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Literature about the Pressure Distribution in the Gap

Starting from the outlet of the feeding funnel the material is accelerated between the rollers, the flowing material then is confined and finally loaded.The space between the rollers is separated into three different areas which - in the following - will be called acceleration zone, compression zone and relaxation zone, see left picture below. The acceleration zone starts at the funnel outlet and ends at the compression angle a0, the compression zone ranges from there to the narrowest gap at a = 0.It follows the relaxation zone which ends at the back strain angle g. Due to the compaction and relaxation an unknown three dimensional stress field is created inside the material.  Experimental and theoretical investigations concentrate on the stress condition on the roller surface which is characterized by the local normal stress respectively by the pressure and by the tangential stress.In the literature this problem is discussed with regard to the briquettingof powders [e.g. 8 to 14]; with regard to the pressure distribution during comminution so far only one experimental study exists where the pressure distribution was measured by a tracer pin which was integrated in the roller [15,16]. Informations about the axial pressure distribution can be obtained by analysing differences in the grinding or comminution effect when material stripes are collected at the mill outlet under the gap between the two rollers [17].

grinding results for different materials

characteristic of different rollers

Pressure Distribution
literature pressure distribution, pressure diagrams, peripheral pressure distribution, axial pressuredistrib., effective pressure and specific grinding force, compression angle and specific throughput

Press Tests
tests with a molding press

mathematic model of the process

Signs and Symbols

Left side: Schematic division of the gap area into acceleration zone, compression zone and relaxation zone. Right side: Characteristic development of the pressure gradient ds/dx against the rotation angle a according Johanson [8].

In the monography of Herrmann [10] different theories about the stress situation during the compaction in briquetting rollers are shown including the theory of Johanson [8] which is commonly ackknowledged today. The core point of his publication is the determination of the compression angle a0 (which Johanson calls nip angle a). For the determination he calculates the stress situation in the acceleration zone with methods of the bulk material mechanics, assuming conditions of stationary flow with constnacy of volume. That means that slip exists between material and rollers. In the compression zone the relation between compression and pressure is approximated with a power law assuming a slip-free material transport. Both physical regularities are extrapolated beyond their area of validity and differentiated in order to determine the stress gradient vertically to the shaft level, see example in the right picture above. Both curves cross each other whereat - due to physical reasons - always only the smaller gradient can exist. The intersection therefore describes the compression angle. This theory does not deliver an explicit equation but a numerical solution for the calculation of a0. The following parameters are part of the calculation scheme: relative gap width (s/D), effective friction angle, outer friction angle, compressibility of the bulk material. Systematic experimental investigations regarding this theory are not existing.

Tundermann and Singer [13,14] have measured the solid volume portion of metal powders in the compression zone.For this purpose a briquetting press was stopped and the material was taken out of the gap and cutted into stripes. The quotient of the densities of two consecutive stripes shows a trend similar to the dotted line in the right picture above.

Herrmann und Rieger [11] investigate the applicability of the Johanson-theory for the design and layout of briquetting machines with regard toroller force and driving power. The compression distribution is not measured. The theoretical values are significantly underestimating the measured values, possible root causes are discussed.

Unfortunately the power law for the compression of a material bed used by Johanson has one disadvantage: It does not comply with the physical constraint that the solid volume portion d can only reach a maximum of one. An approximation which complies with this constraint was proposed in [18] and was also experimentally proven. It is:

q = 1 - exp [- (p/pc)n]

q = (d - d0) / (1 - d0)

Vinogradov and Katashinski [9] were the first who measured compressive and shear forces during the compression of metal powders with a sensor pin (diameter 1,3 mm). The pressure shows the expected trend with a maximum and a steeper decrease than increase. The shear force is changing the prefix during the increase of the pressure. From this the authors conclude that in analogy with the metal rolling that material transport is slip-free only in this one point and that it is slower before and faster behing this point. But this interpretation is questionable as shear forces can also exist without relative movement. The angle coordinate is not shown. Therefore the position of the pressure maximum can not be taken from those results.

Feige used the sensor-pin-method for the measurement of the peripheral and axial pressure distribution during the comminution between two rollers with different diameter [15,16]. The sensor pins were placed in three different levels and had a diameter of 8 mm, the big roller had a diameter of 720 mm and the diameter of the small roller could be changed between 72 and 200 mm.The gap width was fixed. The testing material was a limestone fraction between 0,2 and 3,1 mm and the material flow was adjusted in a way to get solid volume portions between 32 and 54 %. Under these circumstances pressures up to approximately 1 MPa were measured showing a strong pressure decrease towards the edges of the rollers. Significant hints regarding the axial pressure drop are also given by the lower comminution effect and less wear towards the roller edges. The lower comminution effect was observed by Schwarz and von Seebach [17] during tests with cement clinker on an industrial roller mill with D = 1400 mm and L = 660 mm. The wear picture in a roller mill with D = 1700 mm and L = 630 mm was investigated by Galanulis [19].

The objective of Lubjuhn’s work was to investigate and characterize the basics of the material transport and the pressure distribution in high compression roller mills.In terms of experiments that means:

Determination of throughput, observation of particle movement and measurement of the pressure distribution in the gap of a high compression roller mill with variation of

  • type of feed material
  • size of feed material
  • grinding force
  • circumferential speed
  • roller profile


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