# Wear Model of Silicon Nitride Ceramic Balls in Three-Body Coupling Grinding Mode
## 3 Analysis of the Wear Performance of Precision Spheres
### Status of Research on the Wear Model of Silicon Nitride Ceramic Balls  
The surface energy of ceramic balls is low, and the adhesion of grinding media and abrasives is poor. It affects the machining efficiency, surface roughness, and batch diameter variation of ceramic balls. The dimensional accuracy and surface quality of ceramic balls have a very significant impact on the life of shaft bearings, and the pursuit of dimensional accuracy and surface quality will significantly increase the manufacturing cost, so it is of great significance to study high efficiency and low-cost ceramic ball grinding and polishing processing technology. A gentle process with a high removal rate is needed to minimize surface damage and achieve high polishing speeds. This process is called magnetic float polishing (MFP). It was originally developed by [PERSON] and [PERSON] [39], then greatly improved by [PERSON] and [PERSON] [40], [PERSON] et al. [43; 44; 45], [PERSON] et al. [41; 46], and [PERSON] et al. [47; 48] by adding a float to generate a uniform and high polishing force. [PERSON] and [PERSON] [49; 50; 51] developed a non-magnetic fluid grinding process for ceramic balls. In this process, ceramic balls are supported by springs instead of a magnetic force. They also discussed the grinding ratio, magnetic force cost, and non-magnetism. Chemical mechanical polishing (CMP) was also introduced. [PERSON] et al. [52] and [PERSON] et al. [53] demonstrated the feasibility of polishing silicon nitride via chemical mechanical grinding with iron oxide. [PERSON] et al. [54], [PERSON] et al. [55], [PERSON], and [PERSON] et al. [56] studied CMP with various abrasives and discovered that chromium oxide is the most suitable abrasive for polishing silicon nitride. [PERSON] and [PERSON] [57] analyzed the principle of material removal using a chromium oxide abrasive in finishing silicon nitride ceramic balls.  
[PERSON] et al. investigated the micro-frictional wear characteristics and damage behaviors of silicon nitride ceramic balls and ball bearing steel [58]. [PERSON] et al. concluded  
Figure 10: Schematic of balling.  
that grinding speed and pressure have great influences on the removal method and the surface defects and surface quality of ceramic balls [59].  
[PERSON] et al. [44; 45] also discussed ball blank movement and MRR. The volume removal rate \(\mathrm{d}V/\mathrm{d}t\) of the ball blank, which depends on the sliding speed \(U_{\mathrm{s}}\), was established on the basis of two-body wear, and the contact load \(W\) and the hardness \(Hv\) of the ball blank were decided by the abrasive wear principle (with K, the wear coefficient, being approximately 0.06):  
\[\frac{dV}{dt}=\frac{K}{Hv}WU_{\mathrm{s}}. \tag{1}\]  
The above model is based on the fact that the embedded abrasive is located in the shaft surface. It indicates typical two-body wear, which is only related to process parameters and the hardness of the ball blank. In this study, the wear mode was reinvestigated, and a new three-body wear model based on the three-body coupling grinding mode was established to describe the interaction among the wafer, abrasive, and tool. The model is based on the normal distribution of the abrasive particle size on the ball blank-abrasive-tool interface and the plastic contact on the ball blank-tool interface.