Study of Rotation Speed Curve Optimization under the Three-Body Coupling Grinding Mode

The three-body coupling grinding mode of a ball ensures the batch diameter variation and batch consistency of precision ball machining based on the principle of ball forming, resulting in a structure that is simply and feasibly controllable. The change in the rotation angle can be jointly determined using the fixed load of the upper grinding disc and the rotation speed coordination of the inner and outer discs of the lower grinding disc. Related to this, the rotation speed is an important index to guarantee grinding uniformity. To ensure the quality of three-body coupling grinding, this study aims to establish the best mathematical control model of the rotation speed curve of the inner and outer discs in the lower grinding disc. Specifically, it includes two aspects. First, the optimization of the rotation speed curve was mainly studied, and the machining process was simulated with three speed curve combinations: 1, 2, and 3. By analyzing the evaluation index of ball grinding uniformity, the results revealed that the third speed curve combination had the best grinding uniformity, and the three speed curve combinations were optimized on the basis of the traditional triangular wave speed curve. Furthermore, the obtained double trapezoidal speed curve combination not only achieved the traditionally verified stability performance but also overcame the shortcomings of the other speed curves. The mathematical model established in this way was equipped with a grinding control system, which improved the fine control ability of the rotation angle state of the ball blank under the three-body coupling grinding mode. It also obtained the best grinding uniformity and sphericity and laid a theoretical foundation for achieving a grinding effect that was close to the ideal circumstance during mass production. Second, via theoretical comparison and analysis, it was determined that the ball shape and sphericity deviation (SPD) were more accurate than the standard deviation (STD) of the two-dimensional trajectory point distribution. The SPD evaluation method was also investigated via the optimization analysis of the rotation speed curve by means of the ADAMAS simulation. The obtained results coincided with the STD evaluation trend, thus laying a preliminary foundation for subsequent applications.