gbw-animation Modelling


purpose, advantages, inventor


comminution, material throughput, pressure distribution, modelling


plant configuration, roller wear, references


literature survey, references


Other Links
links to suppliers, universities and other institutions


for any questions please contact us


all pages at a glance



High Compression Comminution in a Material Bed

Flakes of limestone - 4 mm (left), Rammelsberg lead-zink-ore - 5 mm (middle) and Rammelsberg lead-zink-ore - 2 mm (right), wet with volume related moisture content between 10 and 20 % (always left) and dry (always right)

In the doctoral thesis of Uwe Lubjuhn [25] two comminution topics are explored. One is the throughput and the material transport in the high compression roller mill, the other is the pressure distribution in the gap at variation of feed material, particle size, grinding force, roller speed and roller profile.

The laboratory mill which was built for these investigations has two rollers with a diameter of D = 200 mm and a length of L = 100 mm which are rotating against each other. The circumferential speed is the same for both rollers and can be varied between u = 0.1 and 3.3 m/s. One of the rollers, the movable roller, is sitting on a horizontal slide bearing and can be moved sideways. Four plate spring packages are pressing the roller against the material bed and are creating together the necessary ginding force for the comminution. The maximal achievable grinding force is F = 200 kN, equal to a maximum specific grinding force of Fsp = F / D L = 10 N/mm². The structure of the roller surface can be changed by installation of roller tyres with different profiles of horizontal bars which have a different width or distance between each other. For the determination of the pressure distribution pressure sensors are installed in three axial shifted positions into the roller. Their angle resolution is 1°. The results of the pressure measurement in different roller layers are complemented by the determination of throughput and production of fines in similarly axial shifted product stripes. Feed materials are quartz and limestone in a particle size range of 0.1 to 8.0 mm. The test rig is equipped with a complex data recording and data processing which consist of four load cells, two torque measurements, two potentiometric displacement sensors, two pressure sensors, one rotation angle sender, one tachometer, depending on the sensor a carrier-frequency- or a DC-amplifier and a 16-channel transient recorder connected to a computer.

At given roller dimensions the throughput is mainly determined by feed material, particle size distribution, circumferential speed and roller profile. In the tested range it is almost independent of the specific grinding force. The product fineness is a function of the energy absorption which again is dependent on the specific grinding force, the roller profile and the compression behavior of the material bed. The compression behavior is characterized by the shape of the pressure distribution in the gap between the two rollers. At equal energy absorptions the loading speed respectively the circumferential roller speed have no influence on the comminution result. According to the test results it seems to be allowed to look at throughput and pressure distribution as independent parameters.


The throughput is displayed as characteristic throughput curve Mt(u) depending on the circumferential roller speed u. The detected characteristic curves rise degressively with increasing circumferential speed.

With the throughput also the specific throughput can be calculated:

n = Mt / r D L u                                                                            (A)

When this parameter is displayed as a function of the relative roller speed z = u/uc with uc = (g D / 2)0.5 then the underproportionally increasing throughput curves are transformed into characteristic (n,z)-lines with negative slope. The equation for those lines is:

n = n0 - z / k                                                                                 (B)

For the laboratory mill is uc = 0.99 m/s. The value of z is therefore in the tested range between 0.1 and 3.3.

The extrapolated throughput number n0 characterizes the throughput level of a specific feed material for a given roller profile. The number is dependent on the static compression angle a0,st, the solid volume portion d0 in the entrance layer of the compression zone and the maximal compression qm. When these parameters are known n0 can be calculated.

n0 = (a0,st2 / 2) d0 [1 + d0 / qm (1 - d0)]                                            (C)

The reciprocal value of the slope value k describes the elasticity of the throughput with increasing roller speed. The elasticity is dependent of the centrifugal effect because of the particle movement along the roller periphery the particles are affected by the centrifugal force which again is depending on the square of the circumferential speed. The centrifugal force is reducing the normal force and therefore also the friction force which is determining the material transport and the throughput. In case of very high centrifugal forces the particles are even temporarily losing the contact to the roller as high speed videos have proven. By this also the material transport may temporarily collapse. The result is a significant decrease of the specific throughput and very unstable mill operation. The centrifugal effect impacts especially the introduction of coarse particles. If the feed material is very fine then additionally the air which is pressed out of the material bed may cause a backflow which is disturbing the material transport. For the tested particle size fractions the latter one can be neglected.

The results indicate a correlation between the throughput number n0 and the throughput elasticity k which is decreasing with increasing n0.

The throughput with profiled rollers exceeds the one with smooth rollers up to 250 %. The profile effect for quartz is bigger than for limestone. With limestone usually a higher throughput is achieved than with quartz. But the material influence is less significant for profiled rollers and the difference becomes smaller the bigger the particles are. With exception of the smooth rollers a particle size influence can be seen. The results are in a systematic order: The throughput decreases with decreasing maximum particle size and increases with increasing width of the particle size distribution. All effects can be explained with different friction conditions in the gap between the rollers and with different bulk densities. The big throughput for limestone, for instance, can be demonstrably related to an adhesive layer of fine limestone on the roller surface which is improving the friction conditions. The profile effect is based on the form fit between roller profile and particle and the resulting activation of the inner friction at the roller surface. The higher throughput of the wider particle size fractions is a result of the higher bulk density. Based on the characteristic throughput curves conclusions about the optimal profile geometry can be drawn.

Pressure distribution

The energy absorption which determines the comminution result is mainly dependent on the maximal pressure in the gap between the rollers and on the width and shape of the peripheral and axial pressure distribution.

The pressure distribution along the roller periphery can be described by the compression angle a0, the location and height of the pressure maximum and the relaxation angle g. Also the force attack angle b results from the pressure distribution which can be directly determined by the measurement of torque and grinding force as well.

The pressure maximum is usually located between 0° and 1°, at higher speeds between 1° and 2° above the narrowest gap. The height of pressure maximum is mainly determined by the specific grinding force. A proportionality exists.

The compression angle a0 characterizes the begin of the comminution respectively of the load on the material bed. This angle is in complex way depending on material, particle size, roller profile and circumferential speed. The compression angle is only for the limit case u → 0 identical with the nip angle. In other cases it is smaller because with bigger roller speed also the acceleration of the feed material decreases and the material transport into the compression zone reduces. For the explanation of those dependencies two cases of the material introduction have to be distinguished. If the maximal particle size is significantly smaller than the gap, means 2 xmax < s, the material will be introduced in the “material bed” condition. For 2 xmax > s almost the “direct contact” condition exists. In the latter case also two particles may be jammed, a calculated average “jamming”-factor of 1.6 was observed.

When the material is introduced as a bed then a0 is depending on the friction between material and roller surface as well as on the inner friction, for direct contact only the first one plays a role. For smooth rollers at a circumferential speed of 0.3 to 1.1 m/s the compression angles for quartz are between a0 = 7° to 13° (0.13 to 0.22) and for limestone between a0 = 9° to 11° (0.15 to 0.19). The grinding force has no influence.

The relaxation angle g is dependent on material and grinding force and is in the range of -3° to -9°, quartz: -2.9° to – 8.6° (-0.05 to -0.15), limestone: -3.4° to -9.2° (-0.06 to -0.16). From this the relaxation can be calculated which is in the range of 15 and 45 % for quartz and 9 to 41 % for limestone. Such big values cannot just be explained by elastic relaxation but have to do with rearranging processes in the compacted material bed.

The force attack angle b is calculated from the torque T and the grinding force F respectively from the specific variables:

b = Tsp / Fsp = T / F D                                                                  (D)

The value of b is almost independent of material and circumferential speed but reduces a little bit with increasing grinding force as the pressure distribution gets steeper. An angle between 1.7° and 2.9° (0.03 and 0.05) results. In transition to the direct contact it reaches a maximum of 3.4° (0.06). The ratio b/a0 is between 0.23 and 0.28.

The axial pressure distribution is surprisingly distinct. At the biggest specific grinding force of 4.5 N/mm² the pressure falls from 170 MPa in the center layer (l = 0 mm) by approximately 70 % to 50 MPa at the outer measurement layer (12 mm away from the edge of the roller, l = 38 mm). The axial pressure distribution is independent of the material. The related distribution p(l) / p(l=0) can be approximated by a power function in the form of 1 – (2|l|)n with l = l / L. The exponent is approximately n = 1.6 and is only slightly depending on the grinding force. Two reasons for the pressure decrease are possible: 1) material leaves through the gap between rollers and side wall and 2) material flow on the sides of the rollers is lower due to friction with the non-moving side wall. The second option could be proven by measurements of the throughput in axial stripes. In the outer stripes the throughput was only 83 % of the throughput in the middle stripe. This relatively small variation is enough to create a significant pressure decrease at such high compression levels as the compression diagram has a steep increase in this area. The comminution effect in the outer stripe is much weaker. The production of fines decreases compared to the middle stripe by 60 %.

As a measure for the integral load intensity the effective pressure peff is determined as an average of the axial pressure distribution in the horizontal shaft layer (a = 0). It is linearly correlated with the specific grinding force. In the tested range of feed materials and grinding forces the almost independent proportionality factor lies between 0.26 and 0.30.

Compression angle and throughput

From the phenomenological considerations regarding the throughput a dependency follows between the throughput number n0 and the static compression angle a0,st, the solid volume portion d0 in the entrance layer and the compression qm, see equation C. The pressure distribution tests delivered the compression angle a0 and the specific throughput n. Under the assumption that the values of n and a0 measured at the low speed of 0.3 m/s are a good approximation for n0 and a0,st the modelling exercises for the throughput number n0 can be checked by using those measured values and the solid volume portion of the loose bulk material dSch. For limestone a good compliance exists but not for quartz. These deviations indicate that there is slip in the entrance layer of the compression zone for quartz because equation C is only valid for slip-free material transport at a0. The high-frequency video recordings showed that in the area above the compression zone the slip between quartz and the roller surface is much higher than between limestone and the roller surface. This is an indication for the permissibility of the given explanation.

The throughput number n0 and the throughput elasticity k are correlated in a way that k decreases with increasing n0. This correlation can be displayed as a trend curve in (k,n0)-diagram.

grinding results for different materials

characteristic of different rollers

Pressure Distribution
pressure diagrams

Press Tests
tests with a molding press

mathematic model of the process

Signs and Symbols

A mathematic modelling of the high compression comminution in a material bed was done by Liu in his doctoral thesis: “Modellierung der Zerkleinerung in einem Gutbett”, Dissertation, TU Clausthal / Germany, 1994

[HCRM-Home] [Idea] [Research] [Praxis] [Literature] [Other Links] [Contact] [Site-Map]

For any questions or remarks please contact the Webmaster.
© Copyright 1992, Dr. Uwe Lubjuhn, all rights reserved