Calculation of Rope Drum

 

 

IDEA

IDEA – WORK STANDARD – DIN 15061

Industrial Designer & Engineer Association

Rope drum

Page : 1 Date : 05-Oct-09 

1.  GENERAL

The rope drum has the function to move the wire rope, to take up the tensile force on the wire rope and to store the whole rope length. When a wire rope is spooled to a drum, each wire of the rrope ope is subject to a  bending moment. The bending moment increases with a smaller drum diameter, thus resulting in a quicker fatigue and easy breakage of each wire. The wire rope deteriorates quickly because of the deformation, the internal friction due to irregular bending and the increasing contact pressure with the drum. The ratio  between rope diameter and drum diameter influences largely the service life of the wire rope and therefore it should not less than the recommended value in this standard. 1.1. Dimensions on drum 1.1.1. Groove profile for rope drum

d r

Δr s h r 2 

= = = = = =

rope diameter in mm groove radius in mm maximum allowable deviation of radius, depending on the rope diameter pitch of groove in mm height of groove in mm, h > 0,375 . d due to rope exit. ( Seil sprung ) edge radius in mm, r 2 is valid for h < 0,4 . d s

50º

h

r2

d

r  t D 130º

The minimum recommended value is : r = 0,53.d and groove hardness of 35 - 42 HRc. The groove  profile may have allowable deviations depending on on rope diameter. See attachment DIN 15 061 bellow. 1.1.2. Diameter of drum

The diameter of drums, sheaves, and compensating sheaves is determined as follows :

D d h1 

D

>

h1 . d

= = =

drum diameters in mm, measured between rope centers. minimum rope diameter in mm coefficient which varies depending on whether a drum considered and takes into account the group of mechanism. The value h1 can be taken from attached DIN 15 020.

Under one and the same rope pull S, ropes having a diameter of up to 1,25 times the calculated diameter d may be provided without affecting their life if the rope reeving components have the diameter D calculated as above. 1.1.3. Thickness of drum

The thickness of a drum is calculated based on the assumption that the drum is a thick-wall, open cylinder, which is loaded by an outer pressure.

 

 

IDEA

IDEA – WORK STANDARD – DIN 15061

Industrial Designer & Engineer Association

Rope drum

Page : 2 Date : 05-Oct-09 

 pa d ϕ

R 

ϕ

     a         d

S

da di R s  pa S

= = = = = =

S

D 2.r da 2.t 0,5 . da pitch of groove outer pressure rope force

= = =

σt

effective outer drum diameter effective inner drum diameter radius of drum

Vertical component of drum force

F

=

2.S

        i         d

=

R . s . pa .

:

dF

π

∫ sin ϕ . d ϕ

R . d ϕ . s . pa . sin ϕ  R . s . pa . sin ϕ . d ϕ 

= = =

R . s . pa .

0 Hence, outer pressure

pa

2.S

=

da . s

[ cos ϕ  ]0π  

σt

= =

σt

S

=

2 . pa . S

. 

da . s . pa

 

The critical point of stress lies in the inner side of the cylinder. With Tangential stress

=

η2 η 2  -  1 da

s . t ( da  -  t )

  =  

 

da

η = 

di

da 2 .    = da . s da 2  -  di 2 4.S

If t 2 . 106

•  ϕd

=

St 52 and equivalent 139 115,8

0,9 + 0,001 . ( h1 - 15 )

•  ϕr depends on the calculated thickness of drum. Therefore, the drum thickness should be estimated first and a calculation check must be done afterwards. ϕr is function of h1 and the ratio h / t. •  ϕE is almost independent from h1 for single layer drum. For E < 100 000 N / mm2  : ϕe = 1,025 2 E = 100 000 N / mm   : ϕe = 1,0 2 E > 100 000 N / mm   : ϕe = 0,974 •  The today winches and hoist are using the wire rope with the filling factor κ  > 0,6, so the factor ϕκ  can be estimated as ϕκ  = 0,97. •  The pitch factor ϕs is as follow : s/d ϕs

1,05 0,956

1,10 0,919

1,15 0,885

1,20 0,855

For pre-calculation purpose, calculate the drum thickness using both methods and take the bigger one. 1.1.4. Number of winding.

The effective number of rope winding depends on the length of wire rope and the drum diameter. The drum should provide at least 3 additional winding, which must be added to the calculated effective winding, to ensure the safe clamping of rope end on the drum. The total number of winding become : n n z f H D

= = = = =

=

z . H .1000

π.D

+ 3 

the total number of rope winding the number of rope reeving number of rope exit from drum lifting height in m drum diameter in mm

1.1.5. Fleet angle

The fleet angle calculation is to check that the wire rope does not spring out of its groove during the operation. Due to the lifting of load, the wire rope is bent into direction in line with pitch groove or in opposite to the groove. The rope should not touch the neighborhood if it goes out from its position. The rope is wound on the drum at an angle β, which is the gradient angle of the drum. The fleet angle is limited to α1 and α2, which maximum value is taken from the table bellow.

 

 

IDEA

IDEA – WORK STANDARD – DIN 15061

Industrial Designer & Engineer Association

Rope drum

tan β  =

s

π.D

Page : 5 Date : 05-Oct-09 

 

t1 

=

1000 . tan ( α1  +

β )

t2 

=

1000 . tan ( α2  -

β )

The value t1 and t2 are depending on the ratio h1.

The maximum fleet angle is prescribed in DIN 15 020 as α1 as well as α2  = 4º for rotating rope and 1,5º for non-rotating rope. There is alternatives to keep fleet angle within the limitation : •  The fleet angle α decreases with the growing distance a between load sheave and drum. •  The maximum possible angle β  + α  can be reduced by shifting the sheave sideways. This measurement is only possible with single layer drum. However the fleet angle on the sheave will increase. •  The drum diameter can be increased to make its width becomes narrow for a given rope length. This solution requires a higher driving torque at slower drum speed. Consequently, it will require stronger gearbox with higher gear ratio. It can be expensive. However, the bigger drum diameter will not only diminish α; it reduces also β considerably, because the shift of the rope on the drum can be distributed over a wider circumference. Consequently the maximum of β  + α is distinctly reduced. In additional, the bending radius of the wire rope becomes bigger and the lifetime of the wire rope is extended. In order to minimize the twist and stop the natural tendency of the rope to unlay, the following rules must  be observed : left-hand drum must be operated with a right-hand lay rope. ••   A A right-hand drum must be operated with a left-hand lay rope.

 

 

IDEA

IDEA – WORK STANDARD – DIN 15061

Industrial Designer & Engineer Association

Rope drum

1.1.6. Possible rope reeving

1.2. Torque and power.

•  The rotational speed on drum: drum: nd z f D

= = = =

nd

:

•  Required power on drum

:

Pd Md nd

= = = =

= = =

= = =

 

Md

=

0,5 . f . S . D

Pd

=

2 . π . Md . nd

ds

=

3  Sb . Md . 16   π . τall

torque on drum number of rope fall from drum rope force drum diameter

required power on drum torque on drum rotational speed of drum

•  Drive shaft diameter on drum : Sb Md τall

f . π . D

rotational speed of drum number of rope reeving number of rope fall from drum drum diameter

•  The torque on drum

Md f S D

z . v

=

service factor torque on drum allowable torsional shear stress

Page : 6 Date : 05-Oct-09