04-05-08

(1)

Grinding theory of

Vertical Mills

and

Roller Presses

(2)

Peder

Hansen

Employed in FLS 2001

Roller Mill Department

Product Manager, HRP and Dryer

Crusher

(3)

Jan Folsberg

Employed in FLS 1979

Roller Mill Department

Product Manager, Atox Mills

Worked with Separators and Roller

Mills

(4)

Aim with this lesson is to create:

•

• a basis for better

a basis for better

understanding of the roller

grinding process and the

design of roller mills.

•

• a basis for optimisation of your

a basis for optimisation of your

own roller mill performance

(5)

Content of presentation, Main topics

1.

1. Roller mills used in cement production

Roller mills used in cement production

2.

2. Basic calculations (roller press)

Basic calculations (roller press)

3.

(6)

1.

1. Roller mills used in cement production

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

(7)

Definition of Roller Mill:

(8)

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

(9)

Roller Press used for raw materials and

cement clinker

•

• Pre

Pre

-

grinding (lumps to pressed cake)

•

(10)

Vertical Mills used for

•

• Pre

Pre

-

grinding of clinker

(lumps to coarse powder)

•

• Finish grinding (lumps to

Finish grinding (lumps to

powder) of

•

• Coal for kiln

Coal for kiln

•

• Raw materials for kiln

Raw materials for kiln

•

(11)

Operational data:

•

• Table speed (rpm)

Table speed (rpm)

•

• Grinding press. (bar) or (kN/m

Grinding press. (bar) or (kN/m

22

₎

•

• Product fineness

Product fineness

(sieve residue, Blaine, etc.)

•

• Capacity (tph)

Capacity (tph)

•

• Mill Motor (kW)/Friction factor (

Mill Motor (kW)/Friction factor (

-

)

•

• Grinding bed thickness (mm)

Grinding bed thickness (mm)

•

(12)

Process inside the roller mill

Evaluation of:

•

• Max pressure pMax pressure p_max_max (MPa)(MPa)

•

• Max grinding bed thickness (mm)Max grinding bed thickness (mm)

•

• Mass flow through roller gap (tph) Mass flow through roller gap (tph)

•

• Spec. Power per roller pass (kWh/t)Spec. Power per roller pass (kWh/t)

•

• Circulation factor for roller (Circulation factor for roller (--))

•

• Friction factor Friction factor µµ ((--))

•

• Retention time in mill (sec)Retention time in mill (sec)

•

• Flow of material on the tableFlow of material on the table

•

• Slip between roller and tableSlip between roller and table

•

(13)

1.

1. Roller mills used in cement production

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

(14)

2. Basic calculations (roller press)

2.1 Nip angle

α

, gripping angle

δ

and

k

_T_T

2.2 Max pressure

p

_max_max

and bed thickness H

2.3 Relation between

p

_max_max

and H

2.4 Power uptake N and N

’

2.5 Circulation factor C

(15)

Evaluation and calculations are

based on

•

• Theoretical considerations

Theoretical considerations

•

• Basic data obtained from test work

Basic data obtained from test work

mainly with roller presses

(16)

Roller Press, single step process.

(17)

L: length of

compaction zone R: roller radius

W: roller width T: roller force

α: nip angle [radian] δ: gripping angle

[radian]

Illustration of the nip angle α and the gripping angle δ.

α small, therefore tg α≈α ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + ⋅ = + = 2 1 2 1 1 1 R R L α α δ

Roller Press, nip angle

(18)

R: roller radius D: roller diameter W: roller width T: roller force

Specific grinding pressure

k

_T_T

1

D

W

T

k

_T

⋅

=

(kN/m

2 )

(19)

Pressure measurements in a roller press

(20)

Typical pressure profile for a compaction of clinker in a roller

Typical pressure profile for a compaction of clinker in a roller press.press. Nip angle 8.3

Nip angle 8.3°° (( 0.14 radians)0.14 radians)

Roller press, pressure measurement

(21)

Compacted material subjected to:

• Extrusion (max. pressure before narrowest gap)

(22)

200 300 100 0 -0.20 -0.10 0 0.04 MPa RAD

Roller Press, Results of test work

(23)

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)

(24)

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

Some typical values of the critical

gripping angle found in practice:

(25)

Calculation of the maximum pressure

p

_max

in the grinding bed.

(26)

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

L

W

T

2 p

max

⋅

≈

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

⋅

≈

max

R

1 R

1 δ

W

T

2 p

1 2 1 R 1 R 1 δ L − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + ⋅ =

(based on triangular pressure distribution

and constant along the roller axis)

Inserting expression for L gives:

(27)

⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + ⋅ ⋅ ≈ 2 1 max R 1 R 1 δ W T 2 p Inserting D₁ = 2*R₁ and D₂ = 2*R₂ gives: ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + ⋅ ⋅ ⋅ ≈ 2 1 1 max D D 1 D W T δ 4 p 1 T D W T k ⋅ = ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + ⋅ ⋅ ≈ 2 1 T max D D 1 k δ 4

(28)

For many raw materials the gripping angle

For many raw materials the gripping angle δδ ≈≈ 1/3 radian (~ 19 1/3 radian (~ 19 ºº), ), which gives: which gives: ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + ⋅ ⋅ ≈ 2 1 T max D D 1 k δ 4 p

Roller press with D1=D2:

Roller press with D1=D2: _max T kT 24 kT

δ 8 1 1 1 k δ 4 p _⎟ = ⋅ = ⋅ ⎠ ⎞ ⎜ ⎝ ⎛ + ⋅ ⋅ ≈

Vertical Mill with D2=

Vertical Mill with D2=∞∞:: _max T kT 12 kT

δ 4 1 1 k δ 4 p _⎟ = ⋅ = ⋅ ⎠ ⎞ ⎜ ⎝ ⎛ ∞ + ⋅ ⋅ ≈

(29)

RP:

VRM:

Example:

Typical gripping angle

Typical gripping angle δδ ≈≈ 1/3 radian for raw materials1/3 radian for raw materials

Roller press: Typical value k_T = 7000 kN/m2 _{=> p}

max ≈ 168 MPa

Vertical roller mill: Typical value k_T = 700 kN/m2 _{=> p}

max ≈ 8.4 MPa T max δ k 8 p ≈ ⋅ T max δ k 4 p ≈ ⋅

(30)

Calculation of the grinding bed

thickness H.

(31)

(

)

(

)

2 (

F

1 )

δ

L

1 F

2 α

α

L

H

1 2

−

⋅

=

−

⋅

+

⋅

=

Grinding bed thickness H Compaction ratio F = ρρ_p/ρρ_f

Based on geometrical considerations we have:

(32)

1 2 1 R 1 R 1 δ L − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + ⋅ =

Using the expression for

Using the expression for gives:

(

F 1

)

D D 1 4 δ D H 2 1 2 1 − ⋅ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⋅ ⋅ =

(

)

D δ D H 2 ⎞ ⎛ + = or

(33)

(

F 1

)

D D 1 4 δ D H 2 1 2 1 ⎟⋅ − ⎠ ⎞ ⎜ ⎝ ⎛ + ⋅ = Roller press: Roller press: Vertical Mill: Vertical Mill:

(

F 1

)

0.014 0.028 1.4% 2.8% 8 δ D H 2 1 − = − = − ⋅ =

(

F 1

)

0.028 0.056 2.8% 5.6% 4 δ D H 2 1 − = − = − ⋅ = Example: Gripping angle

(34)

Relation between

max pressure p

_max_max

and

relative grinding bed thickness H/D

p

(35)

(

F 1

)

D D 1 4 δ D H 2 1 2 1 ⎟⋅ − ⎠ ⎞ ⎜ ⎝ ⎛ + ⋅ = _or_or _δ ₌ ₄_∗_H/D₁ _∗₍₁₊ _D₁_/D₂₎_∗_(F ₋₁₎ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + ⋅ ⋅ ≈ 2 1 T max D D 1 k δ 4 p

When δ is inserted into: we get:

1) (F H/D /D D 1 k 2 1) (F H/D /D D 1 ) D T/(W 2 p 1 2 1 T 1 2 1 1 max _⋅ ₋ + ⋅ ⋅ = − ⋅ + ⋅ ⋅ ⋅ ≈

(36)

1) (F H/D /D D 1 k 2 1) (F H/D /D D 1 ) D T/(W 2 p 1 2 1 T 1 2 1 1 max _⋅ ₋ + ⋅ ⋅ = − ⋅ + ⋅ ⋅ ⋅ ≈

If H is decreased to 50 %, then p

_max

is increased to approx. 140 %

or in other words

(37)

Calculation of the power consumption N (kW):

N = ?

Calculation of the specific power consumption

N

´

(kWh/t):

N

(38)

Dual Drive (symmetrical load)

(

β

)

T

v

T

μ

N

=

⋅

=

₁

+

₂

⋅

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

v = roller speed (m/s)

(39)

Single Drive (asymmetrical load)

(

β

)

T

v

T

μ

N

=

⋅

=

₁

+

₂

⋅

v

T

δ

N

≈

1₃

⋅

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

Valid for both single and dual drive

v = roller speed (m/s)

(40)

Dual Drive (symmetrical load) v T δ N ≈ 1₃ ⋅ ⋅ ⋅ q = ρρ_p* H*W*v Material flow through the roller gap:

Power uptake:

W

H

ρ

T

δ

v

W

H

ρ

v

T

δ

N'

p 3 1 p 3 1

⋅

=

⋅

≈

Specific power consumption:

v = roller speed (m/s)

(41)

Dual Drive (symmetrical load) W H ρ T δ N' p 3 1 ⋅ ⋅ ⋅ ⋅ ≈

Specific power consumption:

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

(

F 1

)

D D 1 4 δ D H 2 1 2 1 − ⋅ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⋅ ⋅ = F = ρρ_p/ρρ_f ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ≈ p f max ρ 1 ρ 1 3 p N' Inserted into gives:

(42)

Dual Drive (symmetrical load) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ≈ p f max ρ 1 ρ 1 3 p N' Example:

For a roller press following is found:

N N´´ = 4 kWh/t = 4= 4 kWh/t = 4··3600 J/kg3600 J/kg Feed material Feed material ρρ_f_f = 1600 kg/m= 1600 kg/m33 Pressed material Pressed material ρρ_p_p = 2400 kg/m= 2400 kg/m33 Calculate Calculate p_max ⋅⋅ MPa 207 2400 1 1600 1 3600 4 3 1 1 N' 3 p_max = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ₋ ⋅ ⋅ = ⎟ ⎟ ⎞ ⎜ ⎜ ⎛ − ⋅ ≈

(43)

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)

(44)

2. Basic calculations (roller press)

(Summary)

:

2.1 Nip angle

α

, gripping angle

δ

and

k

_T_T

2.2 Max pressure

p

_max_max

and bed thickness H

2.3 Relation between

p

_max_max

and H

2.4 Power uptake N and N

’

2.5 Circulation factor C

(45)

3.

3. Calculations used for vertical mills

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

(46)

Vertical Roller Mill

D_O Table diameter [m] µ Friction coefficient [radian] T Roller pressure per roller [kN] k_T Spec. roller pressure [kN/m2_]

D_R Roller diameter [m] W Roller width [m] D_M Mean diameter of track [m] n Table speed [rpm] v Velocity at D_M [m/s] i Number of rollers [-]

N Power [kW]

(47)

Vertical Roller Mill

D_O Table diameter [m] µ Friction coefficient [radian] T Roller pressure per roller [kN] k_T Spec. roller pressure [kN/m2_]

D_R Roller diameter [m] W Roller width [m] D_M Mean diameter of track [m] n Table speed [rpm] v Velocity at D_M [m/s] i Number of rollers [-]

N Power [kW]

P Production [t/h]

For the standard Atox mills i=3, D_R=0.6*D₀, W=0.2*D₀, D_M=0.8*D₀ and n=56*D₀0.5_{, which inserted gives:}

(

k

D

W

) (

D

π

n

60 )

μ

i

v

T

μ

i

N

=

⋅

=

⋅

_T

⋅

_R

⋅

_M

⋅

2.5 O T

D

k

μ

0.844 =

N

⋅

(48)

Friction coefficient µ

Cement raw material

0.09 +/-

0.02 Coal

0.10 +/-

0.02 Cement

0.06 +/-

0.01

(49)

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

Mass inside mill: (t) Retention time: t_r= (sec)

Example:

Atox 40: t_r= (sec)

Retention time for material in the vertical mill

D 0.03 = D 0.03 ) D (1.2 4 3 O 0 2 0 ⋅ ⋅ ⋅ ⋅ ⋅

π

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

(50)

Vertical Roller Mill

Example:

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 k_Tand friction factor µ? The roller force is:

T=¼*π*(0.3π 2_-0.152_{)*160*100 + 245 =} _{1093 kN}

Which means:

(51)

Vertical Roller Mill

Example:

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 ρρ_p of 2000 kg/m3.

What is the maximum pressure p_max, specific power consumption N´ and circulation under the roller C?

p_max = 4*k_T/δ = 4*569/(3*0.104) = 7295 kN/m2

F-1 = ¼ *D_R/H* δ2 = ¼* 2400/50*0.3122 = 1.17 N' = 1/3* p_max*(F-1)/ρρ_p = 1/3*7295*1.17/2000