NSGA-II Based Multi-Objective Optimization on Topologically Modified Pinions for Face Gear Pairs

To reasonably determine the technical parameters in profile modification of face gear pairs, a tooth profile and an axial modification curve both composed of two sections of parabola and a straight line on a spur pinion are created. A topologically modified tooth surface can be represented as a superposition of theoretical tooth surface and the deviation surface obtained by cubic B-splines fitting on the tooth surface grid. Based on the tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) of the face gear pairs, taking the parabolic transmission error curve being symmetrical in geometry, the contact path being limited in the central tooth width, and the minimum wave amplitude of loaded transmission errors as the three optimization objectives, a multi-objective optimization model is established, and the corresponding programs are developed by software Matlab. The fast elitist non-dominated sorting genetic algorithm II(NSGA-II) is selected as the multi-objective optimization algorithm. An optimization example shows that the present method obtains symmetric parabola geometry transmission error and the contact path in the middle of gear tooth width, which greatly reduces the wave amplitude of loaded transmission errors, hence effectively reduces installation error sensitivity, vibration and noise.