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DEUTSCHE NORM

December 2011

D

DIN 22101 ICS 53.040.20

Supersedes DIN 22101:2002-08

Continuous conveyors – Belt conveyors for loose bulk materials – Basis for calculation and dimensioning, English translation of DIN 22101:2011-12 Stetigförderer – Gurtförderer für Schüttgüter – Grundlagen für die Berechnung und Auslegung, Englische Übersetzung von DIN 22101:2011-12 Engins de manutention continue – Transporteurs à bandes pour produits en vrac – Principes de base pour le calcul et la conception, Traduction anglaise de DIN 22101:2011-12

Document comprises 56 pages

Normenausschuss Bergbau (FABERG) im DIN DIN-Sprachendienst

©

No part of this translation may be reproduced without prior permission of DIN Deutsches Institut für Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany, has the exclusive right of sale for German Standards (DIN-Normen).

English price group 21 www.din.de www.beuth.de

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1914862

DIN 22101:2011-12

A comma is used as the decimal marker.

Contents

Page

Foreword ......................................................................................................................................................... 4 1

Scope ................................................................................................................................................. 5

2

Normative references ....................................................................................................................... 5

3

Terms and definitions ...................................................................................................................... 6

4

Symbols and units ............................................................................................................................ 7

5

Volume flow and mass flow ........................................................................................................... 12

6 6.1 6.2 6.2.1 6.2.2 6.2.3 6.3 6.3.1 6.3.2 6.3.3 6.4 6.5 6.5.1 6.5.2

Resistance to motion and required power for the steady operating condition ....................... 14 General ............................................................................................................................................. 14 Primary resistances ........................................................................................................................ 15 General ............................................................................................................................................. 15 Determination of primary resistance FH ....................................................................................... 15 Determination of the hypothetical friction coefficient ................................................................ 16 Secondary resistances ................................................................................................................... 17 General ............................................................................................................................................. 17 Determination of individual secondary resistances ................................................................... 18 Approximate calculation of secondary resistances.................................................................... 19 Gradient resistance ........................................................................................................................ 20 Special resistances ........................................................................................................................ 20 General ............................................................................................................................................. 20 Determination of individual special resistances ......................................................................... 20

7 7.1 7.2 7.2.1 7.2.2 7.2.3 7.2.4 7.2.5 7.3 7.3.1 7.3.2

Design and layout of the drive system ......................................................................................... 21 General ............................................................................................................................................. 21 Location of the drive units, size and number of drive motors ................................................... 22 General ............................................................................................................................................. 22 Horizontal and slightly inclined installations .............................................................................. 22 Uphill conveying installations ....................................................................................................... 23 Downhill conveying installations .................................................................................................. 23 Installations with uphill and downhill sections ........................................................................... 23 Starting, stopping and holding ...................................................................................................... 23 Starting ............................................................................................................................................ 23 Stopping and holding ..................................................................................................................... 24

8 8.1 8.2 8.2.1 8.2.2 8.2.3

Belt tensions and take-up forces .................................................................................................. 25 General ............................................................................................................................................. 25 Required belt tensions ................................................................................................................... 25 General ............................................................................................................................................. 25 Minimum belt tensions required for the transmission of pulley peripheral forces ................. 25 Minimum belt tensions required for the limitation of the belt sag and for correct belt guiding ............................................................................................................................................. 27 Local belt tension variations in the top and return strands ....................................................... 27 General ............................................................................................................................................. 27 Steady operating condition ........................................................................................................... 28 Non-steady operating condition.................................................................................................... 28 Take-up forces and take-up distances ......................................................................................... 29 Local belt tensions in the upper and lower strands .................................................................... 31 General ............................................................................................................................................. 31 Non-steady operating conditions.................................................................................................. 31 Steady operating condition ........................................................................................................... 31

8.3 8.3.1 8.3.2 8.3.3 8.4 8.5 8.5.1 8.5.2 8.5.3

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DIN 22101:2011-12

9 9.1 9.2 9.2.1 9.2.2 9.2.3 9.3 9.3.1 9.3.2

Distribution of belt tensions across the belt width ...................................................................... 31 General ............................................................................................................................................. 31 Transition curves ............................................................................................................................. 32 General ............................................................................................................................................. 32 Distribution of the belt tension for textile conveyor belts ..........................................................34 Distribution of the belt tension for steel cord conveyor belts ....................................................34 Curves............................................................................................................................................... 35 Horizontal curves ............................................................................................................................ 35 Vertical curves ................................................................................................................................. 35

10 10.1 10.2 10.3

Design and layout of the conveyor belt ........................................................................................ 37 General ............................................................................................................................................. 37 Design and layout of the tension member .................................................................................... 37 Design and layout of cover layers ................................................................................................. 40

11

Minimum pulley diameter ............................................................................................................... 41

12 12.1 12.2 12.2.1 12.2.2 12.2.3 12.3 12.3.1 12.3.2 12.3.3

Design and layout of transition curves and vertical curve radii.................................................42 General ............................................................................................................................................. 42 Determination of the minimum transition length ......................................................................... 43 General ............................................................................................................................................. 43 Conveyor belts with textile plies .................................................................................................... 43 Steel cord conveyor belts ............................................................................................................... 43 Determination of the minimum radius of vertical curves ............................................................ 44 General ............................................................................................................................................. 44 Convex curves ................................................................................................................................. 44 Concave curves ............................................................................................................................... 44

13

Dimensioning of belt turnovers ..................................................................................................... 44

Annex A (informative) Explanatory notes .................................................................................................... 46 Annex B (informative) Explanations of relationship of this standard to international standards ........53 Bibliography .................................................................................................................................................. 55

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DIN 22101:2011-12

Foreword This standard has been prepared by Working Committee Fördergurte (Conveyor Belts) of the Normenausschuss Bergbau (FABERG) (Mining Standards Committee). Annexes A and B are provided for information and are informative. This standard relates to the standards ISO 5048:1989, ISO/DIS 3870:1996, ISO 5293:1981 ISO 3684:1990 issued by the International Organization for Standardization (ISO) (see Annex B).

and

Amendments This standard differs from DIN 22101:2002-08 as follows: a) the method for calculating motion resistances has been extended to cover belt conveyors where the number of sections relevant for the calculation varies for the top and bottom strands; b) the start-up factor pA and braking factor pB are now defined; c) the clause “transition curves” has been condensed by combining the theoretical principles common to textile and steel cord belts; d) in the clause on the design and layout of the conveyor belt a factor has been introduced to account for an irregular distribution of belt tension across the belt width; e) information on calculating the pulley load factor has been added in Clause “Minimum pulley diameter”; f)

Clause “Determination of the minimum transition length” has been completely revised;

g) normative references have been updated; h) the standard has been editorially revised. Previous editions DIN BERG 2101 Part 1: 1933-07 DIN BERG 2101 Part 2: 1933-07 DIN BERG 2101 Part 3: 1933-07 DIN 22101: 1942-02, 1982-02, 2002-08

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DIN 22101:2011-12

1

Scope

This standard is applicable to belt conveyor installations for conveying bulk materials, and contains the principles relating to their design. The standard makes it possible to specify essential requirements applicable to major belt conveyor components such as drives, brakes and take-up devices for particular conveying conditions. The standard also gives a description of the design and dimensioning of the conveyor belt.

2

Normative references

The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. DIN 15207-1, Continuous mechanical handling equipment — Idlers for belt conveyors — Main dimensions of idlers for belt conveyors for bulk material DIN 22102-1, Conveyor belts with textile plies for bulk goods — Part 1: Dimensions, specifications, marking DIN 22102-3, Conveyor belts with textile plies for bulk goods — Part 3: Permanent joints DIN 22107, Continuous mechanical handling equipment — Idler sets for belt conveyors for loose bulk materials — Principal dimensions DIN 22109-1, Conveyor belts with textile plies for coal mining — Part 1: Monoply belts for underground applications — Dimensions, requirements DIN 22109-2, Conveyor belts with textile plies for coal mining — Part 2: Rubber-belts with two plies for underground applications — Dimensions, requirements DIN 22109-4, Conveyor belts with textile plies for coal mining — Part 4: Rubber-belts with two plies for above ground applications — Dimensions, requirements DIN 22110-3, Testing methods for conveyor belt joints — Part 3: Determination of time strength for conveyor belt joints (dynamical testing method) DIN 22112-1, Belt conveyors for underground coal mining — Idlers — Part 1: Dimensions DIN 22112-2, Belt conveyors for underground coal mining — Idlers — Part 2: Requirements DIN 22121, Conveyor belts with textile plies for coal mining — Permanent joints for belts with one or two plies — Dimensions, requirements, marking DIN 22129-1, Steel cord conveyor belts for underground coal mining — Dimensions, requirements DIN 22129-4, Steel cord conveyor belts for use in underground coal mining — Belt joints — Dimensions, requirements DIN EN 15236-1 1) Steel cord conveyor belts — Part 1: Design, dimensions and mechanical requirements for conveyor belts for general use ISO 3684:1990-3, Conveyor belts — Determination of minimum pulley diameters

1)

Translator ’s note. The German original is incorrect. The standard number should read “DIN EN ISO 15236-1”.

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DIN 22101:2011-12

3

Terms and definitions

For the purposes of this document, the following term and definition apply. 3.1 belt conveyor continuous belt conveyor for bulk materials with circulating conveyor belts which feature tension members of textile or steel cord ply and cover layers of rubber or plastic supported on carrying idlers and idler stations, and driven or braked by friction grip via pulleys and driving belts where appropriate NOTE Conveyor belts with cover plates made of rubber or plastic are described e.g. in DIN 22102-1, DIN 22109-1, 1) DIN 22109-2, DIN 22109-4, DIN 22129-1 and DIN EN 15236-1 . Idlers and idler sets are described e.g. in DIN 15207-1, DIN 22107, DIN 22112-1 und DIN 22112-2.

1)

Translator ’s note. The German original is incorrect. The standard number should read “DIN EN ISO 15236-1”.

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DIN 22101:2011-12

4

Symbols and units Table 1 — Symbols and units Symbol

Meaning

Unit m2

A

Cross section of fill

A1

Partial cross section above water fill

m2 (mm2) a

A2

Partial cross section with β = 0 (water fill)

m2 (mm2) a

AGr

Effective contact area between cleaner and belt

mm2

B

Belt width

mm

C

Coefficient for the approximate calculation of total secondary resistance

DTr

Pulley diameter

ELGk

Elasticity module related to the width of the belt

Fa

Forces resulting from acceleration/deceleration under non-steady operating conditions

N

FAuf

Inertia resistance of material conveyed and frictional resistance between material conveyed and belt at the feeding point

N

FE

Indentation rolling resistance: Sum of all indentation rolling resistances in the upper and/or lower strands

N

FE,3

Indentation rolling resistance for a 3-roller idler set

N

F' E

Indentation rolling resistance related to the belt width

FGa

Resistances of material transfer devices arranged along the belt conveyor path

N

FGr

Friction resistance caused by belt cleaners

N

FH

Primary resistance: Sum of all primary resistances in the upper and/or lower strands

N

F' M,v

Vertical force related to the belt width

Fn

Normal force acting on an idler

N

FN

Secondary resistance: Sum of all secondary resistances in the upper and/or lower strands

N

FR

Running resistance of idlers: Sum of all running resistances in the upper and/or lower strands

N

FRst

Camber resistance: Sum of all camber resistances for an idler set

N

FS

Special resistance: Sum of all special resistances in the upper and/or lower strands

N

FSch

Friction resistance between material conveyed and lateral chutes outside the acceleration zone of feeding points

N

– mm N/mm

N/m

N/mm

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DIN 22101:2011-12

Table 1 (continued) Symbol

Meaning

Unit

FSchb

Friction resistance between material conveyed and lateral chutes within the acceleration zone of a feeding point

N

FSp

Take-up force at the axis of the take-up pulley

N

FSt

Gradient resistance: Sum of all gradient resistances in the upper and/or lower strands

N

FT

Local belt tension (strand tension)

N

FTm

Mean belt tension of upper strand and lower strand

N

FTr

Total pulley peripheral force

N

FT1

Belt tension (strand tension) of the belt running onto a pulley

N

FT2

Belt tension (strand tension) of the belt running off a pulley

N

FW

Motion resistance: Sum of all resistances to motion in the upper and/or lower strands

N

Im

Mass flow

kg/s

Im,N

Nominal mass flow

kg/s

IV

Volume flow

m3/s

IV,N

Nominal volume flow

m3/s

L

Distance axis-to-axis

m

PM

Total power of drive motors

kW

PM,N

Nominal drive motor capacity

kW

PW

Total power at the periphery of the driving pulley(s) required due to the motion resistances in steady operation

kW

Ra

Radius of a concave vertical transition curve

m (mm)a

Re

Radius of convex vertical transition curve

m (mm)a

S

Safety factor related to the nominal breaking strength of the belt

–

S0

Safety factor taking belt splice manufacturing characteristics into consideration

–

S1

Safety factor taking into consideration expected belt life and operational stresses on belt

–

Smin

Minimum value for the safety factor, related to the minimum nominal breaking strength of the belt

–

Acceleration or deceleration

m/s2

b

Usable belt width

mm

bR

Length of the contact line between belt and idler face

bS

Part of belt lying on a side idler (only for 2- or 3-roller idler sets)

bSch

Clear width between chutes

m

ca

Factor used in the numerical equation describing the indentation rolling resistance determined in relation to the belt width

–

cb

Exponent used in the numerical equation describing the indentation rolling resistance determined in relation to the belt width

–

m mm

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DIN 22101:2011-12

Table 1 (continued) Symbol

Meaning

Unit

cK

Coefficient for determination of the minimum dynamic splice efficiency corresponding to the width related belt tension in the belt edges

–

cR

Coefficient for calculating the masses of the idlers reduced to their periphery

–

cRank

Rankine factor

–

cRst

Coefficient for the calculation of camber resistance

–

cSchb

Coefficient for taking into account additional resistance between material conveyed and lateral chutes in the feeding zones caused by dynamic pressure of the mass flow fed in

–

cTr

Coefficient for the determination of the minimum pulley diameter

–

cÜ

Coefficient for the determination of the standard value for the minimum transition length

–

dGk

Thickness of the load-bearing longitudinal tension member (without outer warp layer or weft, for example)

e

Base of natural logarithms (e = 2,718 28.....)

eK

Distance from the centre line of belt plies at the edge of the belt to the neutral axis of the belt

mm

eM

Distance from the centre line of belt plies at the centre of the belt to the neutral axis of the belt

mm

f

Hypothetical friction coefficient for the approximate calculation of the total primary resistance to motion of the upper and lower strands

–

fi

Hypothetical friction coefficient for the approximate calculation of the primary resistance of a section of the upper or lower strand

–

g

Acceleration due to gravity (g = 9,81 m/s2)

h

Height difference of a section of the upper or lower strand (h > 0 for uphill belt travel, h < 0 for downhill belt travel)

hK0

Distance from the belt edge to the deepest level of the trough

mm

hK1

Distance from the belt edge to the pulley surface level

mm

hrel

Maximum belt sag related to spacing between carrying idlers

hTr

Lift of the pulley in the transition zone above the deepest level of the trough

k

Belt tension related to belt width

N/mm

kK

Tension at belt edge related to belt

N/mm

kM

Tension at belt centre related to belt

N/mm

kN

Nominal belt breaking strength related to belt width

N/mm

kN,min

Minimum nominal belt breaking strength related to belt width

N/mm

kt

Reference dynamic splice efficiency

N/mm

kt,rel

Relative reference dynamic splice efficiency

∆k

Difference between width-related belt tension at the edges and that at the centre of the conveyor belt

l

Length of a section of upper or lower strand

m

lb

Length of the acceleration path in the feeding zone

m

mm –

m/s2 m

– mm

– N/mm

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DIN 22101:2011-12

Table 1 (continued) Symbol

Meaning

Unit

lK

Length of the belt edge in the transition zone

m

lM

Length of the central roller in a 3-roller idler set

lSch

Length of lateral chutes

m

lR

Spacing between carrying idlers

m

lÜ

Length of transition zone

m

lÜ,eff

Reference length of transition zone for steel cord belts

m

∆lÜ

lÜ,eff − lÜ for steel cord belts

m

lW

Belt turnover length

m

Σm

Total of translatorially moving masses and non-driven and non-braked rotating masses reduced to their periphery

kg

m'G

Line load resulting from the conveyor

kg/m

m'L

Line load resulting from the material conveyed

kg/m

m'L,N

Line load resulting from nominal load

kg/m

m'R

Line load resulting from rotating idler parts

kg/m

n

Number of sections of the upper or lower strands of a belt

–

pA

Start-up factor related to the drive pulley: ratio of the total pulley peripheral force at start-up FTr,A , to the force FW determined by the height and distribution of the material conveyed

–

pA0

Start-up factor related to the drive: ratio of the drive torque resulting from the effective drive characteristics during the start-up phase of the conveyor and the nominal torque corresponding to the rated power of the motors actually installed PM,inst

–

pB

Braking factor related to the brake pulley: ratio of the total pulley peripheral force at braking FTr,B to the force FW determined by the height and distribution of the material conveyed

–

pB0

Braking factor related to the brake: ratio of the braking torque resulting from the effective braking characteristics during the braking phase of the conveyor and the nominal torque corresponding to the rated power of the motors actually installed PM,inst

–

pGr

Pressure between belt cleaner and belt

q

Coefficient for the determination of primary resistances for the upper and lower strands

–

sB

Braking distance

m

sSp

Take-up pulley travel

m

tB

Braking time

s

v

Conveying speed

m/s

v0

Feeding speed in the direction of conveying

m/s

zR

Number of carrying idlers in one section (upper strand or lower strand)

–

zRst

Number of carrying idlers in one section (upper or lower strand) set at a tilt

–

mm (m)a

N/mm2

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DIN 22101:2011-12

Table 1 (continued) Symbol

Meaning

Unit

α

Angle of pulley belt wrap

β

Equivalent angle of slope for the calculation of the partial cross-section A1th

°

βdyn

Dynamic angle of slope of the material conveyed

°

δ

Angle of inclination of a section of upper or lower strand, δ > 0 for uphill belt travel, δ < 0 for downhill belt travel)

°

ε

Angle of tilt of a side idler

°

∆ε K

Additional elongation (pos. or neg.) at the edge of the belt in concave or convex transition curves, in relation to the neutral belt axis

–

∆εK∞

Limit of ∆εK at the centre of very long transition curves

–

∆ε M

Additional elongation (pos. or neg.) at the centre of the belt in concave or convex transition curves, in relation to the neutral belt axis

–

∆εM∞

Limit of ∆εM at the centre of very long transition curves

–

∆ε ∞

Difference of elongation at the belt edge and in the middle of very long transition curves

–

ηges

Overall efficiency of all transmission members between motor shaft and pulley shaft

–

λ

Troughing angle of the conveyor belt in the upper strand or lower strand

°

µ

Friction coefficient between belt and pulley

–

µ1

Friction coefficient between belt and material conveyed

–

µ2

Friction coefficient between material conveyed and lateral chutes

–

µ3

Friction coefficient between belt and carrying idler

–

µ4

Friction coefficient between belt and belt cleaner

–

ρ

Bulk density of material conveyed

ϕ

Effective filling ratio

–

ϕ Betr

Filling ratio corresponding to the operating conditions of the conveyor

–

ϕ St

Reduction factor of filling ratio for the theoretical total cross section of fill Ath in the case of inclined installations

–

ϕ St1

Reduction factor of filling ratio for the theoretical partial cross section A1,th in the case of inclined installations

–

a

° or rad

kg/m3

in some equations these variables are used with the unit mentioned in brackets.

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DIN 22101:2011-12

Table 2 — Indices Index A B a eff erf i j inst m max min o s th u zul *

5

Meaning At start-up At stopping (braking) Non-steady operation (start-up, braking) Effective Required Running index for belt strand sections Running index for belt deflection points (at pulleys) Installed Centre idler Maximum Minimum Upper strand Side idler Theoretical Bottom strand Allowable Index for identifying operating conditions

Volume flow and mass flow

The maximum volume flow and mass flow of a belt conveyor is determined by the potential cross section of fill, which is dependent on the dynamic angle of slope of the material conveyed and on the feeding conditions, among other factors. To calculate the maximum volume and mass flow a simple equivalent geometrical cross section needs to be found. This theoretical cross section A th is calculated from the shape of the conveyor belt on the carrying idlers and from the shape of the slope formed by the material conveyed. Figure 1 shows this cross section for a belt supported by a 3 roller idler set, which is commonly used.

Figure 1 — Theoretical cross section of fill in the case of horizontal conveyance and a 3 roller idler set

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DIN 22101:2011-12

The theoretical cross section of fill is dependent on the length and arrangement of the carrying idlers (troughing angle), the usable belt width b and the equivalent slope angle β describing a cross section of the same area as the actual one. In this case, the usable belt width b shall be calculated as a function of the belt width B as follows: B ≤ 2 000mm

b = 0,9 × B − 50 mm

(1)

B > 2 000mm

b = B − 250 mm

(2)

The usable belt width of belt conveyors with horizontal curves and inclined idlers installed to stabilize the belt may be smaller. With 1-, 2- and 3-roller idler sets in horizontal belt conveyors, the theoretical cross section of fill A th that is equivalent to the real cross section of fill can be established using angle β as the sum of partial cross sections A1,th and A2,th (see [1], Figure 1 and Annex A): A1,th = [ lM + (b − lM ) ⋅ cos λ ] 2 ⋅

tanβ 4

(3)

b − lM b − lM A 2,th = lM + ⋅ cos λ ⋅ ⋅ sin λ 2 2

(4)

The selection of an equivalent slope angle depends on the material to be conveyed as well as on the length of the conveying distance. In case of lacking experience in selecting an adequate slope angle, the following standard values can be applied: The value will be β = 20° for materials with normal flow properties. Values below β = 20° down to β = 0° will be characteristic for nearly liquid materials. Equivalent slope angles of more than 20° can be applied only in case of materials with high internal friction. For 1-roller and 2-roller idler sets, the length of the central roller shall be taken to be lM = 0. The following parameters can be calculated on the basis of the theoretical cross section fill:

I V, th = Ath ⋅ v

(5)

ϕ = ϕBetr ⋅ ϕ St

(6)

Nominal volume flow

IV,N = ϕ ⋅ Iv,th

(7)

Nominal mass flow

Im,N = ϕ ⋅ ρ ⋅ Iv,th

(8)

Line load resulting from nominal load

m'L,N = ϕ ⋅ ρ ⋅ Ath

(9)

Theoretical volume flow And on the basis of the effective filling ratio the following can be calculated:

The filling ratio ϕ Betr depends on:

properties of material conveyed lumpiness max. edge length dynamic angle of slope βdyn (characterizing the actual dynamic property of the slope)

operating conditions of the conveyor uniform material feeding tracking of the conveyor belt reserve capacity

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DIN 22101:2011-12

For horizontal, straight conveyors, the theoretical cross section can be fully utilized if uniform feeding of material and straightforward belt movement is ensured (ϕ = ϕ Betr = 1). The reduction factor ϕ St takes into consideration the fact that the partial cross section A1,th is reduced under sloped conveying conditions:

ϕ St = 1 −

A1,th Ath

⋅ (1 − ϕ St 1)

(10)

A properly aligned belt uniformly loaded with non-lumpy material and δ max ≤ β dyn can be calculated as follows:

ϕSt1 =

cos2 δmax − cos2 β dyn 1 − cos2 β dyn

(11)

Applying Equations (10) and (11) it shall be borne in mind that the angle of slope for downhill conveying cannot be higher than the actual dynamic angle of slope βdyn (see also Annex A) and that only the partial cross section A2,th is available for conveying.

6

Resistance to motion and required power for the steady operating condition

6.1 General The method described below for the determination of motion resistances, the required power, and the local belt tensions yields fairly realistic results for state-of-the-art technology, even for complex conveyor installations and all possible operating conditions. Experienced design engineers can simplify the calculation method for ordinary belt conveyors with manageable operating conditions and for those that do not require a high degree of accuracy, provided that safety requirements are met. Prior to calculating the resistance to motion, individual base values shall be estimated. These values shall be checked and corrected, if necessary, after completing the calculation. The calculation shall be repeated as many times as necessary to match the results with the input values. During steady operation, the forces resisting belt movement (resistances to motion) FW are calculated by the summation of friction, weight and mass forces. The required power for the conveyor PW is calculated as a product of the total motion resistance of the upper and lower strands and the conveying speed v. PW = FW ⋅ v

(12)

For the calculation of motional resistances, the following parts are defined:

primary resistance FH

secondary resistance FN

gradient resistance FSt

special resistance FS

The sum of the above types of resistance to motion FW is equal to the total pulley peripheral force FTr to be transmitted to the belt:

FW =

no

∑ i =1

FW,o,i +

nu

∑ FW,u,i = FH + FN + FSt + FS = FTr

(13)

i =1

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DIN 22101:2011-12

The resistances shall be established for individual sections. Each section is characterized by the fact that parameters such as the angle of inclination i of the section, the hypothetical friction coefficients f i and the line loads due to material to be conveyed m'R,i and the rotating idler parts m'L,i have constant values for both the upper and lower strands. Hence it is advisable — particularly with regard to computer calculations — to assign a running index i to the start points and end points of all part sections of the conveyor installation, starting from the tail station toward the head station. Upper strand values shall be identified by index o, lower strand values by index u (see Figure 2). In order to maintain the assigned descriptions, belt deflection points (at pulleys) and their parameters shall be identified by index j (see Figures 5 and 6).

6.2 Primary resistances 6.2.1

General

Primary resistance occurs along the entire length of the conveyor path. The parameters of primary resistance shall be determined for individual sections.

Figure 2 — Creation of belt sections and calculation of motion resistances for each section in a steady operating condition 6.2.2

Determination of primary resistance FH

The primary resistances FH,i of all sections are to be determined separately for the upper and lower strands of each individual section, in a simplified manner assuming a linear relationship between the resistance and the moved load:

[

′ i + (mG ′ + mL, ′ i ) ⋅ cosδ i FH, i = li ⋅ fi ⋅ g ⋅ mR,

]

(14)

The primary resistances of the upper strand sections FH,o,i and lower strand sections FH,u,i are indispensable for the determination of belt tensions (see 8.3). The primary resistance of the conveyor, i.e. the sum of primary resistances for the upper strand FH,o and those for the lower strand FH,u can be calculated as follows:

FH =

no

∑

i =1

F H,o,i +

nu

∑ F H,u,i = FH,o + FH,u

(15)

i =1

Primary resistances for each section shall be calculated for the nominal loading range (filling ratio ϕ within the range 0,7 to 1,1) along the entire conveyance path. For belt conveyors with downhill and uphill sections, and for extreme loading conditions (non-uniform load, partial loading or idling), the cumulative resistance determined under these conditions can deviate significantly from that arising under nominal conditions.

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6.2.3

Determination of the hypothetical friction coefficient

The selection of a hypothetical friction coefficient fi is of major importance as regards the magnitude of primary resistances. This is especially important for conveyors with small gradient resistances. Attempts to be on the safe side with calculations, together with a case-by-case inaccurate description of the operating features and a wide range of possible values can lead to considerable over-dimensioning. In order to avoid disproportional dimensioning, the friction coefficients fi are to be established as precisely as possible for the individual sections. The values for f given in Table 4 can serve as guidelines in a global calculation of the sum of all primary resistances in the top and bottom strands. The friction coefficient fi of a section is defined mainly by the rolling resistance of the carrying idlers and the indentation rolling resistance of the belt. Also the flexing resistance can have a large share in this, if the sag of the conveyor belt is relatively large. For a more precise determination of the friction coefficient fi aiming for a safe conveyor design combined with a minimum investment and lower operational costs, the running resistance of the idlers and the indentation rolling resistance can be measured for given parameters and the other resistances can be estimated (see [2], [3], [4] and [5]). With a normal magnitude of flexing resistance the running resistance of the idlers and rolling indentation resistance of the loaded strand (usually of the upper strand) with a filling ratio ϕ within the range of 0,7 ≤ ϕ ≤ 1,1, generate between 50 % and 85 %, on average 70 %, of the primary resistance FH,o. They amount to approx. 90 % of the primary resistance for the unloaded strand (usually that of the lower strand, FH,u. Considering this following relationships apply: Upper strand (loaded)

FH,o =

1 ⋅ ( FR,o + FE,o ) qo

(16)

Lower strand (unloaded)

FH,u =

1 ⋅ ( FR,u + FE,u ) qu

(17)

with 0,5 ≤ qo ≤ 0,85, on average qo = 0,7 and qu = 0,9. Guidelines for estimating coefficient qo are given in Table 3. Table 3 — Standard values for coefficient q0 for a filling ratio ϕ within the range 0,7 ≤ ϕ ≤ 1,1 Characteristic

Values for characteristic

Relative sag hrel

medium

high, but ≤ 0,01

low

Internal friction of material conveyed

medium

high

low

Running resistance of carrying idlers

medium

low

high

Indentation rolling resistance

medium

low

high

Coefficient qo

Standard value ≈ 0,7

causes reduction of increase of coefficient qo to

0,5

0,85

Equations (16) and (17) can be used to check the plausibility of, and if necessary adjust, the values of the primary resistances determined using the hypothetical friction coefficients f i and the other resistances as in Equations (14) and (15).

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If there are no values which have been obtained by measurement or on the basis of experience, or if only an approximate dimensioning is intended, standard values for the hypothetical friction coefficient f can be selected from Table 4 for estimating the total primary resistance of the upper and lower strands on the basis of the operating conditions and design features (see also Annex A). These values are based on numerous combined upper and lower strand measurements and for the following limiting conditions:

3 roller fixed idler sets in the top run

carrying idlers with antifriction bearings and labyrinth seals

values of relative belt sag hrel ≤ 0,01

filling ratio ϕ within a range from 0,7 to 1,1 Table 4 — Standard values for the hypothetical friction coefficient f for estimating the total primary resistance in the upper and lower strands of conveyors with a filling ratio ϕ within the range 0,7 to 1,1 Characteristic

Values for characteristic

Internal friction of material to be conveyed

medium

low

high

Belt conveyor alignment

medium

good

bad

Belt tension

medium

high

low

Operating conditions (dusty, sticky)

medium

good

bad

Idler diameter

108 to 159

> 159

< 108

Spacing of upper strand idlers in m

1,0 to 1,5

< 1,0

> 1,5

Spacing of lower strand idlers in m

2,5 to 3,5

< 2,5

> 3,5

4 to 6

6

Troughing angle in °

25 to 35

< 25

> 35

Ambient temperature in °C

15 to 25

> 25

< 15

Belt speed in m/s

Friction coefficient f

Standard value ≈ 0,020

causes reduction of increase of friction coefficient f to 0,010 0,040

When the drives function as generators, an assumed smaller friction coefficient f leads to greater safety with regard to the dimensioning; for drives functioning as motors this effect will be achieved by assuming a larger friction coefficient f . The application of these friction coefficients f in the calculation of primary resistances according to Equation (14) is acceptable only if the calculation does not need to be very accurate.

6.3 Secondary resistances 6.3.1

General

Secondary resistances include friction resistances and inertia resistances arising only in some places on the conveyor. Secondary resistances are calculated from several individual resistances. The secondary resistances in the upper strand FN,o,i and in the lower strand FN,u,i are required for the calculation of the belt tensions (see 8.3).

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The secondary resistance of the conveyor belt FN, i.e. the sum of secondary resistances in the upper strand FN,o and in the lower strand FN,u, is calculated as:

FN = 6.3.2

no

∑

i =1

F N,o,i +

nu

∑ F N,u,i = FN,o + FN,u

(18)

i =1

Determination of individual secondary resistances

Inertia resistance of material conveyed and friction resistance between material conveyed and the belt in the feeding zone FAuf = Im ⋅ (v − v0)

(19)

Friction resistance between conveyor belt and lateral chutes in the acceleration zone of a feeding point:

Figure 3 — Chute configuration The following applies to feeding points with 3-roller idler sets and bSch > lM (see [6]):

(

)

2

2 ⋅ Im 2 2 tan λ ⋅ ρ ⋅ g ⋅ l b ⋅ µ 2 FSchb = c Schb ⋅ cRank ⋅ − bSch − lM ⋅ 2 4 bSch (v + v 0 ) ⋅ ρ for 0 ≤ v0 ≤ v 2 2 v − v0 lb > lb,min = 2 ⋅ g ⋅ µ1

(20)

(21)

with

β dyn cRank = tan 2 45° − 2

(22)

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lM = bSch shall be applied for bSch ≤ lM lM = 0 shall be applied for 2-roller idler sets lM = bSch shall be applied for 1-roller idlers The following approach applies to other types of idler set (e.g. 5-roller idler sets): a) determination of the height of material pressing against lateral chute walls on the basis of the volume flow and average conveying speed in the feeding zone (v + v0)/2. b) determination of potential wall pressure caused by a fluid pressing against the side walls of the chute. If applicable, multiply with cSchb and cRank. c) determination of friction resistance from average wall pressure, friction coefficient and size of wall areas The following applies to belt conveyors of customary design: cSchb ⋅ cRank = 1 (see Annex A) As a general rule, the friction coefficients µ1 and µ2 are within the range from 0,5 to 0,7. Friction resistance caused by belt cleaners For the use of scraper bars as belt cleaners, the friction resistance can be determined as follows: FGr = µ4 ⋅ pGr ⋅AGr

(23) 2

2

As a general rule, the contact pressure pGr is within a range of approx. 0,03 N/mm to 0,1 N/mm , whereas the friction coefficient µ4 approximately ranges between 0,6 and 0,7. The total secondary resistance FN is the sum of the secondary resistances of each section.

FN =

no

nu

i =1

i =1

∑ F Auf,o,i + FSchb,o,i + FGr,o,i + ∑ F Auf,u,i + FSchb,u,i + FGr,u,i = FN,o + FN,u

(24)

Further secondary resistances are the bending resistance of the conveyor belt where it runs over a pulley and the resistance of the bearings of non-driven pulleys. These secondary resistances are relatively small in conveyors of customary design as compared with the above mentioned resistances and can be neglected in almost all cases. If necessary, calculation equations can be taken from the referenced documents (e.g. [1]). 6.3.3

Approximate calculation of secondary resistances

If the portion of secondary resistances in the total resistance is small, e.g. with conveyor lengths L > 80 m and conveyors with just one feeding point, an approximate calculation of secondary resistances FN from the primary resistance FH applying coefficient C (see [1]) is permissible:

FN = (C − 1) ⋅ FH

(25)

The coefficient C can be selected from Table 5:

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Table 5 — Standard values for coefficient C for belt conveyor installations with filling ratios ϕ ranging from 0,7 to 1,1 L in m C

80

100

150

200

300

400

500

600

700

800

900

1 000

1 500 ≥ 2 000

1,92

1,78

1,58

1,45

1,31

1,25

1,20

1,17

1,14

1,12

1,10

1,09

1,06

1,05

6.4 Gradient resistance The gradient resistance of the conveyor belt and material conveyed can be calculated as follows for each section:

(

FSt,i = h i ⋅ g ⋅ m' G +m'L,i

)

(26)

The total gradient resistance of the conveyor FSt , that is, the sum of gradient resistances in the upper strand FSt,o and in the lower strand FSt,u , is calculated as follows:

FSt =

no

nu

i =1

i =1

∑ F St,o,i + ∑ F St,u,i = FSt,o + FSt,u

(27)

applying h i = li ⋅ sin δ i

(28)

(for uphill belt travel: h i > 0 and δ i > 0; for downhill belt travel: h i < 0 and δ i < 0)

6.5

Special resistances

6.5.1

General

Special resistances are resistances that do not occur with all belt conveyors. These resistances are calculated on the basis of several individual resistances (see Annex A). The special resistances of a conveyor section i are composed of: FS,i = FRst,i + FSch,i + FGa,i

(29)

The total special resistance of a conveyor FS, i.e. the sum of the special resistances in the upper strand FS,o and in the lower strand FS,u are calculated as follows:

FS = 6.5.2

no

nu

i =1

i =1

∑ (F Rst,o,i + FSch,o,i + FGa,o,i ) + ∑ (F Rst,u,i + FSch,u,i + FGa,u,i ) = FS,o + FS,u

(30)

Determination of individual special resistances

Camber resistance The camber resistance which arises at an individual side carrying idler will depend on its normal force, on the friction coefficient µ3 between the belt and the carrying idler, and also on the angle of tilt ε . The camber resistance FRst,i in section i of the conveyor is then obtained from the total of individual camber resistances, and taking the angle of inclination δ i of the installation into consideration:

FRst,i =

zRst,i zR,i

′ +mL, ′ i) ⋅ li ⋅ cRst,i ⋅ µ3 ⋅ sin ε i ⋅ cos δ i ⋅ g ⋅ (mG

(31)

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The friction coefficient µ3 depends on the angle of tilt ε . For angles ε > 5° it can reach a value of 0,5 (see [7]). In Equation (31), the parameters cRst,i are dependent on the idler arrangement and, in the case of the upper strand, on the geometry of the bulk material. In the case of 3-roller idler sets with rollers of equal length in the upper strand, and with filling ratios ϕ within the range of 0,7 to 1,1 (see [7]) it follows: cRst,o = 0,4 for λ = 30° cRst,o = 0,5 for λ = 45° The following applies to 2-roller idler sets in the (unloaded) lower strand: cRst,u = cos λ Friction resistance between the material conveyed and the lateral chutes outside the feeding points With bSch > lM and 3-roller idler sets (see Figure 3) the relationship below applies:

(

)

2

I ρ ⋅ g ⋅ lSch ⋅ µ2 2 2 tan λ FSch = cRank ⋅ m − bSch − lM ⋅ ⋅ 2 v 4 ρ ⋅ bSch

(32)

As a general rule, the friction coefficient µ2 is within the range from 0,5 to 0,7. lM = bSch shall be applied for bSch < lM; lM = 0 shall be applied for 2-roller idler sets; lM = bSch shall be applied for 1-roller idler sets. Resistances FGa of material transfer devices arranged along the belt conveyor path If, in special cases, material is discharged laterally along the conveying path, e.g. through scrapers serving as belt cleaners, the forces occurring at these locations shall be taken into account as special resistances.

7

Design and layout of the drive system

7.1 General The design and layout of the drive system comprises:

the selection of the location and number of drives

decisions relating to starting aids

the sizing of the drive motors (rated output)

the determination of the required braking forces (stopping and holding)

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7.2 Location of the drive units, size and number of drive motors 7.2.1

General

To minimize belt tension, the drive power is to be distributed among several drive pulleys situated at the head and at the rear of the installation, and in certain cases among intermediate drives, unless there are other considerations to be taken into account. Such other considerations include:

available space

availability of energy

driving and braking options

In order to ensure minimum belt tension, the type and arrangement of drives will depend heavily on the magnitude and local distribution of motion resistances for the conveyor in a steady operating condition, FW,o for the upper strand and FW,u for the lower strand. Variations in belt tension occurring in the direction of belt travel can be calculated by adding the resistances of the conveyor sections i in accordance with Equation (13).

FW =

no

∑

i =1

F W, o,i +

nu

∑ F W,u,i = FW, o + FW,u

(33)

i =1

In the case of extreme loading (non-uniform loading, partial loading or idling) of a belt conveyor with downhill and uphill grade stretches, the maximum force Fw,max can deviate significantly from the force FW determined for the nominal loading range (see 6.2.2): FW,max = FW,o + FW,umax ≥ FW

(34)

PW,max ≥ PW

(35)

This extreme power requirement shall be taken into consideration when selecting the type of drive system — motor drives or generators — however, in due consideration of the thermal rating of the motors. 7.2.2

Horizontal and slightly inclined installations FW,o > 0, FW,u > 0 (for uniformly loaded upper strand)

In the case of belt conveyors with drives at the installation head and rear, but without intermediate drives, the belt tensions will be minimal if the drive power is appropriately distributed between the head and tail stations, i.e. by a proportional distribution of the motion resistances occurring in the upper and lower strands. The required total power of the drive motors can be calculated with the aid of the following equation:

P PM, erf = W, max

ηges

(36)

The rated motor power actually installed, i.e. the sum of the nominal powers of the individual motors PM,N PM,inst =

∑ PM,N

(37)

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is, as a general rule, greater than the required power

P M,inst ≥ P M,erf 7.2.3

(38)

Uphill conveying installations FW,o > 0, FW,u ≤ 0 (for uniformly loaded upper strand)

In such installations, the belt tensions will be minimal if all the drives are arranged at the head of the installation, assuming that no intermediate drives are installed. PM,erf and PM,inst can be calculated using Equations (36), (37) and (38). 7.2.4

Downhill conveying installations

FW,o ≤ 0, FW,u > 0 (for uniformly loaded upper strand) In these installations, to obtain minimum belt tensions it is essential that drives are at the rear end of the installation where the drive is achieved through generators. For the purpose of determining the total power of the drives, the required power of the driving motors at the motor shafts shall be calculated as follows, depending on whether the drives operate as motors (PW,max > 0) or generators (PW,max < 0):

P PM, erf = W, max

where PW,max > 0

(39)

PM,erf = PW, max ⋅ η ges

where PW,max < 0

(40)

ηges

In this design stage it is not possible to precisely determine the overall efficiency ηges. For safety reasons, within the estimated range a higher value for the overall efficiency is to be chosen for a generator drive than for a motor drive. As a rule, the rated power of the motors actually installed (see Equation (37)) is greater than the amount of required power: PM,inst ≥ PM,erf 7.2.5

(41)

Installations with uphill and downhill sections

An appropriate arrangement of the drives for belt conveyor installations with uphill and downhill sections ensuring minimum belt tensions can be suggested only if all actual operating conditions are taken into account.

7.3 Starting, stopping and holding 7.3.1

Starting

In order to achieve minimum belt tensions, it is necessary to limit the total pulley peripheral forces on start-up FTr,A generated at the drive end during run-up to full speed of the belt conveyor installation. However the force FTr,A shall not be allowed to decrease below a given minimum value in order to safeguard the positive control of the initial breakaway and start-up process. The following is recommended especially for large belt conveyors

The maximum pulley peripheral force on start-up FTr,A,max should not exceed 1,7 times the force FW,max in accordance with Equation (34) used for the determination of the installation design. This means: the startup factor pA,max ≤ 1,7.

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In order to break away and accelerate the masses in the upper and lower strands, however, the force available under the most unfavourable start-up conditions (loading condition, distribution of load) should equal at least 20 % of the primary, secondary and special resistances to be taken into account and ensure the starting of the conveyor within the maximum time period allowed in accordance with the thermal rating of the drives (see [8]).

The force FTr,A shall be suitably selected to ensure friction grip between the material conveyed and the conveyor belt for the corresponding start-up acceleration a A . It follows for fine grained bulk material: aA ≤ (µ1 ⋅ cos δ i,max − sin δ i,max) ⋅ g

(42)

(for uphill belt travel: δ i > 0; for downhill belt travel: δ i < 0) The force FTr,A should be introduced into the belt slowly enough to ensure that the installation runs up to full operating speed under quasi steady conditions, and consequently with the small additional dynamic forces (see [8] and [9]). The start-up factor pA,0 related to the nominal torque of all drive motors shall be applied for the determination of the start-up factor pA in accordance with the equation below, where there are relatively small mass inertia torques of the rotating components of drives operating as motors in the steady operating condition, i.e. for horizontal and uphill conveying installations:

pA = pA0 ⋅

PM, inst PM

(43)

For designs according to Equation (35) the following shall be applied: PM = PM,erf 7.3.2

Stopping and holding

The operation of belt conveyor installations generally requires the provision of braking equipment to stop the moving masses, and/or holding devices to hold inclined installations under load. For the dimensioning of the braking equipment the following is to be considered:

total required braking force FTr,B on the periphery of the braked pulleys or the braking factor pB (see 8.3.3)

pB =

FTr, B FW

number and arrangement of brakes

braking frequency and braking time or braking distance

energy of the rotating drive components to be absorbed by braking

(44)

The required braking force FTr,B or the braking factor pB shall be determined for the most unfavourable braking conditions governed by the filling ratio ϕ and by the distribution of the load in downhill and uphill stretches of the installation with the relevant total motion resistance FW. In this connection, either the braking distance sB or braking time tB is to be specified. This will determine the braking deceleration a B , which shall be such that the friction grip between the material conveyed and the belt is maintained. In the case of fine-grained bulk material, the following applies: a B ≤ µ1 ⋅ cos δi,max + sin δi,max ⋅ g

(45)

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The braking factor pB0 related to the nominal torque of all drive motors shall be applied for the determination of the braking factor pB in the case of relatively small mass inertia torques of the rotating components of drives operating as motors in the steady operating condition, i.e. for horizontal and uphill conveyors with the power PM of the drives: pB =

pB0

2 η ges

⋅

PM, inst PM

(46)

It may be necessary to limit the total braking force to a given value FTr,B,max, and consequently the braking deceleration to a limiting value a B,max, in order to reduce the belt stresses and those on other parts of the installation as much as possible, and in order to maintain the friction grip on the braked pulleys (see 8.2.2). As regards the design and dimensioning of holding devices, the maximum gradient resistance FSt,max likely to arise under the maximum permissible loading conditions and most unfavourable load distribution, shall be used as the base value, minus the primary resistance arising under these conditions. For safety reasons, only the minimum primary resistance anticipated shall be used in calculations. If a number of mechanical holding devices are used, the loads shall be suitably distributed.

8 Belt tensions and take-up forces 8.1 General The belt tension in a belt conveyor installation is a quantity which varies along the path of the installation, and which is governed by the following influences (see Figure 5):

length and course of the installation

number and arrangement of drives

characteristics of the driving and braking equipment

type and arrangement of the belt take-up device

operating condition (loading and movement conditions)

Belt tensions should be kept to the lowest possible value in view of the stressing and layout of the belt and of other parts of the installation.

8.2 Required belt tensions 8.2.1

General

The operation of belt conveyor installations requires minimum belt tensions in order to enable the transmission of forces to the belt by friction grip on the drive pulleys, to limit the belt sag and to enable the belt to be guided correctly. 8.2.2

Minimum belt tensions required for the transmission of pulley peripheral forces

The transmission of the maximum pulley peripheral forces which arise during starting, braking, or in the steady operating condition by friction grip on the individual driven or braked pulleys requires certain minimum belt tensions at the point where the belt runs onto and off the pulley. In the case illustrated in Figure 4, with the forces FT1 and FT2 and the associated maximum pulley peripheral force FTr,max > 0 the following applies:

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Figure 4 — Minimum belt tensions at the belt run-on and run-off point on the drive pulley required to ensure transmission of the pulley peripheral force FTr,max FT1 − FT2 = FTr,max

(47)

FT1 ≤ e µ ⋅α , FT2

(48)

where α is to be expressed in radians. It follows that: FT2 ≥

1

e

µ ⋅α

−1

⋅ FTr,max

(49)

FT1 = FT2 + FTr,max

(50)

In the case of more than one driven or braking pulley, whether or not the friction grip is ensured in accordance with Equations (48) and (49) is to be verified for each individual pulley and for all operating conditions. In this connection it shall be borne in mind that the total pulley peripheral forces FTr, FTr,A or FTr,B are distributed onto the individual pulleys in proportion to the torques induced in said pulleys by the driving or braking equipment. Table 6 gives preferred friction coefficients µ for the friction between belts with rubber covers and pulley surfaces of different finishes to be used in the design of belt conveyors for the steady operating condition. Table 6 — Recommended friction coefficients µ for the friction between belts with a rubber cover and pulley surfaces of different finishes (see [10]) for the design of belt conveyor installations for the steady operating condition

Operating condition

a

a

Friction coefficients µ for pulley surfaces of bright metal surface (plain steel pulley)

polyurethane lagging (arrow pattern)

rubber lagging (arrow pattern)

ceramic lagging with pores, (arrow pattern)

dry

0,35 to 0,4

0,35 to 0,4

0,4 to 0,45

0,4 to 0,45

wet (clear water)

0,1

0,35

0,35

0,35 to 0,4

wet dirty (with mud and clay)

0,05 to 0,1

0,2

0,25 to 0,3

0,35

For conveyor belts with a PVC cover approx. 10 % smaller friction coefficients shall be assumed.

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8.2.3

Minimum belt tensions required for the limitation of the belt sag and for correct belt guiding

For the purpose of technical optimization of the belt conveyor installation, especially as regards energy efficiency, the calculated maximum relative belt sag hrel related to the distance between carrying idler centres shall be limited to values lower than 0,01 in the steady operating condition. A greater belt sag is permitted in the non-steady operating condition. The greater the conveying speed and the lumpier the material conveyed, the smaller the sag should be. Greater conveying speeds require either considerably lower sag values or the acceptance of higher primary resistances (see 6.2). The following minimum belt tensions are required for a given maximum belt sag and a given distance between carrying idler centres: Upper strand (with load): FT,o,min =

Lower strand:

FT,u,min =

g ⋅ ( m'L + m'G ) ⋅ lR,o

(51)

g ⋅ m'G ⋅ l R,u

(52)

8 ⋅ hrel

8 ⋅ hrel

If a maximum value of hrel is specified, different distances between carrying idler centres can be allocated to the belt tension occurring along the path of an installation. When these distances between centres are finally selected, the load-carrying capacity of the carrying idlers and the transverse vibration behaviour of the belt shall be taken into account (see [11]). In order to ensure the trouble-free operation of belt conveyor installations, it may be necessary to maintain higher minimum belt tensions in addition to the belt sag, especially for:

belts with turnover in the lower strand (see [12])

belts with a low degree of transverse rigidity

inclined belt conveyor installations at the lower pulley

belts with locally non-uniform force distribution across the belt width (see Clause 9)

8.3 Local belt tension variations in the top and return strands 8.3.1

General

From the point of view of the correct sizing of the belt and of other parts of the installation, sufficient knowledge of the course or pattern of the belt tension along the length of the installation, and in particular the magnitude of the extreme values of the force, is extremely important. Local belt tensions FT,i can be determined by summation of the motion resistances FW, i (see Clause 6) and superimposition of the take-up force (see 8.4) and, where applicable, the acceleration/deceleration force components Fa,i (see 8.3.3).

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Figure 5 — Pulley peripheral forces, resistances to motion and belt tensions illustrated for a conveyor installation with no = nu = 2 sections and 4 pulleys under steady operating condition 8.3.2

Steady operating condition

The calculation of motion resistances Fw,i for the individual sections of a belt conveyor installation in the stationary operating condition is given in Clause 6. 8.3.3

Non-steady operating condition

During the starting and stopping process, the magnitude and pattern of the forces generated by the driving and braking equipment, and the breakaway resistance and motion resistances of a belt conveyor installation result in additional dynamic belt tensions. These additional tensions are a function of the following factors, if we assume a belt acceleration independent of local conditions and, hence, quasi steady operating conditions of the conveyor (see also Annex A):

the total pulley peripheral force FTr,A during starting or FTr,B during stopping

the total acting motion resistance (approximately equal to the motion resistance occurring under steady operation FW)

the masses moving in a straight line and the non-driven or non-braked rotating masses Σ m reduced to their periphery

For the frequently occurring case where the secondary resistance represents only a small proportion of the total resistance, the forces Fa,i resulting from acceleration or deceleration can be determined as follows for an individual section i with the aid of the belt acceleration a : starting:

− FW F F a A = Tr,A = ( pA − 1) ⋅ W > 0 ∑m ∑m

(53)

stopping:

aB =

FTr,B − FW

∑m

= ( pB − 1) ⋅

FW 30 °C

Workspace

normal

roomy

narrow

Qualification of technicians

normal

very good

moderate

Quality of splicing materials

normal

fresh

nearly expired shelf life

Quality of vulcanizing equipment

normal

very good

moderate

Air temperature

cause Safety factor S0

1,1

reduction of

increase of

safety factor to 1,0

1,2

Table 9 — Safety factor S1 based on the classification of operating conditions Characteristics relevant to the dynamic strength of belt and belt splices

Classification

Expected service life

normal

short

long

Consequential damage due to failure

normal

small

large

Chemical/physical stresses

normal

low

high

Starting/stopping processes

> 3/day and < 30/day

≤ 3/day

≥ 30/day

Circulation frequency

> 2/hour < 1/minute

≤ 2/hour

≥ 1/minute causes

Safety factor S1

1,7

decrease

increase

of the safety factor to 1,5

1,9

Hence the minimum dynamic splice efficiency k t,min of the belt and belt splice can be calculated as follows:

k t,min = cK ⋅ kK,max ⋅ S0 ⋅ S1

(75)

For coefficient cK the following applies: for textile conveyor belts:

cK

=1

for steel cord conveyor belts:

cK

= 1,25: troughing transition zones

cK

= 1:

horizontal and vertical curves

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DIN 22101:2011-12

Figure The factor cK is chosen as 1,25 where the width related belt tension at the belt edge is calculated according to the method shown in 9.2.3, whereas a more precise calculation method allows a value cK = 1. 1)

The relative dynamic splice efficiency k t,rel of a belt describes the portion of its nominal breaking strength k N :

k t,rel =

kt kN

(76)

The relative dynamic splice efficiency is characteristic for a certain belt type and its splices. Therefore, it is to be incorporated in future product standards as a minimum requirement. Table 10 contains the relative values of dynamic splice efficiency for several belt types. The following aspects shall be taken into consideration for their application:

The values for conveyor belts with textile plies are standard values based on practical experience. It is likely that they will need to be corrected once a larger number of test results are available.

The values for steel-cord conveyor belts have been determined in numerous tests and can be considered as minimum requirements which need to be verified.

In the calculation of the minimum breaking force k N2) only the actual dynamic splice efficiency k t proven for a certain belt type and a certain type of splice may be applied. Table 10 — Values for the relative dynamic splice efficiency k t,rel Belt type Textile belts with one ply Textile belts with two plies and thick intermediate layer Textile belts with more than two plies Textile belts with one ply Textile belts with two plies Steel cord belts Steel cord belts

Belt design according to

Nominal breaking strength kN N/mm

Splicing according to

Relative dynamic splice efficiency a kt,rel

DIN 22102-3 finger splice

DIN 22102-1

630 to 3 150

DIN 22102-1

200 to 2 000

DIN 22102-3, with intermediate tension member

0,35

DIN 22102-1

315 to 3 150

DIN 22102-3, with stepped splice

0,30

DIN 22109-1

800 to 3 150

DIN 22121

0,35

DIN 22109-2

800 to 1 600

DIN 22129-1 DIN EN ISO 15236-1 Along the lines of DIN ISO 22129-1 DIN EN 15236-1b

DIN 22121 with intermediate tension member

0,35

0,30

1 000 to 5 400

DIN 22129-4

0,45

< 1 000 > 5 400

Along the lines of DIN 22129-4

0,45

a

Please note that it cannot be expected that the standard values are achieved with aged or used belts.

b

Translator ’s note. The German original is incorrect. The standard number should read “DIN EN ISO 15236-1”.

2) The term “nominal breaking strength” cited in this context corresponds to the term “mimimum breaking strength” as applied in DIN 22110-3.

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The minimum nominal breaking force kN,min is calculated as follows applying the highest value k K,max in accordance with Equation (75) and Equation (76) under the steady operating condition:

kN,min =

k t,min k t,rel

= cK ⋅ kK,max ⋅

S 0 ⋅ S1 k t,rel

(77)

Taking the value k N,min calculated according to Equation (77) and the width-related mean belt force k at the point of the value k K,max calculated according to Equation (60), the safety factor Smin related to the mean local belt force can be determined:

S min =

k N ,min k

= cK ⋅

kK,max S 0 ⋅ S1 ⋅ k k t,rel

(78)

In order to avoid extreme stresses in non-steady operating conditions and under those conditions that may arise when belts with a partial load are passing through uphill and downhill stretches of the conveyor installation, it shall be checked that the following limiting conditions are met: kt,min ≥ 1,1 ⋅ cK ⋅ kK,a,max

(79)

If this is not the case, the dimensioning of the tension member shall be corrected applying a higher value k t = 1,1 ⋅ cK ⋅ k K,a,max . According to this method, the tension members of the conveyor belts are dimensioned exclusively on the basis of tensile loads. It shall be checked whether they will provide sufficient resistance against additional stresses and whether their transversal rigidity will be sufficient for supporting the bulk material. They are therefore to be designed with a higher strength, if necessary.

10.3 Design and layout of cover layers The thickness of cover layers shall be suitably selected dependent on the material so as to ensure its protective function, even with progressing wear during the scheduled service life of the conveyor belt; the surface structures of the tension member shall remain adequately covered (see also Annex A). If DIN Standards and other normative regulations do not provide further details, the standard values for the minimum thickness of cover layers indicated in Table 11 and corresponding allowances for the carrying side of the belt as provided in Table 12 can be applied. Certain minimum thickness values are required if a belt protection (transverse reinforcement) is incorporated in the conveyor layers. In order to avoid impermissible cupping of the belt, the ratio of the thickness of the cover layer on the carrying side relative to the cover layer on the running side should not exceed 3:1. Table 11 — Standard values for minimum thickness of cover layers on the carrying side and running side of the belt Material of longitudinal tension member

Minimum thickness of cover layer (standard value)

B (cotton) P (polyamide) E (polyester)

1 mm to 2 mm depending on the textile structure

St (steel cords)

0,7 ⋅ dGk, at least 4 mm, with transverse reinforcement possibly more than 4 mm

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Table 12 — Determination of the standard values for additions to the minimum thickness of carrying side cover layers in accordance with Table 11 Characteristics and their assessment Loading conditions Loading frequency Maximum particle size Bulk density Abrasiveness

favourable average unfavourable low average high small average high low average high low average high

Sum of assessment values

Addition to minimum thickness, mm (standard values)

5 to 6

0 to 1

7 to 8

1 to 3

9 to 11

3 to 6

12 to 13

6 to 10

14 to 15

> 10

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

11 Minimum pulley diameter The method described here for determining the minimum pulley diameters follows ISO 3684:1990. The idea behind the determination of minimum pulley diameters is directly linked with the expectations regarding the service life of the conveyor belt and its splices. The minimum pulley diameters to be determined in accordance with the method described in this clause allows the assumption that the endurance strength of splices will be at least equal to the expected service life of the conveyor belt, provided that the splices are properly executed. Smaller pulley diameters than those determined in accordance with the method described in this document can lead to premature failure; they also facilitate wear and tear of pulley surfaces or lagging. The minimum pulley diameters of a belt conveyor installation will be determined by the design and layout, stresses and splicing method of the belt (see also Annex A). A distinction is made between the following groups of pulleys when determining the minimum diameters:

Group A:

drive pulleys and all other pulleys in the zone of high belt tensions

Group B:

return pulleys in the zone of low belt tensions

Group C:

deflection pulleys (change of direction of belt travel ≤ 30°)

If DIN Standards and other normative regulations do not provide further relevant details, the minimum diameters of Group A pulleys, for the four different groups of pulley load factors provided in Table 14, can be determined as follows: DTr = cTr ⋅ dGk

(80)

The factor cTr is a parameter dependent on the material of the tension member according to Table 13 below:

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Table 13 — Parameter cTr for the determination of the minimum pulley diameter Dtr Material of longitudinal tension member

cTr 80 90 108 145

B (cotton) P (polyamide) E (polyester) St (steel cords)

Each diameter determined for Group A pulleys in accordance with the above description shall be rounded up to the next standard value indicated in Table 14. The minimum diameters of Group B and C pulleys shall be chosen in relation to the pulley load factor from Table 14 that is relevant for Group A. Table 14 — Minimum diameter of Group A, B and C pulleys in relation to the utilization of the maximum pulley load factor in the steady operating condition Minimum diameter in mm (without lagging) DTr as per

Pulley load factor

kmax ⋅ 8 ⋅ 100 % kN

a

Equation

over 100 %

over 60 % to 100 %

over 30 % up to 60 %

up to 30 %

(80)

Pulley group

Pulley group

Pulley group

Pulley group

100 125 160 200 250 315 400 500 630 800 1 000 1 250 1 400 1 600 1 800 2 000 a

A 125 160 200 250 315 400 500 630 800 1 000 1 250 1 400 1 600 1 800 2 000 2 200

B 100 125 160 200 250 315 400 500 630 800 1 000 1 250 1 400 1 600 1 800 2 000

C 100 125 160 200 250 315 400 500 630 800 1 000 1 000 1 250 1 250 1 400

A 100 125 160 200 250 315 400 500 630 800 1 000 1 250 1 400 1 600 1 800 2 000

B

C

A

B

C

A

B

C

100 125 160 200 250 315 400 500 630 800 1 000 1 250 1 250 1 400 1 600

100 125 160 200 250 315 400 500 630 800 1 000 1 000 1 250 1 250

100 125 160 200 250 315 400 500 630 800 1 000 1 250 1 250 1 600 1 600

100 125 160 200 250 315 400 500 630 800 1 000 1 000 1 250 1 250

100 125 160 200 250 315 400 500 630 800 800 1 000 1 000

100 125 160 200 250 315 400 500 630 800 1 000 1 000 1 250 1 250

100 125 160 200 250 315 400 500 630 800 1 000 1 000 1 250 1 250

100 125 160 200 250 315 400 500 630 800 800 1 000 1 000

kmax is the mean width-related tension at the point of maximum belt tension in the zone of Group A pulleys in the steady operating condition.

12 Design and layout of transition curves and vertical curve radii 12.1 General Clause 9 deals with the calculation of belt tensions distributed across the belt width proceeding from the specified design of transition curves or convex curves for the subsequent design and layout of the conveyor belt. This clause deals with the calculation of suitable transitions and vertical curves suitable for a specified belt type.

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12.2 Determination of the minimum transition length 12.2.1 General The following applies to 2-roller and 3-roller carrying idler sets in accordance with the approach illustrated in Figure 8 and Equation (77): kK,zul =

kM =

kN ⋅ k t,rel

(81)

cK ⋅ S0 ⋅ S1

B ⋅ k − bS ⋅ kK,zul B − bS

≥0

and

(82)

∆k = kK, zul − kM 12.2.2

(83)

Conveyor belts with textile plies

With Equation (68):

lK − lÜ ∆k = lÜ ELGk

(84)

Δk is calculated in accordance with Equation (83) applying Equations (82) and (81). In the latter equation the parameter cK = 1,0 is to be used. According to Equation (84) it follows that:

lÜ,min =

2 hTr + 2 ⋅ bS2 − 2 ⋅ bS ⋅ (hTr ⋅ sin λ + bS ⋅ cos λ )

(85)

2

∆k + 1 − 1 ELGk

The transition lengths thus calculated provide sufficient accuracy for textile conveyor belts. 12.2.3 Steel cord conveyor belts Meeting the conditions mentioned in 9.2.3, the minimum transition length can be roughly determined as detailed below. With Equation (71):

l K − lÜ ∆k = lÜ, eff ELGk

(86)

Δk is calculated in accordance with Equation (83) applying Equations (82) and (81). For the latter equation for steel cord belts, the parameter cK is to be considered as explained in the comments to Equation (75). According to Equation (86) it follows that:

lÜ,min =

lÜ,min 2 + hTr 2 + 2 ⋅ bS 2 − 2 ⋅ bS ⋅ (hTr ⋅ sin λ + bS ⋅ cos λ ) − ∆k +1 ELGk

∆k ⋅ ∆lÜ ELGk

(87)

with ΔlÜ in accordance with Equation (70). A comparison of Equations (87) and (85) shows that the minimum troughing length for steel cord belts can only be calculated by iteration.

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Equation (86) and Equation (87) may be applied only if there is a piece of belt of sufficient length provided in front of or behind the belt pulley to compensate for length variations. If there is a convex curve right after a transition, for example, the above condition is not met. In this case lÜ,eff shall be replaced by lÜ so that lÜ,min can explicitly be determined using Equation (85). For more precise calculations in which elongations resulting from superimposition are to be taken into consideration, it is recommended that the methods described in [14] and [16] be used.

12.3 Determination of the minimum radius of vertical curves 12.3.1 General Additional elongations due to convex and concave transition curves can be calculated for small and medium curve lengths only with a relatively great effort (see [16]); however their magnitudes will always be smaller than the elongations arising in the middle of long curves. These elongations form the basis of the calculations below. 12.3.2 Convex curves Proceeding from the assumption that the belt tension in the central zone of the conveyor belt is equal to 0 and the belt is operated with the maximum allowable edge tension kK,zul, the minimum radius of a convex curve can be determined applying Equations (72), (74), (77), with cK = 1, as follows:

Re,min =

bS ⋅ sin λ ⋅ ELGk ⋅ S0 ⋅ S1 kN ⋅ k t,rel

(88)

12.3.3 Concave curves In the case of concave belt guidance there will be additional elongations of the belt centre and compression of the edge of the belt with magnitudes that will amount to the same magnitudes as the additional elongations which arise in the case of convex belt guidance as long as the belt does not lift off the carrying idlers. This lifting can be avoided if the following minimum radius is met under all operating conditions.

Ra, i, min =

FT, i, max ′ ⋅ cos δ i g ⋅ mG

(89)

13 Dimensioning of belt turnovers Belt turnovers are helpful as they reduce the soiling and wear of the conveyor belt and improve belt tracking in the lower strand. The length and type of the belt turnovers are dependent on the following parameters:

Belt width

Belt weight

Transverse rigidity

Elastic characteristics

Conveying speed

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A distinction is made between the types of turnovers of the conveyor belt with different supporting principles as illustrated in Figure 11:

Key top: free turnover middle: guided turnover bottom: supported turnover Figure 11 — Design variants for turnovers Table 15 — Standard values for the dimensioning of turnover lengths lW

Type of belt turnover

Maximum belt width mm

Minimum turnover length lW for conveyor belts with cotton plies

EP plies

steel cord plies

Free turnover

1 200

8⋅B

10 ⋅ B

–

Guided turnover

1 600

10 ⋅ B

12,5 ⋅ B

22 ⋅ B

Supported turnover

2 400

–

10 ⋅ B

15 ⋅ B

The standard values provided in Table 15 will be sufficient if the return strand is subjected to low belt tensions. If this is not the case, a more precise calculation is to be carried out (see [12]).

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DIN 22101:2011-12

Annex A (informative) Explanatory notes General

After a 40-year validity, DIN 22101:1942-02 was completely revised and significantly expanded as DIN 22101:1982-02, of which an official English-language version is also available. The next version was published in 2002-08 with some formal and substantial shortcomings that required an early revision. The working group responsible for revising DIN 22101:1982-02 was required to give a more simple description of relationships, wherever possible. This task appeared to be unrealistic. In fact, the current descriptions are even more complex than those given in the 1982 edition because of new knowledge which needed to be incorporated. The working group came to the conclusion that comprehensive computerized calculations, which are widely practiced, should be preferred in order to find improved technical and economical solutions. Nevertheless, simplified calculation methods are referred to wherever feasible (i.e. in cases not requiring high accuracy). Re Clause 5 Theoretical cross section of fill Ath and equivalent angle of slope β

In the case of a troughed belt, the bulk material cross section comprises the “water cross section” and the slope cross section lying above it. Amongst other factors, the shape of the slope will depend on the properties of the bulk material conveyed (e.g. its lumpiness, internal friction, friction coefficient between the conveyor belt and the material conveyed) and also on the operating conditions of the belt conveyor installation (e.g. type of belt feed, tracking of the belt, frequency and duration of vibrations (jarring) of the bulk material conveyed). The slope cross section which actually takes shape is markedly smaller than the cross section given by the static angle of slope. A calculation of this actual cross section can therefore in general only be undertaken under idealized assumptions. In the case of belt conveyor installations with a horizontal layout, in German technical literature the slope cross section is nearly always idealized in the form of a triangular cross section, whilst in International Standard ISO 5048:1989 it is idealized in the form of a segment of a parabola. The working group considered the adoption of the approach according to ISO 5048 and its incorporation in this revision, but finally refrained from this intention for the following reasons: ─ The latest editions of international and German standards use a triangular cross section as a basis (see ISO 7189 or DIN 22200). ─ ISO 3435 uses the “angle of repose” instead of referring to the “surcharge angle” (as mentioned in ISO 5048). ─ Hence it can be assumed that in its next revision, ISO 5048 will use an idealized triangular cross section. Reduction factor ϕ st

When using Equations (10), (11) it shall be borne in mind that the equivalent angle β = 15° used in a large number of calculations of the cross section of fill represents a precautionary value. In the case of inclined installations, to avoid determining cross sections of fill that are considerably too small when using this value, it will be necessary to calculate the factor φ st which is dependent on the inclination, with an angle of slope βdyn close to the static angle of slope (the angle of internal static friction). If accurate values are required in borderline cases, such values are to be determined by tests carried out under conditions which approximate the actual application conditions as closely as possible. Re 6.2

For the calculation of resistances, even complex equations are not excluded here, since computerized calculations of this type are widely practiced.

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In deviation from DIN 22101:1982-02 preference is given to the determination of resistances in each conveyor section. The simplest conceivable layout of a belt conveyor installation consists of two sections only: upper strand and lower strand. Simplifying a belt conveyor installation with uphill and downhill part sections as an installation with only two part sections may yield extremely false results. Re 6.2.3

In order to enable a high degree of accuracy of design and layout, the hypothetical friction coefficient f should be determined more precisely by measuring two major parts of the resistance to motion, i.e. ─ the indentation rolling resistance of the conveyor belt ─ the idler running resistance and by giving an estimate of the remaining portions (see [5]). The indentation rolling resistance is generally measured with a single idler under consideration of the conveyor specific parameters. For the transformation to the indentation rolling resistance of a complete set of idlers, the values of the normal forces acting on each idler must be known. Figure A.1 shows schematically the idealized distribution of the normal forces and the indentation rolling resistance resulting thereof for an idler configuration with three rollers of equal length in a horizontal and straight conveyor [20].

Key 1 Bulk material 2 Direction of travel 3 Load over length on side idler 4 Load over length on centre idler 5 Related indentation rolling resistance on centre idler F'E,m 6 Related indentation rolling resistance on side idler F'E,s Figure A.1 — Idealized distribution of the normal forces and the resulting indentation rolling resistance for a 3-roller idler set with rollers of equal length The dependence of the relevant indentation rolling resistance F'E on the vertical force F'M,v for a single idler can generally be described using the following numerical equation [20]: ′ v ) cb FE′ = ca ⋅ ( FM,

(A.1)

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Here the values ca and cb vary depending on the measured function of the relevant indentation rolling resistance. The indentation rolling resistance FE,3 acting on each idler of a 3-roller idler set is determined by integrating the locally varying value of F'E along the contact line bR under consideration of the local line load. For the total indentation rolling resistance acting on the idler set the following numeric equation applies [20]:

FE,3

Fn,m = ca ⋅ b R, m

cb

ca ⋅ bR,s 2 ⋅ Fn,s ⋅ bR,m + 2 ⋅ ⋅ cb + 1 bR,s

cb

(A.2)

In order to demonstrate the importance of the indentation rolling resistance for a safe dimensioning while at the same time minimizing investments and operating costs, Figure A.2 can be used as it shows examples of the distribution of parts of motion resistances for long belt conveyors: Left column: belt conveyor installation with horizontal layout Right column: belt conveyor installation with approx. 5 % inclination It should be borne in mind that, especially as regards the interpretation of the left column, in the future an increasing use of energy-optimized belts will accordingly reduce the portion of the indentation rolling resistance in the total resistance to motion. Furthermore, the information shown in Figure A.2 should not be taken as basis for the design of conveyors, in view of the dependence of the single parts of the resistance to motion on the operational and design-related parameters of the conveyor.

Key Gradient resistances Special resistances Secondary resistances Flexing resistance of the belt Flexing resistance of the bulk material Idler running resistance Indentation rolling resistance

Figure A.2 — Comparison of the portions of resistance of two long belt conveyor installations of identical design, with different inclinations

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Re 6.3.2

For the secondary resistances a determination of each part is preferable to the determination of a generalized value for the portion of the primary resistance. In determining the friction resistance between conveyor belt and lateral chutes in the acceleration zone of a β dyn , which has an effect on the pressure feeding point, not only shall the Rankine factor cRank = tan 2 45° − 2 exerted on the chute walls by the material in the chute zone, be taken into consideration, but also the coefficient cSchb (information on the magnitudes of βdyn is given in the explanatory notes on the reduction factor φ St). This factor characterizes the increase of the resistance due to additional pressure on the chute walls caused by the dynamic pressure of the material flow of feed material. Consequently, the magnitude of the coefficient cSchb will be equal to 1 for the transfer height 0; it then increases with rising conveying speeds and dropping heights. For the design and layout of customary belt conveyor installations, the product will be cSchb · cRank = 1, whilst the coefficient will be applied as cSchb = 1 for hopper discharge conveyors with high loading heights. Re 6.5

A distinction has not been made between special resistances arising along the entire stretch of the installation and those occurring in individual sections only, as introduced by ISO 5048. The calculation approach detailed in this standard requires the calculation of resistance values for individual sections which implies the consideration of special resistances. Detailed information on the magnitudes of the dynamic angle of slope βdyn in the Rankine factor cRank applied in the calculation of the resistance arising at the material guide bars can be seen from the above comments on the reduction factor φ st. Re 8.3.3

A belt conveyor installation for which the rate of increase of the pulley peripheral forces is limited during starting or stopping procedures, and where the belt is in motion along the entire installation, exhibits a belt acceleration which is independent of location; it behaves in a quasi steady-state fashion, and enables the dynamic additional forces to be determined as mass forces. If the non-quasi steady operating conditions, e.g. the breakaway process, of a belt conveyor installation are to be calculated, it is necessary to determine the additional dynamic forces which arise in this connection with the aid of very complex calculation methods (see [9]). Re 8.4

For the calculations, a distinction is to be made between take-up devices with a fixed take-up pulley and those with a flying take-up pulley. Take-up devices with a fixed pulley are devices on which the position of the driven and non-driven pulleys remains unaltered for every operating condition of the conveyor. The desired adjustment of the tensile force is effected, for example, by means of spindles (screws) or jacks. Depending on the prevailing operating condition, a fixed take-pulley will result in varying forces at the tensioning location. Conversely, the total of the local belt elongations in the upper strand and the lower strand will remain constant; it is equal to twice the take-up pulley travel during the take-up process (take-up pulley path s*Sp). * = const ∑ Δli = 2 ⋅ sSp

(A.3)

Take-up devices with a flying take-up pulley are devices which generate tensile forces which are either independent of the operating conditions and practically constant, or which are suitably matched to the prevailing operating conditions. This is achieved, for example with the aid of take-up weights, pneumatic or hydraulic devices and force-controlled jacks in the case of take-up pulleys with an adequate travel facility. Their mode of operation is, therefore, characterized by the fact that the total of the local belt elongations in the upper strand and the lower strand and consequently the take-up pulley travel vary:

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* ≠ const ∑ Δli = 2 ⋅ sSp

(A.4)

For the calculation of Δli a linear relationship between the elastic elongations and the belt tensions k related to the belt width is generally assumed as a simplification, and this is expressed by means of a mean widthrelated longitudinal modulus of elasticity related to the belt ELGk. Take-up forces that can be adjusted by suitable means shall be adjusted with an adequate speed in order to avoid sliding and slipping on the drive pulleys. In this context, it may be helpful to adjust the take-up force to a higher degree than the calculated one in order to ensure an adequate belt tension at any time. Re Clause 9

The determination of belt tensions in accordance with DIN 22101:1982-02 solely focussed on mean belt tensions. Non-uniform distribution of tensions over the width of a troughed belt as arising in transitions or curves was accounted for by a deduction r1 introduced for this particular purpose. This, however, no longer represents the state of the art in respect of the design and layout of conveyor belts with a high demand of accuracy. For the consideration and determination of additional elongations of the conveyor belt, a distinction shall be made between belts with textile plies and steel-cord belts because of their extremely different elastic characteristics. Elongations of belt edges in the transition zones shall be calculated proceeding from the geometrical approach suggested by Laier (see [13]). Applying this approach, length variations and — for conveyor belts with textile plies — elongations and additional loads can be determined with sufficient accuracy. Length compensations of steel-cord belts involve considerably large belt portions adjacent to the transition zone, which is why higher belt tensions than those which actually arise will be calculated if the approach recommended for conveyor belts with textile plies is applied to steel-cord belts. In the referenced literature (see [12) and [14]) descriptions of safe methods for the precise calculation of steel-cord conveyor belts are provided, which can be applied without problems using computerised support, provided that the mechanical characteristics of these belts are available. If no mechanical characteristics of the belt are available, empirical relationships are provided for conveyor belts in accordance with DIN 22129-1 or DIN EN 15236-11) and steel-cord belts of similar design. These relationships will enable a sufficiently precise prediction of the stresses arising in conveyor belts installed on 2-roller idlers and the more frequently used 3-roller idlers, in many cases. However, the relationships can only be referred to as being correct if the elastic characteristics of the belt currently ensured according to common practice, but not as specified in the applicable standards, are maintained, except for insignificant modifications. Re 9.2

The belt pulley should not be arranged at a level which is lower than the deepest trough level as this requires greater transition lengths or may aggravate the non-uniform distribution of belt tensions across the cross section of the belt. This also increases the load on idlers and bearings. There is also an increasing risk of damage to the belt as the belt may run into the gap between the rollers of the carrying idlers. Re 10.2 Deviating from DIN 22101:1982-02, the belt tensions arising in non-steady operating conditions are not directly taken into consideration in the design and layout of the conveyor belt. Instead, one single limiting condition has been specified which will be applicable only to extremely high stresses in the non-steady operating conditions. Safety factors are to be selected (Table 8 of the previous edition of this standard) in order to take the frequency of non-steady operating conditions into consideration. For this reason the deduction r2 is no longer required for the global consideration of these stresses.

The load-bearing capacity of a conveyor belt is primarily dependent on the dynamic strength of the conveyor belt and belt splices. DIN 22101:1982-02 accounts for this aspect by applying the factor r0. By testing the belt in accordance with DIN 22110-3 the dynamic splice efficiency of the conveyor belt and the belt splices can be 1)

Translator ’s note. The German original is incorrect. The standard number should read “DIN EN ISO 15236-1”.

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determined. The characteristics of the belt splice manufacture are represented by the safety factors S0 provided in Table 8. The magnitude of stresses is expressed by the safety factor S1 to be selected from Table 9. The values in Table 8 and 9 have been verified by comparison with the values obtained from existing and proven heavy-duty conveyor installations. The relationship of the safety factors S0 and S1 to the safety factor Smin in steady operation which is based on the mean belt force over the width of the belt is given in Equation (78). Its use leads to the results in Table A.1. From them the influence of belt specific parameters (k t,rel, S0) and conveyor-specific parameters (S1, k K,max) on the safety factor Smin can be seen. Table A.1 — Minimum values for the safety factor Smin related to the minimum nominal breaking strength of the belt as a function of the parameters S0, S1, kt,rel , cK and k K,max S0 * S1 / k t,rel

cK · k K,max / k

The safety factor S which is related to the nominal breaking strength of the belt k N, as opposed to the value kN,min can be determined analogously to Equation (78) as:

S = Smin ⋅

kN

(A.5)

kN,min

Re 10.3

Because the relevant DIN Standards, International Standards and currently available drafts of European Standards do not contain data regarding the selection of the cover layer thickness, recommendations in this respect have been incorporated in this standard. The cover layer thickness on the running side of the conveyor belt is determined to a great extent by the tension member, or in some cases by the transverse reinforcement, whilst the cover layer thickness on the carrying side of the belt is determined mainly by the stressing of the belt by the material conveyed, and consequently by the following influencing quantities: ─ Nature of material conveyed:

particle size and shape, density, abrasiveness

─ Loading condition:

drop height, resilience of the belt support, difference in speed between bulk material and conveyor belt

─ Loading frequency:

frequency of belt revolutions and scheduled service life of the conveyor belt, number of feeding points

The thickness on the carrying side shall be at least equal to the thickness on the running side of the belt.

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Re Clause 11

The principle and general contents of the method of calculating minimum pulley diameters is identical with that described in ISO 3684:1990. The design and layout according to the ISO Standard is based on the percentage of utilized RMBT (Recommended Maximum Belt Tension), which was defined in DIN 22101:1982-02 k k ⋅ S sta ⋅ 100 % . This standard defines this variable as N and derived from this, the pulley load factor is as 8 kN kmax ⋅ 8 ⋅ 100% , where according to Table 14 k max is the mean width-related tension at the point kN of maximum belt tension in the zone of Group A pulleys in the steady operating condition.

calculated as

This pulley load factor can have values higher than 100 %. Therefore, a fourth category has been introduced for pulleys with loads exceeding the permissible values defined in DIN 22101:1982-02 and ISO 3684:1990. Re Clause 13

This standard contains empirical values for minimum turnover lengths for different belt types and turnover principles.

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Annex B (informative) Explanations of relationship of this standard to international standards The following ISO Standards have been taken into consideration for the revision of this standard: ISO 5048:1989 “Continuous mechanical handling equipment — Belt conveyors with carrying idlers — Calculation of operating power and tensile forces”

The recommendations contained in the above document for the determination of —

the material flow and the troughing cross section

—

the resistance to motion, driving force and power requirement

—

the belt tensions

are in accordance with the contents of this standard, but for the following important exceptions. In the ISO document, the cross section of fill of a troughed belt is composed of an equal sided trapezium or triangle surmounted by a segment of a parabola. In this standard (see Clause 5), the upper portion of the cross section of fill is idealized in the form of an isosceles triangle, in accordance with the German technical literature. This approach has been maintained as it can be assumed that the standard ISO 5048:1989 — like other ISO Standards — will also be revised to refer to a triangular cross section (see Annex A, explanatory notes to Clause 5). According to the recommendations contained in the ISO document for the calculation of the secondary and special resistances, the resistances due to the belt cleaners are deemed to be special resistances. However, as belt cleaners form part of the standard equipment of belt conveyor installations for bulk materials, the associated resistances have been allotted to the secondary resistances in this standard (see 6.3). The ISO document takes the maximum belt tension calculated as a mean value across the belt width as a basis for the design and layout of the conveyor belt. It is expressly limited to simple, but frequently occurring cases. The present standard accounts for non-uniform belt tensions distributed across the cross section of troughed conveyor belts taking into consideration the endurance strength of the conveyor belt and belt splices subject to dynamic loads. ISO/DIS 3870:1996 “Conveyor belts for loose bulk-materials — Description of types and adjustment of take-up devices”

In the above standard, recommendations are given in respect of different types of take-up devices. It defines the standard values of elongation and other influencing variables for the calculation of the take-up distances applicable to tension members of different materials. ISO/DIS 3870:1996, Annex A provides an option for the determination of adequate take-up distances dependent on the belt tensions determined for a belt conveyor installation. Applying the relationships provided in this standard (see 8.4), the elastic elongations of the conveyor belt and the corresponding take-up pulley path can be determined with a relatively high degree of accuracy proceeding from the distribution of belt tensions and the characteristics of the conveyor belt.

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ISO 5293: 1981 “Conveyor belts — Determination of minimum on three idler rollers”

The above standard gives detailed recommendations for the determination of transition distances (transition lengths). It is based on simplified assumptions which were made by Laier (see [13]). The present standard does not give priority to the retroactive calculation of an adequate transition distance, but takes the maximum belt tensions resulting from a given transition distance (or curve layout) as a basis for the design and layout of the conveyor belt. ISO 3684: 1990 “Conveyor belts — Determination of minimum pulley diameter”

The recommendations contained in the above standard for the determination of minimum pulley diameters for belt conveyor installations have been incorporated in this standard in a more concise form adapted to their field of application (see Clause 11). This standard does not contain any variables corresponding to the term “recommended maximum belt tension” (RMBT), which had been introduced in ISO 3684. A pulley load factor k k has been introduced as max ⋅ 8 ⋅ 100 in % with the reference value N . kN 8 Here kmax according to Table 14 is the mean width-related tension at the point of maximum belt tension in the zone of Group A pulleys in the steady operating condition.

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Bibliography DIN 22103, Flame resistant steel cord conveyor belts — Requirements and method of test DIN 22109-5, Conveyor belts with textile plies for coalmining — Branding DIN 22109-6, Conveyor belts with textile plies for coalmining — Part 6: Testing DIN 22110-2, Testing methods for conveyor belt joints — Part 2: Endurance running tests, determination of running time of belt joints at conveyor belts with textile plies DIN 22111, Belt conveyors for underground coal mining — Light construction DIN 22112-3, Belt conveyors for underground coalmining — Idlers — Part 3: Testing DIN 22114, Belt conveyors for underground coalmining — Heavy construction DIN 22118, Conveyor belts with textile plies for use in coal mining — Fire testing DIN 22120, Elastomere scraper plates for belt conveyors in hard coal mines DIN 22200, Continuous mechanical handling equipment — Apron conveyors — Principles for calculation DIN EN ISO 284, Conveyor belts — Electrical conductivity — Specification and test method DIN EN ISO 340, Conveyor belts — Laboratory scale flammability characteristics — Requirements and test method DIN EN ISO 1120, Conveyor belts — Determination of strength of mechanical fastenings — Static test method ISO 1537, Continuous mechanical handling equipment for loose bulk materials — Troughed belt conveyors (other than portable conveyors) — Idlers ISO 3435, Continuous mechanical handling equipment — Classification and symbolization of bulk materials ISO 5048, Continuous mechanical handling equipment belt conveyors with carrying idlers — Calculation of operating power and tensile forces ISO 5293, Conveyor belts — Determination of minimum transition distance on three idler rollers ISO 7189, Continuous mechanical handling equipment — Apron conveyors — Design rules [1]

Vierling, A.: Zum Stand der Berechungsgrundlagen für Gurtförderanlagen. Braunkohle. Wärme und Energie 19 (1967) No. 9, pp. 309–315.

[2]

Schwarz, F.; Zum Eindrückrollwiderstand zwischen Fördergurt und Tragrolle. fördern und heben 17 (1967) No. 12, pp. 712–719.

[3]

Behrens, U.: Untersuchungen zum Walkwiderstand schwerer Förderbandanlagen. Braunkohle, Wärme und Energie 20 (1968) No. 7, pp. 222–231.

[4]

Hager, M. and A. Hintz: The Energy-Saving Design of Belts for Long Conveyor-Systems. Bulk Solids Handling 13 (1993) No. 4, pp. 749–758.

[5]

Hager, M. and H. Simonsen: Berechnung und Auslegung von Gurtförderern für Schüttgut. Braunkohle/Surface Mining 52 (2000) No. 3, pp. 245–259.

[6]

Grimmer, K.-J. and D. Thormann: Zur Problematik der Kraft- und Bewegungsverhältnisse des Schüttgutes an Aufgabestellen von Förderbandanlagen, fördern und heben 17 (1967) No. 6, pp. 345–351.

[7]

Grimmer, K.-J.: Zwei ausgewählte Probleme der Bandfördertechnik. Fortschrittberichte VDI-Zeitschrift, series 13, No. 10, September 1968.

[8]

Funke, H.: Zur Auslegung von Anlaufhilfen für Gurtförderanlagen nach Entwurf DIN 22101. Braunkohle 31 (1979) No. 6, pp. 188–194.

[9]

Funke, H. and F.K. Könneker: Experimental Investigations and Theory for the Design of a Long-Distance Belt Conveyor System. Bulk Solids Handling 8 (1988) No. 5, pp. 567-579.

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[10] Grimmer, K.-J.: Der Einfluss von Trommelbelägen und Feuchtigkeit auf den Reibungsbeiwert zwischen Fördergurt und Antriebstrommel. Braunkohle, Wärme und Energie 18 (1966) No. 9, pp. 325–332. [11] VDI-Guideline 2341; Belt conveyors for bulk material — Idler rolls and idler roll distances. [12] Oehmen, K. H.: Berechnung der Dehnungsverteilung in Fördergurten infolge Muldungsübergang, Gurtwendung und Seilunterbrechung. Braunkohle 31 (1979) No. 12. pp. 394–402. [13] Laier, D.: Ein Versuch zur rechnerischen Erfassung der zusätzlichen Dehnung in der Muldungsstrecke von Fördergurten. Braunkohle, Wärme und Energie 18 (1966) No. 1, pp. 14–19. [14] Hager, M. and S. Tappeiner: Additional Strain in Conveyor Belts Caused by Curves and Transition Geometry. Bulk Solids Handling 13 (1993) No. 4, pp. 695–703. [15] Grimmer, K.-J. and F. Kessler: Spezielle Betrachtungen zur Gurtführung bei Gurtförderern mit Horizontalkurven. Part 1: Anmerkungen and Part 2: Verbesserungen zu herkömmlichen Berechnungsverfahren. Berg- und Hüttenmännische Monatshefte 132 (1987), No. 2, pp. 27–32 and No. 6, pp. 206–211. [16] Oehmen, K. H.: Einfluß vertikaler und horizontaler Kurven auf die Dehnungsverteilung in Fördergurten – Theorie und Anwendung. Braunkohle 31 (1979) No. 12, pp. 340–348. [17] Hager, M.: Stand der Entwicklung von Verbindungen hochfester Stahlseilgurte Braunkohle 39 (1987) No. 7, pp. 251–253. [18] Flebbe, H.: Dynamic Splice Strength-Design Criterion for Conveyor Belts Bulk Solids Handling 8 (1988) No. 5. pp. 581–586. [19] Hager, M. and H.v.d.Wroge: Design of Steel Cord Conveyor Belt Splices. Bulk Solids Handling 11 (1991) No. 4, pp. 849–860. [20] Wennekamp, T.: Tribologie und rheologische Eigenschaften von Fördergurten Dissertation Leibniz Universität Hannover 2008

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December 2011

D

DIN 22101 ICS 53.040.20

Supersedes DIN 22101:2002-08

Continuous conveyors – Belt conveyors for loose bulk materials – Basis for calculation and dimensioning, English translation of DIN 22101:2011-12 Stetigförderer – Gurtförderer für Schüttgüter – Grundlagen für die Berechnung und Auslegung, Englische Übersetzung von DIN 22101:2011-12 Engins de manutention continue – Transporteurs à bandes pour produits en vrac – Principes de base pour le calcul et la conception, Traduction anglaise de DIN 22101:2011-12

Document comprises 56 pages

Normenausschuss Bergbau (FABERG) im DIN DIN-Sprachendienst

©

No part of this translation may be reproduced without prior permission of DIN Deutsches Institut für Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany, has the exclusive right of sale for German Standards (DIN-Normen).

English price group 21 www.din.de www.beuth.de

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1914862

DIN 22101:2011-12

A comma is used as the decimal marker.

Contents

Page

Foreword ......................................................................................................................................................... 4 1

Scope ................................................................................................................................................. 5

2

Normative references ....................................................................................................................... 5

3

Terms and definitions ...................................................................................................................... 6

4

Symbols and units ............................................................................................................................ 7

5

Volume flow and mass flow ........................................................................................................... 12

6 6.1 6.2 6.2.1 6.2.2 6.2.3 6.3 6.3.1 6.3.2 6.3.3 6.4 6.5 6.5.1 6.5.2

Resistance to motion and required power for the steady operating condition ....................... 14 General ............................................................................................................................................. 14 Primary resistances ........................................................................................................................ 15 General ............................................................................................................................................. 15 Determination of primary resistance FH ....................................................................................... 15 Determination of the hypothetical friction coefficient ................................................................ 16 Secondary resistances ................................................................................................................... 17 General ............................................................................................................................................. 17 Determination of individual secondary resistances ................................................................... 18 Approximate calculation of secondary resistances.................................................................... 19 Gradient resistance ........................................................................................................................ 20 Special resistances ........................................................................................................................ 20 General ............................................................................................................................................. 20 Determination of individual special resistances ......................................................................... 20

7 7.1 7.2 7.2.1 7.2.2 7.2.3 7.2.4 7.2.5 7.3 7.3.1 7.3.2

Design and layout of the drive system ......................................................................................... 21 General ............................................................................................................................................. 21 Location of the drive units, size and number of drive motors ................................................... 22 General ............................................................................................................................................. 22 Horizontal and slightly inclined installations .............................................................................. 22 Uphill conveying installations ....................................................................................................... 23 Downhill conveying installations .................................................................................................. 23 Installations with uphill and downhill sections ........................................................................... 23 Starting, stopping and holding ...................................................................................................... 23 Starting ............................................................................................................................................ 23 Stopping and holding ..................................................................................................................... 24

8 8.1 8.2 8.2.1 8.2.2 8.2.3

Belt tensions and take-up forces .................................................................................................. 25 General ............................................................................................................................................. 25 Required belt tensions ................................................................................................................... 25 General ............................................................................................................................................. 25 Minimum belt tensions required for the transmission of pulley peripheral forces ................. 25 Minimum belt tensions required for the limitation of the belt sag and for correct belt guiding ............................................................................................................................................. 27 Local belt tension variations in the top and return strands ....................................................... 27 General ............................................................................................................................................. 27 Steady operating condition ........................................................................................................... 28 Non-steady operating condition.................................................................................................... 28 Take-up forces and take-up distances ......................................................................................... 29 Local belt tensions in the upper and lower strands .................................................................... 31 General ............................................................................................................................................. 31 Non-steady operating conditions.................................................................................................. 31 Steady operating condition ........................................................................................................... 31

8.3 8.3.1 8.3.2 8.3.3 8.4 8.5 8.5.1 8.5.2 8.5.3

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9 9.1 9.2 9.2.1 9.2.2 9.2.3 9.3 9.3.1 9.3.2

Distribution of belt tensions across the belt width ...................................................................... 31 General ............................................................................................................................................. 31 Transition curves ............................................................................................................................. 32 General ............................................................................................................................................. 32 Distribution of the belt tension for textile conveyor belts ..........................................................34 Distribution of the belt tension for steel cord conveyor belts ....................................................34 Curves............................................................................................................................................... 35 Horizontal curves ............................................................................................................................ 35 Vertical curves ................................................................................................................................. 35

10 10.1 10.2 10.3

Design and layout of the conveyor belt ........................................................................................ 37 General ............................................................................................................................................. 37 Design and layout of the tension member .................................................................................... 37 Design and layout of cover layers ................................................................................................. 40

11

Minimum pulley diameter ............................................................................................................... 41

12 12.1 12.2 12.2.1 12.2.2 12.2.3 12.3 12.3.1 12.3.2 12.3.3

Design and layout of transition curves and vertical curve radii.................................................42 General ............................................................................................................................................. 42 Determination of the minimum transition length ......................................................................... 43 General ............................................................................................................................................. 43 Conveyor belts with textile plies .................................................................................................... 43 Steel cord conveyor belts ............................................................................................................... 43 Determination of the minimum radius of vertical curves ............................................................ 44 General ............................................................................................................................................. 44 Convex curves ................................................................................................................................. 44 Concave curves ............................................................................................................................... 44

13

Dimensioning of belt turnovers ..................................................................................................... 44

Annex A (informative) Explanatory notes .................................................................................................... 46 Annex B (informative) Explanations of relationship of this standard to international standards ........53 Bibliography .................................................................................................................................................. 55

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Foreword This standard has been prepared by Working Committee Fördergurte (Conveyor Belts) of the Normenausschuss Bergbau (FABERG) (Mining Standards Committee). Annexes A and B are provided for information and are informative. This standard relates to the standards ISO 5048:1989, ISO/DIS 3870:1996, ISO 5293:1981 ISO 3684:1990 issued by the International Organization for Standardization (ISO) (see Annex B).

and

Amendments This standard differs from DIN 22101:2002-08 as follows: a) the method for calculating motion resistances has been extended to cover belt conveyors where the number of sections relevant for the calculation varies for the top and bottom strands; b) the start-up factor pA and braking factor pB are now defined; c) the clause “transition curves” has been condensed by combining the theoretical principles common to textile and steel cord belts; d) in the clause on the design and layout of the conveyor belt a factor has been introduced to account for an irregular distribution of belt tension across the belt width; e) information on calculating the pulley load factor has been added in Clause “Minimum pulley diameter”; f)

Clause “Determination of the minimum transition length” has been completely revised;

g) normative references have been updated; h) the standard has been editorially revised. Previous editions DIN BERG 2101 Part 1: 1933-07 DIN BERG 2101 Part 2: 1933-07 DIN BERG 2101 Part 3: 1933-07 DIN 22101: 1942-02, 1982-02, 2002-08

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1

Scope

This standard is applicable to belt conveyor installations for conveying bulk materials, and contains the principles relating to their design. The standard makes it possible to specify essential requirements applicable to major belt conveyor components such as drives, brakes and take-up devices for particular conveying conditions. The standard also gives a description of the design and dimensioning of the conveyor belt.

2

Normative references

The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. DIN 15207-1, Continuous mechanical handling equipment — Idlers for belt conveyors — Main dimensions of idlers for belt conveyors for bulk material DIN 22102-1, Conveyor belts with textile plies for bulk goods — Part 1: Dimensions, specifications, marking DIN 22102-3, Conveyor belts with textile plies for bulk goods — Part 3: Permanent joints DIN 22107, Continuous mechanical handling equipment — Idler sets for belt conveyors for loose bulk materials — Principal dimensions DIN 22109-1, Conveyor belts with textile plies for coal mining — Part 1: Monoply belts for underground applications — Dimensions, requirements DIN 22109-2, Conveyor belts with textile plies for coal mining — Part 2: Rubber-belts with two plies for underground applications — Dimensions, requirements DIN 22109-4, Conveyor belts with textile plies for coal mining — Part 4: Rubber-belts with two plies for above ground applications — Dimensions, requirements DIN 22110-3, Testing methods for conveyor belt joints — Part 3: Determination of time strength for conveyor belt joints (dynamical testing method) DIN 22112-1, Belt conveyors for underground coal mining — Idlers — Part 1: Dimensions DIN 22112-2, Belt conveyors for underground coal mining — Idlers — Part 2: Requirements DIN 22121, Conveyor belts with textile plies for coal mining — Permanent joints for belts with one or two plies — Dimensions, requirements, marking DIN 22129-1, Steel cord conveyor belts for underground coal mining — Dimensions, requirements DIN 22129-4, Steel cord conveyor belts for use in underground coal mining — Belt joints — Dimensions, requirements DIN EN 15236-1 1) Steel cord conveyor belts — Part 1: Design, dimensions and mechanical requirements for conveyor belts for general use ISO 3684:1990-3, Conveyor belts — Determination of minimum pulley diameters

1)

Translator ’s note. The German original is incorrect. The standard number should read “DIN EN ISO 15236-1”.

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3

Terms and definitions

For the purposes of this document, the following term and definition apply. 3.1 belt conveyor continuous belt conveyor for bulk materials with circulating conveyor belts which feature tension members of textile or steel cord ply and cover layers of rubber or plastic supported on carrying idlers and idler stations, and driven or braked by friction grip via pulleys and driving belts where appropriate NOTE Conveyor belts with cover plates made of rubber or plastic are described e.g. in DIN 22102-1, DIN 22109-1, 1) DIN 22109-2, DIN 22109-4, DIN 22129-1 and DIN EN 15236-1 . Idlers and idler sets are described e.g. in DIN 15207-1, DIN 22107, DIN 22112-1 und DIN 22112-2.

1)

Translator ’s note. The German original is incorrect. The standard number should read “DIN EN ISO 15236-1”.

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4

Symbols and units Table 1 — Symbols and units Symbol

Meaning

Unit m2

A

Cross section of fill

A1

Partial cross section above water fill

m2 (mm2) a

A2

Partial cross section with β = 0 (water fill)

m2 (mm2) a

AGr

Effective contact area between cleaner and belt

mm2

B

Belt width

mm

C

Coefficient for the approximate calculation of total secondary resistance

DTr

Pulley diameter

ELGk

Elasticity module related to the width of the belt

Fa

Forces resulting from acceleration/deceleration under non-steady operating conditions

N

FAuf

Inertia resistance of material conveyed and frictional resistance between material conveyed and belt at the feeding point

N

FE

Indentation rolling resistance: Sum of all indentation rolling resistances in the upper and/or lower strands

N

FE,3

Indentation rolling resistance for a 3-roller idler set

N

F' E

Indentation rolling resistance related to the belt width

FGa

Resistances of material transfer devices arranged along the belt conveyor path

N

FGr

Friction resistance caused by belt cleaners

N

FH

Primary resistance: Sum of all primary resistances in the upper and/or lower strands

N

F' M,v

Vertical force related to the belt width

Fn

Normal force acting on an idler

N

FN

Secondary resistance: Sum of all secondary resistances in the upper and/or lower strands

N

FR

Running resistance of idlers: Sum of all running resistances in the upper and/or lower strands

N

FRst

Camber resistance: Sum of all camber resistances for an idler set

N

FS

Special resistance: Sum of all special resistances in the upper and/or lower strands

N

FSch

Friction resistance between material conveyed and lateral chutes outside the acceleration zone of feeding points

N

– mm N/mm

N/m

N/mm

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Table 1 (continued) Symbol

Meaning

Unit

FSchb

Friction resistance between material conveyed and lateral chutes within the acceleration zone of a feeding point

N

FSp

Take-up force at the axis of the take-up pulley

N

FSt

Gradient resistance: Sum of all gradient resistances in the upper and/or lower strands

N

FT

Local belt tension (strand tension)

N

FTm

Mean belt tension of upper strand and lower strand

N

FTr

Total pulley peripheral force

N

FT1

Belt tension (strand tension) of the belt running onto a pulley

N

FT2

Belt tension (strand tension) of the belt running off a pulley

N

FW

Motion resistance: Sum of all resistances to motion in the upper and/or lower strands

N

Im

Mass flow

kg/s

Im,N

Nominal mass flow

kg/s

IV

Volume flow

m3/s

IV,N

Nominal volume flow

m3/s

L

Distance axis-to-axis

m

PM

Total power of drive motors

kW

PM,N

Nominal drive motor capacity

kW

PW

Total power at the periphery of the driving pulley(s) required due to the motion resistances in steady operation

kW

Ra

Radius of a concave vertical transition curve

m (mm)a

Re

Radius of convex vertical transition curve

m (mm)a

S

Safety factor related to the nominal breaking strength of the belt

–

S0

Safety factor taking belt splice manufacturing characteristics into consideration

–

S1

Safety factor taking into consideration expected belt life and operational stresses on belt

–

Smin

Minimum value for the safety factor, related to the minimum nominal breaking strength of the belt

–

Acceleration or deceleration

m/s2

b

Usable belt width

mm

bR

Length of the contact line between belt and idler face

bS

Part of belt lying on a side idler (only for 2- or 3-roller idler sets)

bSch

Clear width between chutes

m

ca

Factor used in the numerical equation describing the indentation rolling resistance determined in relation to the belt width

–

cb

Exponent used in the numerical equation describing the indentation rolling resistance determined in relation to the belt width

–

m mm

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DIN 22101:2011-12

Table 1 (continued) Symbol

Meaning

Unit

cK

Coefficient for determination of the minimum dynamic splice efficiency corresponding to the width related belt tension in the belt edges

–

cR

Coefficient for calculating the masses of the idlers reduced to their periphery

–

cRank

Rankine factor

–

cRst

Coefficient for the calculation of camber resistance

–

cSchb

Coefficient for taking into account additional resistance between material conveyed and lateral chutes in the feeding zones caused by dynamic pressure of the mass flow fed in

–

cTr

Coefficient for the determination of the minimum pulley diameter

–

cÜ

Coefficient for the determination of the standard value for the minimum transition length

–

dGk

Thickness of the load-bearing longitudinal tension member (without outer warp layer or weft, for example)

e

Base of natural logarithms (e = 2,718 28.....)

eK

Distance from the centre line of belt plies at the edge of the belt to the neutral axis of the belt

mm

eM

Distance from the centre line of belt plies at the centre of the belt to the neutral axis of the belt

mm

f

Hypothetical friction coefficient for the approximate calculation of the total primary resistance to motion of the upper and lower strands

–

fi

Hypothetical friction coefficient for the approximate calculation of the primary resistance of a section of the upper or lower strand

–

g

Acceleration due to gravity (g = 9,81 m/s2)

h

Height difference of a section of the upper or lower strand (h > 0 for uphill belt travel, h < 0 for downhill belt travel)

hK0

Distance from the belt edge to the deepest level of the trough

mm

hK1

Distance from the belt edge to the pulley surface level

mm

hrel

Maximum belt sag related to spacing between carrying idlers

hTr

Lift of the pulley in the transition zone above the deepest level of the trough

k

Belt tension related to belt width

N/mm

kK

Tension at belt edge related to belt

N/mm

kM

Tension at belt centre related to belt

N/mm

kN

Nominal belt breaking strength related to belt width

N/mm

kN,min

Minimum nominal belt breaking strength related to belt width

N/mm

kt

Reference dynamic splice efficiency

N/mm

kt,rel

Relative reference dynamic splice efficiency

∆k

Difference between width-related belt tension at the edges and that at the centre of the conveyor belt

l

Length of a section of upper or lower strand

m

lb

Length of the acceleration path in the feeding zone

m

mm –

m/s2 m

– mm

– N/mm

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DIN 22101:2011-12

Table 1 (continued) Symbol

Meaning

Unit

lK

Length of the belt edge in the transition zone

m

lM

Length of the central roller in a 3-roller idler set

lSch

Length of lateral chutes

m

lR

Spacing between carrying idlers

m

lÜ

Length of transition zone

m

lÜ,eff

Reference length of transition zone for steel cord belts

m

∆lÜ

lÜ,eff − lÜ for steel cord belts

m

lW

Belt turnover length

m

Σm

Total of translatorially moving masses and non-driven and non-braked rotating masses reduced to their periphery

kg

m'G

Line load resulting from the conveyor

kg/m

m'L

Line load resulting from the material conveyed

kg/m

m'L,N

Line load resulting from nominal load

kg/m

m'R

Line load resulting from rotating idler parts

kg/m

n

Number of sections of the upper or lower strands of a belt

–

pA

Start-up factor related to the drive pulley: ratio of the total pulley peripheral force at start-up FTr,A , to the force FW determined by the height and distribution of the material conveyed

–

pA0

Start-up factor related to the drive: ratio of the drive torque resulting from the effective drive characteristics during the start-up phase of the conveyor and the nominal torque corresponding to the rated power of the motors actually installed PM,inst

–

pB

Braking factor related to the brake pulley: ratio of the total pulley peripheral force at braking FTr,B to the force FW determined by the height and distribution of the material conveyed

–

pB0

Braking factor related to the brake: ratio of the braking torque resulting from the effective braking characteristics during the braking phase of the conveyor and the nominal torque corresponding to the rated power of the motors actually installed PM,inst

–

pGr

Pressure between belt cleaner and belt

q

Coefficient for the determination of primary resistances for the upper and lower strands

–

sB

Braking distance

m

sSp

Take-up pulley travel

m

tB

Braking time

s

v

Conveying speed

m/s

v0

Feeding speed in the direction of conveying

m/s

zR

Number of carrying idlers in one section (upper strand or lower strand)

–

zRst

Number of carrying idlers in one section (upper or lower strand) set at a tilt

–

mm (m)a

N/mm2

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DIN 22101:2011-12

Table 1 (continued) Symbol

Meaning

Unit

α

Angle of pulley belt wrap

β

Equivalent angle of slope for the calculation of the partial cross-section A1th

°

βdyn

Dynamic angle of slope of the material conveyed

°

δ

Angle of inclination of a section of upper or lower strand, δ > 0 for uphill belt travel, δ < 0 for downhill belt travel)

°

ε

Angle of tilt of a side idler

°

∆ε K

Additional elongation (pos. or neg.) at the edge of the belt in concave or convex transition curves, in relation to the neutral belt axis

–

∆εK∞

Limit of ∆εK at the centre of very long transition curves

–

∆ε M

Additional elongation (pos. or neg.) at the centre of the belt in concave or convex transition curves, in relation to the neutral belt axis

–

∆εM∞

Limit of ∆εM at the centre of very long transition curves

–

∆ε ∞

Difference of elongation at the belt edge and in the middle of very long transition curves

–

ηges

Overall efficiency of all transmission members between motor shaft and pulley shaft

–

λ

Troughing angle of the conveyor belt in the upper strand or lower strand

°

µ

Friction coefficient between belt and pulley

–

µ1

Friction coefficient between belt and material conveyed

–

µ2

Friction coefficient between material conveyed and lateral chutes

–

µ3

Friction coefficient between belt and carrying idler

–

µ4

Friction coefficient between belt and belt cleaner

–

ρ

Bulk density of material conveyed

ϕ

Effective filling ratio

–

ϕ Betr

Filling ratio corresponding to the operating conditions of the conveyor

–

ϕ St

Reduction factor of filling ratio for the theoretical total cross section of fill Ath in the case of inclined installations

–

ϕ St1

Reduction factor of filling ratio for the theoretical partial cross section A1,th in the case of inclined installations

–

a

° or rad

kg/m3

in some equations these variables are used with the unit mentioned in brackets.

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DIN 22101:2011-12

Table 2 — Indices Index A B a eff erf i j inst m max min o s th u zul *

5

Meaning At start-up At stopping (braking) Non-steady operation (start-up, braking) Effective Required Running index for belt strand sections Running index for belt deflection points (at pulleys) Installed Centre idler Maximum Minimum Upper strand Side idler Theoretical Bottom strand Allowable Index for identifying operating conditions

Volume flow and mass flow

The maximum volume flow and mass flow of a belt conveyor is determined by the potential cross section of fill, which is dependent on the dynamic angle of slope of the material conveyed and on the feeding conditions, among other factors. To calculate the maximum volume and mass flow a simple equivalent geometrical cross section needs to be found. This theoretical cross section A th is calculated from the shape of the conveyor belt on the carrying idlers and from the shape of the slope formed by the material conveyed. Figure 1 shows this cross section for a belt supported by a 3 roller idler set, which is commonly used.

Figure 1 — Theoretical cross section of fill in the case of horizontal conveyance and a 3 roller idler set

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DIN 22101:2011-12

The theoretical cross section of fill is dependent on the length and arrangement of the carrying idlers (troughing angle), the usable belt width b and the equivalent slope angle β describing a cross section of the same area as the actual one. In this case, the usable belt width b shall be calculated as a function of the belt width B as follows: B ≤ 2 000mm

b = 0,9 × B − 50 mm

(1)

B > 2 000mm

b = B − 250 mm

(2)

The usable belt width of belt conveyors with horizontal curves and inclined idlers installed to stabilize the belt may be smaller. With 1-, 2- and 3-roller idler sets in horizontal belt conveyors, the theoretical cross section of fill A th that is equivalent to the real cross section of fill can be established using angle β as the sum of partial cross sections A1,th and A2,th (see [1], Figure 1 and Annex A): A1,th = [ lM + (b − lM ) ⋅ cos λ ] 2 ⋅

tanβ 4

(3)

b − lM b − lM A 2,th = lM + ⋅ cos λ ⋅ ⋅ sin λ 2 2

(4)

The selection of an equivalent slope angle depends on the material to be conveyed as well as on the length of the conveying distance. In case of lacking experience in selecting an adequate slope angle, the following standard values can be applied: The value will be β = 20° for materials with normal flow properties. Values below β = 20° down to β = 0° will be characteristic for nearly liquid materials. Equivalent slope angles of more than 20° can be applied only in case of materials with high internal friction. For 1-roller and 2-roller idler sets, the length of the central roller shall be taken to be lM = 0. The following parameters can be calculated on the basis of the theoretical cross section fill:

I V, th = Ath ⋅ v

(5)

ϕ = ϕBetr ⋅ ϕ St

(6)

Nominal volume flow

IV,N = ϕ ⋅ Iv,th

(7)

Nominal mass flow

Im,N = ϕ ⋅ ρ ⋅ Iv,th

(8)

Line load resulting from nominal load

m'L,N = ϕ ⋅ ρ ⋅ Ath

(9)

Theoretical volume flow And on the basis of the effective filling ratio the following can be calculated:

The filling ratio ϕ Betr depends on:

properties of material conveyed lumpiness max. edge length dynamic angle of slope βdyn (characterizing the actual dynamic property of the slope)

operating conditions of the conveyor uniform material feeding tracking of the conveyor belt reserve capacity

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DIN 22101:2011-12

For horizontal, straight conveyors, the theoretical cross section can be fully utilized if uniform feeding of material and straightforward belt movement is ensured (ϕ = ϕ Betr = 1). The reduction factor ϕ St takes into consideration the fact that the partial cross section A1,th is reduced under sloped conveying conditions:

ϕ St = 1 −

A1,th Ath

⋅ (1 − ϕ St 1)

(10)

A properly aligned belt uniformly loaded with non-lumpy material and δ max ≤ β dyn can be calculated as follows:

ϕSt1 =

cos2 δmax − cos2 β dyn 1 − cos2 β dyn

(11)

Applying Equations (10) and (11) it shall be borne in mind that the angle of slope for downhill conveying cannot be higher than the actual dynamic angle of slope βdyn (see also Annex A) and that only the partial cross section A2,th is available for conveying.

6

Resistance to motion and required power for the steady operating condition

6.1 General The method described below for the determination of motion resistances, the required power, and the local belt tensions yields fairly realistic results for state-of-the-art technology, even for complex conveyor installations and all possible operating conditions. Experienced design engineers can simplify the calculation method for ordinary belt conveyors with manageable operating conditions and for those that do not require a high degree of accuracy, provided that safety requirements are met. Prior to calculating the resistance to motion, individual base values shall be estimated. These values shall be checked and corrected, if necessary, after completing the calculation. The calculation shall be repeated as many times as necessary to match the results with the input values. During steady operation, the forces resisting belt movement (resistances to motion) FW are calculated by the summation of friction, weight and mass forces. The required power for the conveyor PW is calculated as a product of the total motion resistance of the upper and lower strands and the conveying speed v. PW = FW ⋅ v

(12)

For the calculation of motional resistances, the following parts are defined:

primary resistance FH

secondary resistance FN

gradient resistance FSt

special resistance FS

The sum of the above types of resistance to motion FW is equal to the total pulley peripheral force FTr to be transmitted to the belt:

FW =

no

∑ i =1

FW,o,i +

nu

∑ FW,u,i = FH + FN + FSt + FS = FTr

(13)

i =1

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DIN 22101:2011-12

The resistances shall be established for individual sections. Each section is characterized by the fact that parameters such as the angle of inclination i of the section, the hypothetical friction coefficients f i and the line loads due to material to be conveyed m'R,i and the rotating idler parts m'L,i have constant values for both the upper and lower strands. Hence it is advisable — particularly with regard to computer calculations — to assign a running index i to the start points and end points of all part sections of the conveyor installation, starting from the tail station toward the head station. Upper strand values shall be identified by index o, lower strand values by index u (see Figure 2). In order to maintain the assigned descriptions, belt deflection points (at pulleys) and their parameters shall be identified by index j (see Figures 5 and 6).

6.2 Primary resistances 6.2.1

General

Primary resistance occurs along the entire length of the conveyor path. The parameters of primary resistance shall be determined for individual sections.

Figure 2 — Creation of belt sections and calculation of motion resistances for each section in a steady operating condition 6.2.2

Determination of primary resistance FH

The primary resistances FH,i of all sections are to be determined separately for the upper and lower strands of each individual section, in a simplified manner assuming a linear relationship between the resistance and the moved load:

[

′ i + (mG ′ + mL, ′ i ) ⋅ cosδ i FH, i = li ⋅ fi ⋅ g ⋅ mR,

]

(14)

The primary resistances of the upper strand sections FH,o,i and lower strand sections FH,u,i are indispensable for the determination of belt tensions (see 8.3). The primary resistance of the conveyor, i.e. the sum of primary resistances for the upper strand FH,o and those for the lower strand FH,u can be calculated as follows:

FH =

no

∑

i =1

F H,o,i +

nu

∑ F H,u,i = FH,o + FH,u

(15)

i =1

Primary resistances for each section shall be calculated for the nominal loading range (filling ratio ϕ within the range 0,7 to 1,1) along the entire conveyance path. For belt conveyors with downhill and uphill sections, and for extreme loading conditions (non-uniform load, partial loading or idling), the cumulative resistance determined under these conditions can deviate significantly from that arising under nominal conditions.

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DIN 22101:2011-12

6.2.3

Determination of the hypothetical friction coefficient

The selection of a hypothetical friction coefficient fi is of major importance as regards the magnitude of primary resistances. This is especially important for conveyors with small gradient resistances. Attempts to be on the safe side with calculations, together with a case-by-case inaccurate description of the operating features and a wide range of possible values can lead to considerable over-dimensioning. In order to avoid disproportional dimensioning, the friction coefficients fi are to be established as precisely as possible for the individual sections. The values for f given in Table 4 can serve as guidelines in a global calculation of the sum of all primary resistances in the top and bottom strands. The friction coefficient fi of a section is defined mainly by the rolling resistance of the carrying idlers and the indentation rolling resistance of the belt. Also the flexing resistance can have a large share in this, if the sag of the conveyor belt is relatively large. For a more precise determination of the friction coefficient fi aiming for a safe conveyor design combined with a minimum investment and lower operational costs, the running resistance of the idlers and the indentation rolling resistance can be measured for given parameters and the other resistances can be estimated (see [2], [3], [4] and [5]). With a normal magnitude of flexing resistance the running resistance of the idlers and rolling indentation resistance of the loaded strand (usually of the upper strand) with a filling ratio ϕ within the range of 0,7 ≤ ϕ ≤ 1,1, generate between 50 % and 85 %, on average 70 %, of the primary resistance FH,o. They amount to approx. 90 % of the primary resistance for the unloaded strand (usually that of the lower strand, FH,u. Considering this following relationships apply: Upper strand (loaded)

FH,o =

1 ⋅ ( FR,o + FE,o ) qo

(16)

Lower strand (unloaded)

FH,u =

1 ⋅ ( FR,u + FE,u ) qu

(17)

with 0,5 ≤ qo ≤ 0,85, on average qo = 0,7 and qu = 0,9. Guidelines for estimating coefficient qo are given in Table 3. Table 3 — Standard values for coefficient q0 for a filling ratio ϕ within the range 0,7 ≤ ϕ ≤ 1,1 Characteristic

Values for characteristic

Relative sag hrel

medium

high, but ≤ 0,01

low

Internal friction of material conveyed

medium

high

low

Running resistance of carrying idlers

medium

low

high

Indentation rolling resistance

medium

low

high

Coefficient qo

Standard value ≈ 0,7

causes reduction of increase of coefficient qo to

0,5

0,85

Equations (16) and (17) can be used to check the plausibility of, and if necessary adjust, the values of the primary resistances determined using the hypothetical friction coefficients f i and the other resistances as in Equations (14) and (15).

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DIN 22101:2011-12

If there are no values which have been obtained by measurement or on the basis of experience, or if only an approximate dimensioning is intended, standard values for the hypothetical friction coefficient f can be selected from Table 4 for estimating the total primary resistance of the upper and lower strands on the basis of the operating conditions and design features (see also Annex A). These values are based on numerous combined upper and lower strand measurements and for the following limiting conditions:

3 roller fixed idler sets in the top run

carrying idlers with antifriction bearings and labyrinth seals

values of relative belt sag hrel ≤ 0,01

filling ratio ϕ within a range from 0,7 to 1,1 Table 4 — Standard values for the hypothetical friction coefficient f for estimating the total primary resistance in the upper and lower strands of conveyors with a filling ratio ϕ within the range 0,7 to 1,1 Characteristic

Values for characteristic

Internal friction of material to be conveyed

medium

low

high

Belt conveyor alignment

medium

good

bad

Belt tension

medium

high

low

Operating conditions (dusty, sticky)

medium

good

bad

Idler diameter

108 to 159

> 159

< 108

Spacing of upper strand idlers in m

1,0 to 1,5

< 1,0

> 1,5

Spacing of lower strand idlers in m

2,5 to 3,5

< 2,5

> 3,5

4 to 6

6

Troughing angle in °

25 to 35

< 25

> 35

Ambient temperature in °C

15 to 25

> 25

< 15

Belt speed in m/s

Friction coefficient f

Standard value ≈ 0,020

causes reduction of increase of friction coefficient f to 0,010 0,040

When the drives function as generators, an assumed smaller friction coefficient f leads to greater safety with regard to the dimensioning; for drives functioning as motors this effect will be achieved by assuming a larger friction coefficient f . The application of these friction coefficients f in the calculation of primary resistances according to Equation (14) is acceptable only if the calculation does not need to be very accurate.

6.3 Secondary resistances 6.3.1

General

Secondary resistances include friction resistances and inertia resistances arising only in some places on the conveyor. Secondary resistances are calculated from several individual resistances. The secondary resistances in the upper strand FN,o,i and in the lower strand FN,u,i are required for the calculation of the belt tensions (see 8.3).

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DIN 22101:2011-12

The secondary resistance of the conveyor belt FN, i.e. the sum of secondary resistances in the upper strand FN,o and in the lower strand FN,u, is calculated as:

FN = 6.3.2

no

∑

i =1

F N,o,i +

nu

∑ F N,u,i = FN,o + FN,u

(18)

i =1

Determination of individual secondary resistances

Inertia resistance of material conveyed and friction resistance between material conveyed and the belt in the feeding zone FAuf = Im ⋅ (v − v0)

(19)

Friction resistance between conveyor belt and lateral chutes in the acceleration zone of a feeding point:

Figure 3 — Chute configuration The following applies to feeding points with 3-roller idler sets and bSch > lM (see [6]):

(

)

2

2 ⋅ Im 2 2 tan λ ⋅ ρ ⋅ g ⋅ l b ⋅ µ 2 FSchb = c Schb ⋅ cRank ⋅ − bSch − lM ⋅ 2 4 bSch (v + v 0 ) ⋅ ρ for 0 ≤ v0 ≤ v 2 2 v − v0 lb > lb,min = 2 ⋅ g ⋅ µ1

(20)

(21)

with

β dyn cRank = tan 2 45° − 2

(22)

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DIN 22101:2011-12

lM = bSch shall be applied for bSch ≤ lM lM = 0 shall be applied for 2-roller idler sets lM = bSch shall be applied for 1-roller idlers The following approach applies to other types of idler set (e.g. 5-roller idler sets): a) determination of the height of material pressing against lateral chute walls on the basis of the volume flow and average conveying speed in the feeding zone (v + v0)/2. b) determination of potential wall pressure caused by a fluid pressing against the side walls of the chute. If applicable, multiply with cSchb and cRank. c) determination of friction resistance from average wall pressure, friction coefficient and size of wall areas The following applies to belt conveyors of customary design: cSchb ⋅ cRank = 1 (see Annex A) As a general rule, the friction coefficients µ1 and µ2 are within the range from 0,5 to 0,7. Friction resistance caused by belt cleaners For the use of scraper bars as belt cleaners, the friction resistance can be determined as follows: FGr = µ4 ⋅ pGr ⋅AGr

(23) 2

2

As a general rule, the contact pressure pGr is within a range of approx. 0,03 N/mm to 0,1 N/mm , whereas the friction coefficient µ4 approximately ranges between 0,6 and 0,7. The total secondary resistance FN is the sum of the secondary resistances of each section.

FN =

no

nu

i =1

i =1

∑ F Auf,o,i + FSchb,o,i + FGr,o,i + ∑ F Auf,u,i + FSchb,u,i + FGr,u,i = FN,o + FN,u

(24)

Further secondary resistances are the bending resistance of the conveyor belt where it runs over a pulley and the resistance of the bearings of non-driven pulleys. These secondary resistances are relatively small in conveyors of customary design as compared with the above mentioned resistances and can be neglected in almost all cases. If necessary, calculation equations can be taken from the referenced documents (e.g. [1]). 6.3.3

Approximate calculation of secondary resistances

If the portion of secondary resistances in the total resistance is small, e.g. with conveyor lengths L > 80 m and conveyors with just one feeding point, an approximate calculation of secondary resistances FN from the primary resistance FH applying coefficient C (see [1]) is permissible:

FN = (C − 1) ⋅ FH

(25)

The coefficient C can be selected from Table 5:

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DIN 22101:2011-12

Table 5 — Standard values for coefficient C for belt conveyor installations with filling ratios ϕ ranging from 0,7 to 1,1 L in m C

80

100

150

200

300

400

500

600

700

800

900

1 000

1 500 ≥ 2 000

1,92

1,78

1,58

1,45

1,31

1,25

1,20

1,17

1,14

1,12

1,10

1,09

1,06

1,05

6.4 Gradient resistance The gradient resistance of the conveyor belt and material conveyed can be calculated as follows for each section:

(

FSt,i = h i ⋅ g ⋅ m' G +m'L,i

)

(26)

The total gradient resistance of the conveyor FSt , that is, the sum of gradient resistances in the upper strand FSt,o and in the lower strand FSt,u , is calculated as follows:

FSt =

no

nu

i =1

i =1

∑ F St,o,i + ∑ F St,u,i = FSt,o + FSt,u

(27)

applying h i = li ⋅ sin δ i

(28)

(for uphill belt travel: h i > 0 and δ i > 0; for downhill belt travel: h i < 0 and δ i < 0)

6.5

Special resistances

6.5.1

General

Special resistances are resistances that do not occur with all belt conveyors. These resistances are calculated on the basis of several individual resistances (see Annex A). The special resistances of a conveyor section i are composed of: FS,i = FRst,i + FSch,i + FGa,i

(29)

The total special resistance of a conveyor FS, i.e. the sum of the special resistances in the upper strand FS,o and in the lower strand FS,u are calculated as follows:

FS = 6.5.2

no

nu

i =1

i =1

∑ (F Rst,o,i + FSch,o,i + FGa,o,i ) + ∑ (F Rst,u,i + FSch,u,i + FGa,u,i ) = FS,o + FS,u

(30)

Determination of individual special resistances

Camber resistance The camber resistance which arises at an individual side carrying idler will depend on its normal force, on the friction coefficient µ3 between the belt and the carrying idler, and also on the angle of tilt ε . The camber resistance FRst,i in section i of the conveyor is then obtained from the total of individual camber resistances, and taking the angle of inclination δ i of the installation into consideration:

FRst,i =

zRst,i zR,i

′ +mL, ′ i) ⋅ li ⋅ cRst,i ⋅ µ3 ⋅ sin ε i ⋅ cos δ i ⋅ g ⋅ (mG

(31)

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DIN 22101:2011-12

The friction coefficient µ3 depends on the angle of tilt ε . For angles ε > 5° it can reach a value of 0,5 (see [7]). In Equation (31), the parameters cRst,i are dependent on the idler arrangement and, in the case of the upper strand, on the geometry of the bulk material. In the case of 3-roller idler sets with rollers of equal length in the upper strand, and with filling ratios ϕ within the range of 0,7 to 1,1 (see [7]) it follows: cRst,o = 0,4 for λ = 30° cRst,o = 0,5 for λ = 45° The following applies to 2-roller idler sets in the (unloaded) lower strand: cRst,u = cos λ Friction resistance between the material conveyed and the lateral chutes outside the feeding points With bSch > lM and 3-roller idler sets (see Figure 3) the relationship below applies:

(

)

2

I ρ ⋅ g ⋅ lSch ⋅ µ2 2 2 tan λ FSch = cRank ⋅ m − bSch − lM ⋅ ⋅ 2 v 4 ρ ⋅ bSch

(32)

As a general rule, the friction coefficient µ2 is within the range from 0,5 to 0,7. lM = bSch shall be applied for bSch < lM; lM = 0 shall be applied for 2-roller idler sets; lM = bSch shall be applied for 1-roller idler sets. Resistances FGa of material transfer devices arranged along the belt conveyor path If, in special cases, material is discharged laterally along the conveying path, e.g. through scrapers serving as belt cleaners, the forces occurring at these locations shall be taken into account as special resistances.

7

Design and layout of the drive system

7.1 General The design and layout of the drive system comprises:

the selection of the location and number of drives

decisions relating to starting aids

the sizing of the drive motors (rated output)

the determination of the required braking forces (stopping and holding)

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7.2 Location of the drive units, size and number of drive motors 7.2.1

General

To minimize belt tension, the drive power is to be distributed among several drive pulleys situated at the head and at the rear of the installation, and in certain cases among intermediate drives, unless there are other considerations to be taken into account. Such other considerations include:

available space

availability of energy

driving and braking options

In order to ensure minimum belt tension, the type and arrangement of drives will depend heavily on the magnitude and local distribution of motion resistances for the conveyor in a steady operating condition, FW,o for the upper strand and FW,u for the lower strand. Variations in belt tension occurring in the direction of belt travel can be calculated by adding the resistances of the conveyor sections i in accordance with Equation (13).

FW =

no

∑

i =1

F W, o,i +

nu

∑ F W,u,i = FW, o + FW,u

(33)

i =1

In the case of extreme loading (non-uniform loading, partial loading or idling) of a belt conveyor with downhill and uphill grade stretches, the maximum force Fw,max can deviate significantly from the force FW determined for the nominal loading range (see 6.2.2): FW,max = FW,o + FW,umax ≥ FW

(34)

PW,max ≥ PW

(35)

This extreme power requirement shall be taken into consideration when selecting the type of drive system — motor drives or generators — however, in due consideration of the thermal rating of the motors. 7.2.2

Horizontal and slightly inclined installations FW,o > 0, FW,u > 0 (for uniformly loaded upper strand)

In the case of belt conveyors with drives at the installation head and rear, but without intermediate drives, the belt tensions will be minimal if the drive power is appropriately distributed between the head and tail stations, i.e. by a proportional distribution of the motion resistances occurring in the upper and lower strands. The required total power of the drive motors can be calculated with the aid of the following equation:

P PM, erf = W, max

ηges

(36)

The rated motor power actually installed, i.e. the sum of the nominal powers of the individual motors PM,N PM,inst =

∑ PM,N

(37)

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is, as a general rule, greater than the required power

P M,inst ≥ P M,erf 7.2.3

(38)

Uphill conveying installations FW,o > 0, FW,u ≤ 0 (for uniformly loaded upper strand)

In such installations, the belt tensions will be minimal if all the drives are arranged at the head of the installation, assuming that no intermediate drives are installed. PM,erf and PM,inst can be calculated using Equations (36), (37) and (38). 7.2.4

Downhill conveying installations

FW,o ≤ 0, FW,u > 0 (for uniformly loaded upper strand) In these installations, to obtain minimum belt tensions it is essential that drives are at the rear end of the installation where the drive is achieved through generators. For the purpose of determining the total power of the drives, the required power of the driving motors at the motor shafts shall be calculated as follows, depending on whether the drives operate as motors (PW,max > 0) or generators (PW,max < 0):

P PM, erf = W, max

where PW,max > 0

(39)

PM,erf = PW, max ⋅ η ges

where PW,max < 0

(40)

ηges

In this design stage it is not possible to precisely determine the overall efficiency ηges. For safety reasons, within the estimated range a higher value for the overall efficiency is to be chosen for a generator drive than for a motor drive. As a rule, the rated power of the motors actually installed (see Equation (37)) is greater than the amount of required power: PM,inst ≥ PM,erf 7.2.5

(41)

Installations with uphill and downhill sections

An appropriate arrangement of the drives for belt conveyor installations with uphill and downhill sections ensuring minimum belt tensions can be suggested only if all actual operating conditions are taken into account.

7.3 Starting, stopping and holding 7.3.1

Starting

In order to achieve minimum belt tensions, it is necessary to limit the total pulley peripheral forces on start-up FTr,A generated at the drive end during run-up to full speed of the belt conveyor installation. However the force FTr,A shall not be allowed to decrease below a given minimum value in order to safeguard the positive control of the initial breakaway and start-up process. The following is recommended especially for large belt conveyors

The maximum pulley peripheral force on start-up FTr,A,max should not exceed 1,7 times the force FW,max in accordance with Equation (34) used for the determination of the installation design. This means: the startup factor pA,max ≤ 1,7.

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In order to break away and accelerate the masses in the upper and lower strands, however, the force available under the most unfavourable start-up conditions (loading condition, distribution of load) should equal at least 20 % of the primary, secondary and special resistances to be taken into account and ensure the starting of the conveyor within the maximum time period allowed in accordance with the thermal rating of the drives (see [8]).

The force FTr,A shall be suitably selected to ensure friction grip between the material conveyed and the conveyor belt for the corresponding start-up acceleration a A . It follows for fine grained bulk material: aA ≤ (µ1 ⋅ cos δ i,max − sin δ i,max) ⋅ g

(42)

(for uphill belt travel: δ i > 0; for downhill belt travel: δ i < 0) The force FTr,A should be introduced into the belt slowly enough to ensure that the installation runs up to full operating speed under quasi steady conditions, and consequently with the small additional dynamic forces (see [8] and [9]). The start-up factor pA,0 related to the nominal torque of all drive motors shall be applied for the determination of the start-up factor pA in accordance with the equation below, where there are relatively small mass inertia torques of the rotating components of drives operating as motors in the steady operating condition, i.e. for horizontal and uphill conveying installations:

pA = pA0 ⋅

PM, inst PM

(43)

For designs according to Equation (35) the following shall be applied: PM = PM,erf 7.3.2

Stopping and holding

The operation of belt conveyor installations generally requires the provision of braking equipment to stop the moving masses, and/or holding devices to hold inclined installations under load. For the dimensioning of the braking equipment the following is to be considered:

total required braking force FTr,B on the periphery of the braked pulleys or the braking factor pB (see 8.3.3)

pB =

FTr, B FW

number and arrangement of brakes

braking frequency and braking time or braking distance

energy of the rotating drive components to be absorbed by braking

(44)

The required braking force FTr,B or the braking factor pB shall be determined for the most unfavourable braking conditions governed by the filling ratio ϕ and by the distribution of the load in downhill and uphill stretches of the installation with the relevant total motion resistance FW. In this connection, either the braking distance sB or braking time tB is to be specified. This will determine the braking deceleration a B , which shall be such that the friction grip between the material conveyed and the belt is maintained. In the case of fine-grained bulk material, the following applies: a B ≤ µ1 ⋅ cos δi,max + sin δi,max ⋅ g

(45)

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DIN 22101:2011-12

The braking factor pB0 related to the nominal torque of all drive motors shall be applied for the determination of the braking factor pB in the case of relatively small mass inertia torques of the rotating components of drives operating as motors in the steady operating condition, i.e. for horizontal and uphill conveyors with the power PM of the drives: pB =

pB0

2 η ges

⋅

PM, inst PM

(46)

It may be necessary to limit the total braking force to a given value FTr,B,max, and consequently the braking deceleration to a limiting value a B,max, in order to reduce the belt stresses and those on other parts of the installation as much as possible, and in order to maintain the friction grip on the braked pulleys (see 8.2.2). As regards the design and dimensioning of holding devices, the maximum gradient resistance FSt,max likely to arise under the maximum permissible loading conditions and most unfavourable load distribution, shall be used as the base value, minus the primary resistance arising under these conditions. For safety reasons, only the minimum primary resistance anticipated shall be used in calculations. If a number of mechanical holding devices are used, the loads shall be suitably distributed.

8 Belt tensions and take-up forces 8.1 General The belt tension in a belt conveyor installation is a quantity which varies along the path of the installation, and which is governed by the following influences (see Figure 5):

length and course of the installation

number and arrangement of drives

characteristics of the driving and braking equipment

type and arrangement of the belt take-up device

operating condition (loading and movement conditions)

Belt tensions should be kept to the lowest possible value in view of the stressing and layout of the belt and of other parts of the installation.

8.2 Required belt tensions 8.2.1

General

The operation of belt conveyor installations requires minimum belt tensions in order to enable the transmission of forces to the belt by friction grip on the drive pulleys, to limit the belt sag and to enable the belt to be guided correctly. 8.2.2

Minimum belt tensions required for the transmission of pulley peripheral forces

The transmission of the maximum pulley peripheral forces which arise during starting, braking, or in the steady operating condition by friction grip on the individual driven or braked pulleys requires certain minimum belt tensions at the point where the belt runs onto and off the pulley. In the case illustrated in Figure 4, with the forces FT1 and FT2 and the associated maximum pulley peripheral force FTr,max > 0 the following applies:

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Figure 4 — Minimum belt tensions at the belt run-on and run-off point on the drive pulley required to ensure transmission of the pulley peripheral force FTr,max FT1 − FT2 = FTr,max

(47)

FT1 ≤ e µ ⋅α , FT2

(48)

where α is to be expressed in radians. It follows that: FT2 ≥

1

e

µ ⋅α

−1

⋅ FTr,max

(49)

FT1 = FT2 + FTr,max

(50)

In the case of more than one driven or braking pulley, whether or not the friction grip is ensured in accordance with Equations (48) and (49) is to be verified for each individual pulley and for all operating conditions. In this connection it shall be borne in mind that the total pulley peripheral forces FTr, FTr,A or FTr,B are distributed onto the individual pulleys in proportion to the torques induced in said pulleys by the driving or braking equipment. Table 6 gives preferred friction coefficients µ for the friction between belts with rubber covers and pulley surfaces of different finishes to be used in the design of belt conveyors for the steady operating condition. Table 6 — Recommended friction coefficients µ for the friction between belts with a rubber cover and pulley surfaces of different finishes (see [10]) for the design of belt conveyor installations for the steady operating condition

Operating condition

a

a

Friction coefficients µ for pulley surfaces of bright metal surface (plain steel pulley)

polyurethane lagging (arrow pattern)

rubber lagging (arrow pattern)

ceramic lagging with pores, (arrow pattern)

dry

0,35 to 0,4

0,35 to 0,4

0,4 to 0,45

0,4 to 0,45

wet (clear water)

0,1

0,35

0,35

0,35 to 0,4

wet dirty (with mud and clay)

0,05 to 0,1

0,2

0,25 to 0,3

0,35

For conveyor belts with a PVC cover approx. 10 % smaller friction coefficients shall be assumed.

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8.2.3

Minimum belt tensions required for the limitation of the belt sag and for correct belt guiding

For the purpose of technical optimization of the belt conveyor installation, especially as regards energy efficiency, the calculated maximum relative belt sag hrel related to the distance between carrying idler centres shall be limited to values lower than 0,01 in the steady operating condition. A greater belt sag is permitted in the non-steady operating condition. The greater the conveying speed and the lumpier the material conveyed, the smaller the sag should be. Greater conveying speeds require either considerably lower sag values or the acceptance of higher primary resistances (see 6.2). The following minimum belt tensions are required for a given maximum belt sag and a given distance between carrying idler centres: Upper strand (with load): FT,o,min =

Lower strand:

FT,u,min =

g ⋅ ( m'L + m'G ) ⋅ lR,o

(51)

g ⋅ m'G ⋅ l R,u

(52)

8 ⋅ hrel

8 ⋅ hrel

If a maximum value of hrel is specified, different distances between carrying idler centres can be allocated to the belt tension occurring along the path of an installation. When these distances between centres are finally selected, the load-carrying capacity of the carrying idlers and the transverse vibration behaviour of the belt shall be taken into account (see [11]). In order to ensure the trouble-free operation of belt conveyor installations, it may be necessary to maintain higher minimum belt tensions in addition to the belt sag, especially for:

belts with turnover in the lower strand (see [12])

belts with a low degree of transverse rigidity

inclined belt conveyor installations at the lower pulley

belts with locally non-uniform force distribution across the belt width (see Clause 9)

8.3 Local belt tension variations in the top and return strands 8.3.1

General

From the point of view of the correct sizing of the belt and of other parts of the installation, sufficient knowledge of the course or pattern of the belt tension along the length of the installation, and in particular the magnitude of the extreme values of the force, is extremely important. Local belt tensions FT,i can be determined by summation of the motion resistances FW, i (see Clause 6) and superimposition of the take-up force (see 8.4) and, where applicable, the acceleration/deceleration force components Fa,i (see 8.3.3).

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Figure 5 — Pulley peripheral forces, resistances to motion and belt tensions illustrated for a conveyor installation with no = nu = 2 sections and 4 pulleys under steady operating condition 8.3.2

Steady operating condition

The calculation of motion resistances Fw,i for the individual sections of a belt conveyor installation in the stationary operating condition is given in Clause 6. 8.3.3

Non-steady operating condition

During the starting and stopping process, the magnitude and pattern of the forces generated by the driving and braking equipment, and the breakaway resistance and motion resistances of a belt conveyor installation result in additional dynamic belt tensions. These additional tensions are a function of the following factors, if we assume a belt acceleration independent of local conditions and, hence, quasi steady operating conditions of the conveyor (see also Annex A):

the total pulley peripheral force FTr,A during starting or FTr,B during stopping

the total acting motion resistance (approximately equal to the motion resistance occurring under steady operation FW)

the masses moving in a straight line and the non-driven or non-braked rotating masses Σ m reduced to their periphery

For the frequently occurring case where the secondary resistance represents only a small proportion of the total resistance, the forces Fa,i resulting from acceleration or deceleration can be determined as follows for an individual section i with the aid of the belt acceleration a : starting:

− FW F F a A = Tr,A = ( pA − 1) ⋅ W > 0 ∑m ∑m

(53)

stopping:

aB =

FTr,B − FW

∑m

= ( pB − 1) ⋅

FW 30 °C

Workspace

normal

roomy

narrow

Qualification of technicians

normal

very good

moderate

Quality of splicing materials

normal

fresh

nearly expired shelf life

Quality of vulcanizing equipment

normal

very good

moderate

Air temperature

cause Safety factor S0

1,1

reduction of

increase of

safety factor to 1,0

1,2

Table 9 — Safety factor S1 based on the classification of operating conditions Characteristics relevant to the dynamic strength of belt and belt splices

Classification

Expected service life

normal

short

long

Consequential damage due to failure

normal

small

large

Chemical/physical stresses

normal

low

high

Starting/stopping processes

> 3/day and < 30/day

≤ 3/day

≥ 30/day

Circulation frequency

> 2/hour < 1/minute

≤ 2/hour

≥ 1/minute causes

Safety factor S1

1,7

decrease

increase

of the safety factor to 1,5

1,9

Hence the minimum dynamic splice efficiency k t,min of the belt and belt splice can be calculated as follows:

k t,min = cK ⋅ kK,max ⋅ S0 ⋅ S1

(75)

For coefficient cK the following applies: for textile conveyor belts:

cK

=1

for steel cord conveyor belts:

cK

= 1,25: troughing transition zones

cK

= 1:

horizontal and vertical curves

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Figure The factor cK is chosen as 1,25 where the width related belt tension at the belt edge is calculated according to the method shown in 9.2.3, whereas a more precise calculation method allows a value cK = 1. 1)

The relative dynamic splice efficiency k t,rel of a belt describes the portion of its nominal breaking strength k N :

k t,rel =

kt kN

(76)

The relative dynamic splice efficiency is characteristic for a certain belt type and its splices. Therefore, it is to be incorporated in future product standards as a minimum requirement. Table 10 contains the relative values of dynamic splice efficiency for several belt types. The following aspects shall be taken into consideration for their application:

The values for conveyor belts with textile plies are standard values based on practical experience. It is likely that they will need to be corrected once a larger number of test results are available.

The values for steel-cord conveyor belts have been determined in numerous tests and can be considered as minimum requirements which need to be verified.

In the calculation of the minimum breaking force k N2) only the actual dynamic splice efficiency k t proven for a certain belt type and a certain type of splice may be applied. Table 10 — Values for the relative dynamic splice efficiency k t,rel Belt type Textile belts with one ply Textile belts with two plies and thick intermediate layer Textile belts with more than two plies Textile belts with one ply Textile belts with two plies Steel cord belts Steel cord belts

Belt design according to

Nominal breaking strength kN N/mm

Splicing according to

Relative dynamic splice efficiency a kt,rel

DIN 22102-3 finger splice

DIN 22102-1

630 to 3 150

DIN 22102-1

200 to 2 000

DIN 22102-3, with intermediate tension member

0,35

DIN 22102-1

315 to 3 150

DIN 22102-3, with stepped splice

0,30

DIN 22109-1

800 to 3 150

DIN 22121

0,35

DIN 22109-2

800 to 1 600

DIN 22129-1 DIN EN ISO 15236-1 Along the lines of DIN ISO 22129-1 DIN EN 15236-1b

DIN 22121 with intermediate tension member

0,35

0,30

1 000 to 5 400

DIN 22129-4

0,45

< 1 000 > 5 400

Along the lines of DIN 22129-4

0,45

a

Please note that it cannot be expected that the standard values are achieved with aged or used belts.

b

Translator ’s note. The German original is incorrect. The standard number should read “DIN EN ISO 15236-1”.

2) The term “nominal breaking strength” cited in this context corresponds to the term “mimimum breaking strength” as applied in DIN 22110-3.

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The minimum nominal breaking force kN,min is calculated as follows applying the highest value k K,max in accordance with Equation (75) and Equation (76) under the steady operating condition:

kN,min =

k t,min k t,rel

= cK ⋅ kK,max ⋅

S 0 ⋅ S1 k t,rel

(77)

Taking the value k N,min calculated according to Equation (77) and the width-related mean belt force k at the point of the value k K,max calculated according to Equation (60), the safety factor Smin related to the mean local belt force can be determined:

S min =

k N ,min k

= cK ⋅

kK,max S 0 ⋅ S1 ⋅ k k t,rel

(78)

In order to avoid extreme stresses in non-steady operating conditions and under those conditions that may arise when belts with a partial load are passing through uphill and downhill stretches of the conveyor installation, it shall be checked that the following limiting conditions are met: kt,min ≥ 1,1 ⋅ cK ⋅ kK,a,max

(79)

If this is not the case, the dimensioning of the tension member shall be corrected applying a higher value k t = 1,1 ⋅ cK ⋅ k K,a,max . According to this method, the tension members of the conveyor belts are dimensioned exclusively on the basis of tensile loads. It shall be checked whether they will provide sufficient resistance against additional stresses and whether their transversal rigidity will be sufficient for supporting the bulk material. They are therefore to be designed with a higher strength, if necessary.

10.3 Design and layout of cover layers The thickness of cover layers shall be suitably selected dependent on the material so as to ensure its protective function, even with progressing wear during the scheduled service life of the conveyor belt; the surface structures of the tension member shall remain adequately covered (see also Annex A). If DIN Standards and other normative regulations do not provide further details, the standard values for the minimum thickness of cover layers indicated in Table 11 and corresponding allowances for the carrying side of the belt as provided in Table 12 can be applied. Certain minimum thickness values are required if a belt protection (transverse reinforcement) is incorporated in the conveyor layers. In order to avoid impermissible cupping of the belt, the ratio of the thickness of the cover layer on the carrying side relative to the cover layer on the running side should not exceed 3:1. Table 11 — Standard values for minimum thickness of cover layers on the carrying side and running side of the belt Material of longitudinal tension member

Minimum thickness of cover layer (standard value)

B (cotton) P (polyamide) E (polyester)

1 mm to 2 mm depending on the textile structure

St (steel cords)

0,7 ⋅ dGk, at least 4 mm, with transverse reinforcement possibly more than 4 mm

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Table 12 — Determination of the standard values for additions to the minimum thickness of carrying side cover layers in accordance with Table 11 Characteristics and their assessment Loading conditions Loading frequency Maximum particle size Bulk density Abrasiveness

favourable average unfavourable low average high small average high low average high low average high

Sum of assessment values

Addition to minimum thickness, mm (standard values)

5 to 6

0 to 1

7 to 8

1 to 3

9 to 11

3 to 6

12 to 13

6 to 10

14 to 15

> 10

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

11 Minimum pulley diameter The method described here for determining the minimum pulley diameters follows ISO 3684:1990. The idea behind the determination of minimum pulley diameters is directly linked with the expectations regarding the service life of the conveyor belt and its splices. The minimum pulley diameters to be determined in accordance with the method described in this clause allows the assumption that the endurance strength of splices will be at least equal to the expected service life of the conveyor belt, provided that the splices are properly executed. Smaller pulley diameters than those determined in accordance with the method described in this document can lead to premature failure; they also facilitate wear and tear of pulley surfaces or lagging. The minimum pulley diameters of a belt conveyor installation will be determined by the design and layout, stresses and splicing method of the belt (see also Annex A). A distinction is made between the following groups of pulleys when determining the minimum diameters:

Group A:

drive pulleys and all other pulleys in the zone of high belt tensions

Group B:

return pulleys in the zone of low belt tensions

Group C:

deflection pulleys (change of direction of belt travel ≤ 30°)

If DIN Standards and other normative regulations do not provide further relevant details, the minimum diameters of Group A pulleys, for the four different groups of pulley load factors provided in Table 14, can be determined as follows: DTr = cTr ⋅ dGk

(80)

The factor cTr is a parameter dependent on the material of the tension member according to Table 13 below:

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Table 13 — Parameter cTr for the determination of the minimum pulley diameter Dtr Material of longitudinal tension member

cTr 80 90 108 145

B (cotton) P (polyamide) E (polyester) St (steel cords)

Each diameter determined for Group A pulleys in accordance with the above description shall be rounded up to the next standard value indicated in Table 14. The minimum diameters of Group B and C pulleys shall be chosen in relation to the pulley load factor from Table 14 that is relevant for Group A. Table 14 — Minimum diameter of Group A, B and C pulleys in relation to the utilization of the maximum pulley load factor in the steady operating condition Minimum diameter in mm (without lagging) DTr as per

Pulley load factor

kmax ⋅ 8 ⋅ 100 % kN

a

Equation

over 100 %

over 60 % to 100 %

over 30 % up to 60 %

up to 30 %

(80)

Pulley group

Pulley group

Pulley group

Pulley group

100 125 160 200 250 315 400 500 630 800 1 000 1 250 1 400 1 600 1 800 2 000 a

A 125 160 200 250 315 400 500 630 800 1 000 1 250 1 400 1 600 1 800 2 000 2 200

B 100 125 160 200 250 315 400 500 630 800 1 000 1 250 1 400 1 600 1 800 2 000

C 100 125 160 200 250 315 400 500 630 800 1 000 1 000 1 250 1 250 1 400

A 100 125 160 200 250 315 400 500 630 800 1 000 1 250 1 400 1 600 1 800 2 000

B

C

A

B

C

A

B

C

100 125 160 200 250 315 400 500 630 800 1 000 1 250 1 250 1 400 1 600

100 125 160 200 250 315 400 500 630 800 1 000 1 000 1 250 1 250

100 125 160 200 250 315 400 500 630 800 1 000 1 250 1 250 1 600 1 600

100 125 160 200 250 315 400 500 630 800 1 000 1 000 1 250 1 250

100 125 160 200 250 315 400 500 630 800 800 1 000 1 000

100 125 160 200 250 315 400 500 630 800 1 000 1 000 1 250 1 250

100 125 160 200 250 315 400 500 630 800 1 000 1 000 1 250 1 250

100 125 160 200 250 315 400 500 630 800 800 1 000 1 000

kmax is the mean width-related tension at the point of maximum belt tension in the zone of Group A pulleys in the steady operating condition.

12 Design and layout of transition curves and vertical curve radii 12.1 General Clause 9 deals with the calculation of belt tensions distributed across the belt width proceeding from the specified design of transition curves or convex curves for the subsequent design and layout of the conveyor belt. This clause deals with the calculation of suitable transitions and vertical curves suitable for a specified belt type.

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12.2 Determination of the minimum transition length 12.2.1 General The following applies to 2-roller and 3-roller carrying idler sets in accordance with the approach illustrated in Figure 8 and Equation (77): kK,zul =

kM =

kN ⋅ k t,rel

(81)

cK ⋅ S0 ⋅ S1

B ⋅ k − bS ⋅ kK,zul B − bS

≥0

and

(82)

∆k = kK, zul − kM 12.2.2

(83)

Conveyor belts with textile plies

With Equation (68):

lK − lÜ ∆k = lÜ ELGk

(84)

Δk is calculated in accordance with Equation (83) applying Equations (82) and (81). In the latter equation the parameter cK = 1,0 is to be used. According to Equation (84) it follows that:

lÜ,min =

2 hTr + 2 ⋅ bS2 − 2 ⋅ bS ⋅ (hTr ⋅ sin λ + bS ⋅ cos λ )

(85)

2

∆k + 1 − 1 ELGk

The transition lengths thus calculated provide sufficient accuracy for textile conveyor belts. 12.2.3 Steel cord conveyor belts Meeting the conditions mentioned in 9.2.3, the minimum transition length can be roughly determined as detailed below. With Equation (71):

l K − lÜ ∆k = lÜ, eff ELGk

(86)

Δk is calculated in accordance with Equation (83) applying Equations (82) and (81). For the latter equation for steel cord belts, the parameter cK is to be considered as explained in the comments to Equation (75). According to Equation (86) it follows that:

lÜ,min =

lÜ,min 2 + hTr 2 + 2 ⋅ bS 2 − 2 ⋅ bS ⋅ (hTr ⋅ sin λ + bS ⋅ cos λ ) − ∆k +1 ELGk

∆k ⋅ ∆lÜ ELGk

(87)

with ΔlÜ in accordance with Equation (70). A comparison of Equations (87) and (85) shows that the minimum troughing length for steel cord belts can only be calculated by iteration.

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Equation (86) and Equation (87) may be applied only if there is a piece of belt of sufficient length provided in front of or behind the belt pulley to compensate for length variations. If there is a convex curve right after a transition, for example, the above condition is not met. In this case lÜ,eff shall be replaced by lÜ so that lÜ,min can explicitly be determined using Equation (85). For more precise calculations in which elongations resulting from superimposition are to be taken into consideration, it is recommended that the methods described in [14] and [16] be used.

12.3 Determination of the minimum radius of vertical curves 12.3.1 General Additional elongations due to convex and concave transition curves can be calculated for small and medium curve lengths only with a relatively great effort (see [16]); however their magnitudes will always be smaller than the elongations arising in the middle of long curves. These elongations form the basis of the calculations below. 12.3.2 Convex curves Proceeding from the assumption that the belt tension in the central zone of the conveyor belt is equal to 0 and the belt is operated with the maximum allowable edge tension kK,zul, the minimum radius of a convex curve can be determined applying Equations (72), (74), (77), with cK = 1, as follows:

Re,min =

bS ⋅ sin λ ⋅ ELGk ⋅ S0 ⋅ S1 kN ⋅ k t,rel

(88)

12.3.3 Concave curves In the case of concave belt guidance there will be additional elongations of the belt centre and compression of the edge of the belt with magnitudes that will amount to the same magnitudes as the additional elongations which arise in the case of convex belt guidance as long as the belt does not lift off the carrying idlers. This lifting can be avoided if the following minimum radius is met under all operating conditions.

Ra, i, min =

FT, i, max ′ ⋅ cos δ i g ⋅ mG

(89)

13 Dimensioning of belt turnovers Belt turnovers are helpful as they reduce the soiling and wear of the conveyor belt and improve belt tracking in the lower strand. The length and type of the belt turnovers are dependent on the following parameters:

Belt width

Belt weight

Transverse rigidity

Elastic characteristics

Conveying speed

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A distinction is made between the types of turnovers of the conveyor belt with different supporting principles as illustrated in Figure 11:

Key top: free turnover middle: guided turnover bottom: supported turnover Figure 11 — Design variants for turnovers Table 15 — Standard values for the dimensioning of turnover lengths lW

Type of belt turnover

Maximum belt width mm

Minimum turnover length lW for conveyor belts with cotton plies

EP plies

steel cord plies

Free turnover

1 200

8⋅B

10 ⋅ B

–

Guided turnover

1 600

10 ⋅ B

12,5 ⋅ B

22 ⋅ B

Supported turnover

2 400

–

10 ⋅ B

15 ⋅ B

The standard values provided in Table 15 will be sufficient if the return strand is subjected to low belt tensions. If this is not the case, a more precise calculation is to be carried out (see [12]).

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Annex A (informative) Explanatory notes General

After a 40-year validity, DIN 22101:1942-02 was completely revised and significantly expanded as DIN 22101:1982-02, of which an official English-language version is also available. The next version was published in 2002-08 with some formal and substantial shortcomings that required an early revision. The working group responsible for revising DIN 22101:1982-02 was required to give a more simple description of relationships, wherever possible. This task appeared to be unrealistic. In fact, the current descriptions are even more complex than those given in the 1982 edition because of new knowledge which needed to be incorporated. The working group came to the conclusion that comprehensive computerized calculations, which are widely practiced, should be preferred in order to find improved technical and economical solutions. Nevertheless, simplified calculation methods are referred to wherever feasible (i.e. in cases not requiring high accuracy). Re Clause 5 Theoretical cross section of fill Ath and equivalent angle of slope β

In the case of a troughed belt, the bulk material cross section comprises the “water cross section” and the slope cross section lying above it. Amongst other factors, the shape of the slope will depend on the properties of the bulk material conveyed (e.g. its lumpiness, internal friction, friction coefficient between the conveyor belt and the material conveyed) and also on the operating conditions of the belt conveyor installation (e.g. type of belt feed, tracking of the belt, frequency and duration of vibrations (jarring) of the bulk material conveyed). The slope cross section which actually takes shape is markedly smaller than the cross section given by the static angle of slope. A calculation of this actual cross section can therefore in general only be undertaken under idealized assumptions. In the case of belt conveyor installations with a horizontal layout, in German technical literature the slope cross section is nearly always idealized in the form of a triangular cross section, whilst in International Standard ISO 5048:1989 it is idealized in the form of a segment of a parabola. The working group considered the adoption of the approach according to ISO 5048 and its incorporation in this revision, but finally refrained from this intention for the following reasons: ─ The latest editions of international and German standards use a triangular cross section as a basis (see ISO 7189 or DIN 22200). ─ ISO 3435 uses the “angle of repose” instead of referring to the “surcharge angle” (as mentioned in ISO 5048). ─ Hence it can be assumed that in its next revision, ISO 5048 will use an idealized triangular cross section. Reduction factor ϕ st

When using Equations (10), (11) it shall be borne in mind that the equivalent angle β = 15° used in a large number of calculations of the cross section of fill represents a precautionary value. In the case of inclined installations, to avoid determining cross sections of fill that are considerably too small when using this value, it will be necessary to calculate the factor φ st which is dependent on the inclination, with an angle of slope βdyn close to the static angle of slope (the angle of internal static friction). If accurate values are required in borderline cases, such values are to be determined by tests carried out under conditions which approximate the actual application conditions as closely as possible. Re 6.2

For the calculation of resistances, even complex equations are not excluded here, since computerized calculations of this type are widely practiced.

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In deviation from DIN 22101:1982-02 preference is given to the determination of resistances in each conveyor section. The simplest conceivable layout of a belt conveyor installation consists of two sections only: upper strand and lower strand. Simplifying a belt conveyor installation with uphill and downhill part sections as an installation with only two part sections may yield extremely false results. Re 6.2.3

In order to enable a high degree of accuracy of design and layout, the hypothetical friction coefficient f should be determined more precisely by measuring two major parts of the resistance to motion, i.e. ─ the indentation rolling resistance of the conveyor belt ─ the idler running resistance and by giving an estimate of the remaining portions (see [5]). The indentation rolling resistance is generally measured with a single idler under consideration of the conveyor specific parameters. For the transformation to the indentation rolling resistance of a complete set of idlers, the values of the normal forces acting on each idler must be known. Figure A.1 shows schematically the idealized distribution of the normal forces and the indentation rolling resistance resulting thereof for an idler configuration with three rollers of equal length in a horizontal and straight conveyor [20].

Key 1 Bulk material 2 Direction of travel 3 Load over length on side idler 4 Load over length on centre idler 5 Related indentation rolling resistance on centre idler F'E,m 6 Related indentation rolling resistance on side idler F'E,s Figure A.1 — Idealized distribution of the normal forces and the resulting indentation rolling resistance for a 3-roller idler set with rollers of equal length The dependence of the relevant indentation rolling resistance F'E on the vertical force F'M,v for a single idler can generally be described using the following numerical equation [20]: ′ v ) cb FE′ = ca ⋅ ( FM,

(A.1)

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Here the values ca and cb vary depending on the measured function of the relevant indentation rolling resistance. The indentation rolling resistance FE,3 acting on each idler of a 3-roller idler set is determined by integrating the locally varying value of F'E along the contact line bR under consideration of the local line load. For the total indentation rolling resistance acting on the idler set the following numeric equation applies [20]:

FE,3

Fn,m = ca ⋅ b R, m

cb

ca ⋅ bR,s 2 ⋅ Fn,s ⋅ bR,m + 2 ⋅ ⋅ cb + 1 bR,s

cb

(A.2)

In order to demonstrate the importance of the indentation rolling resistance for a safe dimensioning while at the same time minimizing investments and operating costs, Figure A.2 can be used as it shows examples of the distribution of parts of motion resistances for long belt conveyors: Left column: belt conveyor installation with horizontal layout Right column: belt conveyor installation with approx. 5 % inclination It should be borne in mind that, especially as regards the interpretation of the left column, in the future an increasing use of energy-optimized belts will accordingly reduce the portion of the indentation rolling resistance in the total resistance to motion. Furthermore, the information shown in Figure A.2 should not be taken as basis for the design of conveyors, in view of the dependence of the single parts of the resistance to motion on the operational and design-related parameters of the conveyor.

Key Gradient resistances Special resistances Secondary resistances Flexing resistance of the belt Flexing resistance of the bulk material Idler running resistance Indentation rolling resistance

Figure A.2 — Comparison of the portions of resistance of two long belt conveyor installations of identical design, with different inclinations

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Re 6.3.2

For the secondary resistances a determination of each part is preferable to the determination of a generalized value for the portion of the primary resistance. In determining the friction resistance between conveyor belt and lateral chutes in the acceleration zone of a β dyn , which has an effect on the pressure feeding point, not only shall the Rankine factor cRank = tan 2 45° − 2 exerted on the chute walls by the material in the chute zone, be taken into consideration, but also the coefficient cSchb (information on the magnitudes of βdyn is given in the explanatory notes on the reduction factor φ St). This factor characterizes the increase of the resistance due to additional pressure on the chute walls caused by the dynamic pressure of the material flow of feed material. Consequently, the magnitude of the coefficient cSchb will be equal to 1 for the transfer height 0; it then increases with rising conveying speeds and dropping heights. For the design and layout of customary belt conveyor installations, the product will be cSchb · cRank = 1, whilst the coefficient will be applied as cSchb = 1 for hopper discharge conveyors with high loading heights. Re 6.5

A distinction has not been made between special resistances arising along the entire stretch of the installation and those occurring in individual sections only, as introduced by ISO 5048. The calculation approach detailed in this standard requires the calculation of resistance values for individual sections which implies the consideration of special resistances. Detailed information on the magnitudes of the dynamic angle of slope βdyn in the Rankine factor cRank applied in the calculation of the resistance arising at the material guide bars can be seen from the above comments on the reduction factor φ st. Re 8.3.3

A belt conveyor installation for which the rate of increase of the pulley peripheral forces is limited during starting or stopping procedures, and where the belt is in motion along the entire installation, exhibits a belt acceleration which is independent of location; it behaves in a quasi steady-state fashion, and enables the dynamic additional forces to be determined as mass forces. If the non-quasi steady operating conditions, e.g. the breakaway process, of a belt conveyor installation are to be calculated, it is necessary to determine the additional dynamic forces which arise in this connection with the aid of very complex calculation methods (see [9]). Re 8.4

For the calculations, a distinction is to be made between take-up devices with a fixed take-up pulley and those with a flying take-up pulley. Take-up devices with a fixed pulley are devices on which the position of the driven and non-driven pulleys remains unaltered for every operating condition of the conveyor. The desired adjustment of the tensile force is effected, for example, by means of spindles (screws) or jacks. Depending on the prevailing operating condition, a fixed take-pulley will result in varying forces at the tensioning location. Conversely, the total of the local belt elongations in the upper strand and the lower strand will remain constant; it is equal to twice the take-up pulley travel during the take-up process (take-up pulley path s*Sp). * = const ∑ Δli = 2 ⋅ sSp

(A.3)

Take-up devices with a flying take-up pulley are devices which generate tensile forces which are either independent of the operating conditions and practically constant, or which are suitably matched to the prevailing operating conditions. This is achieved, for example with the aid of take-up weights, pneumatic or hydraulic devices and force-controlled jacks in the case of take-up pulleys with an adequate travel facility. Their mode of operation is, therefore, characterized by the fact that the total of the local belt elongations in the upper strand and the lower strand and consequently the take-up pulley travel vary:

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* ≠ const ∑ Δli = 2 ⋅ sSp

(A.4)

For the calculation of Δli a linear relationship between the elastic elongations and the belt tensions k related to the belt width is generally assumed as a simplification, and this is expressed by means of a mean widthrelated longitudinal modulus of elasticity related to the belt ELGk. Take-up forces that can be adjusted by suitable means shall be adjusted with an adequate speed in order to avoid sliding and slipping on the drive pulleys. In this context, it may be helpful to adjust the take-up force to a higher degree than the calculated one in order to ensure an adequate belt tension at any time. Re Clause 9

The determination of belt tensions in accordance with DIN 22101:1982-02 solely focussed on mean belt tensions. Non-uniform distribution of tensions over the width of a troughed belt as arising in transitions or curves was accounted for by a deduction r1 introduced for this particular purpose. This, however, no longer represents the state of the art in respect of the design and layout of conveyor belts with a high demand of accuracy. For the consideration and determination of additional elongations of the conveyor belt, a distinction shall be made between belts with textile plies and steel-cord belts because of their extremely different elastic characteristics. Elongations of belt edges in the transition zones shall be calculated proceeding from the geometrical approach suggested by Laier (see [13]). Applying this approach, length variations and — for conveyor belts with textile plies — elongations and additional loads can be determined with sufficient accuracy. Length compensations of steel-cord belts involve considerably large belt portions adjacent to the transition zone, which is why higher belt tensions than those which actually arise will be calculated if the approach recommended for conveyor belts with textile plies is applied to steel-cord belts. In the referenced literature (see [12) and [14]) descriptions of safe methods for the precise calculation of steel-cord conveyor belts are provided, which can be applied without problems using computerised support, provided that the mechanical characteristics of these belts are available. If no mechanical characteristics of the belt are available, empirical relationships are provided for conveyor belts in accordance with DIN 22129-1 or DIN EN 15236-11) and steel-cord belts of similar design. These relationships will enable a sufficiently precise prediction of the stresses arising in conveyor belts installed on 2-roller idlers and the more frequently used 3-roller idlers, in many cases. However, the relationships can only be referred to as being correct if the elastic characteristics of the belt currently ensured according to common practice, but not as specified in the applicable standards, are maintained, except for insignificant modifications. Re 9.2

The belt pulley should not be arranged at a level which is lower than the deepest trough level as this requires greater transition lengths or may aggravate the non-uniform distribution of belt tensions across the cross section of the belt. This also increases the load on idlers and bearings. There is also an increasing risk of damage to the belt as the belt may run into the gap between the rollers of the carrying idlers. Re 10.2 Deviating from DIN 22101:1982-02, the belt tensions arising in non-steady operating conditions are not directly taken into consideration in the design and layout of the conveyor belt. Instead, one single limiting condition has been specified which will be applicable only to extremely high stresses in the non-steady operating conditions. Safety factors are to be selected (Table 8 of the previous edition of this standard) in order to take the frequency of non-steady operating conditions into consideration. For this reason the deduction r2 is no longer required for the global consideration of these stresses.

The load-bearing capacity of a conveyor belt is primarily dependent on the dynamic strength of the conveyor belt and belt splices. DIN 22101:1982-02 accounts for this aspect by applying the factor r0. By testing the belt in accordance with DIN 22110-3 the dynamic splice efficiency of the conveyor belt and the belt splices can be 1)

Translator ’s note. The German original is incorrect. The standard number should read “DIN EN ISO 15236-1”.

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determined. The characteristics of the belt splice manufacture are represented by the safety factors S0 provided in Table 8. The magnitude of stresses is expressed by the safety factor S1 to be selected from Table 9. The values in Table 8 and 9 have been verified by comparison with the values obtained from existing and proven heavy-duty conveyor installations. The relationship of the safety factors S0 and S1 to the safety factor Smin in steady operation which is based on the mean belt force over the width of the belt is given in Equation (78). Its use leads to the results in Table A.1. From them the influence of belt specific parameters (k t,rel, S0) and conveyor-specific parameters (S1, k K,max) on the safety factor Smin can be seen. Table A.1 — Minimum values for the safety factor Smin related to the minimum nominal breaking strength of the belt as a function of the parameters S0, S1, kt,rel , cK and k K,max S0 * S1 / k t,rel

cK · k K,max / k

The safety factor S which is related to the nominal breaking strength of the belt k N, as opposed to the value kN,min can be determined analogously to Equation (78) as:

S = Smin ⋅

kN

(A.5)

kN,min

Re 10.3

Because the relevant DIN Standards, International Standards and currently available drafts of European Standards do not contain data regarding the selection of the cover layer thickness, recommendations in this respect have been incorporated in this standard. The cover layer thickness on the running side of the conveyor belt is determined to a great extent by the tension member, or in some cases by the transverse reinforcement, whilst the cover layer thickness on the carrying side of the belt is determined mainly by the stressing of the belt by the material conveyed, and consequently by the following influencing quantities: ─ Nature of material conveyed:

particle size and shape, density, abrasiveness

─ Loading condition:

drop height, resilience of the belt support, difference in speed between bulk material and conveyor belt

─ Loading frequency:

frequency of belt revolutions and scheduled service life of the conveyor belt, number of feeding points

The thickness on the carrying side shall be at least equal to the thickness on the running side of the belt.

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Re Clause 11

The principle and general contents of the method of calculating minimum pulley diameters is identical with that described in ISO 3684:1990. The design and layout according to the ISO Standard is based on the percentage of utilized RMBT (Recommended Maximum Belt Tension), which was defined in DIN 22101:1982-02 k k ⋅ S sta ⋅ 100 % . This standard defines this variable as N and derived from this, the pulley load factor is as 8 kN kmax ⋅ 8 ⋅ 100% , where according to Table 14 k max is the mean width-related tension at the point kN of maximum belt tension in the zone of Group A pulleys in the steady operating condition.

calculated as

This pulley load factor can have values higher than 100 %. Therefore, a fourth category has been introduced for pulleys with loads exceeding the permissible values defined in DIN 22101:1982-02 and ISO 3684:1990. Re Clause 13

This standard contains empirical values for minimum turnover lengths for different belt types and turnover principles.

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Annex B (informative) Explanations of relationship of this standard to international standards The following ISO Standards have been taken into consideration for the revision of this standard: ISO 5048:1989 “Continuous mechanical handling equipment — Belt conveyors with carrying idlers — Calculation of operating power and tensile forces”

The recommendations contained in the above document for the determination of —

the material flow and the troughing cross section

—

the resistance to motion, driving force and power requirement

—

the belt tensions

are in accordance with the contents of this standard, but for the following important exceptions. In the ISO document, the cross section of fill of a troughed belt is composed of an equal sided trapezium or triangle surmounted by a segment of a parabola. In this standard (see Clause 5), the upper portion of the cross section of fill is idealized in the form of an isosceles triangle, in accordance with the German technical literature. This approach has been maintained as it can be assumed that the standard ISO 5048:1989 — like other ISO Standards — will also be revised to refer to a triangular cross section (see Annex A, explanatory notes to Clause 5). According to the recommendations contained in the ISO document for the calculation of the secondary and special resistances, the resistances due to the belt cleaners are deemed to be special resistances. However, as belt cleaners form part of the standard equipment of belt conveyor installations for bulk materials, the associated resistances have been allotted to the secondary resistances in this standard (see 6.3). The ISO document takes the maximum belt tension calculated as a mean value across the belt width as a basis for the design and layout of the conveyor belt. It is expressly limited to simple, but frequently occurring cases. The present standard accounts for non-uniform belt tensions distributed across the cross section of troughed conveyor belts taking into consideration the endurance strength of the conveyor belt and belt splices subject to dynamic loads. ISO/DIS 3870:1996 “Conveyor belts for loose bulk-materials — Description of types and adjustment of take-up devices”

In the above standard, recommendations are given in respect of different types of take-up devices. It defines the standard values of elongation and other influencing variables for the calculation of the take-up distances applicable to tension members of different materials. ISO/DIS 3870:1996, Annex A provides an option for the determination of adequate take-up distances dependent on the belt tensions determined for a belt conveyor installation. Applying the relationships provided in this standard (see 8.4), the elastic elongations of the conveyor belt and the corresponding take-up pulley path can be determined with a relatively high degree of accuracy proceeding from the distribution of belt tensions and the characteristics of the conveyor belt.

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ISO 5293: 1981 “Conveyor belts — Determination of minimum on three idler rollers”

The above standard gives detailed recommendations for the determination of transition distances (transition lengths). It is based on simplified assumptions which were made by Laier (see [13]). The present standard does not give priority to the retroactive calculation of an adequate transition distance, but takes the maximum belt tensions resulting from a given transition distance (or curve layout) as a basis for the design and layout of the conveyor belt. ISO 3684: 1990 “Conveyor belts — Determination of minimum pulley diameter”

The recommendations contained in the above standard for the determination of minimum pulley diameters for belt conveyor installations have been incorporated in this standard in a more concise form adapted to their field of application (see Clause 11). This standard does not contain any variables corresponding to the term “recommended maximum belt tension” (RMBT), which had been introduced in ISO 3684. A pulley load factor k k has been introduced as max ⋅ 8 ⋅ 100 in % with the reference value N . kN 8 Here kmax according to Table 14 is the mean width-related tension at the point of maximum belt tension in the zone of Group A pulleys in the steady operating condition.

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Bibliography DIN 22103, Flame resistant steel cord conveyor belts — Requirements and method of test DIN 22109-5, Conveyor belts with textile plies for coalmining — Branding DIN 22109-6, Conveyor belts with textile plies for coalmining — Part 6: Testing DIN 22110-2, Testing methods for conveyor belt joints — Part 2: Endurance running tests, determination of running time of belt joints at conveyor belts with textile plies DIN 22111, Belt conveyors for underground coal mining — Light construction DIN 22112-3, Belt conveyors for underground coalmining — Idlers — Part 3: Testing DIN 22114, Belt conveyors for underground coalmining — Heavy construction DIN 22118, Conveyor belts with textile plies for use in coal mining — Fire testing DIN 22120, Elastomere scraper plates for belt conveyors in hard coal mines DIN 22200, Continuous mechanical handling equipment — Apron conveyors — Principles for calculation DIN EN ISO 284, Conveyor belts — Electrical conductivity — Specification and test method DIN EN ISO 340, Conveyor belts — Laboratory scale flammability characteristics — Requirements and test method DIN EN ISO 1120, Conveyor belts — Determination of strength of mechanical fastenings — Static test method ISO 1537, Continuous mechanical handling equipment for loose bulk materials — Troughed belt conveyors (other than portable conveyors) — Idlers ISO 3435, Continuous mechanical handling equipment — Classification and symbolization of bulk materials ISO 5048, Continuous mechanical handling equipment belt conveyors with carrying idlers — Calculation of operating power and tensile forces ISO 5293, Conveyor belts — Determination of minimum transition distance on three idler rollers ISO 7189, Continuous mechanical handling equipment — Apron conveyors — Design rules [1]

Vierling, A.: Zum Stand der Berechungsgrundlagen für Gurtförderanlagen. Braunkohle. Wärme und Energie 19 (1967) No. 9, pp. 309–315.

[2]

Schwarz, F.; Zum Eindrückrollwiderstand zwischen Fördergurt und Tragrolle. fördern und heben 17 (1967) No. 12, pp. 712–719.

[3]

Behrens, U.: Untersuchungen zum Walkwiderstand schwerer Förderbandanlagen. Braunkohle, Wärme und Energie 20 (1968) No. 7, pp. 222–231.

[4]

Hager, M. and A. Hintz: The Energy-Saving Design of Belts for Long Conveyor-Systems. Bulk Solids Handling 13 (1993) No. 4, pp. 749–758.

[5]

Hager, M. and H. Simonsen: Berechnung und Auslegung von Gurtförderern für Schüttgut. Braunkohle/Surface Mining 52 (2000) No. 3, pp. 245–259.

[6]

Grimmer, K.-J. and D. Thormann: Zur Problematik der Kraft- und Bewegungsverhältnisse des Schüttgutes an Aufgabestellen von Förderbandanlagen, fördern und heben 17 (1967) No. 6, pp. 345–351.

[7]

Grimmer, K.-J.: Zwei ausgewählte Probleme der Bandfördertechnik. Fortschrittberichte VDI-Zeitschrift, series 13, No. 10, September 1968.

[8]

Funke, H.: Zur Auslegung von Anlaufhilfen für Gurtförderanlagen nach Entwurf DIN 22101. Braunkohle 31 (1979) No. 6, pp. 188–194.

[9]

Funke, H. and F.K. Könneker: Experimental Investigations and Theory for the Design of a Long-Distance Belt Conveyor System. Bulk Solids Handling 8 (1988) No. 5, pp. 567-579.

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[10] Grimmer, K.-J.: Der Einfluss von Trommelbelägen und Feuchtigkeit auf den Reibungsbeiwert zwischen Fördergurt und Antriebstrommel. Braunkohle, Wärme und Energie 18 (1966) No. 9, pp. 325–332. [11] VDI-Guideline 2341; Belt conveyors for bulk material — Idler rolls and idler roll distances. [12] Oehmen, K. H.: Berechnung der Dehnungsverteilung in Fördergurten infolge Muldungsübergang, Gurtwendung und Seilunterbrechung. Braunkohle 31 (1979) No. 12. pp. 394–402. [13] Laier, D.: Ein Versuch zur rechnerischen Erfassung der zusätzlichen Dehnung in der Muldungsstrecke von Fördergurten. Braunkohle, Wärme und Energie 18 (1966) No. 1, pp. 14–19. [14] Hager, M. and S. Tappeiner: Additional Strain in Conveyor Belts Caused by Curves and Transition Geometry. Bulk Solids Handling 13 (1993) No. 4, pp. 695–703. [15] Grimmer, K.-J. and F. Kessler: Spezielle Betrachtungen zur Gurtführung bei Gurtförderern mit Horizontalkurven. Part 1: Anmerkungen and Part 2: Verbesserungen zu herkömmlichen Berechnungsverfahren. Berg- und Hüttenmännische Monatshefte 132 (1987), No. 2, pp. 27–32 and No. 6, pp. 206–211. [16] Oehmen, K. H.: Einfluß vertikaler und horizontaler Kurven auf die Dehnungsverteilung in Fördergurten – Theorie und Anwendung. Braunkohle 31 (1979) No. 12, pp. 340–348. [17] Hager, M.: Stand der Entwicklung von Verbindungen hochfester Stahlseilgurte Braunkohle 39 (1987) No. 7, pp. 251–253. [18] Flebbe, H.: Dynamic Splice Strength-Design Criterion for Conveyor Belts Bulk Solids Handling 8 (1988) No. 5. pp. 581–586. [19] Hager, M. and H.v.d.Wroge: Design of Steel Cord Conveyor Belt Splices. Bulk Solids Handling 11 (1991) No. 4, pp. 849–860. [20] Wennekamp, T.: Tribologie und rheologische Eigenschaften von Fördergurten Dissertation Leibniz Universität Hannover 2008

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