Computerized Design and Optimization of Tooth Modifications on Pinions for Face Gear Drives

This paper presents a novel design and optimization method for tooth modifications on pinions for face gear drives that spans a variety of modification types. A tooth profile and an axial modification curve on a spur pinion are designed to consist of a straight line and two sections of parabola, and the topologically modified tooth surface of the pinion is expressed as a superposition of the theoretical tooth surface and the deviation surface determined by fitting cubic B-splines on the tooth surface grid. The design method can accurately control the modification amount, modification lengths and deviation surface. Based on tooth contact analysis and loaded tooth contact analysis of the face gear drives, a multi-objective optimization model is established with a uniform tooth surface load distribution, minimum wave amplitude of loaded transmission error (WALTE) and minimum tooth surface flash temperature (TSFT) as the three objectives. Optimization variables include the eight parameters of the modification curves, and a fast elitist nondominated sorting genetic algorithm (NSGA-II) is applied to solve the model. The simulation results show that the maximum TSFT can be reduced by up to 36.32%, the WALTE can be reduced by up to 59.26%, and the maximum load density can be reduced by up to 9.84%, which proves the proposed method is feasible and satisfactory for face gear drives.