CHENG Ziyao a， LI Pengdab， LIANG Shaominb，c， ZHANG Qi b
a. College of Mechanical Engineering， b. College of Aeronautics and Astronautics， c. Shanxi Key Laboratory ofMaterial Strength and Structural Impact， Taiyuan University of Technology， Taiyuan 030024， China
Abstract
Objective To solve the problems of high energy consumption per unit output and low energy utilization efficiency of ball mills， it is necessary to reduce energy consumption as much as possible while improving the yield of target particles and ensuring the quality of products after material particle breakage， thereby achieving optimal overall grinding performance.
Methods Based the software EDEM， the grinding process of the ball mill was numerically simulated， and the grinding efficiency of the ball mill was analyzed accordingly. The research was conducted in the following steps. First， a geometric model of the ball mill cylinder equipped with trapezoidal liners was established. Second， an cumulative energy loss-based breakage model， capable of counting the cumulative energy loss of bonded particles during multiple collisions， was established， and the validity of the proposed model was verified. Finally， the effects of various key parameters on the grinding efficiency were investigated separately， including the rotational speed of the cylinder， number of cylinder liners， radius and material of the grinding media balls， particle shape of the material， and ball-to-material ratio.
Results and Discussion With a grinding ball diameter of 20 mm， a ball-to-material ratio of 1：1， and steel balls as the grinding media balls， grinding performance was compared at the cylinder rotational speeds of 20， 30， 40， 50， and 60 r/min， and the numbers of liners of 8， 10， 12， and 14， respectively. The results showed that when the number of liners was 12 and the cylinder speed was 40 r/min， the comprehensive grinding efficiency was the best， the average number of collisions was the highest， the mass fraction of over-crushed particles was the smallest， and the mass fraction of target particles was 32.7%. When the cylinder speed was at 40 r/min， the number of liners was 12， and the ball-to-material ratio was 1：1， grinding performance was compared with the grinding ball radii of 20， 30， 40， and 50 mm， and the mass ratio of steel ball to ceramic ball set to 9：1， 7：3， 5：5， 3：7 and 1：9， respectively. The results showed that when the radius of grinding medium ball was 20 mm and the mass ratio of steel ball to ceramic ball was 7：3， the comprehensive grinding efficiency was the best， and the yield of target particles was the highest， with the mass fraction reaching 32.2%. After breakage， strip-shaped materials exhibited the largest mass fraction of target particles and the highest number of collisions， but the over-crushing phenomenon was the most severe. Sheet-like materials ranked second. Blocky materials exhibited the lowest mass fraction of target particles after breakage and were the most difficult to break， requiring secondary grinding or the use of larger-diameter grinding balls. The target particle yield was optimal when the ball-to-material ratio was 3：2.
Conclusion Low-energy and high-frequency collision can ensure a reasonable breakage rate while controlling the over-crushing phenomenon， so that the breakage efficiency and the target particle yield can reach an optimal balance. An excessively small grinding media ball radius can easily lead to low yield， while an excessively large radius can cause problems of over-crushing and uneven grinding. Incorporating ceramic balls into grinding media balls can effectively inhibit the phenomenon of over-crushing， but an excessive proportion of ceramic balls will weaken the overall crushing efficiency. Although an excessively high ball-to-material ratio can increase the number of collisions， it will lead to the aggravation of over-crushing.
Keywords： cumulative energy loss-based breakage model； discrete element method； ball mill； grinding efficiency
Get Citation: CHENG Ziyao， LI Pengda， LIANG Shaomin， et al. Grinding efficiency analysis of ball mills based on cumulative energy loss-based breakage model［J］. China Powder Science and Technology， 2026， 32（3）： 1-13.
Received:2025-06-09 , Revised:2026-01-09 , Online: 2026-01-26.
Funding： The research was supported by National Natural Science Foundation of China (Grant No. 12302512) and the Basic Research Program of Shanxi Province (Grant No. 202203021222118).
DOI：10.13732/j.issn.1008-5548.2026.03.012
CLC No: TB44；Q39 Type Code: A
Serial No:1008-5548（2026）03-0001-13
