Minimization of Non-repeatable Runout (NRRO) in High-Speed Spindle Bearings 2021-01-5023

The production with high quality at the lowest production time can be a key means to success in the competitive environment of manufacturing companies. Therefore, in recent years, the need for extra precise and high-speed machine tools has been impressively increased in manufacturing applications. One of the main sources of errors in the motion of high-speed spindles is the occurrence of non-repetitive runouts (NRRO) in the bearing. The NRRO can be caused by some factors such as the form of balls, the waviness of rings, the number of balls, and the permutation of one or two balls in the ball bearing. In this paper, a Taguchi-based approach is proposed for the optimal design of high-speed spindle bearings by minimizing the NRRO in the machine tools compatible with corresponding standards. First, the optimal design of the high-speed spindle bearings to minimize the NRRO is formulated. To reach this aim, a two-dimensional (2D) model for formulating the NRRO in the ball bearings of the spindle is presented based on the Hertzian contact theory. Subsequently, the objective function and the constraints are formulated in terms of the design parameters for the simulations and the optimization processes. To find the effective parameters with significant impact, above 95% confidence level, the sensitivity analysis is carried out based on the Plackett-Burman design. The optimal robust design of high-speed spindle bearings for minimizing the NRRO is carried out through the Taguchi optimization method. For numerical optimization, the optimal design is formulated in two scenarios based on the Response Surface Method (RSM), and then it is solved by Genetic Algorithm (GA). For verification, the obtained results are compared and discussed.