# Finite element analysis of contact stress of spur gear

The mechanical properties of spur gear system have an important influence on the whole transmission. In recent years, the research on the mechanical characteristics of spur gear system mainly focuses on two aspects: one is the research on the contact stress and strain of tooth surface of spur gear in the meshing process; The second is the research on the dynamics of spur gear pair in the transmission process. It can be seen that the direction of spur gear transmission is still important in the research of spur gear transmission. The contact problem of gear teeth is a highly nonlinear behavior, which studies the local stress and deformation of two or more objects under load. At present, the finite element analysis of spur gear contact stress mainly adopts the finite element contact analysis method to establish the finite element model of spur gear, and use the three-dimensional contact element to solve the contact stress and strain of spur gear under certain load. Hertz first proposed the load distribution formula on the contact surface of two elastic cylinders, which laid the theoretical foundation for the calculation of tooth contact strength.

Videoky first applied the Hertz contact stress theory to calculate the tooth surface stress, and obtained the variation diagram of the maximum contact stress along the meshing line. Conry uses the programming method to study the elastic deformation of gear teeth and the stress distribution in the contact area, while Tsay uses the gap element to calculate the contact deformation and stiffness of gear teeth.

Vijayarangan, s and others studied the contact stress between gear teeth by using the finite element method, and discussed the influence of friction coefficient on the contact stress. J Wang and others have done a lot of analysis and Research on the finite element analysis of spur gear meshing process, discussed the change law of meshing stiffness of spur gear in the transmission process, established the finite element model of spur gear in ANSYS software, carried out finite element analysis on the meshing of gear teeth, and obtained the contact stress and stress of gear teeth in the meshing process. With the wide application of finite element software in China, more and more domestic scholars have also begun to study the contact performance of spur gears in the meshing process. Yang Shenghua and others used the contact finite element method to analyze the loaded deformation of spur gear teeth, and came to the conclusion that the tooth contact finite element analysis can accurately calculate the tooth deformation. Long Hui and others discussed the distribution of contact load and the size and distribution of contact stress of spur gear teeth in a meshing cycle by using finite element software. Ma Xuejie and others used ANSYS / LS-DYNA software to conduct dynamic contact analysis of hypoid gear, and obtained the magnitude and distribution trend of contact stress and strain on the meshing tooth surface when the gear pair and two pairs of teeth participate in meshing. Li Shanshan and others applied ANSYS and ANSYS / LS-DYNA software to study the meshing condition of the driving wheel in a pair of spur gear pair in the process of tooth meshing, obtained the dynamic and static stress nephogram of the gear pair, and reached the conclusion that the bending strength at the tooth root of the driving tooth end is the weakest and it is easy to break when the gear pair is meshed. Sheng Yun et al. Studied the change law of meshing impact force and impact speed of involute spur gear in the transmission process based on the dynamic model of spur gear transmission, and discussed the influence law of load, transmission ratio and modulus on the impact force of spur gear in the meshing process.

Tang Jinyuan and others analyzed and studied the impact problem of spur gear meshing, numerically simulated the meshing impact process of gear teeth by using ANSYS / LS-DYNA software, discussed the relationship between gear tooth width and impact force, impact speed and impact force, and obtained more accurate impact time. The contact stress of spur gear is studied from two aspects of driven and static state, such as Fu Shuangxue, and the calculated results are compared with the results obtained by empirical formula. It is proved that the contact analysis of spur gear by finite element method is feasible; At the same time, it is concluded that the dynamic and static simulation data are reasonable, but the dynamic contact calculation can more accurately simulate the working state of spur gear than the static contact calculation. Based on the static contact analysis of spur gears, Lu Yongjian used the multi-body dynamics simulation method and the complete method to analyze the dynamic contact of a pair of spur gears. Li Fengji used ANSYS / LS-DYNA software to analyze the dynamic contact finite element of double involute gear, obtained the cloud diagram of equivalent stress distribution of spur gear and the variation diagram of total contact force with time, and pointed out that the contact simulation including spur gear axle and support can be considered in the dynamic and static structural simulation of spur gear.

To sum up, many scholars at home and abroad have conducted a series of studies on the contact characteristics of spur gears in the meshing process from many different aspects.

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