Vibration analysis method for hub motor drive reducer based on bending-torsional shaft vertical coupling dynamics model

Abstract

This invention relates to a vibration analysis method for a hub electric drive reducer based on a bending-torsional-axis-vertical coupling dynamic model. The method includes: dividing the gear meshing stiffness into end-face meshing stiffness and axial meshing stiffness, constructing a time-varying meshing stiffness model, characterizing the time-varying meshing stiffness using Fourier series, and establishing a bending-torsional-axis coupling dynamic model for the reducer; introducing road surface excitation to determine the vertical coupling relationship between the tire / rim and the reducer, and constructing a refined vertical dynamic model; combining the bending-torsional-axis coupling dynamic model and the vertical dynamic model, considering the coupling effect between road surface excitation and the reducer meshing excitation in the hub electric drive system, constructing a bending-torsional-axis-vertical coupling dynamic model, and solving it using numerical integration to obtain the vibration characteristic analysis results of the hub electric drive reducer system under real-world operating conditions. Compared with existing technologies, this invention can accurately describe the dynamic behavior of the hub electric drive reducer system and accurately analyze the vibration characteristics of the reducer system.

Description

Technical Field

[0001] This invention relates to the field of hub electric drive technology, and in particular to a vibration analysis method for hub electric drive reducers based on a bending-torsional shaft-vertical coupling dynamic model. Background Technology

[0002] Hub electric drive systems are mainly divided into two types: hub electric drive direct drive systems and hub electric drive reduction systems. Among them, hub electric drive reduction systems use high-power density high-speed motors, and the reduction devices have high torque density, which can make up for the shortcomings of existing hub direct drive electric wheels. Due to its high structural integration, diversified excitation, and complex working environment, it has become a configuration that has attracted much attention and development in the industry. However, due to its complex structural characteristics, it is prone to a series of vehicle dynamics problems.

[0003] In existing dynamic modeling of hub electric drive reducers, common methods include finite element models, lumped mass models, and rigid-flexible coupling models. Finite element models can simulate precise contact between gears, but they are time-consuming and involve more complex model optimization designs. Rigid-flexible coupling models combine finite element models and lumped mass models, ensuring improved model accuracy within a limited timeframe. However, compared to the former two, lumped mass models simplify model parameters and offer faster computation. Existing research often uses lumped mass models for dynamic modeling of gear transmission systems, simplifying each mechanism of the planetary gear into a lumped mass rigid body, with different components connected by spring damping. Depending on the selected degrees of freedom, these models are often divided into torsional models and bending-torsional-axis coupling models. Torsional dynamic models are the basic form in planetary gear dynamic modeling, typically considering only the axial torsional degrees of freedom of each component. They are used to study the influence of each component on the system's vibration characteristics and are suitable for systems with high support stiffness. Bending-torsional-axis coupling models can simultaneously consider the lateral, longitudinal, and vertical translational degrees of freedom of the planetary gears, as well as their axial degrees of freedom, and are commonly used to analyze the inherent characteristics and dynamic response of gears.

[0004] Furthermore, in the complex vibration environment of hub-driven electric drive reducers, road surface excitation and sprung mass are key external excitation sources. Road surface excitation, as a major and complex external input in vehicle dynamics, causes random excitation that is transmitted to the reducer through the tires, rims, and planetary carriers. This results in the superposition and coupling of external road surface excitation and internal meshing excitation within the reducer, leading to complex dynamic responses in gear meshing forces, bearing loads, and the motion states of the sun gear and planetary gears. Sprung mass also generates dynamic responses under road surface excitation, directly affecting the meshing state of the reducer gears and the dynamic load on the bearings. These characteristics are key factors influencing vehicle comfort, reliability, lifespan, and NVH performance during operation. Therefore, establishing a vehicle dynamics system that reflects the time-varying meshing characteristics of gears and includes road surface excitation and sprung mass is of significant theoretical and engineering value for accurately predicting the vibration and noise behavior of the system under real-world operating conditions, evaluating the reliability of transmission components, and achieving positive optimization of NVH performance.

[0005] Existing research on hub electric drive reducer systems mostly focuses on simplified models such as planar meshing stiffness, single-dimensional load input, or indirect coupling inference, neglecting the coupling effect between the internal excitation of the gear system and the dynamic feedback of the sprung mass. Therefore, it is difficult to characterize the dynamic characteristics of multi-source coupled vibration induced by road surface excitation under real working conditions, which is not conducive to subsequent vibration and noise optimization work. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art by providing a vibration analysis method for hub electric drive reducers based on a bending-torsional-axis-vertical coupling dynamic model, which can accurately describe the dynamic behavior of the hub electric drive reducer system and accurately analyze the vibration characteristics of the reducer system based on this.

[0007] The objective of this invention can be achieved through the following technical solution: a vibration analysis method for a hub electric drive reducer based on a bending-torsional-axis-vertical coupling dynamic model, comprising the following steps: Based on the slicing method, the meshing stiffness of the gear slice is divided into end face meshing stiffness and axial meshing stiffness. A time-varying meshing stiffness model is constructed, and Fourier series is used to characterize the time-varying meshing stiffness. A dynamic model of bending and torsion shaft coupling of the reducer is established. By introducing road surface excitation, the vertical coupling relationship between the tire rim and the reducer is determined, thereby constructing a refined vertical dynamic model of the interaction between the tire rim, the shell, the sprung mass, and the components of the planetary gear train. Combining the bending-torsional-axis coupled dynamic model and the vertical dynamic model, and considering the coupling effect between the road surface excitation and the meshing excitation of the wheel hub electric drive system reducer, a bending-torsional-axis vertical coupled dynamic model of the wheel hub electric drive reducer is constructed. The numerical integration method is used to solve the vertical coupling dynamic model of the bending and torsion shaft, and the key evaluation indicators of vertical dynamic response, bearing dynamic load, dynamic transmission error and dynamic meshing force are obtained, thus obtaining the vibration characteristic analysis results of the hub electric drive reducer system under real working conditions.

[0008] Furthermore, the process of constructing the time-varying meshing stiffness model includes: Based on the slicing method, the helical gear is sliced ​​along the tooth width direction. The meshing stiffness of the gear slice is divided into end face meshing stiffness and axial meshing stiffness. The end face meshing stiffness includes Hertzian contact stiffness, matrix deformation stiffness, and combined bending, shear, and compression stiffness. The axial meshing stiffness includes axial bending stiffness, axial torsional stiffness, and axial matrix deformation stiffness. Based on the end face overlap and axial overlap, the multi-tooth meshing interval is determined, and a time-varying meshing stiffness model of the planetary gear train is constructed.

[0009] For end-face meshing stiffness, Hertzian contact stiffness is the elastic deformation stiffness of the tooth surface under meshing force in gear transmission. Since the tooth contact surface is a high-pair contact, a linear method is used to calculate the contact stiffness based on Hertzian theory. End-face matrix deformation stiffness mainly focuses on the deformation stiffness of the external gear matrix. The combined bending, shear, and compressive stiffness considers the internal and external meshing of the planetary gear train. By analyzing the tooth profiles of the internal and external gears and the forces on the gear end faces, the bending, shear, and radial compressive stiffness are obtained with the load angle during meshing as the independent variable.

[0010] For axial meshing stiffness, to intuitively reflect the gear rotation angle during the calculation of axial bending and torsional stiffness, the same treatment method as for end face stiffness is adopted, and the integral variable in the integral formula of axial bending and torsional stiffness is expressed as angular displacement. Axial base deformation stiffness mainly focuses on the deformation stiffness of the external gear base.

[0011] Furthermore, the process of establishing the coupled dynamic model of the reducer's bending and torsional shafts includes: The translational and torsional degrees of freedom of the planetary gear train of the reducer are defined, including the translational and torsional degrees of freedom of the sun gear, ring gear, planet carrier, and planet gears. The time-varying meshing stiffness in the time-varying meshing stiffness model is characterized by Fourier series. The bending and torsional shaft coupling dynamic model of the reducer is established based on the internal and external meshing.

[0012] Furthermore, the time-varying meshing stiffness characterized by Fourier series is specifically as follows: in, Let N be the components of the stiffness of the external and internal meshing meshes, respectively, with a frequency of 0. Taking the first N orders of the Fourier series, then... External meshing and internal meshing stiffness respectively The amplitude of the first-order component, The stiffness of external meshing and internal meshing are respectively the first. Phase of the first-order component, f m The meshing frequency, t For time, γ sn For external meshing phase coefficient, γ rn For internal meshing phase coefficient, T m For the meshing cycle, γ rs It is the relative phase difference coefficient between internal and external meshing.

[0013] Furthermore, the process of constructing the refined vertical dynamic model includes: By introducing road surface excitation as the external excitation for vertical dynamics, a time-domain model of road surface unevenness is established based on the white noise method. At the same time, considering the interaction force between gears, the meshing stiffness of the gears is equivalent to the vertical stiffness. By analyzing the vertical coupling relationship between the tire rim and the reducer under the equivalent stiffness of the tire, the rim mass, and the vertical component of the reducer meshing force, a refined vertical dynamic model of the hub electric drive system is established, which includes the interaction of the tire rim, the shell, the sprung mass, and the components of the planetary gear system.

[0014] In this study, white noise was used to simulate road surface roughness. National standard GB7031-86 and international standard ISO / DIS8608, through processing a large amount of randomly measured road data, provided a fitting expression for the road surface based on statistical parameters, and derived a time-domain model of road surface roughness based on this expression.

[0015] Furthermore, the vertical coupling relationship between the tire rim and the reducer is specifically as follows: Considering the interaction force between gears, the inherent connection between the motor stator and the housing, and the inherent connection between the motor rotor and the sun gear shaft, and ignoring the influence of the braking system and speed, since the interaction force between gears is along the meshing direction of helical gears, it cannot be directly used as the vertical stiffness. It is necessary to convert the internal and external meshing stiffness and damping into vertical stiffness and calculate them. At the same time, only the vertical displacement of each component of the planetary gear train is considered, and the static meshing force between gears is projected into the vertical direction.

[0016] Furthermore, the process of constructing the bending-torsional-vertical coupling dynamic model of the hub electric drive reducer includes: Combining the bending-torsional-axis coupled dynamic model and the vertical dynamic model, and considering the coupling effect between the road surface excitation and the meshing excitation of the wheel hub electric drive system reducer, the bending-torsional-axis vertical coupled dynamic model of the wheel hub electric drive reducer is constructed by analyzing the transmission path of bending-torsional-axis vertical coupled vibration of the sprung mass, housing, tire rim and planetary gear train components.

[0017] Furthermore, the process of analyzing the transmission path of bending, torsion, and vertical coupling vibrations of the spring mass, housing, tire rim, and various components of the planetary gear train includes: First, the road surface excitation is transmitted to the rim through the tire, and then to the planetary carrier through the hub. Secondly, there are three transmission paths starting from the planetary carrier: one is through the hub bearing to the housing, and through the suspension to the sprung mass; the second is through the planetary carrier to the planet gears, through gear meshing to the sun gear and ring gear, and in the ring gear part to the housing, and then to the suspension and sprung mass; the third is through the planetary carrier to the sun gear through the bearings, and then through the bearings to the housing and through the suspension to the sprung mass.

[0018] Furthermore, the construction of the bending-torsional-shaft-vertical coupling dynamic model of the hub electric drive reducer specifically involves analyzing the inherent characteristics of the reducer system based on a linear time-invariant model. Considering the relatively low rotational speed of the planetary carrier, the stiffness matrix terms related to Coriolis acceleration and centripetal acceleration in the dynamic equations are omitted. Simultaneously, system damping and external excitation are ignored, resulting in the simplified dynamic equations for the reducer system's bending-torsional-shaft-vertical coupling: in, For the quality matrix, For generalized coordinate vectors, These are the support stiffness matrix and the meshing stiffness matrix, respectively.

[0019] Furthermore, the process of obtaining the key evaluation indicators of vertical dynamic response, bearing dynamic load, dynamic transmission error, and dynamic meshing force includes: The simplified dynamic equations of the reducer system's bending, torsional, and sag were solved using the numerical integration method. This yielded vibration characteristic indicators of the hub electric drive reducer system under real-world operating conditions, including vertical vibration response, bearing dynamic load, dynamic transmission error, and dynamic meshing force. Time-frequency domain analysis of these indicators was then performed to obtain the corresponding key evaluation indicators.

[0020] Compared with the prior art, the present invention has the following advantages: This invention first uses a slicing method to divide the gear meshing stiffness into end-face meshing stiffness and axial meshing stiffness, constructing a time-varying meshing stiffness model. Fourier series is used to characterize the time-varying meshing stiffness, establishing a bending-torsional shaft coupling dynamic model for the reducer. Then, road surface excitation is introduced to determine the vertical coupling relationship between the tire / rim and the reducer, thus constructing a refined vertical dynamic model. Next, combining the bending-torsional shaft coupling dynamic model and the vertical dynamic model, and considering the coupling effect between road surface excitation and the reducer meshing excitation in the hub electric drive system, a bending-torsional shaft-vertical coupling dynamic model for the hub electric drive reducer is constructed. Finally, the numerical integration method is used to solve the bending-torsional shaft-vertical coupling dynamic model to obtain key evaluation indicators such as vertical dynamic response, bearing dynamic load, dynamic transmission error, and dynamic meshing force. Therefore, by establishing a dynamic model of the hub electric drive reducer that considers bending-torsional shaft-vertical coupling, accurate modeling and analysis of the multi-dimensional coupled dynamics of the hub electric drive reducer system are achieved. This model can accurately describe the dynamic behavior of the reducer system and accurately determine the vibration characteristics of the hub electric drive reducer system under real-world operating conditions.

[0021] This invention comprehensively considers the decoupling effect of the end face meshing stiffness and axial meshing stiffness of the helical planetary gear train, simplifies the load angle calculation by combining the effective meshing length, solves the time-varying meshing stiffness, and expresses the nonlinear transmission characteristics of the time-varying excitation through Fourier series. It establishes a bending-torsional shaft coupled dynamic model of the helical planetary gear train, realizing a unified characterization of the Coriolis effect, phase coupling and other multi-physics field effects under a single model framework, improving the calculation accuracy and efficiency of the model, and laying a high-precision foundation for subsequent coupled modeling.

[0022] This invention comprehensively considers the energy transfer path of the helical planetary gear train and the vertical vibration of the whole vehicle under road excitation, and establishes a refined vertical dynamic model of the hub electric drive system. This model takes into account the influence of gear interaction on the vertical vibration of the hub electric drive system, and convolves and couples the random road excitation with the time-varying stiffness of the gears in the time domain, reducing the prediction error of the vertical acceleration of the hub electric drive system, and providing a more comprehensive dynamic quantitative basis for vertical vibration optimization.

[0023] Based on the helical planetary gear train bending-torsional shaft coupling dynamic model and the hub electric drive system vertical dynamic model, this invention establishes a hub electric drive reducer bending-torsional shaft vertical coupling dynamic model that considers the coupling effect of road surface excitation and reducer meshing excitation. This model constructs a three-dimensional coupling transfer matrix of "gear meshing excitation - structural vibration response - road surface random excitation", realizing accurate quantitative correlation analysis of dynamics from microscopic gear contact to macroscopic vehicle vibration. It breaks through the limitation of traditional single-dimensional models that cannot characterize the multi-dimensional excitation coupling effect, and realizes comprehensive and accurate prediction of the vibration characteristics of the hub electric drive reducer system.

[0024] This invention is based on a bending-torsional-axis vertical coupling dynamic model. By solving this dynamic model, vibration characteristic indicators such as vertical vibration response, bearing dynamic load, dynamic transmission error, and dynamic meshing force are obtained. Through time-frequency domain analysis of these indicators, corresponding key evaluation indicators are obtained. Thus, the vibration characteristics of the hub electric drive reduction system under real working conditions are analyzed from four dimensions: vertical dynamic response, bearing dynamic load, dynamic transmission error, and dynamic meshing force. The frequency characteristics and amplitude range of key indicators are quantified, which can effectively reflect the modal characteristics and dynamic response of the reducer system, reveal the important laws of key vibration sources, and facilitate subsequent accurate vibration and noise optimization work. Attached Figure Description

[0025] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram illustrating the application process of the embodiment; Figure 3 This is a schematic diagram of the bending-torsional shaft coupling dynamics model in the embodiment; Figure 4 This is a schematic diagram of the refined vertical dynamics model in the embodiment; Figure 5 This is a schematic diagram of the bending and torsional shaft sag dynamics model in the embodiment; Figures 6a-6b The above diagram shows the time and frequency domain plots of the vertical acceleration of the spring mass in the embodiment. Figures 7a-7b The above are time-domain and frequency-domain plots of the vertical acceleration of the tire rim in the embodiment. Figures 8a-8d The dynamic load time-domain diagrams of bearing 1 and hub bearing in the Y-direction bending-torsional shaft-vertical coupling model and the refined vertical dynamic model are shown in the embodiment. Figures 9a-9b The above is a time-domain response diagram of the dynamic transmission error between the bending-torsional shaft vertical coupling model and the bending-torsional shaft coupling model in the embodiment. Figures 10a-10b The diagram shows the dynamic meshing force of the sun gear-ring gear-planet gear in the vertical coupling model and the vertical coupling model of the bending-torsion shaft in the embodiment. Detailed Implementation

[0026] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0027] Example like Figure 1 As shown, a vibration analysis method for a hub electric drive reducer based on a bending-torsional-axis-vertical coupling dynamic model includes the following steps: Based on the slicing method, the meshing stiffness of the gear slice is divided into end face meshing stiffness and axial meshing stiffness. A time-varying meshing stiffness model is constructed, and Fourier series is used to characterize the time-varying meshing stiffness. A dynamic model of bending and torsion shaft coupling of the reducer is established. By introducing road surface excitation, the vertical coupling relationship between the tire rim and the reducer is determined, thereby constructing a refined vertical dynamic model of the interaction between the tire rim, the shell, the sprung mass, and the components of the planetary gear train. Combining the bending-torsional-axis coupled dynamic model and the vertical dynamic model, and considering the coupling effect between the road surface excitation and the meshing excitation of the wheel hub electric drive system reducer, a bending-torsional-axis vertical coupled dynamic model of the wheel hub electric drive reducer is constructed. The numerical integration method is used to solve the vertical coupling dynamic model of the bending and torsion shaft, and the key evaluation indicators of vertical dynamic response, bearing dynamic load, dynamic transmission error and dynamic meshing force are obtained, thus obtaining the vibration characteristic analysis results of the hub electric drive reducer system under real working conditions.

[0028] This embodiment applies the above-described solution, such as... Figure 2 As shown, the main contents include: Step 1: Based on the slicing method, the helical gear is sliced ​​along the tooth width direction. The meshing stiffness of the gear slice is divided into end face meshing stiffness and axial meshing stiffness. Based on the end face overlap and axial overlap, the multi-tooth meshing interval is determined, and a time-varying meshing stiffness model of the planetary gear train is constructed. Then, the translational and torsional degrees of freedom of the sun gear, ring gear, planet carrier, and planet gears are considered, and the time-varying meshing stiffness is characterized by Fourier series to establish a bending-torsional shaft coupling dynamic model of the planetary gear train.

[0029] Step 2: Establish a time-domain model of road surface unevenness based on the white noise method, introduce road surface excitation as external excitation of vertical dynamics, consider the interaction force between gears, ignore the influence of braking system and speed, and convert the internal and external meshing stiffness of gears into vertical stiffness. By studying the vertical coupling relationship between the tire, rim, and reducer under the equivalent stiffness of the tire, rim mass, and vertical component of the reducer meshing force, a refined vertical dynamic model of the hub electric drive system is established, which involves the interaction of the tire, rim, shell, sprung mass, and various components of the planetary gear system.

[0030] Step 3: Based on the planetary gear train bending-torsional shaft coupling dynamic model and the hub electric drive system vertical dynamic model, and fully considering the coupling effect between the road surface excitation and the meshing excitation of the hub electric drive system reducer, the hub electric drive reducer bending-torsional shaft vertical coupling dynamic model is established by analyzing the transmission path of bending-torsional shaft vertical coupling vibration of the sprung mass, housing, tire rim and each component of the planetary gear train.

[0031] Step 4: Based on the bending-torsional-vertical coupling dynamic model, a method for analyzing the vibration characteristics of the hub electric drive reducer system under working conditions is proposed. Based on numerical solutions, key evaluation indicators such as vertical dynamic response, bearing dynamic load, dynamic transmission error, and dynamic meshing force are obtained, enabling accurate analysis of the vibration characteristics of the hub electric drive reducer system under real working conditions. This provides practical engineering suggestions for the design of the hub electric drive reducer system.

[0032] In step 1, based on the slicing method, the helical gear is sliced ​​along the tooth width direction, and the meshing stiffness of the gear slice is divided into end face meshing stiffness and axial meshing stiffness. The multi-tooth meshing interval is determined based on the end face overlap and axial overlap, thus constructing a time-varying meshing stiffness model for the planetary gear train. Next, the translational and torsional degrees of freedom of the sun gear, ring gear, planet carrier, and planet gears are considered, and the time-varying meshing stiffness is characterized using Fourier series. Based on the internal and external meshing forces and Newton's second law, a bending-torsional shaft coupling dynamic model of the planetary gear train is established, as follows: Figure 3 As shown.

[0033] The end-face meshing stiffness includes Hertzian contact stiffness, matrix deformation stiffness, and combined bending, shear, and compression stiffness. Hertzian contact stiffness is the elastic deformation stiffness of the tooth surface under meshing force in gear transmission. Since the tooth contact surface is a high-pair contact, the contact stiffness is calculated using a linear method based on Hertzian theory. End-face matrix deformation stiffness primarily focuses on the deformation stiffness of the external gear matrix. Combined bending, shear, and compression stiffness considers the internal and external meshing of the planetary gear train. By analyzing the tooth profiles of the internal and external gears and the forces on the gear end faces, the bending, shear, and radial compression stiffness are obtained with the load angle during meshing as the independent variable.

[0034] The specific load angle is: in, The load angle when the driven wheel enters the meshing point A2.

[0035] The expressions for the end face bending, shear, and radial compressive stiffness with the load angle as the independent variable are: The involute section and the end face section are combined to obtain the end face bending, shear, and radial compressive stiffness. The expression is: Axial meshing stiffness includes axial bending stiffness, axial torsional stiffness, and axial base deformation stiffness. To visually represent the gear rotation angle during the calculation of axial bending and torsional stiffness, the same treatment method as for end face stiffness is adopted, and the integral variable in the integral formulas for axial bending and torsional stiffness is expressed as angular displacement. Axial base deformation stiffness mainly focuses on the deformation stiffness of the external gear base.

[0036] The expressions for axial bending, torsion, and matrix stiffness are as follows: End face gear to slice overall meshing stiffness Specifically: For end face contact stiffness, For the deformation stiffness of the matrix. For bending deformation stiffness, For shear deformation stiffness, For radial compressive stiffness, the superscript is specified. Taking 1 represents the driving wheel. Let 2 represent the driven wheel.

[0037] Axial direction gear-to-slice combined meshing stiffness Specifically: in, For axial bending deformation stiffness, For torsional deformation stiffness, This represents the deformation stiffness of the matrix.

[0038] Helical gear slice overall meshing stiffness : The time-varying meshing stiffness of a planetary gear train is calculated using Fourier series as follows: in, These are the components where the stiffness frequency of the external and internal meshing is 0, respectively. Taking the first Nth order components of the Fourier series, then... External meshing and internal meshing stiffness respectively The amplitude of the first-order component, The stiffness of external meshing and internal meshing are respectively the first. Phase of the first-order component, f m The meshing frequency, t For time, γ sn For external meshing phase coefficient, γ rn For internal meshing phase coefficient, T m For the meshing cycle, γ rs It is the relative phase difference coefficient between internal and external meshing.

[0039] In step 2, white noise is used to simulate road surface roughness during excitation. National standard GB7031-86 and international standard ISO / DIS8608, through processing a large amount of randomly measured road data, provide a fitting expression for the road surface based on statistical parameters. The time-domain model of road surface roughness derived from this expression is as follows: in, The cutoff spatial frequency under road surface unevenness. Corresponding to the maximum road surface wavelength ; For vehicle speed, the unit is _____. .

[0040] Considering the interaction forces between gears, it is necessary to project the vertical displacement of each meshing gear onto the meshing direction, and calculate its static meshing force based on the average meshing stiffness. Ignoring the influence of the braking system and rotational speed, the internal and external meshing stiffness of the gears is equivalent to the vertical stiffness. The vertical projection of the static meshing force of the internal and external meshing of the planetary gear train is as follows: in, For the first First natural frequency, It is the mode shape vector corresponding to it.

[0041] Next, by studying the vertical coupling relationship between the tire and rim / reducer under the equivalent stiffness of the tire, rim mass, and the vertical component of the reducer meshing force, a refined vertical dynamic model of the hub electric drive system is established, considering the interaction of the tire, rim, shell, sprung mass, and various components of the planetary gear train. Figure 4 As shown.

[0042] In step 3, based on the planetary gear train bending-torsional shaft coupling dynamic model and the hub electric drive system vertical dynamic model, a hub electric drive reducer bending-torsional shaft vertical coupling dynamic model is established, such as... Figure 5 As shown. The transmission paths of the bending, torsional, and axial coupled vibrations of each component are as follows: First, the road surface excitation is transmitted to the rim through the tire, and then to the planetary carrier through the hub. Second, there are three transmission paths from the planetary carrier: one is transmitted to the housing through the hub bearing, and then to the sprung mass through the suspension; the second is transmitted to the planetary gears through the planetary carrier, and then to the sun gear and ring gear through gear meshing, and finally to the housing in the ring gear section, and then to the suspension and sprung mass; the third is transmitted to the sun gear through bearing 2 in the planetary carrier, and then to the housing through bearing 1 and finally to the sprung mass through the suspension.

[0043] The transmission path of this model considers not only the connection between the hub electric drive housing and the suspension, sprung mass, and planetary gear train along the bending and torsional axes, but also the vertical connection between the planetary gear train, housing, sprung mass, and tire rim under road excitation. Let For road surface excitation, Then the dynamic equations for the sprung mass, the housing, and the tire and rim are: The inherent characteristics of the system are analyzed based on a linear time-invariant model. Assuming that the planetary carrier rotation speed is relatively small, the stiffness matrix terms caused by Coriolis acceleration and centripetal acceleration in the equations are neglected. At the same time, the system damping and external excitation are ignored, and the dynamic equations of bending, torsion and sag of the system are simplified to: in, For the quality matrix, For generalized coordinate vectors, These are the support stiffness matrix and the meshing stiffness matrix, respectively.

[0044] The system characteristic equation is: in, It is an eigenvalue, representing the square of the i-th natural frequency of the system. It is an eigenvector that describes the relative vibration amplitude and phase relationship of each generalized coordinate of the system at the i-th natural frequency.

[0045] In step 4, by considering the internal meshing excitation of the gears and the random external vertical excitation of the road surface, a bending-torsional-axis-vertical coupled dynamic model of the hub electric drive reducer system is constructed. The dynamic equations are solved by numerical integration to obtain the vibration characteristics of the hub electric drive reducer system under actual working conditions, including vertical vibration response, bearing dynamic load, dynamic transmission error, and dynamic meshing force. By performing time-frequency domain analysis on these indicators, key evaluation indicators are obtained, thereby providing practical engineering suggestions for the design of the hub electric drive reducer system.

[0046] (1) Vertical dynamic response Comparing the vertical vibration response of the sprung mass in the bending-torsional shaft vertical coupling model and the refined vertical dynamics model: the vertical displacement and vertical acceleration of the sprung mass show the same trend in both models. After considering the dynamic meshing excitation inside the gears, the displacement and acceleration response of the sprung mass is earlier than that in the pure vertical dynamics model. The acceleration response of the bending-torsional shaft vertical dynamics model has high-frequency harmonic components. The difference in vertical acceleration of the sprung mass between the bending-torsional shaft vertical coupling model and the vertical dynamics model is shown in the figure. Figures 6a-6b As shown. From the time domain perspective, the maximum acceleration difference is 0.51 m / s². 2From the frequency domain perspective, the high-frequency signals that the bending-torsional shaft vertical model has compared to the refined vertical dynamic model are mainly 737Hz, 773Hz, 1417Hz and 1861Hz. Among them, 773Hz is the meshing frequency and the main excitation frequency, which shows that the gear meshing excitation has an important influence on the acceleration of the sprung mass.

[0047] Comparing the tire vertical vibration response of the bending-torsional-vertical coupling model and the refined vertical dynamics model: both models show the same displacement trend, but the displacement response of the bending-torsional-vertical coupling model is earlier. The maximum acceleration of the bending-torsional-vertical coupling model is 44.23 m / s². 2 The maximum tire acceleration in the vertical dynamics model is 6.21 m / s². 2 The acceleration response amplitude of this model is significantly larger than that of the vertical dynamic model. The acceleration difference between the bending-torsional axis vertical coupling model and the vertical dynamic model is as follows: Figures 7a-7b As shown, the high-frequency harmonics added by the bending-torsional shaft vertical model compared to the refined vertical dynamic model are mainly 737Hz, 773Hz, 1888Hz and 3306Hz. Among them, 773Hz is the meshing frequency and the main excitation frequency, which shows that gear meshing excitation has an important influence on tire acceleration.

[0048] bearing dynamic load In the X-direction bending-torsional-axis coupling model, the maximum dynamic loads of bearing 1 and hub bearing are 6940N and 4140N, respectively. The main excitation frequencies of the two bearings are 737Hz and 773Hz, with 773Hz being the meshing frequency. Both bearing 1 and hub bearing have the maximum amplitude response at 737Hz.

[0049] In the time domain of the dynamic loads of bearing 1 and hub bearing in the bending-torsional shaft-vertical coupling model and the refined vertical dynamic model in the Y direction, as shown... Figures 8a-8d As shown. For bearing 1 and hub bearing, the bending-torsional shaft vertical coupling model and the vertical dynamic model have the same trend. The main excitation frequencies of the bending-torsional shaft vertical coupling model are 1.63Hz, 737Hz and 773Hz, while the main excitation frequency of the vertical dynamic model is 1.63Hz. It can be seen that when considering the internal meshing excitation of the gear, the dynamic load in the Y direction of the bearing has high-frequency harmonic components, of which 773Hz is the meshing frequency, and the maximum response amplitude is at this frequency.

[0050] In the Z-direction bending-torsional shaft-vertical coupling model, the maximum dynamic loads of bearing 1 and hub bearing are 2776 N and 796 N, respectively. The main excitation frequencies for bearing 1 are 641 Hz and 1289 Hz, with the largest amplitude response at 641 Hz. For hub bearing, the main excitation frequencies are 641 Hz, 834 Hz, and 1289 Hz, with the largest amplitude response at 1289 Hz. Both bearing 1 and hub bearing correspond to an "axial-torsional vibration mode," while the meshing frequency contributes relatively little to the Z-direction bearing dynamic load.

[0051] Dynamically propagated error The dynamic transmission error and internal / external meshing time-domain response of the bending-torsional shaft coupling model and the bending-torsional shaft coupling model of the hub electric drive reducer system are as follows: Figures 9a-9b As shown. Analysis of the bending-torsional shaft vertical coupling model: the mean dynamic transmission error of the external meshing is 2.91 × 10⁻⁶. -6 m, the peak-to-peak value of the propagation error is 6.23 × 10 -6 m; the mean value of the internal meshing dynamic transmission error is 2.09 × 10⁻⁶. -6 m, the peak-to-peak value of the propagation error is 3.65 × 10 -6 The dynamic transmission errors of both external meshing and internal meshing models are greater. The dynamic transmission errors of the bending-torsional shaft-vertical coupling model are smaller for both external and internal meshing than those of the bending-torsional shaft-coupled model, but the peak-to-peak value of the transmission error for both external and internal meshing is greater for the bending-torsional shaft-coupled model. The main excitation frequencies of the bending-torsional shaft-vertical coupling model are 773Hz and 1290Hz, while those of the bending-torsional shaft-coupled model are 1200Hz, 1291Hz, 1810Hz, and 2970Hz, with 773Hz corresponding to the meshing frequency. The harmonic components of the dynamic transmission error in the bending-torsional shaft-coupled model are relatively small at the meshing frequency, and exhibit significant harmonic components at the meshing frequency, better reflecting the importance of meshing excitation to the transmission error. This explains why the peak-to-peak value of the transmission error in the bending-torsional shaft-vertical coupling model is greater than that in the bending-torsional shaft-coupled model.

[0052] (4) Dynamic meshing force The dynamic meshing force of the sun gear-ring gear-planet gears in the bending-torsional shaft coupling model and the bending-torsional shaft coupling model of the hub electric drive reducer system are shown in the following time-domain response: Figures 10a-10bAs shown. Analysis of the bending-torsional shaft coupling model: The average dynamic meshing force of the external meshing is 1610 N, and the peak-to-peak value of the dynamic meshing force is 3415 N; the average dynamic meshing force of the internal meshing is 1610 N, and the peak-to-peak value of the meshing force is 2767 N. The average dynamic meshing forces of the internal and external meshing are the same in both models; the dynamic meshing force of the external meshing is greater than that of the internal meshing; the average dynamic meshing force of the internal and external meshing in the bending-torsional shaft coupling model is smaller than that in the bending-torsional shaft coupling model, but the peak-to-peak value of the internal and external meshing forces is greater than that in the bending-torsional shaft coupling model. The main excitation frequencies of the bending-torsional shaft dynamics are 773 Hz and 1290 Hz, while the main excitation frequencies of the bending-torsional shaft coupling model are 1200 Hz, 1291 Hz, 1810 Hz, and 2970 Hz, where 773 Hz corresponds to the meshing frequency. The harmonic components of the dynamic transmission error in the bending-torsional shaft coupling model are relatively small at the meshing frequency, but exhibit significant harmonic components at the meshing frequency. The peak-to-peak value of the dynamic meshing force in the bending-torsional shaft coupling model is greater than that in the bending-torsional shaft coupling model, demonstrating the importance of meshing excitation to the transmission error.

[0053] Therefore, in practical engineering, using the bending-torsional shaft sag dynamic model for system design can effectively avoid dynamic transmission errors and the motor operating speed range where the peak meshing force occurs: 3900 rpm, 5850 rpm, and 7100 rpm. It also assists in optimizing the gear micro-parameters of the auxiliary hub electric drive reduction system, including displacement coefficients and profile design, to reduce meshing stiffness fluctuations. Furthermore, it can accurately predict vibration loads under actual operating conditions, providing a quantitative basis for design. In summary, this scheme takes the hub electric drive reducer system as the research object, considering the coupling effect between road excitation and internal excitation such as reducer meshing excitation. A bending-torsional shaft coupling dynamic model and a refined vertical dynamic model are established using theoretical modeling methods. Based on this, a bending-torsional shaft-vertical coupling dynamic model is established, and the dynamic characteristics of vibration of each component under the coupling effect of road excitation and meshing excitation are analyzed. This achieves accurate modeling and analysis of multi-dimensional coupled dynamics of the hub electric drive system, enabling accurate prediction of vibration loads under actual working conditions and providing quantitative design basis.

[0054] This scheme, by considering the dynamic response of road surface excitation and sprung mass, and integrating the translational and torsional degrees of freedom of the gears in the lateral, longitudinal, and vertical directions, achieves accurate analysis of the multi-source coupled dynamics of the hub electric drive reducer system under road surface excitation. This significantly improves the accuracy of dynamic response analysis, thereby providing reliable theoretical support for vibration and noise suppression, transmission reliability design, and intelligent control of the hub electric drive system, and bringing greater impetus to the innovative development of hub electric drive reduction systems.

[0055] In practical engineering, the use of bending and torsional shaft sag dynamic model for system design and vibration analysis can effectively avoid dynamic transmission errors and the motor operating speed range where the peak meshing force is located. It can also help optimize the gear micro parameters of the hub electric drive reduction system, including displacement coefficient and profile design, to reduce meshing stiffness fluctuations. Furthermore, it can accurately predict the vibration load under actual working conditions, providing a quantitative design basis for system structure and parameter optimization, and ultimately achieving effective suppression of vibration and noise in the hub electric drive reduction system.

Claims

1. A vibration analysis method for a hub electric drive reducer based on a bending-torsional-axis-vertical coupling dynamic model, characterized in that, Includes the following steps: Based on the slicing method, the meshing stiffness of the gear slice is divided into end face meshing stiffness and axial meshing stiffness. A time-varying meshing stiffness model is constructed, and Fourier series is used to characterize the time-varying meshing stiffness. A dynamic model of bending and torsion shaft coupling of the reducer is established. By introducing road surface excitation, the vertical coupling relationship between the tire rim and the reducer is determined, thereby constructing a refined vertical dynamic model of the interaction between the tire rim, the shell, the sprung mass, and the components of the planetary gear train. Combining the bending-torsional-axis coupled dynamic model and the vertical dynamic model, and considering the coupling effect between the road surface excitation and the meshing excitation of the wheel hub electric drive system reducer, a bending-torsional-axis vertical coupled dynamic model of the wheel hub electric drive reducer is constructed. The numerical integration method is used to solve the vertical coupling dynamic model of the bending and torsion shaft, and the key evaluation indicators of vertical dynamic response, bearing dynamic load, dynamic transmission error and dynamic meshing force are obtained, thus obtaining the vibration characteristic analysis results of the hub electric drive reducer system under real working conditions.

2. The vibration analysis method for a hub electric drive reducer based on a bending-torsional-axis-vertical coupling dynamic model according to claim 1, characterized in that, The process of constructing the time-varying meshing stiffness model includes: Based on the slicing method, the helical gear is sliced ​​along the tooth width direction. The meshing stiffness of the gear slice is divided into end face meshing stiffness and axial meshing stiffness. The end face meshing stiffness includes Hertzian contact stiffness, matrix deformation stiffness, and combined bending, shear, and compression stiffness. The axial meshing stiffness includes axial bending stiffness, axial torsional stiffness, and axial matrix deformation stiffness. Based on the end face overlap and axial overlap, the multi-tooth meshing interval is determined, and a time-varying meshing stiffness model of the planetary gear train is constructed.

3. The vibration analysis method for a hub electric drive reducer based on a bending-torsional-axis-vertical coupling dynamic model according to claim 1, characterized in that, The process of establishing the coupled dynamic model of the reducer's bending and torsional shafts includes: The translational and torsional degrees of freedom of the planetary gear train of the reducer are defined, including the translational and torsional degrees of freedom of the sun gear, ring gear, planet carrier, and planet gears. The time-varying meshing stiffness in the time-varying meshing stiffness model is characterized by Fourier series. The bending and torsional shaft coupling dynamic model of the reducer is established based on the internal and external meshing.

4. The vibration analysis method for a hub electric drive reducer based on a bending-torsional-axis-vertical coupling dynamic model according to claim 3, characterized in that, The time-varying meshing stiffness characterized by Fourier series is specifically as follows: in, Let N be the components of the stiffness of the external and internal meshing meshes, respectively, with a frequency of 0. Taking the first N orders of the Fourier series, then... The stiffness of external meshing and internal meshing respectively The amplitude of the first-order component, The stiffness of external meshing and internal meshing are respectively the first. Phase of the first-order component, f m The meshing frequency, t For time, γ sn For external meshing phase coefficient, γ rn The internal meshing phase coefficient, T m For the meshing cycle, γ rs It is the relative phase difference coefficient between internal and external meshing.

5. The vibration analysis method for a hub electric drive reducer based on a bending-torsional-axis-vertical coupling dynamic model according to claim 1, characterized in that, The process of constructing the refined vertical dynamics model includes: By introducing road surface excitation as the external excitation for vertical dynamics, a time-domain model of road surface unevenness is established based on the white noise method. At the same time, considering the interaction force between gears, the meshing stiffness of the gears is equivalent to the vertical stiffness. By analyzing the vertical coupling relationship between the tire rim and the reducer under the equivalent stiffness of the tire, the rim mass, and the vertical component of the reducer meshing force, a refined vertical dynamic model of the hub electric drive system is established, which includes the interaction of the tire rim, the shell, the sprung mass, and the components of the planetary gear system.

6. The vibration analysis method for a hub electric drive reducer based on a bending-torsional-axis-vertical coupling dynamic model according to claim 5, characterized in that, The vertical coupling relationship between the tire rim and the reducer is specifically as follows: Considering the interaction force between gears, the inherent connection between the motor stator and the housing, and the inherent connection between the motor rotor and the sun gear shaft, and ignoring the influence of the braking system and speed, since the interaction force between gears is along the meshing direction of helical gears, it cannot be directly used as the vertical stiffness. It is necessary to convert the internal and external meshing stiffness and damping into vertical stiffness and calculate them. At the same time, only the vertical displacement of each component of the planetary gear train is considered, and the static meshing force between gears is projected into the vertical direction.

7. The vibration analysis method for a hub electric drive reducer based on a bending-torsional-axis-vertical coupling dynamic model according to claim 1, characterized in that, The process of constructing the bending-torsional-vertical coupling dynamic model of the hub electric drive reducer includes: Combining the bending-torsional-axis coupled dynamic model and the vertical dynamic model, and considering the coupling effect between the road surface excitation and the meshing excitation of the wheel hub electric drive system reducer, the bending-torsional-axis vertical coupled dynamic model of the wheel hub electric drive reducer is constructed by analyzing the transmission path of bending-torsional-axis vertical coupled vibration of the sprung mass, housing, tire rim and planetary gear train components.

8. The vibration analysis method for a hub electric drive reducer based on a bending-torsional-axis-vertical coupling dynamic model as described in claim 7, characterized in that, The process of analyzing the transmission path of bending, torsional, and vertical coupling vibrations between the spring mass, the housing, the tire rim, and each component of the planetary gear train includes: First, the road surface excitation is transmitted to the rim through the tire, and then to the planetary carrier through the hub. Secondly, there are three transmission paths starting from the planetary carrier: one is through the hub bearing to the housing, and through the suspension to the sprung mass; the second is through the planetary carrier to the planet gears, through gear meshing to the sun gear and ring gear, and in the ring gear part to the housing, and then to the suspension and sprung mass; the third is through the planetary carrier to the sun gear through the bearings, and then through the bearings to the housing and through the suspension to the sprung mass.

9. The vibration analysis method for a hub electric drive reducer based on a bending-torsional-axis-vertical coupling dynamic model as described in claim 7, characterized in that, The aforementioned construction of the bending-torsional-shaft-vertical coupled dynamic model of the hub electric drive reducer is specifically based on the analysis of the inherent characteristics of the reducer system using a linear time-invariant model. Considering the relatively low rotational speed of the planetary carrier, the stiffness matrix terms related to Coriolis acceleration and centripetal acceleration in the dynamic equations are neglected. At the same time, system damping and external excitation are ignored, resulting in the simplified dynamic equations of the reducer system's bending-torsional-shaft-vertical coupling: in, For the quality matrix, For generalized coordinate vectors, These are the support stiffness matrix and the meshing stiffness matrix, respectively.

10. A vibration analysis method for a hub electric drive reducer based on a bending-torsional-axis-vertical coupling dynamic model as described in claim 9, characterized in that, The process of obtaining the key evaluation indicators of vertical dynamic response, bearing dynamic load, dynamic transmission error, and dynamic meshing force includes: The simplified dynamic equations of the reducer system's bending, torsional, and sag were solved using the numerical integration method. This yielded vibration characteristic indicators of the hub electric drive reducer system under real-world operating conditions, including vertical vibration response, bearing dynamic load, dynamic transmission error, and dynamic meshing force. Time-frequency domain analysis of these indicators was then performed to obtain the corresponding key evaluation indicators.

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