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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.

This article proposes the application of a profile-shifted grinding disc to generate an offset, non-orthogonal and profile-shifted face gear. A detailed investigation of the modelling, tooth geometry and contact characteristics of the offset, non-orthogonal and profile-shifted face gear has been conducted. The mathematical models of the profile-shifted shaper cutter, profile-shifted pinion, profile-shifted grinding disc and offset, non-orthogonal and profile-shifted face gear are established. Considering the topological modification, the tooth surface equation of the offset, non-orthogonal and profile-shifted face gear is deduced. Based on the undercutting and pointing of the tooth surface, the limiting tooth width of the offset, non-orthogonal and profile-shifted face gear is determined, and a mathematical model of tooth contact analysis of the offset, non-orthogonal and profile-shifted face gear drive is established with the alignment errors. Using the approach presented in this article, an example of an offset, non-orthogonal and profile-shifted face gear drive and analytical results are presented.