Gray Relational Optimization of the Surface Performance of Splines Formed by Cold Roll-Beating

Surface roughness, residual stress, and work hardening are the key parameters characterizing the mechanical properties of a spline surface after undergoing cold roll-beating. A comprehensive optimization of the mechanical properties of such surfaces has not been previously reported. To improve the performance of the spline surface, gray theory is used to study the relationships between the surface roughness, residual stress, and work hardening in the pitch diameter of spline teeth. This method addresses the surface performance optimization of an involute spline as influenced by the cold roll-beating speed and feed rate as the main parameters during the cold roll-beating process. The results show that the surface roughness and hardening degree of the splines increase with an increasing feed rate but decrease with an increasing cold roll-beating speed; the residual stress of the spline decreases with an increasing feed rate and increases with an increasing cold roll-beating speed. The results also show that the feed rate has a strong influence on the surface performance of splines produced by cold roll-beating. The optimal process parameters in terms of the spline surface performance are a cold roll-beating speed of 1428 r/min and a feed rate of 42 mm/min. The results of the present work emphasize the significance of improving the surface performance of the cold roll-beating spline-forming process and determining the optimal process parameters.