# Wear Model of Silicon Nitride Ceramic Balls in Three-Body Coupling Grinding Mode
## 2 Comprehensive Performance Analysis of Precision Ball Grinding Methods at Home and Abroad
### Three-Body Coupling Grinding Mode  
Although the rotation angle actively controlled grinding method can adjust the rotation angle of the ball to achieve a uniform machining trajectory by controlling the rotation speed changes of three independent rotating grinding disks, its structure is complicated. To reduce the complexity of the mechanism and the power source of the grinding equipment, the team of the Ultra-precision Machining Research Center of Zhejiang University of Technology improved the grinding mode on the basis of the active control of the rotation angle; combined it with the process control of the rotation speed change of the grinding disk; and proposed a three-body coupling grinding mode, the principle of which is shown in Figure 7[23]. In this grinding mode, the upper grinding disk does not need to rotate. The relative orientation of the ball's rotation and revolution axes can be adjusted by controlling the rotation speed changes of the inner and outer disks of the lower grinding disk, such that the grinding trajectory evenly covers the ball surface, thus achieving efficient and high-precision ball grinding. Given that the number of driving and transmission devices is reduced from three to two, the structure of the equipment can be greatly simplified, and the precision requirements of processing and assembly are relatively reduced. Therefore, the rotation angle can be continuously changed within the range of [\(-90^{\circ}\), \(90^{\circ}\)]. In addition, the grinding trajectory can cover the whole ball to significantly improve the processing accuracy in the mass production of precision balls. This effect is highly suitable for the small-batch production of precision balls; meets the increasing demand for precision balls; and further compensates for the defects of the traditional processing method, such as low efficiency and high costs[37]. [PERSON] et al. and [PERSON] et al. [20; 32] analyzed the rotation angle actually controlled grinding mode and discovered that the driving of the upper grinding disk in the grinding device was redundant and that the rotation of the upper grinding disk only increased by a relative movement velocity. A new grinding method--the three-body coupling grinding device--was proposed to reduce complexity. Figure 1 provides a schematic of the grinding structure of the three-body coupling grinding method. The upper grinding disk is under motion redundancy. The grinding movement with variable relative orientation can be realized just by controlling the rotation speed change of the lower inner and outer grinding disks, such that the grinding trajectory is evenly distributed on the ball surface. The high-efficiency and high-precision grinding of the ball blanks can thus be realized. Given that the number of driving and transmission devices is reduced from three to two, the structure of the equipment can be greatly simplified, and the precision requirements of processing and assembly are relatively reduced. This effect is highly suitable for the small-batch production of high-precision ceramic balls. [PERSON] et al. [20] manufactured silicon nitride ceramic balls with high precision (roundness: <0.05 \(\upmu\)m, surface roughness: Ra < 5 nm)by combining key technology and newly developed processing equipment. In 1984, [PERSON] and [PERSON] [33] proposed using the MFP for facilitating the efficient grinding of precision spheres. This method has been improved by many scholars [40; 41] and has greatly enhanced the machining efficiency of precision spheres. Its principle is illustrated in Figure 8. This method uses a magnetic fluid abrasive. When a magnetic field is imposed, the magnetic fluid pushes the floating disk upward and loads the ball. The high-efficiency machining of precision balls can be realized as a result of the very high shaft  
Figure 7: Schematic of the three-body coupling grinding mode. rotation speed (above 10,000 rpm). However, this method has limited applications due to the high cost and short service life of magnetic fluids. [PERSON] et al.