Correlation of grinding rate of gibbsite with impact energy in tumbling mill with mono-size balls

In our previous paper, we proposed a corresponding Work Index Wi. c which is proportional to the Work Index Wi. Wi. c can be determined from the zero-order increasing rate constant in a ball mill grinding.In this paper, we propose an application of Wi. c to compare fine grindability in dry and wet grinding. The grinding tests were carried out by using a mill made of alumina with a diameter 144mm and grinding balls of alumina with a diameter 20mm. The feed sample was silica glass with density of 2, 150kg·m-3 and vickers hardness of 465kgf·mm-2. In the case of wet grinding, the volume of water added was twice of the feed sample.The relationship between Wi. c and the particle size was studied in dry and wet grinding. As a result, Wi. c in wet grinding was smaller than Wi. c in dry grinding. It was suggested that Wi. c could be useful for evaluating a fine grindability in dry and wet grinding.

https://www.jstage.jst.go.jp/article/sptj1978/35/11/35_11_792/_pdf

Comparison of Fine Grindability in Dry and Wet Grinding based on Work Index

Work Index is an important factor in designing grinding processes. In previous papers, the authors proposed a Corresponding Work Index which is proportional to the Work Index. The Corresponding Work Index could be estimated by examination of the zero-order grinding rate constant using various grinding mills.In this study, grinding experiments were carried out with five types of solid materials using a ball mill, a vibration mill and a planetary mill. The relationships between the Corresponding Work Index and particle size were evaluated. For these mills, the Corresponding Work Indices of silica glass, quartz and feldspar increased up to a certain particle size and became approximately constant. However, the Indices of limestone and gypsum had a minimum when the evaluated size was nearly the same as that of grain size. The Corresponding Work Index can be useful for evaluating the fine grindability of solid materials in these mills.

Evaluation of Fine Grindability of Solid Materials by Ball, Vibration and Planetary Mills.

Comminution plays a major role in many processes where raw materials are converted into intermediate or final products. The efficiency of comminution is very low, and research and development to save the comminution energy have been performed. Then, it is necessary to estimate correctly the comminution energy. Work Index proposed by Bond is an important factor in designing comminution processes and has been widely used. Work Index is measured by a ball mill grinding and the measurement procedure is closely defined in JIS (Japanese Industrial Standard) but the optimum grinding condition is varied with samples. Then, it would be possible to overestimate the comminution energy to get products. In this paper, the above was studied by grinding conditions for the measurement of a Corresponding Work Index which was proportional to the Work Index. The feed size, the mass of feed and the mass of ball were investigated as the grinding conditions when the rotational speed of mill and the ball diameter were constant. The samples used were silica glass, quartz, feldspar, limestone and gypsum. The result indicated that the comminution energy based on the Bond's theory might be larger than the energy required to get fine particles.

粉砕仕事指数(Work Index)の測定条件に対する一考察

In the previous report4), we suggested that the grindability or the rate of grinding of particles was closely connected with the size distribution pattern of the ground material, which ranged from the bulk crushing to the surface grinding. We assumed, also, that the size distribution of the ground material was affected by the strength of grinding force.This paper is intended to verify the above-mentioned assumption by means of the ball-mill grinding, which is the most general operation pattern comprizing factors we can easily vary.Silica balls with four different diameters (and naturally of different weights) and sintercorund balls with one diameter were respectively employed at various rotational speeds of the mill. To investigate the results of the experiment, we assumed the characteristic number of β, which indicates a characteristic of the size distribution relative to the ratio of cumulative weight percent of the coarse part (Y(r)to that of the fine part (Y(f)). (Cf. Fig. 4).When the ball weight or the speed of rotation increased, (or the grinding force increased), β also increased as shown in Eq. 4-2 and Figs. 8 and 9. The values of kβ and kx were closely related to the particle diameters, viz., when the fed particles were small, the effect of grinding force was small.From this we may conclude that in fine grinding, the weight of a ball does not count much.It was observed that in general the grinding rate of particle (X) was determined by the grindability of particle (Γ) and the mechanical efficiency of grinding (ηm), which is the probability of ball impact or that of other grinding forces. Therefore, in fine grinding, Γ becomes negligible, and ηm essential.Upon this, we assumed that ηm (or impact number per one rotation of the mill) was constant irrespective of the speed of rotation of the mill, and obtained by experiment the relative values of ηm as shown in Fig. 10.Furthermore, according to H.E. Rose's suggestion9), from the supposed contact area of a couple of balls and probability of impact of balls in the mill., we derived relative efficiency of ball impact, as shown in Eq. 5-13, and ascertained the experimental results and Eq. 5-13, as shown in Fig. 17.

https://www.jstage.jst.go.jp/article/kakoronbunshu1953/23/3/23_3_138/_pdf

Genji Jinbo

Papers

On the Mechanism of Ball Mill Grinding