04-05-08

Grinding theory of Vertical Mills and Roller Presses FLSmidth 2008, all rights reserved.

Lecture: 04-05

Peder Hansen Employed in FLS 2001 Roller Mill Department Product Manager, HRP and Dryer Crusher

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Jan Folsberg Employed in FLS 1979 Roller Mill Department Product Manager, Atox Mills Worked with Separators and Roller Mills FLSmidth 2008, all rights reserved.

Lecture: 04-05

Aim with this lesson is to create: • a basis for better understanding of the roller grinding process and the design of roller mills. • a basis for optimisation of your own roller mill performance

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Content of presentation, Main topics 1. Roller mills used in cement production 2. Basic calculations (roller press) 3. Calculations used for vertical mills

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1. Roller mills used in cement production 1.1 Definition of roller mill 1.2 Use of roller press and vertical mills 1.3 Operational parameters and values

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Definition of Roller Mill: ?

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Definition: A roller mill is characterised in that a bed of loosely packed material is compacted and thereby ground between two rolling surfaces pressed against each other, and that at least one of the rolling surfaces is a roller. The gap between the rolling surfaces is not fixed but varies with change in the material properties.

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Roller Press used for raw materials and cement clinker • Pre-grinding (lumps to pressed cake) • Finish Grinding (lumps to powder)

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Vertical Mills used for • Pre-grinding of clinker (lumps to coarse powder) • Finish grinding (lumps to powder) of • Coal for kiln • Raw materials for kiln • Cement, OPC or mixed • Slag, pure or mixed FLSmidth 2008, all rights reserved.

Lecture: 04-05

Operational data: • Table speed (rpm) • Grinding press. (bar) or (kN/m2) • Product fineness (sieve residue, Blaine, etc.) • Capacity (tph) • Mill Motor (kW)/Friction factor (-) • Grinding bed thickness (mm) FLSmidth 2008, all rights reserved.

• Vibration level (mm/s)

Lecture: 04-05

Process inside the roller mill Evaluation of: • Max pressure pmax (MPa) • Max grinding bed thickness (mm) • Mass flow through roller gap (tph) • Spec. Power per roller pass (kWh/t) • Circulation factor for roller (-) • Friction factor µ (-) • Retention time in mill (sec) • Flow of material on the table • Slip between roller and table • Wear FLSmidth 2008, all rights reserved.

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1. Roller mills used in cement production (Summary) 1.1 Definition of roller mill 1.2 Use of roller press and vertical mills 1.3 Operational parameters and values

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2. Basic calculations (roller press) 2.1 Nip angle α, gripping angle δ and kT 2.2 Max pressure pmax and bed thickness H 2.3 Relation between pmax and H 2.4 Power uptake N and N’ 2.5 Circulation factor C

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Evaluation and calculations are based on • Theoretical considerations • Basic data obtained from test work mainly with roller presses

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Roller Press, single step process.

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Roller Press, nip angle α and gripping angle δ L: length of compaction zone R: roller radius W: roller width T: roller force α: nip angle [radian] δ: gripping angle [radian] α small, therefore tg α≈α ⎛1 1⎞ δ = α1 + α2 = L ⋅ ⎜⎜ + ⎟⎟ ⎝ R1 R2 ⎠

Illustration of the nip angle α and the gripping angle δ. FLSmidth 2008, all rights reserved.

Lecture: 04-05

Specific grinding pressure kT R: D: W: T:

T kT = W ⋅ D1 FLSmidth 2008, all rights reserved.

roller radius roller diameter roller width roller force

2 (kN/m )

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Pressure measurements in a roller press Ø1000*260 mm

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Roller press, pressure measurement

Typical pressure profile for a compaction of clinker in a roller press. Nip angle 8.3° ( 0.14 radians) FLSmidth 2008, all rights reserved.

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Compacted material subjected to: • Extrusion (max. pressure before narrowest gap) • Elastic behaviour (pressure after narrowest gap)

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Roller Press, Results of test work 300

200 MPa

100

0

-0.20

-0.10

RAD

0

0.04

Compaction profiles of a clinker press at different pressures 100-300 MPa FLSmidth 2008, all rights reserved.

Lecture: 04-05

Nip angle α and gripping angle δ dependent of: • Angle of repose for material (internal friction) (type, moisture, granulometry, fluidisation) • Friction coefficient between material and grinding surface (smooth/ropes) • Degree of material filling in gap (choke feed/starving)

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Some typical values of the critical gripping angle found in practice: δ [radian] Fine ground cement and slag

0.20-0.25

Cement clinker

0.25-0.35

Limestone/rawmeal

0.35-0.45

Coal

0.40-0.50

Note: 0.1 radians = 5.7 º FLSmidth 2008, all rights reserved.

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Calculation of the maximum pressure pmax in the grinding bed. pmax = ?

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⎛ 1 1 ⎞ ⎟⎟ δ = α1 + α 2 = L ⋅ ⎜⎜ + ⎝ R1 R 2 ⎠

⎛ 1 1 ⎞ ⎜ ⎟⎟ L = δ⋅⎜ + ⎝ R1 R 2 ⎠

p

max

2⋅T ≈ W⋅L

−1

(based on triangular pressure distribution and constant along the roller axis)

Inserting expression for L gives:

p

max

2⋅T ⎛ 1 1 ⎞ ⎜⎜ ⎟⎟ ≈ + W ⋅ δ ⎝ R1 R 2 ⎠

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p

max

2⋅T ⎛ 1 1 ⎞ ⎜⎜ ⎟⎟ + ≈ W ⋅ δ ⎝ R1 R 2 ⎠

Inserting D1 = 2*R1 and D2 = 2*R2 gives: p p

max

max

4 T ≈ ⋅ δ W ⋅ D1 4 ≈ ⋅ kT δ

⎛ D ⎞ ⋅ ⎜⎜1 + 1 ⎟⎟ ⎝ D2 ⎠

⎛ D1 ⎞ ⎟⎟ ⋅ ⎜⎜1 + ⎝ D2 ⎠

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T kT = W ⋅ D1

General for all kind of roller mills

Lecture: 04-05

p

max

≈

4 ⋅ kT δ

⎛ D ⎞ ⋅ ⎜⎜1 + 1 ⎟⎟ ⎝ D2 ⎠

For many raw materials the gripping angle δ ≈ 1/3 radian (~ 19 º), which gives: Roller press with D1=D2: p

max

Vertical Mill with D2=∞: p max

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≈

4 ⎛ 1⎞ 8 ⋅ k T ⋅ ⎜1 + ⎟ = ⋅ k T = 24 ⋅ k T δ ⎝ 1⎠ δ

4 1⎞ 4 ⎛ ≈ ⋅ k T ⋅ ⎜1 + ⎟ = ⋅ k T = 12 ⋅ k T δ ⎝ ∞⎠ δ

Lecture: 04-05

RP: VRM:

p p

max

max

≈

8 ⋅ kT δ

4 ≈ ⋅ kT δ

Example: Typical gripping angle δ ≈ 1/3 radian for raw materials Roller press: Typical value kT = 7000 kN/m2 =>

pmax ≈ 168 MPa

Vertical roller mill: Typical value kT = 700 kN/m2 => pmax ≈ 8.4 MPa

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Calculation of the grinding bed thickness H. H=?

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Grinding bed thickness H Compaction ratio F = ρp/ρf α small, therefore tg α ≈ α Based on geometrical considerations we have:

L ⋅ (α1 + α 2 ) L⋅δ H= = 2 ⋅ (F − 1) 2 ⋅ (F − 1) FLSmidth 2008, all rights reserved.

Lecture: 04-05

−1

⎛ 1 1 ⎞ ⎜ ⎟⎟ gives: Using the expression for L = δ ⋅ ⎜ + ⎝ R1 R 2 ⎠

or

D1 ⋅ δ 2 H= ⎞ ⋅ (F − 1) 4 ⋅ ⎛⎜1 + D1 ⎟ D 2⎠ ⎝ H δ2 = D 1 4 ⋅ ⎛1 + D 1 ⎞ ⋅ (F − 1) ⎜ D 2 ⎟⎠ ⎝

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H δ2 = D 1 4 ⋅ ⎛1 + D 1 ⎞ ⋅ (F − 1) ⎜ D 2 ⎟⎠ ⎝

Example: Gripping angle δ ≈ 1/3 radian and compaction factor F=1.5-2: Roller press:

H δ2 = = 0.014 − 0.028 = 1.4% − 2.8% D1 8 ⋅ (F − 1)

Vertical Mill:

H δ2 = = 0.028 − 0.056 = 2.8% − 5.6% D1 4 ⋅ (F − 1)

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Relation between max pressure pmax and relative grinding bed thickness H/D pmax = f(H/D) ? FLSmidth 2008, all rights reserved.

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H δ2 = D 1 4 ⋅ ⎛1 + D 1 ⎞ ⋅ (F − 1) ⎜ D 2 ⎟⎠ ⎝

or δ = 4 ∗ H/D1 ∗ (1 + D1 /D 2 ) ∗ (F − 1)

When δ is inserted into: p max

p max

⎛ D1 ⎞ 4 ⎜ ⎟⎟ we get: ≈ ⋅ k T ⋅ ⎜1 + δ ⎝ D2 ⎠

1 + D1 /D 2 1 + D1 /D 2 = 2⋅ kT ⋅ ≈ 2 ⋅ T/(W ⋅ D1 ) ⋅ H/D1 ⋅ (F − 1) H/D1 ⋅ (F − 1)

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p max

1 + D1 /D 2 1 + D1 /D 2 = 2⋅ kT ⋅ ≈ 2 ⋅ T/(W ⋅ D1 ) ⋅ H/D1 ⋅ (F − 1) H/D1 ⋅ (F − 1)

If H is decreased to 50 %, then pmax is increased to approx. 140 % or in other words If H is increased 100 %, then pmax is decreased to approx. 70 % FLSmidth 2008, all rights reserved.

Lecture: 04-05

Calculation of the power consumption N (kW): N=? Calculation of the specific power consumption N´ (kWh/t): N´ = ? FLSmidth 2008, all rights reserved.

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Dual Drive (symmetrical load)

v = roller speed (m/s)

N = μ ⋅ T ⋅ v = (β1 + β 2 ) ⋅ T ⋅ v For triangular load the angle of reaction β ≈ α/3 i.e. μ ≈ δ/3, which gives:

N≈ FLSmidth 2008, all rights reserved.

1

3

⋅δ⋅T⋅v Lecture: 04-05

Single Drive (asymmetrical load)

v = roller speed (m/s)

N = μ ⋅ T ⋅ v = (β1 + β 2 ) ⋅ T ⋅ v

For triangular load the angle of reaction β ≈ α/3 i.e. μ ≈ δ/3, which gives:

N≈

1

3

⋅δ⋅T⋅v

Valid for both single and dual drive FLSmidth 2008, all rights reserved.

Lecture: 04-05

Dual Drive (symmetrical load)

v = roller speed (m/s)

Power uptake:

N≈

Material flow through the roller gap:

q = ρp* H*W*v

Specific power consumption:

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1

3

⋅δ⋅T ⋅v

1 ⋅δ⋅T ⋅δ⋅T⋅ v N' ≈ = 3 ρp ⋅ H ⋅ W ⋅ v ρp ⋅ H ⋅ W 1

3

Lecture: 04-05

Dual Drive (symmetrical load)

p

max

⎛ D1 ⎞ 4 T ⎟⎟ ≈ ⋅ ⋅ ⎜⎜1 + δ W ⋅ D1 ⎝ D 2 ⎠

D1 ⋅ δ 2 H= 4 ⋅ ⎛⎜1 + D1 ⎞⎟ ⋅ (F − 1) D2 ⎠ ⎝

F = ρp/ρf

Inserted into 1 ⋅δ⋅T N' ≈ 3 ρp ⋅ H ⋅ W gives: Specific power consumption:

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p N' ≈ max 3

⎛1 1⎞ ⎜ − ⎟ ⎜ρ ρ ⎟ p ⎠ ⎝ f Lecture: 04-05

Dual Drive (symmetrical load)

p max N' ≈ 3

⋅

Example: For a roller press following is found: N´ = 4 kWh/t = 4·3600 J/kg Feed material ρf = 1600 kg/m3 Pressed material ρp = 2400 kg/m3 Calculate pmax p max

⎛1 1⎞ ⎜ − ⎟ ⎜ρ ρ ⎟ p ⎠ ⎝ f

3 ⋅ N'

3 ⋅ 4 ⋅ 3600 ≈ = = 207 MPa 1 ⎞ ⎛1 1⎞ ⎛ 1 − ⎜ − ⎟ ⎜ ⎟ ⎜ ρ ρ ⎟ ⎝ 1600 2400 ⎠ p ⎠ ⎝ f

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Circulation factor C = (N/P)/N’ C: circulation factor (-) P: capacity for finished product (t/h) N: power uptake for roller mill (kW) N’: specific power uptake (kWh/t)

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Lecture: 04-05

2. Basic calculations (roller press) (Summary): 2.1 Nip angle α, gripping angle δ and kT 2.2 Max pressure pmax and bed thickness H 2.3 Relation between pmax and H 2.4 Power uptake N and N’ 2.5 Circulation factor C

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3. Calculations used for vertical mills 3.1 Power uptake 3.2 Friction factor 3.3 Retention time inside mill 3.4 Optimisation of vertical mill operation

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Vertical Roller Mill DO µ T kT DR W DM n v i N P

Table diameter Friction coefficient Roller pressure per roller Spec. roller pressure Roller diameter Roller width Mean diameter of track Table speed Velocity at DM Number of rollers Power Production

[m] [radian] [kN] [kN/m2] [m] [m] [m] [rpm] [m/s] [-] [kW] [t/h]

Vertical and horizontal components of roller load FLSmidth 2008, all rights reserved.

Lecture: 04-05

Vertical Roller Mill

DO µ T kT DR W DM n v i N P

Table diameter Friction coefficient Roller pressure per roller Spec. roller pressure Roller diameter Roller width Mean diameter of track Table speed Velocity at DM Number of rollers Power Production

[m] [radian] [kN] [kN/m2] [m] [m] [m] [rpm] [m/s] [-] [kW] [t/h]

N = i ⋅ μ ⋅ T ⋅ v = i ⋅ μ ⋅ (k T ⋅ D R ⋅ W ) ⋅ (D M ⋅ π ⋅ n 60 ) For the standard Atox mills i=3, DR=0.6*D0, W=0.2*D0, DM=0.8*D0 and n=56*D00.5, which inserted gives:

N = 0.844 ⋅ μ ⋅ k T ⋅ D O2.5 FLSmidth 2008, all rights reserved.

Lecture: 04-05

Friction coefficient µ Cement raw material 0.09 +/- 0.02 Coal 0.10 +/- 0.02 Cement 0.06 +/- 0.01

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Retention time for material in the vertical mill Assumption: • Mill capacity P = 7*D02.5 (~225 tph for Atox 40) • Material layer thickness of 3 % of the table diameter continues over the nozzle ring to a diameter of about 1.2*D0. • Density approx. 1 t/m3

π

Mass inside mill: Retention time: Example: Atox 40:

4

⋅ (1.2 ⋅ D 0 ) 2 ⋅ 0.03 ⋅ D 0 = 0.03 ⋅ D 3O (t)

(0.03 ⋅ D 3O ) tr = ⋅ 3600 = 15 ⋅ D 0 (sec) 2.5 (7 ⋅ D O ) tr=15 ⋅ 4 = 15 ⋅ 2 = 30 (sec)

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Lecture: 04-05

Example:

Vertical Roller Mill

An Atox 40 raw mill running with 160 bar hydraulic pressure consumes 1600 kW. The cylinder diameter is Ø300/150 mm. Weight of each roller is 25 ton ~ 245 kN. Calculate specific grinding pressure kT and friction factor µ? The roller force is: T=¼*π*(0.32-0.152)*160*100 + 245 =

1093 kN

Which means: kT = T/(0.6*0.2*D02) = 1093/(0.12*42) = 569 kN/m2 µ = N/(0.844*kT*D02.5) = 1600/(0.844*569*42.5) = 0.104 FLSmidth 2008, all rights reserved.

Lecture: 04-05

Example:

Vertical Roller Mill

The Atox 40 raw mill produces 250 tph with a grinding bed H of 50 mm and assuming a density of the compacted material under the rollers ρp of 2000 kg/m3. What is the maximum pressure pmax, specific power consumption N´ and circulation under the roller C? pmax

= 4*kT/δ = 4*569/(3*0.104) =

7295 kN/m2

F-1

= ¼ *DR/H* δ2 = ¼* 2400/50*0.3122 =

N'

= 1/3* pmax*(F-1)/ρp = 1/3*7295*1.17/2000

1.17

= 1.42 kJ/kg = 1.42 /3.6 = 0.395 kWh/t C = (N/P)/N´= (1600/250)/0.395 = 6.4/0.395 = 16 times FLSmidth 2008, all rights reserved.

Lecture: 04-05

Optimisation of mill operation. •Increase of friction coefficient of material: Inject water on table • Higher power uptake • Lower vibration level •Increase thickness of material: Increase height of dam ring • Higher power uptake • Lower vibration level • Decreased grinding efficiency •Increase thickness of material: Reduce table speed (to 80-100%) • Lower vibration level (for finer materials) • Increased friction factor but lower power uptake FLSmidth 2008, all rights reserved.

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3. Calculations used for vertical mills (Summary) 3.1 Power uptake 3.2 Friction factor 3.3 Retention time inside mill 3.4 Optimisation of vertical mill operation

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Content of presentation, Main topics (Summary) • Roller mills used in cement production • Basic calculations (roller press) • Calculations used for vertical mills

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End of lesson FLSmidth 2008, all rights reserved.

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