Profile modification is to remove trace material from the tooth surface along the direction of tooth height, so as to change the shape of tooth profile. The three elements of tooth profile modification are modification amount, modification length and modification curve. Since the correlation between the vibration and noise of gear system and the static transmission error has been widely proved, the basic principle of tooth profile modification is to reduce the static transmission fluctuation. Lin et al defined the specific combination of the first 12 harmonic amplitude values of static transmission error as “equivalent error”. It was found that with the change of tooth profile modification amount, the equivalent error curve has a high similarity with the dynamic load coefficient curve of gear pair, indicating that the equivalent error can be used as an index to check the effect of tooth profile modification in the design stage. Harris et al. Obtained a set of static transmission error curves (known as Harris map) under different loads by using experimental measurement and theoretical calculation respectively. It is confirmed that there is a special “design load” to minimize the fluctuation of static transmission error for the gear pair with specific modification parameters. Because the calculation of static transmission error is the key of tooth profile modification, pears and others studied the calculation method of static transmission error of fixedand planetary gear train by slice method and finite element method respectively.
Tavakoli and Houser considered the comprehensive effects of bending and shear deformation of gear teeth, torsional deformation of gear body and contact deformation of gear teeth at the same time, and established the calculation program of static transmission error of gear pair. Then, with the objective of minimizing the harmonic amplitude combination of static transmission error, the optimal profile modification parameters under specific load were obtained. Tesfahunegn et al. Used ABAQUS as a tool to compare the differences of different tooth profile modification curves from three aspects of static transmission error, tooth root bending stress and tooth surface contact stress. The results show that the optimal tooth profile modification amount is related to the tooth profile modification curve. Lin et al. Simulated and compared the dynamic response characteristics of the straight-line modification and parabolic modification. Sundaresan et al. Studied the problem of tooth profile modification design considering machining error. Ghribi et al. Introduced the concept of robustness in the tooth profile modification design, and studied the optimal tooth profile modification design when the load changes in a certain range. Wang Cheng et al. Analyzed the tooth profile modification of involutetransmission under the action of fluctuating torque. Based on the nonlinear dynamic model of transverse torsional pendulum coupling of gear transmission system, Wang Cheng proposed the design idea of tooth profile modification considering the actual motion state of gear. Chapron et al. Studied the tooth profile modification of internal and external meshing pair of planetary gear considering the flexibility of ring gear. Jiang Jinke et al., Fonseca et al., bonori et al. Used genetic algorithm to find the optimal tooth profile modification parameters.
Terauchi et al. Measured the dynamic load and noise of the modified gear pair. Sun Yuehai et al. Studied the vibration and noise of three kinds of involute spur gears with different profile modification parameters. Bahk and Parker established the analytical expressions of the external and internal meshing excitation of the planetary gear train considering the tooth profile modification. The approximate analytical solution of the dynamic response of the planetary gear train was obtained by the perturbation method, and the effectiveness of the approximate solution was verified by the finite element simulation. In order to minimize the fluctuation amplitude of static transmission error, velex et al. Bruy è re et al. Modified the formula of the optimum tooth profile modification parameters for straight-line modification by considering the change of single tooth meshing stiffness along the tooth profile direction. Velex et al. Discussed the tooth profile modification criterion of multi-stage gear system, and theoretically deduced that if and only if the fluctuation amplitude of local static transmission error of each gear pair in multi-stage gear transmission system is the smallest, the dynamic load of the whole gear system is the smallest. In order to minimize the sum of local static transfer error amplitude of all gear pairs, fackfack et al. Established and solved the optimization model of tooth profile modification of an aviation multi-stage gear transmission system.