# Research on gear stiffness excitation at China and abroad

In the process of calculating the meshing stiffness of gears with energy method, the gear teeth are usually assumed to be a cantilever beam with variable cross-section, so the cantilever theory is applied to the calculation of gear meshing stiffness. Yang and Lin first used the energy method to calculate the meshing stiffness of gears. It was pointed out that the total energy of gears in the meshing process included Hertz contact energy, bending energy and axial compression energy. Through the above three energies, Hertz contact stiffness, bending stiffness and axial compression stiffness could be calculated respectively, but the shear energy of gear mesh was ignored. In the following research, Tian and Zuo took the shear energy as another form of the total energy in the gear meshing process, and the shear stiffness could be calculated by the shear energy.

Four kinds of energy in the process of gear meshing can be obtained: Hertz contact energy, bending energy, axial compression energy and shear energy. The energy method is widely used to calculate the stiffness Four kinds of gear stiffness (Hertz contact stiffness, bending stiffness, axial compression stiffness and shear stiffness) are calculated respectively. The comprehensive time-varying meshing stiffness of the gear is obtained by superposition. The gear meshing stiffness is taken as the internal excitation of the gear system. The dynamic simulation analysis of the gearbox system is carried out by using the dynamic model of the gear system. The dynamic response of the gear system is analyzed Make a diagnosis.

Ma et al. Calculated the meshing stiffness of gear with spalling defect based on energy method. In the calculation, the influence of delayed meshing, nonlinear contact stiffness and tooth spalling defect was considered. The time-varying meshing stiffness analysis model of gear spalling fault was established, and the influence of spalling width, spalling length and spalling position on meshing stiffness was studied. The results show that the meshing stiffness of gears decreases sharply with the increase of spalling width, especially in the process of single tooth meshing; the spalling length of tooth surface only affects the starting and ending positions of gear meshing stiffness reduction; the spalling position of tooth surface will affect the range of reduction of meshing stiffness; when the spalling position is close to the top of the tooth, the reduction range of meshing stiffness will be reduced.