# Analysis of the Influencing Factors of Grinding Uniformity under Three-Body Coupling Grinding Mode
## 1 Introduction
They replaced the magnetic fluid with amitxture of cheap water and glycerin, replaced the grinding discs with a resin binder diamond wheel, and produced adaptive supporting forces with a spiral spring [21; 22; 23; 24; 25; 26; 27]. In the traditional V-shaped groove grinding mode, the rotating angular velocity (\(\theta\)) is only determined by the diameters of the ball and the groove on the lower grinding disc, \(\theta\) is hardly changed during processing, and it is small [29; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44]. The ball can only make the grinding motion with \"constant relative direction\" (the included angle between the rotating axis and the revolving axis of the ball does not change). The grinding tracks formed by the contact points between the ball and the grinding disc on the spherical surface are groups of rings around the rotating axis of the ball [21]. These rings are disadvantageous for the spherical surface to achieve uniform grinding quickly and restrict the improvement of the processing precision and efficiency of the ball. [PERSON] et al. from Kanazawa University proposed a grinding mode with positive control over rotating angular velocity (known as coaxial three-disc grinding mode, Figure 4) [38; 39; 40; 41; 42; 43; 44]. The lower grinding disc in the V-shaped groove grinding mode is cut at the V-shaped groove; thus, the whole system is composed of three pieces of grinding discs that can rotate independently. The rotating angular velocity of the ball-billet is adjusted by controlling the rotating speed changes of these three grinding discs. Grinding tracks are spatial spherical curves around the rotating axis of the ball-billet, and they can cover the whole ball-billet surface. Such grinding device has complicated systems, thus restricting its use in practical production. Figure 3: Structural schematic of nonmagnetic fluid. Figure 2: Structural schematic of magnetic fluid:1—grinding groove; 2—ceramic ball-billet; 3—driving axis; 4—mixture of magnetic fluid and abrasive materials; 5—floating plate; 6—magnet. To reduce the structural complexity and decrease the power source of the grinding equipment, the rotating angular velocity can change continuously within \([-90^{\circ},90^{\circ}]\). Grinding tracks can cover the whole spherical surface. [PERSON] and [PERSON] et al. [21; 40] analyzed the grinding mode with positive control over the rotating angular velocity and found that the driving of the upper grinding disc in the grinding device was redundant and it meets the increasing needs of precision balls better. As a result, it offsets the low efficiency and high cost of traditional processing techniques [32]. The principle of the three-body coupling grinding mode is shown in Figure 1[24]. The three-body coupling grinding mode is appropriate for the small-lot production of high-precision balls [32]; it can realize grinding movement with \"variable relative directions\" by only controlling rotating speed changes of the inner and outer discs of the lower grinding disc. It makes grinding tracks cover the spherical surface uniformly, thus achieving high-efficiency and high-precision grinding of the ball-billet. Given that the driving and gearing devices decrease from three to two, the equipment structure is simplified considerably. The requirements for processing and assembly precision are decreased accordingly. Through the above analysis, 3B-CGM has obvious comprehensive advantages in machining accuracy, machining efficiency, and mechanical structure.