The electric drive axle is a big and complex flexible system composed of a planetary gear system, an axle system, bearings and housing, etc. The unavoidable excitation of gear eccentricity error and the time-varying meshing stiffness of gears cause signal modulation, which severely affects the vibration characteristics of the system. Although an equivalent dynamics model of the system established by using spatial beam units can effectively solve the vibration response, it requires a long computation time for large and complex systems.

An efficient dynamics calculation method for electric drive axles is proposed herein. This method considers the excitation of gear eccentricity error. First, the beam element of each component in the driveline was used to reduce the dimensions of the stiffness and mass matrices using the modal synthesis method. Only the essential connection nodes and the main modal order were retained. Since the housing was not suitable for beam unit modeling due to its complex structure, the bearing connection nodes and test measurement nodes were retained on the basis of the housing finite element solid element to obtain the reduced housing stiffness matrix and mass matrix. Second, the magnitude of the eccentricity error for each gear in the planetary gear system was determined using the results of the gear detection accuracy. It was assumed that the magnitude of the eccentricity error of each planetary gear was consistent, but the direction was random; the eccentricity error state of the planetary gear was regarded as consistent when the same planetary gear was in the sun-planet and ring-planet gear pairs simultaneously. Accordingly, the detailed expression of eccentricity error excitation for sun-planet n and ring-planet n gear pair was deduced. Finally, using the reduced stiffness matrix and mass matrix of each component, which considered the eccentric error excitation of each gear pair of the planetary gear system, a combined modal integrated dynamics model of the electric drive axle system was obtained. The vibration response was solved by using the Newmark method.

The analysis results revealed the following: (1) Compared with the finite element model of the beam element with an unreduced system, the proposed model had fewer degrees of freedom—2788×2788 for the former model but only 1515×1515 for the latter model (an effective reduction of 45.7%)—and significantly higher computational efficiency. (2) Pronounced side-frequency phenomena were observed in the frequency-domain response of the system calculated by the proposed method. In addition, amplitude fluctuations were observed in the time-domain response. These phenomena are consistent with the experimental measurement results. These phenomena did not arise when the eccentricity error excitation was not considered.

In summary, this study proposed an efficient dynamic modeling and analysis method for overcoming the problem of time-consuming dynamics solution and signal modulation in determining the dynamic response of large and complex systems, such as electric drive axles. The accuracy of the method was verified, and the necessity of considering the excitation of eccentricity error through numerical calculation and experimental measurement was established.

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.

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.

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.

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.