Abstract：[Objective] The face-hobbing hypoid gear is a crucial component of drive axles owing to its continuous indexing processing capabilities. However, in practical engineering applications, gear pairs rarely operate under ideal conditions. Instead, they frequently experience heavy-load and high-speed conditions. These conditions result in substantial system deformation and a complex meshing state of the tooth surface. Under heavy-load conditions, considerable skewing of the load on the tooth surface can occur, greatly affecting the performance of the gear pair and drive axles. Currently, the system deformation factor under actual working conditions is not sufficiently considered, making it challenging to address the aforementioned issue. Consequently, this paper proposes the analysis of the tooth surface load distribution by employing a semi-analytic loaded tooth contact analysis method to accurately predict the tooth surface load distribution. Based on a load distribution analysis, a highly accurate calculation method for gear meshing efficiency is proposed.[Methods] This paper proposes a calculation method for gear meshing efficiency under mixed-lubrication conditions for hypoid gears in drive axles operating under complex working conditions. First, a multi-support shaft system modeling method is employed to analyze the drive axles system. This method can calculate the forces acting on various components, such as gears and bearings, as well as the gear misalignment caused by system deformation under various load conditions. Second, by simulating the spatial motion process of the actual gear machining machine, the coordinates of the tool cutting point are transformed to the coordinate system of the gear blank via coordinate transformation. This process results in the correspondence of the tooth profile with the actual machining parameters. The time-varying friction coefficient distribution of the tooth surface under different working conditions is derived by combining the point contact mixed-lubrication friction coefficient model of the tooth surface with its relative motion relationship. Then, taking into account the tooth surface deformation equilibrium equation, tooth surface torque equilibrium equation, and tooth surface contact pressure equilibrium equation, a gear frictional loaded tooth contact analysis method is established. This method accurately calculates the tooth surface load distribution and mesh efficiency of gears under different working conditions through an iterative solution. Finally, the calculation results of the tooth surface load distribution under various working conditions are compared with the experimental results obtained from a loading experiment conducted on the entire drive axles. The meshing efficiency of the gear pair under various working conditions is determined by conducting a system no-load efficiency experiment and loading efficiency experiment and comparing the results with those obtained by calculations.[Results] In the gear no-load experiment, the contact patterns of the gear tooth surface were compared under forward and reverse working conditions. The experimental results were found to be in good agreement with theoretical calculations, verifying the accuracy of the tooth surface calculation method and no-load tooth contact analysis. Subsequently, a loading experiment was conducted on the drive axles system, indicating that the system deformation had a considerable impact on the load distribution of the hypoid gear tooth surface. For instance, in the experiment drive axles, under heavy-load conditions, system deformation caused the tooth surface load on the driving side of the gear pair to shift toward the outside, while the tooth surface loaded on the driven side shifts toward the inside. The meshing efficiency experiment results revealed that system deformation considerably impacted the gear meshing efficiency under heavy-load and high-speed working conditions. In addition, the vehicle speed had a considerable impact on the meshing efficiency, with an increase in speed from 10 to 80 km/h, resulting in a 1% improvement in meshing efficiency.[Conclusions] By comprehensively considering gear meshing misalignment caused by system deformation and the mixed-lubrication state of the tooth surface, the tooth surface load distribution and meshing efficiency can be accurately calculated under loaded conditions. Therefore, the proposed process enhances the accuracy of calculating the drive axles system efficiency while providing a solid foundation for gear optimization research.
王钦, 贺迪, 桂良进, 胡智宇, 彭金, 范子杰. 考虑系统变形的驱动桥准双曲面齿轮啮合效率计算方法[J]. 清华大学学报（自然科学版）, 2024, 64(1): 33-43.
WANG Qin, HE Di, GUI Liangjin, HU Zhiyu, PENG Jin, FAN Zijie. Calculation method of hypoid gear meshing efficiency of drive axles with considering system deformation. Journal of Tsinghua University(Science and Technology), 2024, 64(1): 33-43.
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2024, Vol. 64 
