# Material mechanics calculation method of gear vibration characteristics under time varying meshing stiffness excitation

The meshing stiffness of gears refers to the ability of gear teeth to resist elastic deformation under the action of meshing force. Stiffness excitation is a very important system parameter and one of the main causes of vibration and noise of gear system. The time-varying of gear meshing stiffness is a very important reason to aggravate the noise and vibration in the transmission process of gear system. Its mean value and amplitude have a significant impact on the stability and vibration characteristics of gear transmission system. When there are defects on the tooth surface, the increase of meshing stiffness fluctuation will cause greater vibration response of the system. Therefore, it is important to study the dynamic excitation principle and dynamic characteristics of gear meshing stiffness systematically to study the causes of vibration and noise of gear transmission system.

The calculation method of material mechanics is one of the earliest and widely used methods. The gear tooth is simplified as a cantilever beam structure, and then according to the elastic deformation calculation method in material mechanics, the meshing stiffness of the gear is obtained after calculating the deformation under the action of the meshing force. The time-varying meshing stiffness of the gear can be obtained by calculating the meshing stiffness of multiple meshing positions. However, the material mechanics method does not consider the deformation of the tooth matrix and can not be refined when there are many pairs of teeth meshing The normal load of the gear is obtained, so the calculated value will be larger than the actual value.

Compared with the finite element method, the mechanical method of materials is still widely used because of its early development and perfect theory. However, due to the low accuracy of the method, many scholars have improved it and improved the accuracy of the method. Li Yapeng and Chang Lehao improved the Ishikawa formula, which improved the calculation efficiency and accuracy, and calculated and studied the influence of various parameters of gear on the calculated value of time-varying meshing stiffness by using the improved formula.

Wang et al. Calculated the meshing stiffness of helical gear by slice method, and analyzed the influence of helical angle on the time-varying meshing stiffness and system vibration characteristic response of helical gear, and compared with the simulation results of finite element model; Tang et al. Based on the integral potential energy method, proposed a high-efficiency calculation method of gear meshing stiffness; Han et al S á nchez et al. Proposed the meshing stiffness equation of Spur Gear Considering Hertz effect, and gave the approximate equation relationship between meshing stiffness and load distribution coefficient.

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