# Time varying meshing stiffness of hypoid gear of automobile drive axle

The motion transmission error of hypoid gear is the main excitation of gear vibration energy. In most hypoid gear equipment, it will cause other parts to vibrate and radiate outward in the form of noise, making people feel irritable. For the hypoid gear system in the main reducer of the automobile drive axle, the previous research mainly focused on simulating the machining process of the hypoid gear, so as to obtain the high-precision outer contour of the hypoid gear, and optimize the geometric parameters of the hypoid gear and the machining parameters of the machine tool through the geometric contact analysis of the hypoid gear, Then the quasi hyperbolic gear static finite element method calculates the tooth root stress, load distribution and motion transmission error of the hypoid gear, but these calculation results can not fully reflect the vibration and noise response of the hypoid gear system in the meshing process of the hypoid gear. Many disgusting problems of the meshing noise of the hypoid gear still exist in the vehicle drive axle.

Therefore, many researchers have established the dynamic response mathematical model of the gear system of the main reducer, studied the influence of the stiffness, damping and inertia mass of each component in the hypoid gear system on the gear dynamic system, and established the correlation between the static analysis of the hypoid gear and the dynamic response of the system through the meshing stiffness. When establishing the dynamics system of hypoid gear, the biggest difference between hypoid gear and spur gear is gear meshing stiffness, which is mainly due to the fact that the direction of meshing force of spur involute gear remains basically unchanged. There are relatively mature calculation methods and empirical formulas, but the geometric shape and meshing process of hypoid gear are complex, In the process of gear meshing, the direction of meshing force and the position of meshing point change with the change of gear rotation angle and loading force. Compared with spur gear, there is less research on meshing stiffness of this kind of gear.

In foreign countries, teik et al. Established the multi degree of freedom model of quasi double-sided gear meshing, and used a constant constant and trigonometric series to approximate the meshing stiffness of quasi hyperbolic gear. Mohammadpour et al. Obtained the time-varying meshing stiffness of hypoid gear through the professional finite element software calyx, simplified the meshing stiffness of hypoid gear into trigonometric series, and finally obtained the empirical formula of meshing stiffness of hypoid gear.

In China, Fang Zongde establishes the dynamic meshing model of hypoid gear according to the static stress state of gear meshing, but this model does not take into account the time-varying characteristics of meshing stiffness in the meshing process of hypoid gear. Tang Jinyuan and others calculated the meshing stiffness of a single tooth based on the basic theory of hypoid gear stiffness, and then obtained the meshing stiffness of multiple teeth when meshing at the same time from the superposition of a single tooth. This model ignores the influence of the direction of gear meshing force changing with the meshing position of hypoid gear in the process of hypoid meshing.

According to the above analysis, the corresponding calculation method of time-varying meshing stiffness of hypoid gear has been proposed abroad, and the meshing stiffness has been approximated by Fourier series, and the meshing stiffness expression of hypoid gear is directly output through software. However, the actual Fourier series can not fully characterize the meshing stiffness characteristics of hypoid gear, and the specific calculation details are not disclosed, At present, there is little research on the meshing stiffness of hypoid gear based on the widely used ABAQUS or ANSYS finite element.

In China, there are few studies that truly reflect the meshing characteristics of hypoid gears, and there are few applications of software calyx. There are still difficulties in establishing accurate hypoid geometric model and finite element model. Therefore, this paper proposes a complete time-varying stiffness calculation method of hypoid gears, and obtains the tooth surface coordinate points of gears by using the current mature numerical calculation software MATLAB, Then it is imported into CATIA to establish the three-dimensional model of hypoid gear, then the finite element model modeling process of hypoid gear is described in detail by using ABAQUS software, and the finite element calculation results are post processed to obtain the time-varying meshing stiffness of hypoid gear. This meshing stiffness of hypoid gear can be applied to the dynamic analysis of hypoid gear system without any other assumptions. Therefore, it can provide a basis for better predicting the dynamic response of hypoid gear transmission system of automobile drive axle.

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