Design and Analysis for Actively Modified Gear with Zero Amplitude of Loaded Transmission Error

To eliminate stiffness excitation, this paper proposed an approach of design and analysis for actively modified gears with zero amplitude of loaded transmission error (ALTE). Firstly, the maximum bearing deformation of mesh cycle was obtained based on tooth contact analysis and loaded tooth contact analysis (LTCA) for predesign modified gears. Secondly, taking bearing deformations of meshing period being equal to the maximum value as the known condition, a novel equation for LTCA was developed, then compensating tooth gaps from pitch error (additional modifications) were determined by solving the equation in reverse. Thirdly, the compensating gaps characterized by equal values along instantaneous contact line of tooth were constrained according to the meshing positions, and was added to the predesigned modified pinion to produce novel modified gears with zero ALTE. The method integrated geometric analysis and mechanical analysis of tooth, and it can accurately and quickly obtain any modified gears with zero ALTE. The results show that shape and size determined by the compensating gaps surface are related to the locations of tooth, the predesign modification and load. On the one hand, when the differences of predesigned modification is small, the rule of compensation modification curve is basically opposite to the ALTE of predesigned tooth modification, that is, the larger the bearing deformation is, the smaller the compensation gaps is. Then the overall compensation modification is also small due to only compensating the bearing deformation differences actually. On the other hand, when the differences of the predesigned modification is large, the overall compensation modification is also large due to compensating the differences of both bearing deformation and predesigned modification at the meshing position. Besides, the tooth contact pattern is not changed with the compensation modification and ALTE are reduced on wider loads for gears with zero ALTE based on preset topology modification. Appropriate locations and predesign modifications make the additional modification well integrate into the predesigned and modified surface, so as to obtain the machinable modified pinion with zeros ALTE. It provides a theoretical reference for design and analysis of tooth with vibration reduction and high performances.