# Analysis of the Influencing Factors of Grinding Uniformity under Three-Body Coupling Grinding Mode
## 1 Introduction  
Precision balls area core basic element in roundness-measuring instruments, peg-tops, precision bearings, ball crews, spherical guides, and precision-measuring instruments. It has huge requirements and has been extensively applied to various fields, such as precision machinery, petrochemical engineering, military science, national defense, aerospace, etc. [1; 2; 3; 4; 5; 6; 7]. The precision and batch consistency of spheres considerably influence the performance of precision functional components [8; 9; 10; 11]. At present, industries, such as precision instruments and precision machine tools are proposing increasing demands for precision balls. Thus, the development of a whole set of high-efficiency and high-precision spherical technology and equipment for batch processing is urgent. To increase further the ultra-precision machining technological level, developed countries developing new methods and techniques to achieve new breakthroughs. The batch processing of precision balls mainly inherits the traditional steel ball processing technique (V-shaped groove processing technique) [12]. It leads to poor processing precision and poor batch consistency [13]. High-precision balls are usually picked outof batch-processing balls, which has been a challenge in the field of high-precision ball processing in China and foreign countries [10; 11]. Moreover, the degree of production automation is low, and production technology is influenced by human factors [14; 15; 16; 17; 18; 19; 20]. The project team innovatively proposed a three-body coupling grinding technique that can realize ultra-precision ball grinding. It guarantees high precision, lot diameter variation, and batch consistency during the processing of precision balls. The working principle of the three-body coupling grinding technique is shown in Figure 1[21]. However, many factors influence grinding precision. Given factors, such as changes in processing conditions or structural errors of grinding equipment, the ball does not move in the theoretically predicted way, thus influencing the processing precision. To address these problems, influencing factors of grinding uniformity, which can further affect balling precision in practical processing, were chosen and analyzed theoretically one by one. The influencing laws of these factors on grinding uniformity were deduced, thus further improving dynamic mechanical precision control ability during processing. This deduction assures that precision balls can achieve high precision and batch consistency stably and effectively under the three-body coupling grinding mode. 2 Comprehensive Performance Analysis of Precision Ball Grinding Modes in China and Foreign Countries  
To reduce the processing cost and improve the processing precision, efficiency, and consistency of balls, many scholars have proposed several new processing methods in accordance with the characteristics of ball processing, such as the magnetic fluid grinding method, grinding mode with positive control over rotating angular velocity, three-body coupling grinding mode, and so on [21; 22; 23; 24; 25; 26; 27]. To realize the high-efficiency grinding of precision balls, [PERSON] and [PERSON] [28] proposed the magnetic fluid processing (MFP) of precision balls. After improvement by many scholars [29; 30], the processing efficiency of precision balls has been improved remarkably. The principle is shown in Figure 2. MFP uses magnetic fluid as the abraser. Given that a high rotating speed (>10,000 rpm) of the main shaft was applied, it can realize the high-efficiency processing of precision balls. However, its applications are restricted by the high cost and short service life of the magnetic fluid. Figure 1: Principle of dual-disc rotatory grinding. [PERSON] et al. [31; 32; 33] developed the nonmagnetic fluid grinding mode of ceramic balls (Figure 3).