Specific throughput of quartz and limestone, smooth rollers / Dissertation U. Lubjuhn, 1992 [25]

To proove the effect of the undercoating some tests with blank rollers were performed and the throughput during the first rotation was measured, see specific throughputs. In this case the increase of throughput compared to quartz is only 26 % for the graining 1,6/6,3 mm and 45 % for the graining 0,25/1,0 mm According to this the undercoating contributes 69 % respectively 42 % to the throughput increase. The smaller effect of the undercoating for the fine fraction could be explained by the fact that - looking at the maximum particle size - a material bed situation exists (s = 3,6 mm) whereas for the coarser graining almost direct contact exists (s = 4,9 mm). In the last-mentioned case only the friction between material and roller is decisive, for the material bed situation also the friction inside the material bed is important.

The width of the graining has an additional but minor effect. With smaller graining width the throughput decreases a little bit because the bulk density is a little bit lower.It can be seen in the next diagram which shows the specific throuput for fractions with a graining width ratio of 1:1,3 and the best-fit lines taken from the previous diagram..

Specific throughput of quartz and limestone, smooth rollers, coarse narrow fractions / Dissertation U. Lubjuhn, 1992 [25]

b) Influence of the profile

In the following six diagram all results of the throughput measurements are shown.The most significant findings are that (1.) the throughput with corrugated rollers is up to 250 % higher than with smooth rollers, (2.) for corrugated rollers the material influence is substantially lower than for smooth rollers and (3.) a significant influence of the graining is visible. The throughput numbers for limestone are generally higher than for quartz but decline a little bit sharper what means the throughput characteristic is less elastic.

Specific throughput quartz 0,25/1,0 mm with different roller profiles / Dissertation Lubjuhn, 1992 [25]

Specific throughput quartz 1,6/6,3 mm with different roller profiles / Dissertation Lubjuhn, 1992 [25]

Specific throughput quartz 0,1/6,3 mm with different roller profiles / Dissertation Lubjuhn, 1992 [25]

Specific throughput limestone 0,25/1,0 mm with different roller profiles / Dissert. Lubjuhn, 1992 [25]

Specific throughput limestone 1,6/6,3 mm with different roller profiles / Dissert. Lubjuhn, 1992 [25]

Specific throughput limestone 0,1/6,3 mm with different roller profiles / Dissert. Lubjuhn, 1992 [25]

The throughput is obviously determined by the geometric conditions which are a result of the choosen roller profile and the filling of the corrugation grooves with material coatings. For open profiles the first sketch demonstrates the situation true to scale for the maximum particle sizes of the different grainings. The next picture shows the condition for the profile B (1-8-3/4) after grinding a limestone grinding 0,1/6,3 mm.In the second sketch the conditions for different roller profiles and materials are shown. The observations show the following tendencies:

• As expected, the softer the material is, the smaller the groove width is and the higher the grinding force is the easier the grooves are filled with material coatings.
• For quartz only the grooves of profile A with 2 mm width are filled with material when the speed is low and only if grainings are used which have a certain amount of fines (0,25/1,0 and 0,1/6,3 mm).
• Limestone creates on all profiles very strong and closed undercoatings, especially if grainings are used which have a certain amount of fines. Only for profile C with a grovve width of b_N = 10 mm the corrugation structure can still be seen at the roller surface.

In the throughput curves above the small profile influence for the smallest graining 0,25/1,0 mm is noticeable. For limestone the friction conditions don’t change much compared to the smooth rollers with material coating as the grooves are more or less completely filled with material. A significant profile effect can therefore not be expected.

Only the little bit bigger roughness of the thicker material coating in the grooves of profile B and C lead to a throughput increase of approximately 20 %. Profile A shows almost no difference compared to smooth rollers. Material coatings of quartz on the rollers are not visible or only of minor account. Nevertheless it has to be expected that the grooves during the grinding process are completely filled with particles and by this a slip-free transported particle layer is created. For the acceleration and introduction of the material therefore also the inner friction is decisive. As all profiles have the same groove width of 1 mm and the maximum particle size is also 1 mm the influence of the profile pitch is small.

For the quartz grainings 1,6/6,3 and 0,1/6,3 mm the throughput curves are in an order according to the profiles A, B and C. This can be explained by the fact that the profiles in the mentioned order create a better and better form closure between particles and roller which leads to a better material introduction and transport with positive influence on the throughput. The following theoretical thoughts should confirm this conclusion.

The groove width b_N which is necessary for a form closure can be calculated for a given corrugation height h_S and a spheric particle as follows, see picture below:

sin a = (x/2 - h_S’) / (x/2)

cos a = (b_N/2) / (x/2)

with h_S’ = depth of impression and x = particle size. With sin² a + cos² a = 1 it follows:

 b_N = 2h_S’ [(x/h_S’)-1]^0,5

The best form closure is achieved if the depth of impression h_S’ is equal to the corrugation height h_S and the profile pitch is adjusted to the maximum particle size x_max.

 b_N = 2h_S [(x_max/h_S)-1]^0,5

A comparison of tests with the quartz fractions 1,6/6,3 and 2,0/8,0 mm and the profiles B (1-8-3/4) and C (1-12-5/6) shows that the ratio of h_S/x_max should not be less than 0,15. Otherwise a significant roll over of particles on the corrugation will occur. This has partly already at lower roller speeds a negative impact on the throughput characteristik, see following diagram.

For  h_S = (0,1...0,2) x_max the following indication value for the groove width can be given:

 b_N ~ (0,6...0,8) x_max                            (12)

The following spreadsheet shows all b_N/x_max-ratios of the used profiles and their effective part of the roller circumference which means the summarized width of all grooves in relation to the roller circumference (= ratio of groove width to corrugation pitch). Closest to the theoretically deducted b_N/x_max-ratio is the profile B. For the more narrow profile A the dpeth of impression for large particles is to small. On the opposite the depth of impression for profile C is similar to profile B but inside the large grooves slip may occur, similar to a smooth roller surface.

Table: b_N/x_max-ratios of the different profiles for x_max = 6,3 mm

The highest throughput for limestone 0,1/6,3 mm is achieved with profile C but it has to be taken into account that in this case the effective width and depth of the corrugation is reduced by material coatings. By this effect the surface geometry of profile C gets obviously closer to the optimum than profile B. For the coarser fraction 1,6/6,3 mm a similar tendency can be seen although the throughput decrease with speed  for profile B is less than for profile A and C. A stringent explanation for this could not be found.

Knowing the particle size distribution of the feed material the optimal profile geometry for the roller surface can be deducted based on the before shown results and interpretations.For the design of a profile three points should be considered:

• The highest throughput is achieved by a slip-free and form-closed corrugation of the roller. The depth of the corrugation and the ratio between corrugation depth and groove width should allow a sufficient form closure on the one hand and should avoid slip inside the groove on the other hand.
• The width of the corrugation bars has no effect on the form closure. This width should be minimized (considering the necessary strength of the design) to maximize the number of grooves on the roller circumference.
• The smaller the height of the corrugation bars is the smaller their width can be. Therefore the profile should not be deeper as it is necessary to assure a sufficient form closure between particle and roller.