# Wear Model of Silicon Nitride Ceramic Balls in Three-Body Coupling Grinding Mode
###### Abstract  
Silicon nitride ceramic balls are the key basic components of bearings in major equipment. Their key performance indices are accuracy and batch consistency. A grinding method with the most appropriate comprehensive performance is the basis and guarantee for optimizing these performance indices. In this study, an accurate wear model was established to predict the material removal rates (MRRs) of grinding methods and improve the dynamic grinding control ability of machinery during grinding, thus enabling the mass production of high-grade silicon nitride ceramic balls. A comprehensive analysis of various grinding and polishing methods revealed that the factors affecting sphericity were mainly manifested by the increase in ball sliding and the improvement in MRRs. More over, the three-body coupling grinding mode was considered as the grinding mode that was most applicable to silicon nitride ceramic balls. The upper disk served as an external nonlinear load, and the combination of the rotating speeds of the inner and outer disks of the lower grinding disk could actively control the ball's angle of rotation. This three-body wear mode can fully envelop the grinding trajectory and ensure uniform grinding. The traditional two-body wear model was unsuitable for three-body coupling grinding. A wear model based on three-body wear was established to predict MRRs and understand the principle of material removal in the grinding of precision spheres. Theoretical analysis and experimental verification revealed that the MRRs of silicon nitride ceramic balls during wear are not only related to the process parameters of external load and speed but also to the physical properties and geometric parameters of balls, abrasives, and processing machinery. The wear model results of silicon nitride ceramic balls in the three-body coupling grinding mode can be obtained stably on the basis of the established wear model by removing adverse effects and adopting optimized processing parameters, thus verifying the correctness of the theoretical and simulation analyses. type: _applied_  
_sciences_  
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Footnote 1: College of Electrical and Information Engineering, Quzhou University, Quzhou 324000, China  
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Footnote 2: Key Laboratory of E&M, Zhejiang University of Technology, Hangzhou 310014, China  
as precision instruments and precision machine tools, and complete sets of batch processing technology and equipment for high-efficiency precision spheres are urgently needed. All developed countries are working hard to study new methods and processes to achieve new breakthroughs for further elevating ultra-precision machining technology. The 14 th Five-Year Plan for China's machinery industry also proposes considerably improving the design and technical level of major technical equipment and markedly enhancing the international competitiveness of products. In particular, the bottleneck of key parts that restrict the development of high-end equipment should be broken. The development of precision balls, which are the key parts of supporting components in high-end equipment, is particularly important. In recent years, the market demand for precision balls has increased at a rate of 15% and reached approximately80 billion in 2021. The batch processing of precision balls mainly follows the traditional steel ball processing method (V-groove processing method), during which the spin angle of the balls is constant [12]. The processing orientation is changed through the random movement of the circulation slot and is followed by repeated circular processing [7], which leads to low processing accuracy and poor batch consistency. Usually, precision balls are picked individually from batch-processed balls; this situation has been a difficulty perplexing the domestic and foreign fields of precision balling processing [10; 11]. Moreover, production has a low automation degree and its process is affected by human factors [13; 14; 15; 16; 17; 18; 19].