Vibration analysis method and device of vehicle electric driving system, medium and equipment

Abstract

The invention discloses a vibration analysis method, device, medium and equipment for a vehicle electric driving system, and relates to the technical field of electric digital data processing, and the method comprises the steps: analyzing excitation characteristics and gear engagement dynamic load parameters based on a motor electromagnetic excitation and gear system dynamics model, and taking the excitation characteristics and the gear engagement dynamic load parameters as a mechanical excitation coupling motor, gear, bearing and shell model; according to the method, a rigid-flexible coupling dynamic model is formed, after the rigid-flexible coupling dynamic model is converted into a state-space equation, multivariable time-domain data are obtained through nondimensionalization and piecewise linear method solving, and then the transmission efficiency value of vibration energy among a motor, a gear, a bearing and all parts of a shell is calculated based on excitation characteristic parameters, gear meshing dynamic load parameters and the multivariable time-domain data. And positioning a key noise transmission path of the vehicle electric driving system according to the transmission efficiency value. By comprehensively analyzing the vibration characteristics of the system, the NVH problem of high-frequency howling and the like under the high-speed working condition is effectively solved.

Description

Technical Field

[0001] The present application relates to the technical field of electrical digital data processing, and in particular to a vibration analysis method, device, medium, and equipment for a vehicle electric drive system. Background Art

[0002] With the rapid development of the global new energy vehicle industry, electric drive systems, as the core power unit of new energy vehicles, are rapidly evolving towards higher speeds and greater integration. Unlike traditional internal combustion engine drive systems, electric drive systems lack the masking effect of engine noise, making problems such as motor electromagnetic noise and gear meshing order noise increasingly prominent. Especially under high-speed operating conditions, the system's dynamic response frequency reaches the sensitive range of the human ear, and high-frequency whine noise is particularly prominent during acceleration or load conditions, severely impacting the vehicle's NVH (noise, vibration, and harshness) performance. At the same time, the internal coupling of electric drive systems has significantly increased, involving the coordinated interaction of multiple components such as the motor, reducer, and controller. Its dynamic characteristics require comprehensive consideration of multi-physics coupling effects such as electromagnetic excitation, mechanical excitation, and structural deformation, placing higher demands on the vibration analysis of electric drive systems.

[0003] In order to solve the vibration and noise problems of electric drive systems, the existing technologies mainly use single physical field modeling or simplified multi-field coupling models for analysis. For example, some solutions only establish dynamic models for the mechanical vibration of the gear system, and fail to fully consider the influence of the electromagnetic excitation of the motor; other solutions, although electromagnetic excitation is taken into account, have deficiencies in dealing with the bending-torsion-axis coupling vibration of the gear pair and the flexible support of the housing, resulting in low model accuracy. In terms of solution methods, traditional time domain or frequency domain solutions often face problems such as low computational efficiency and poor convergence for strongly nonlinear and multivariable coupled dynamic systems, making it difficult to achieve accurate calculation of the multivariable vibration characteristics of the electric drive system. Therefore, the existing technology cannot comprehensively and accurately analyze the vibration characteristics of the electric drive system, resulting in a lack of reliable theoretical basis for the optimization design of the noise problem, and it is difficult to effectively solve NVH problems such as high-frequency howling under high-speed conditions. Summary of the Invention

[0004] In view of this, the present application provides a vibration analysis method, device, medium and equipment for an automotive electric drive system, which can effectively solve NVH problems such as high-frequency howling under high-speed conditions by comprehensively and accurately analyzing the vibration characteristics of the electric drive system.

[0005] According to a first aspect of the present application, a vibration analysis method for a vehicle electric drive system is provided, comprising: Based on the established motor electromagnetic excitation model and gear system dynamics model, the excitation characteristic parameters and gear meshing dynamic load parameters are analyzed; The excitation characteristic parameters and the gear meshing dynamic load parameters are used as mechanical excitations of the gear system, and the motor electromagnetic excitation model, the gear system dynamics model, the bearing rigidity model, and the housing flexibility model are coupled to form a rigid-flexible coupling dynamics model; Converting the rigid-flexible coupling dynamic model into a state-space equation, solving the state-space equation by dimensionless transformation and piecewise linear method to obtain multivariate time-domain data; Based on the excitation characteristic parameters, the gear meshing dynamic load parameters and the multivariate time domain data, the transmission efficiency values ​​of the vibration energy among the motor, gears, bearings and housing components are calculated, and the key noise transmission paths of the vehicle electric drive system are located according to the size of the transmission efficiency values.

[0006] According to a second aspect of the present application, there is provided a vibration analysis device for a vehicle electric drive system, comprising: An analysis module is used to analyze the excitation characteristic parameters and gear meshing dynamic load parameters based on the established motor electromagnetic excitation model and gear system dynamics model; a coupling module, configured to use the excitation characteristic parameters and the gear meshing dynamic load parameters as mechanical excitations of the gear system, and couple the motor electromagnetic excitation model, the gear system dynamics model, the bearing rigidity model, and the housing flexibility model to form a rigid-flexible coupling dynamics model; A first computing module is configured to convert the rigid-flexible coupling dynamics model into a state-space equation, solve the state-space equation by dimensionless transformation and piecewise linear method, and obtain multivariate time-domain data; The second calculation module is used to calculate the transmission efficiency value of vibration energy among the motor, gears, bearings and housing components based on the excitation characteristic parameters, the gear meshing dynamic load parameters and the multivariate time domain data, and locate the key noise transmission path of the vehicle electric drive system according to the size of the transmission efficiency value.

[0007] According to a third aspect of the present application, a storage medium is provided, on which a computer program is stored. When the program is executed by a processor, the vibration analysis method of the vehicle electric drive system is implemented.

[0008] According to a fourth aspect of the present application, an electronic device is provided, comprising a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor, wherein the processor implements the above-mentioned vibration analysis method for an electric vehicle drive system when executing the program.

[0009] By means of the above technical solutions, the vibration analysis method, device, medium, and equipment for an electric vehicle drive system provided in this application can effectively solve the problems of insufficient single-physics field modeling accuracy and low solution efficiency in the existing technology through multi-physics field coupling modeling and efficient solution methods. Specifically, based on the motor electromagnetic excitation model and the gear system dynamics model, the excitation characteristic parameters and meshing dynamic load parameters are analyzed, which can fully consider the interaction between electromagnetic excitation and gear coupled vibration. The motor, gear, bearing, and housing models are coupled to form a rigid-flexible coupling dynamic model, which can accurately reflect the influence of the housing flexible support on the system vibration, and make up for the shortcomings of traditional simplified models in multi-physics field coupling analysis and characterization of the influence of housing flexibility. Through state-space equation transformation, dimensionless transformation, and piecewise linear solution, it can not only solve the problem of poor computational convergence of strongly nonlinear systems, but also improve the solution efficiency of multivariable coupled systems, and realize the accurate calculation of multivariable time-domain data such as vibration displacement and velocity. Based on multi-source data, the energy transfer efficiency is calculated and the key noise path is located, which can provide a quantitative basis for noise optimization and can specifically solve NVH problems such as high-frequency whine under high-speed conditions, making the optimization design for noise problems more theoretically supported.

[0010] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 A schematic flow chart of a vibration analysis method for a vehicle electric drive system provided in an embodiment of the present application is shown; Figure 2 A schematic flow chart of a vibration analysis method for a vehicle electric drive system provided in another embodiment of the present application is shown; Figure 3 A schematic structural diagram of a vibration analysis device for a vehicle electric drive system provided in an embodiment of the present application is shown; Figure 4 A schematic structural diagram of another vibration analysis device for an electric drive system for a vehicle provided in an embodiment of the present application is shown. DETAILED DESCRIPTION

[0012] The present application will be described in detail below with reference to the accompanying drawings and in combination with embodiments. It should be noted that, unless there is a conflict, the embodiments and features in the embodiments of the present application can be combined with each other.

[0013] In order to solve the above technical problems, an embodiment of the present invention provides a vibration analysis method for a vehicle electric drive system, such as Figure 1 As shown, the method includes: Step 110: Analyze the excitation characteristic parameters and the gear meshing dynamic load parameters based on the created motor electromagnetic excitation model and gear system dynamics model.

[0014] Among them, the motor electromagnetic excitation model is a mathematical model used to describe the excitations such as tangential electromagnetic force, axial electromagnetic force and torque fluctuation generated by the electromagnetic effect when the motor is running. Based on the motor electromagnetic excitation model, the electromagnetic excitation characteristics can be solved by the finite element simulation method; the gear system dynamic model is a dynamic model that considers the bending-torsion-axis coupling vibration of the helical gear pair, multi-stage gear transmission and multi-gear switching. It uses tangential, axial and torsional displacements as variables and describes the multi-degree-of-freedom vibration characteristics of the gear system through a set of differential equations; the excitation characteristic parameters are key parameters that characterize the electromagnetic excitation of the motor, including tangential electromagnetic force, axial electromagnetic force and torque fluctuation; the gear meshing dynamic load parameters are parameters that describe the dynamic load during the gear meshing process, including tangential / axial dynamic meshing force, torsional vibration load spectrum and load change data.

[0015] For the disclosed embodiments, a motor electromagnetic excitation model and a gear system dynamics model can be constructed first, and then the excitation characteristic parameters such as the tangential electromagnetic force, axial electromagnetic force, and torque fluctuation can be solved from the motor electromagnetic excitation model. At the same time, from the helical gear coupling vibration equations for multiple pairs of gear pairs, multiple gears, and containing tangential, axial, and torsional degrees of freedom established by the gear system dynamics model, the gear meshing dynamic load parameters such as the tangential dynamic meshing force and axial dynamic meshing force of the gear pairs, as well as the torsional vibration load spectrum and load change data during multi-gear meshing can be solved. Among them, the helical gear coupling vibration equations refer to a differential equation group containing tangential, axial, and torsional degrees of freedom, which couples the vibrations in the three directions through the mass matrix, damping matrix, and stiffness matrix to reflect the dynamic load characteristics during the meshing process of the helical gear pair.

[0016] By analyzing the excitation characteristic parameters and gear meshing dynamic load parameters, we can comprehensively obtain the specific data of the motor electromagnetic excitation and gear meshing dynamic load in the electric drive system, providing accurate excitation input for the subsequent construction of the rigid-flexible coupling dynamic model, enabling the model to more realistically reflect the dynamic characteristics of the electric drive system and provide a reliable basis for the analysis and optimization of system vibration and noise problems.

[0017] Step 120: Using the excitation characteristic parameters and the gear meshing dynamic load parameters as the mechanical excitation of the gear system, the motor electromagnetic excitation model, the gear system dynamics model, the bearing rigidity model, and the housing flexibility model are coupled to form a rigid-flexible coupling dynamics model.

[0018] Among them, the bearing rigidity model is a model established with stiffness as the core based on the relationship between bearing displacement deformation and external force load. It is used to characterize the support characteristics of the bearing, and can determine the bearing support stiffness matrix to reflect the supporting effect of the bearing on the vibration of the gear system; the shell flexibility model is a model obtained by shrinking the shell using the finite element substructure analysis method. It contains the shell mass matrix, the shell damping matrix and the shell shrinkage stiffness matrix, which is used to describe the flexible vibration characteristics of the shell and reflect the influence of the shell flexibility on the system vibration; the rigid-flexible coupling dynamic model is a model formed by coupling the motor electromagnetic excitation model, the gear system dynamics model (rigid components) with the bearing rigidity model and the shell flexibility model (flexible components) through the mechanical transmission path. It can comprehensively consider the interaction between the rigid and flexible components in the system and accurately reflect the dynamic characteristics of the electric drive system.

[0019] For the embodiments of the present disclosure, the excitation characteristic parameters such as tangential electromagnetic force, axial electromagnetic force, torque fluctuation, etc. obtained from the analysis of the motor electromagnetic excitation model, and the gear meshing dynamic load parameters such as tangential dynamic meshing force, axial dynamic meshing force, torsional vibration load spectrum and change data of the gear pair obtained from the gear system dynamics model can be used as input excitations of the gear system. The motor electromagnetic excitation model, the gear system dynamics model, the bearing rigidity model established with stiffness as the core, and the shell flexibility model obtained by condensation processing using the finite element substructure analysis method are connected and combined in a certain way, thereby constructing a rigid-flexible coupling dynamic model that takes into account both rigid and flexible components.

[0020] By coupling multi-source excitation parameters with multi-component models, accurate modeling of the multi-physics field and multi-degree-of-freedom vibration characteristics of the electric drive system can be achieved. On the one hand, the introduction of excitation characteristic parameters and gear mesh dynamic load parameters ensures that the synergistic effect of the motor electromagnetic excitation and the gear mesh excitation is accurately reflected. On the other hand, the coupling of the bearing rigidity model and the housing flexibility model enables the rigid-flexible coupling dynamic model to consider the reaction of the housing flexible support to the system vibration, compensating for the shortcomings of traditional simplified models in dealing with rigid-flexible coupling problems, ensuring that the rigid-flexible coupling dynamic model accurately restores the actual working state of the electric drive system, and providing a more reliable model foundation for subsequent system vibration response analysis, energy transfer efficiency calculation, and noise path location.

[0021] Step 130: Convert the rigid-flexible coupling dynamics model into a state-space equation, solve the state-space equation by dimensionless transformation and piecewise linear method, and obtain multivariate time-domain data.

[0022] Among them, the state-space equation is a set of first-order differential equations based on modern control theory, with the system state vector (such as displacement and velocity) as variables; dimensionless conversion is to introduce characteristic reference quantities (such as displacement nominal scale and time nominal scale) to convert physical parameters into dimensionless quantities, eliminating the influence of dimension differences on calculations; the piecewise linear method is to divide the nonlinear characteristics of time-varying parameters (such as gear meshing stiffness) into multiple linear intervals according to the working conditions, and use the linear system solution method in each interval to achieve approximate solution of nonlinear problems; multivariable time domain data is the change data of each system state variable (such as tangential / axial vibration displacement, velocity, torsional angular displacement, etc.) in the time dimension obtained by solving the state-space equation, which is used to describe the dynamic response process of the system.

[0023] For the embodiments of the present disclosure, the second-order differential equation corresponding to the rigid-flexible coupling dynamic model including components such as the motor, gears, bearings, and housing can be first converted into a first-order state-space equation by defining a state vector including the system displacement and velocity; then, characteristic reference quantities are selected for physical parameters such as time and displacement in the state-space equation, and they are converted into dimensionless quantities to obtain the dimensionless state-space equation; finally, based on the nonlinear characteristics of the rigid-flexible coupling dynamic model, the time-varying parameters in the state-space equation (such as the time-varying meshing stiffness of the gear) are divided into multiple linear intervals according to different working conditions, and the dimensionless state-space equation is linearly solved in each interval to obtain multivariate time-domain data of each state variable of the system (such as vibration displacement and velocity) changing with time.

[0024] Converting the rigid-flexible coupling dynamic model into a state-space equation and solving it through dimensionless transformation and piecewise linearization can effectively address the problems of low computational efficiency and poor convergence of traditional time-domain or frequency-domain solutions when dealing with strongly nonlinear, multivariable coupled dynamic systems. This enables accurate calculation of the multivariable vibration characteristics of the electric drive system, and provides an efficient and accurate method for obtaining multivariable time-domain data such as the vibration displacement and velocity of each component of the system, thereby laying a data foundation for subsequent vibration energy transfer efficiency analysis and key noise transmission path positioning, making the analysis of vibration and noise problems of the electric drive system more accurate and reliable.

[0025] Step 140: Based on the excitation characteristic parameters, the gear meshing dynamic load parameters, and the multivariate time domain data, calculate the transmission efficiency of the vibration energy among the motor, gears, bearings, and housing components, and locate the key noise transmission paths of the vehicle electric drive system based on the transmission efficiency values.

[0026] Among them, the transfer efficiency value is the ratio of vibration energy transfer between various components in the automotive electric drive system. For example, the efficiency from motor to gear is the ratio of the energy received by the gear to the energy input by the motor. It is used to quantitatively evaluate the energy transfer efficiency in the system and provide a quantitative basis for noise path positioning; the key noise transfer path is a path with higher energy transfer efficiency selected according to the size of the transfer efficiency value, such as the high-efficiency sub-path in "motor→gear→bearing→housing", which is the main channel for noise generation and propagation in the electric drive system and provides a target for structural optimization.

[0027] For the embodiments of the present disclosure, the tangential electromagnetic force, axial electromagnetic force and torque fluctuation in the excitation characteristic parameters can be used as the motor input energy, combined with the tangential / axial meshing force in the gear meshing dynamic load parameters, and the gear displacement, bearing displacement, housing displacement and speed in the multivariate time domain data, and the motor input energy, gear received energy, bearing received energy and housing vibration energy are calculated by integration, and then the transmission efficiency value between each component is obtained through the energy ratio. Finally, the noise transmission path with high energy transfer efficiency is screened out according to the efficiency value.

[0028] By fusion-based energy transfer efficiency calculations using multi-source data, quantitative analysis of electric drive system noise paths is possible. Combining excitation parameters with mesh load parameters ensures the integrity of electromagnetic excitation and gear mesh excitation in energy calculations. Furthermore, multivariate time-domain data is used to accurately characterize the vibration response of each component, making transfer efficiency calculations more accurate to actual operating conditions. Identifying critical noise paths through efficiency comparison provides clear targets for noise optimization, avoiding the blinding nature of traditional trial-and-error methods and improving the efficiency and accuracy of solving NVH issues in electric drive systems.

[0029] In summary, the vibration analysis method of the electric drive system for a vehicle provided by the present invention can effectively solve the problems of insufficient accuracy and low solution efficiency of single physical field modeling in the existing technology through multi-physics field coupling modeling and efficient solution method. Specifically, based on the analysis of the excitation characteristic parameters and meshing dynamic load parameters of the motor electromagnetic excitation model and the gear system dynamic model, the interaction between the electromagnetic excitation and the gear coupling vibration can be fully considered; the motor, gear, bearing and housing models are coupled to form a rigid-flexible coupling dynamic model, which can accurately reflect the influence of the housing flexible support on the system vibration, and make up for the defects of the traditional simplified model in multi-physics field coupling analysis and housing flexibility influence characterization; through state space equation transformation, dimensionless and piecewise linear method solution, it can not only solve the problem of poor convergence of strong nonlinear system calculation, but also improve the solution efficiency of multivariable coupling system, and realize the accurate calculation of multivariable time domain data such as vibration displacement and velocity; based on multi-source data, the energy transfer efficiency is calculated and the key noise path is located, which can provide a quantitative basis for noise optimization, and can solve NVH problems such as high-frequency howling under high-speed conditions in a targeted manner, so that the optimization design for noise problems has more theoretical support.

[0030] Furthermore, as a refinement and expansion of the specific implementation of the above embodiment, in order to fully illustrate the implementation of this embodiment, this embodiment also provides another vibration analysis method for a vehicle electric drive system, such as Figure 2 As shown, the method includes: Step 210: Use finite element simulation software to simulate the electromagnetic excitation model of the motor to solve the excitation characteristic parameters including tangential electromagnetic force, axial electromagnetic force and torque fluctuation.

[0031] In the disclosed embodiments, finite element simulation software is used to simulate the constructed motor electromagnetic excitation model, thereby solving for the excitation characteristic parameters covering the tangential electromagnetic force, axial electromagnetic force, and torque fluctuation. Specifically, the tangential electromagnetic force density can be calculated using the Maxwell stress tensor method, and then multiplied by the effective area to obtain the tangential electromagnetic force. The axial electromagnetic force is then solved based on parameters such as electromagnetic power, motor speed, and core length. The tangential electromagnetic force is then integrated along the circumference to calculate the electromagnetic torque. At the same time, the torque fluctuation is obtained by combining the non-sinusoidal distribution characteristics of the permanent magnet magnetic field obtained by simulation. Finally, the tangential electromagnetic force, axial electromagnetic force, and torque fluctuation are determined as the excitation characteristic parameters.

[0032] Accordingly, as a possible implementation, step 210 may include the following steps: Step 210 - 1 , using finite element simulation software to simulate the electromagnetic excitation model of the motor, calculating the tangential electromagnetic force density using the Maxwell stress tensor method and multiplying it by the effective area to obtain the tangential electromagnetic force.

[0033] Among them, finite element simulation software is a software that performs numerical calculations by discretizing the model into a finite number of units. It can be used to simulate the electromagnetic field distribution and electromagnetic force calculation in the electromagnetic excitation model of the motor; the Maxwell stress tensor method is a method based on electromagnetic field theory that determines the electromagnetic force density by calculating the stress tensor of the electromagnetic field in space. It is suitable for calculating the electromagnetic force in the air gap of the motor; the tangential electromagnetic force density is the tangential electromagnetic force per unit area. It is an intermediate calculation result of the Maxwell stress tensor method. The total amount of the tangential electromagnetic force needs to be further solved in combination with the effective area; the effective area is the area of ​​the stator and rotor surface or air gap area where the tangential electromagnetic force acts in the electromagnetic excitation model of the motor. It is determined by finite element mesh division and is used to convert the electromagnetic force density into actual force; the tangential electromagnetic force is the force generated by the electromagnetic effect in the tangential direction when the motor is running.

[0034] In the disclosed embodiments, when simulating the motor's electromagnetic excitation model using finite element simulation software, the Maxwell stress tensor method can be used to calculate the tangential electromagnetic force density exerted by the electromagnetic field in the air gap on the motor's stator and rotor surfaces. This tangential electromagnetic force density is then multiplied by the corresponding area of ​​action to obtain the specific value of the tangential electromagnetic force. Based on electromagnetic field theory, this method converts the complex electromagnetic interactions within the motor into stress tensor calculations. Finite element discretization is then used to accurately determine the tangential electromagnetic force.

[0035] The Maxwell stress tensor method combined with finite element simulation to calculate the tangential electromagnetic force fully accounts for the nonlinear characteristics of the motor's air gap magnetic field distribution and the influence of the stator and rotor structures. Compared to traditional simplified algorithms, this method more accurately reflects the dynamic changes of the electromagnetic force under different operating conditions. This step provides precise tangential excitation input for subsequent vibration analysis of the electric drive system, enabling the model to more realistically simulate the effects of the motor's electromagnetic excitation on the gear system and housing vibration, effectively improving the accuracy of multi-physics coupling analysis and laying a solid foundation for locating the root causes of noise and vibration problems.

[0036] Step 210 - 2 : Based on the electromagnetic power, motor speed, and core length parameters, the axial electromagnetic force is obtained by solving.

[0037] Among them, electromagnetic power is the power converted from electromagnetic energy when the motor is running, which is equal to the product of electromagnetic torque and motor angular velocity, and its unit is watt (W). It is a key parameter to characterize the energy conversion efficiency of the motor and is used to establish a mathematical relationship between electromagnetic force and speed; motor speed is the rotation speed of the motor rotor per unit time, usually in revolutions per minute (r / min), which directly affects the magnetic field rotation frequency and the fluctuation characteristics of the electromagnetic force, and is a dynamic input parameter in the calculation of axial electromagnetic force; core length is the axial length of the motor stator or rotor core, which affects the distribution range and magnetic flux density of the axial magnetic field. It is a geometric parameter to characterize the structural characteristics of the motor in the calculation of axial electromagnetic force, and is used to correct the effective area of ​​the magnetic field; axial electromagnetic force is the force along the motor axis generated by the interaction of the electromagnetic field when the motor is running, which may cause axial movement of the motor shaft or changes in the axial load of the bearing, and is an important excitation source causing axial vibration of the electric drive system.

[0038] In the disclosed embodiments, when solving for the axial electromagnetic force based on the parameters of electromagnetic power, motor speed, and core length, the electromagnetic torque can be first calculated based on the relationship that electromagnetic power equals the product of electromagnetic torque and motor angular velocity, combined with the motor speed. The effect of core length on the distribution range of the axial magnetic field is then considered. An axial electromagnetic force calculation model that includes electromagnetic power, motor speed, and core length is established through electromagnetic theory to further solve for the axial electromagnetic force. Specifically, electromagnetic power reflects the efficiency of motor energy conversion, motor speed determines the frequency of magnetic field rotation, and core length affects the range of the axial magnetic field. These three factors together contribute to the quantitative calculation of the axial electromagnetic force, ultimately resulting in the specific numerical value of the axial electromagnetic force through a mathematical model.

[0039] By integrating multiple parameters, such as electromagnetic power, motor speed, and core length, to solve for the axial electromagnetic force, the energy conversion characteristics and structural parameter effects of the motor's actual operation are fully considered, avoiding the limitations of traditional simplified models that only consider a single magnetic field component. The solved axial electromagnetic force accurately reflects the changes in the motor's axial magnetic pull at different speeds, providing a key input for the calculation of bearing support forces in subsequent rigid-flexible coupling dynamic models. This enables the model to more realistically simulate the effects of motor axial vibration on the gear system and housing, improving the accuracy of multi-physics coupling analysis of electric drive systems and providing a reliable theoretical basis for controlling axial vibration noise.

[0040] Step 210 - 3 : Calculate the electromagnetic torque by integrating the tangential electromagnetic force along the circumference, and obtain the torque fluctuation by combining the non-sinusoidal distribution characteristics of the permanent magnet magnetic field obtained by simulation.

[0041] Among them, the circular integral refers to the integration operation of the tangential electromagnetic force on the entire circumference of the motor stator and rotor air gap, which is used to solve the resultant torque of the tangential electromagnetic force on the axis at each point, that is, the electromagnetic torque. It is a calculation method for converting force into torque. The electromagnetic torque is the torque that drives the motor rotor to rotate obtained by the circumferential integration of the tangential electromagnetic force, and its unit is , its size and stability directly affect the power output and vibration characteristics of the motor; the non-sinusoidal distribution characteristic of the permanent magnet magnetic field is that the magnetic field generated by the permanent magnet is not an ideal sinusoidal waveform distribution in space, but contains high-order harmonic components. This characteristic is determined by factors such as the nonlinearity of the magnetization curve of the permanent magnet material, the shape of the magnetic poles and the arrangement, which will cause electromagnetic torque fluctuations; torque fluctuations are the periodic fluctuations caused by the change of electromagnetic torque with the rotor position during the operation of the motor. It is usually characterized by fluctuation amplitude and frequency. It is one of the important reasons for motor vibration and noise, especially under high-speed conditions. The impact is more significant.

[0042] In the disclosed embodiments, the electromagnetic torque is calculated by integrating the tangential electromagnetic force along the circumference, and then combined with the non-sinusoidal distribution characteristics of the permanent magnet magnetic field obtained by simulation to obtain torque fluctuations. Specifically, the distribution of the tangential electromagnetic force on the circumference of the motor's stator and rotor air gap is not uniform and constant, and an integral operation is required to calculate the resultant torque on the entire circumference, i.e., the electromagnetic torque. However, due to the material properties and structural design of the permanent magnet magnetic field, this non-sinusoidal characteristic causes the electromagnetic torque to fluctuate periodically during the motor's rotation. By simulating and analyzing the magnetic field distribution and introducing this characteristic, the amplitude and frequency characteristics of the torque fluctuations can be accurately calculated.

[0043] By integrating the electromagnetic torque and combining it with the non-sinusoidal distribution characteristics of the permanent magnet's magnetic field, the dynamic changes in torque during motor operation can be accurately reflected. Traditional methods often assume a sinusoidal magnetic field distribution, ignoring the impact of actual non-sinusoidal characteristics on torque. This step accurately obtains the magnetic field distribution through simulation, making the calculation of torque fluctuations more consistent with the actual operating conditions of the motor. This provides more accurate torsional excitation input for subsequent vibration analysis of the electric drive system. In particular, for noise issues such as high-frequency whine caused by torque fluctuations, it can be accurately quantified at the excitation source level, providing a reliable basis for the formulation of noise control strategies.

[0044] Step 210 - 4 : Determine the tangential electromagnetic force, the axial electromagnetic force, and the torque fluctuation as excitation characteristic parameters.

[0045] Among them, the tangential electromagnetic force reflects the electromagnetic driving force in the direction of motor rotation, the axial electromagnetic force reflects the magnetic pull characteristics of the motor's axial direction, and the torque fluctuation quantifies the dynamic changes in torque caused by the non-sinusoidal distribution of the magnetic field. The three together constitute the core parameter system that describes the electromagnetic excitation of the motor.

[0046] Identifying tangential electromagnetic force, axial electromagnetic force, and torque fluctuation as excitation characteristic parameters comprehensively captures the multi-dimensional characteristics of the motor's electromagnetic excitation, providing standardized excitation input for the dynamic analysis of electric drive systems. By integrating the tangential and axial force components and torque fluctuation parameters during motor operation, this step avoids the one-sidedness of traditional single-parameter analysis. This enables the subsequent rigid-flexible coupling dynamic model to simultaneously consider the effects of the motor's electromagnetic excitation in different directions, as well as the impact of torque fluctuation on the gear system's torsional vibration. This improves the completeness and accuracy of the system's vibration characteristic analysis, providing a multi-dimensional quantitative basis for noise source identification and optimized design.

[0047] Step 220: Based on the gear system dynamics model, a helical gear coupling vibration equation group is established for multiple gear pairs, multiple gears, and the three degrees of freedom (tangential, axial, and torsional). Based on the helical gear coupling vibration equation group, the gear meshing dynamic load parameters, including the tangential dynamic meshing force and axial dynamic meshing force of the gear pairs, the torsional vibration load spectrum during multi-gear meshing, and the load variation data, are calculated.

[0048] For the embodiments of the present disclosure, a coupled vibration equation set for helical gears with multiple pairs of gear pairs, multiple gears, and three degrees of freedom (tangential, axial, and torsional) can be established based on the dynamic model of the gear system. Specifically, based on the dynamic model of the gear system, the three degrees of freedom of the helical gears in the tangential, axial, and torsional directions are considered for the working conditions of multiple pairs of gear pairs and multiple gear switching, and a coupled vibration equation set that can reflect the vibration characteristics in these three directions is established. By comprehensively considering the effects of the motor's electromagnetic excitation, the internal excitation of the helical gears, and the multi-stage transmission, the equation set is solved to obtain the tangential dynamic meshing force and axial dynamic meshing force of the gear pair. The torsional vibration load spectrum and load variation data are then calculated using the gear base circle radius and the load torque, ultimately determining the dynamic load parameters of the gear meshing.

[0049] For the embodiment of the present disclosure, as a possible implementation, calculating the gear meshing dynamic load parameters based on the helical gear coupled vibration equations in step 220 may include the following steps: Step 220 - 1 : Based on the helical gear coupled vibration equations, a dynamic equation including tangential, axial, and torsional vibration characteristics is established.

[0050] Among them, the tangential vibration characteristic is the translational vibration of the gear in the tangential direction of the circle, which is caused by the tangential dynamic meshing force, corresponds to the displacement variable in the y direction in the dynamic equation, and affects the smoothness of the gear rotation; the axial vibration characteristic is the translational vibration of the gear along the axis, which is caused by the axial dynamic meshing force and the axial component force generated by the helix angle of the helical gear, corresponds to the displacement variable in the z direction, and is related to the axial load of the bearing and the axial vibration of the housing; the torsional vibration characteristic is the rotational vibration of the gear around the axis, which is caused by the torque and torque fluctuation generated by the tangential force through the base circle radius, corresponds to the angular displacement variable θ, and is the main factor causing the torsional vibration noise of the gear pair.

[0051] For the embodiments of the present disclosure, based on the constructed multiple pairs of gear pairs, multiple gears and three-degree-of-freedom helical gear coupling vibration equations, the displacements of the gear pairs in the tangential (translational vibration), axial (translational vibration) and torsional (rotational vibration) directions are used as variables, and the inertial force, damping force and elastic force of the vibration in each direction are described by the mass matrix, damping matrix and stiffness matrix, thereby establishing a dynamic equation that takes into account the three-directional coupling effect.

[0052] By establishing three-degree-of-freedom coupled dynamic equations, a unified description of the multi-directional vibration characteristics of helical gear transmission systems can be achieved. Compared with traditional single-degree-of-freedom or decoupled models, this can more accurately reflect the bending-torsion-axis coupled vibration characteristics of helical gear pairs in actual operation. For example, the dynamic meshing force in the tangential vibration equation will affect the torsional vibration equation through the base circle radius, and the bearing support stiffness in the axial vibration equation will couple with the housing flexibility model. This multi-dimensional coupled modeling provides a theoretical basis for the precise solution of the dynamic load parameters of gear meshing, allowing the calculated tangential / axial dynamic meshing forces and torsional vibration loads to more realistically reflect the stress state of the gear system under complex operating conditions, laying a key foundation for subsequent rigid-flexible coupling dynamic analysis.

[0053] Step 220-2: Comprehensively consider the influence of the motor electromagnetic excitation, the internal excitation of the helical gear, and the multi-stage transmission, solve the dynamic equation, and obtain the tangential dynamic meshing force and the axial dynamic meshing force of the gear pair.

[0054] Among them, the electromagnetic excitation of the motor is the tangential electromagnetic force, axial electromagnetic force and torque fluctuation generated by the interaction of the electromagnetic field when the motor is running. It is input into the dynamic equation as an external excitation and affects the vibration characteristics of the gear pair. The internal excitation of the helical gear is the excitation generated by factors such as time-varying meshing stiffness, gear manufacturing error, meshing impact, etc. during the helical gear transmission process. It is the internal cause of the dynamic meshing force fluctuation of the gear pair and needs to be reflected in the dynamic equation through the stiffness matrix and time-varying parameters. The influence of multi-stage transmission is the transmission ratio, load distribution and shaft stiffness of each gear pair in the multi-stage gear transmission system. The influence of the dynamic meshing force of the target gear pair needs to be reflected through the coupling of the mass matrix and the stiffness matrix in the dynamic equation; the tangential dynamic meshing force is the dynamic force acting along the tangential direction of the circumference during the meshing process of the gear pair, which is generated by the combined action of the tangential electromagnetic force of the motor, the tangential component of the helical gear meshing and the time-varying stiffness excitation, which can affect the smoothness of gear rotation; the axial dynamic meshing force is the dynamic force acting along the axial direction during the meshing process of the gear pair, which is determined by the axial electromagnetic force of the motor, the axial component generated by the helix angle of the helical gear and the bearing support stiffness, which can affect the axial load of the bearing and the vibration of the housing.

[0055] For the embodiments of the present disclosure, based on the established helical gear coupled vibration dynamics equations containing tangential, axial and torsional degrees of freedom, the tangential electromagnetic force, axial electromagnetic force and torque fluctuation in the motor electromagnetic excitation can be used as external excitation inputs. At the same time, internal excitations such as the time-varying meshing stiffness and error excitation of the helical gears, as well as the load distribution relationship of each gear pair in the multi-stage gear transmission are considered. The dynamic equations are iteratively solved through numerical methods (such as the Runge-Kutta method), and finally the dynamic meshing force of the gear pair that changes with time in the tangential and axial directions is obtained.

[0056] By solving the dynamic equations through multi-source excitation coupling, accurate calculation of the dynamic load of the gear pair can be achieved. The introduction of motor electromagnetic excitation enables the model to reflect the influence of electromagnetic force fluctuations on gear meshing. The consideration of the internal excitation of the helical gear can ensure that the effects of factors such as time-varying meshing stiffness and manufacturing errors on the dynamic meshing force are accurately characterized, while the inclusion of the influence of multi-stage transmission ensures the rationality of the load distribution of multiple gear pairs. The solved tangential / axial dynamic meshing force can truly reflect the gear stress state of the electric drive system under complex working conditions, and can provide key data support for gear strength verification, bearing life calculation and system vibration and noise analysis, effectively improving the reliability and optimization accuracy of the electric drive system design.

[0057] Step 220 - 3 : Calculate the torsional vibration load using the gear base circle radius and the load torque, and obtain the torsional vibration load spectrum and load variation data when multiple gears are engaged.

[0058] Among them, the gear base circle radius is the radius of the gear base circle and is one of the basic geometric parameters of the gear. It is used to calculate the gear tooth shape and meshing characteristics. In the calculation of torsional vibration load, it is used to convert torque into tangential force. The load torque is the torque borne by the gear during the transmission process. It is obtained by distributing the motor output torque through multiple transmission stages and reflects the load size of the gear pair under actual working conditions. The torsional vibration load is the dynamic load borne by the gear in the torsional direction. It is generated by the tangential force through the base circle radius. Its fluctuation will cause torsional vibration of the gear and is one of the important factors causing vibration and noise in the gear system. Multi-gear meshing refers to the meshing state of the gear transmission system in different gears. Different gears correspond to different transmission ratios and torque distributions. The torsional vibration load will change with the gear position. The torsional vibration load spectrum is the frequency-amplitude distribution diagram obtained by Fourier transforming the torsional vibration load. It is used to analyze the frequency components of the torsional vibration load and the amplitude of each frequency component. The load change data is the data of the torsional vibration load changing over time, recording the load values ​​at different times and used to describe the dynamic change process of the load.

[0059] In the disclosed embodiments, the tangential force of the meshing gear pair can be determined by multiplying the load torque and the base circle radius, based on the known base circle radius. This is combined with the multi-gear transmission ratios and the torque distribution relationships within each gear to calculate the torsional vibration loads during meshing at different gears. By performing a Fourier transform on the torsional vibration load, its spectral characteristics are obtained, and the load variation over time is recorded, thereby obtaining the torsional vibration load spectrum and load variation data.

[0060] By combining the base circle radius with the load torque to calculate the torsional vibration load, the torsional stress state of the gear pair under different gears can be accurately reflected. The base circle radius, as a basic geometric parameter of the gear, directly affects the conversion of torque to tangential force; the load torque reflects the load magnitude under actual working conditions. The torsional vibration load calculated by combining the two can truly reflect the load changes during multi-gear engagement. The load spectrum characteristics obtained through spectral analysis can reveal the frequency components of the torsional vibration load, providing a basis for identifying the resonant frequency and vibration noise source of the gear system; the load change data provides quantitative support for gear strength design and system dynamic characteristics analysis, helping to improve the operating reliability of the electric drive system under multi-gear conditions.

[0061] Step 220-4: Determine the gear pair's tangential dynamic meshing force, axial dynamic meshing force, torsional vibration load spectrum, and load variation data as gear meshing dynamic load parameters.

[0062] Among them, the tangential dynamic meshing force reflects the dynamic force along the tangential direction when the gear pair is meshing, the axial dynamic meshing force reflects the load characteristics in the axial direction, the torsional vibration load spectrum quantifies the frequency component of the torsional direction load, and the load change data records the dynamic changes of the load over time under each gear. The four together constitute the core parameter system that describes the dynamic load of gear meshing.

[0063] Determining the gear pair's tangential dynamic meshing force, axial dynamic meshing force, torsional vibration load spectrum, and load variation data as gear meshing dynamic load parameters comprehensively covers the multi-dimensional load characteristics during gear meshing, providing standardized load input for the dynamic analysis of electric drive systems. This step avoids the one-sidedness of traditional single-parameter analysis by integrating the gear pair's tangential and axial force components and the torsional load spectrum and variation data. This enables the subsequent rigid-flexible coupling dynamic model to simultaneously consider the effects of gear meshing loads in different directions, as well as the dynamic changes in loads during multi-gear shifting. This improves the completeness and accuracy of the system's vibration characteristic analysis and provides a multi-dimensional quantitative basis for gear strength verification, bearing life calculation, and noise source identification.

[0064] Step 230: Using the excitation characteristic parameters and the gear meshing dynamic load parameters as the mechanical excitation of the gear system, the motor electromagnetic excitation model, the gear system dynamics model, the bearing rigidity model, and the housing flexibility model are coupled to form a rigid-flexible coupling dynamics model.

[0065] In the disclosed embodiments, excitation characteristic parameters such as the tangential electromagnetic force, axial electromagnetic force, and torque fluctuation obtained from the motor electromagnetic excitation model, along with gear meshing dynamic load parameters such as the tangential dynamic meshing force, axial dynamic meshing force, torsional vibration load spectrum, and load variation data obtained from the gear system dynamics model, can be used as mechanical excitation sources and input into the corresponding models. By considering the force transmission relationship between the motor and gear, the support constraints between the gear and bearing, and the rigid-flexible coupling between the bearing and housing, the dynamic equations of each model are combined to establish a multi-physics coupled dynamic equation that includes the motor electromagnetic excitation, gear system vibration, bearing rigid support, and housing flexible deformation, thereby forming a rigid-flexible coupled dynamic model that comprehensively reflects the dynamic interaction between the rigid and flexible components of the electric drive system. This model enables coupled analysis of the dynamic characteristics of key components such as the motor, gears, shaft, bearing, and housing, covering the gear system's multi-degree-of-freedom vibration variables in the tangential, axial, and torsional directions, providing a more accurate model foundation for vibration and noise analysis of the electric drive system.

[0066] Accordingly, step 230 may include the following steps: Step 230 - 1 : Establish a bearing support stiffness matrix corresponding to the bearing rigidity model, and perform condensation processing on the shell flexibility model to obtain a shell mass matrix, a shell damping matrix, and a shell condensation stiffness matrix.

[0067] For the disclosed embodiments, a bearing rigidity model with stiffness as the core can be established based on the relationship between bearing displacement deformation and external force load, and a bearing support stiffness matrix that characterizes the bearing support characteristics can be determined based on the bearing rigidity model. Specifically, the displacement deformation generated by the bearing when subjected to radial, axial and other external force loads can be analyzed, and a mathematical relationship between load and displacement can be established using Hooke's law (stress is proportional to strain), thereby constructing a bearing rigidity model with stiffness as the core. This model simplifies the bearing into a support element with specific stiffness parameters, obtains the stiffness values ​​of the bearing in different directions through experimental testing or theoretical calculations, and then forms a stiffness matrix that characterizes the bearing support characteristics, which is used to describe the bearing's ability to resist deformation in each degree of freedom.

[0068] At the same time, the finite element substructure analysis method can also be used to condense the shell flexible model to obtain the shell mass matrix, shell damping matrix and shell condensed stiffness matrix used to describe the flexible vibration characteristics of the shell. Specifically, the shell structure can be divided into multiple substructures, and the dynamic equations of the complete shell model can be established using the finite element method. Then, through modal analysis or static condensation methods, the high-order degree of freedom system can be condensed into a low-order system, retaining key modal information. The mass matrix, damping matrix and condensed stiffness matrix obtained after the condensation process can significantly reduce the model's degrees of freedom while ensuring calculation accuracy, efficiently describe the flexible vibration characteristics of the shell, and provide parameter support for the shell's flexible deformation for the rigid-flexible coupling dynamic model.

[0069] Among them, bearing displacement deformation is the radial, axial or angular displacement deformation generated by the bearing when it is subjected to external force load. Its size is proportional to the load and is the basic parameter for establishing the bearing rigidity model; the bearing rigidity model simplifies the bearing into a mechanical model with specific stiffness properties, ignores the complex internal structure of the bearing, and describes its support characteristics with stiffness as the core, which is used for rigid-flexible coupling dynamic analysis; the bearing support stiffness matrix is ​​a matrix composed of the stiffness values ​​of the bearing in each degree of freedom (such as radial, axial, and torsion), which characterizes the ability of the bearing to resist deformation in different directions and is used to describe support constraints in dynamic equations; the finite element substructure analysis method is a finite element method that divides a complex structure into multiple substructures, solves them separately and then assembles them, which can reduce the degree of freedom of the model and improve calculation efficiency; The body flexibility model is a dynamic model that takes into account the elastic deformation of the shell structure. It is used to describe the flexible characteristics of the shell under vibration load, which is different from the rigid model that ignores deformation; the condensation treatment is the process of reducing the high-order finite element model to a low-order model through methods such as modal truncation or static condensation, retaining the main vibration modes to ensure calculation accuracy; the shell mass matrix is ​​a matrix that characterizes the mass distribution of the shell, describes the inertia force in the dynamic equation, and is obtained through finite element discretization calculation; the shell damping matrix is ​​a matrix that describes the energy dissipation characteristics of the shell during vibration, reflecting the attenuation effect of material damping and structural damping on vibration; the shell condensation stiffness matrix is ​​a matrix that characterizes the elastic stiffness of the shell after condensation treatment, which is used to describe the relationship between the flexible deformation of the shell and the load, retaining key stiffness characteristics.

[0070] By establishing a bearing rigidity model and determining the bearing support stiffness matrix, a quantitative description of the bearing support characteristics can be achieved. This model accurately reflects the rigid support effect of the bearing under different loads, providing reliable boundary conditions for gear system vibration analysis. Using finite element substructuring analysis to shrink the housing model reduces model complexity while preserving the housing's key vibration characteristics, improving the computational efficiency of the rigid-flexible coupling dynamics model.

[0071] Step 230 - 2 : Based on the bearing support stiffness matrix and the housing condensation stiffness matrix, connect the gear system dynamics model and the housing flexibility model to establish a mechanical transmission path between the gear system and the housing.

[0072] Among them, the mechanical transmission path refers to the path through which the vibration of the gear system is transmitted to the housing through the bearing, and at the same time the flexible reaction force of the housing is fed back to the gear system. It is jointly constructed by the bearing support stiffness matrix and the housing contraction stiffness matrix. It is a mechanical bridge connecting the gear system and the housing, and can realize the two-way transmission of vibration between the two.

[0073] For the embodiment of the present disclosure, based on the bearing support stiffness matrix and the shell contraction stiffness matrix, the gear system dynamic model and the shell flexibility model are connected. The essence is to build a mechanical bridge for transmitting the vibration of the gear system to the shell through the bearing: the vibration generated by the gear system under the electromagnetic excitation of the motor and the dynamic load of the gear meshing will be converted into a force on the shell through the bearing support stiffness matrix, and the flexible response characteristics of the shell are quantified by the shell contraction stiffness matrix. At the same time, the flexible reaction force of the shell will also be fed back to the gear system through this path, thereby realizing the two-way transmission of vibration between the two and forming a complete mechanical transmission path.

[0074] Realizing the mechanical coupling between the gear system and the housing through the bearing support stiffness matrix can significantly improve the accuracy and completeness of the rigid-flexible coupling dynamics model. First, by coordinating the bearing support stiffness matrix with the housing contraction stiffness matrix, the accuracy of the vibration transmission path can be ensured, so that the excitation of the gear system vibration on the housing and the reaction of the housing flexibility on the gear system can be accurately quantified; second, combining the mass matrix and damping matrix after the housing contraction process can provide a reliable parameter basis for the subsequent construction of the rigid-flexible coupling dynamics equation, thereby improving the accuracy of the rigid-flexible coupling dynamics model of the entire electric drive system; third, this connection method takes into account the coupling effect between multiple components, so that the model can more realistically reflect the dynamic characteristics of the electric drive system, providing effective theoretical support for analyzing system vibration, noise and other issues, and helping to optimize the NVH performance of the electric drive system.

[0075] Step 230 - 3 : Substitute the excitation characteristic parameters and the gear meshing dynamic load parameters into the gear system dynamics model to achieve coupling between the motor electromagnetic excitation model and the gear system dynamics model.

[0076] The excitation characteristic parameters are derived from the motor's electromagnetic excitation model and include tangential electromagnetic force, axial electromagnetic force, and torque fluctuation. These parameters are transmitted to the driving gear via the motor shaft, driving the gear system to produce tangential, axial, and torsional vibrations. The gear meshing dynamic load parameters, such as tangential and axial meshing forces, are intrinsic excitations calculated based on the meshing characteristics of the gear pair in the gear system's dynamics model. These quantify the dynamic loads during the meshing process. When these two parameters are input into the gear system's dynamics model as mechanical excitation, the motor's electromagnetic energy is converted into the gear system's mechanical vibration energy through electromagnetic force, torque, and other forms. This creates a linkage between the motor's electromagnetic excitation and the gear system's vibration response, thereby achieving dynamic coupling between the two models.

[0077] The effects of this coupling method are mainly reflected in three aspects: First, it realizes the precise correlation between the energy and mechanical transmission between the motor and the gear system, so that the model can truly reflect the transformation process of "electromagnetic excitation-mechanical vibration" in the electric drive system, overcoming the defect of the traditional model that separates the connection between the motor and the gear system; Second, by integrating exogenous electromagnetic excitation and endogenous gear meshing excitation, it can fully capture the composite vibration inducement of the gear system, improve the accuracy of the dynamic model's representation of the system's vibration characteristics, and provide a reliable basis for analyzing noise problems such as high-frequency howling under high-speed conditions; Third, it lays the foundation for the subsequent construction of a rigid-flexible coupling model including bearings and housings, making the multi-component coupling analysis of the entire electric drive system more coherent, and helping to optimize the system structure to improve NVH performance.

[0078] Step 230-4: Integrate the output excitation of the motor electromagnetic excitation model and the gear meshing intrinsic excitation, combine the shell mass matrix, shell damping matrix and shell condensation stiffness matrix, and construct the rigid-flexible coupling dynamic equation corresponding to the rigid-flexible coupling dynamic model.

[0079] Among them, the output excitation is obtained by the electromagnetic excitation model of the motor through electromagnetic mechanical energy conversion, and the gear meshing endogenous excitation is calculated based on the meshing characteristics of the gear pair in the gear system dynamics model.

[0080] In the disclosed embodiments, the mechanical excitation (i.e., output excitation) generated by the motor's electromagnetic excitation through energy conversion can be coupled with the intrinsic excitation generated by time-varying stiffness and other characteristics during the meshing of the gear pair. The mass, damping, and condensation stiffness parameters of the housing's flexible model are then introduced to establish multi-physics field simultaneous equations. Specifically, the electromagnetic excitation is transmitted to the gear system via the motor shaft, driving the tangential, axial, and torsional vibrations of the gears. The intrinsic excitation of the gear meshing further enhances the dynamic load effect, while the mass, damping, and stiffness characteristics of the housing are coupled to the gear system via the bearing support stiffness matrix, forming a rigid-flexible coupling dynamic equation encompassing the motor, gear, bearing, and housing, achieving a mathematical description of the dynamic interactions among the multiple components of the electric drive system.

[0081] By integrating multi-source excitation and shell flexibility parameters to construct rigid-flexible coupling dynamic equations, the accuracy and completeness of the electric drive system model can be significantly improved. The coupling of the motor's electromagnetic excitation and the intrinsic excitation of the gear meshing ensures that the model can capture the complete transmission process from electromagnetic energy to mechanical vibration; the introduction of shell flexibility parameters enables the model to reflect the reaction of the shell's elastic deformation to the system's vibration, avoiding the limitations of traditional rigid models. The constructed dynamic equations can be solved to obtain the vibration response of components such as the motor rotor, gears, and shell in multiple degrees of freedom, such as gear tangential displacement and shell axial vibration acceleration, providing a quantitative basis for system vibration and noise source identification, component strength verification, and optimized design.

[0082] Step 240: Convert the rigid-flexible coupling dynamics model into a state-space equation, solve the state-space equation by dimensionless transformation and piecewise linear method, and obtain multivariate time-domain data.

[0083] For the embodiment of the present disclosure, step 240 may include the following steps: Step 240 - 1 : By defining a state vector including the displacement and velocity of the system, the rigid-flexible coupling dynamics equation corresponding to the rigid-flexible coupling dynamics model is transformed from a second-order differential equation to a first-order state space equation group.

[0084] For the embodiments of the present disclosure, the displacement variables (such as the tangential displacement of the gear and the axial deformation of the housing) and their first-order derivatives (velocity) in the rigid-flexible coupling dynamic model can be combined into a state vector, and then the second-order differential equations can be reconstructed into a first-order equation group using matrix operations.

[0085] State-space transformation can improve the solution efficiency and applicability of rigid-flexible coupling dynamic models. First-order state-space equations are more suitable for iterative solution using numerical integration algorithms (such as the Runge-Kutta method), which significantly reduces the amount of computation compared to second-order differential equations and is particularly suitable for transient response analysis of complex systems with multiple degrees of freedom. Furthermore, the state-space form facilitates the introduction of system analysis methods from modern control theory (such as modal analysis and frequency-domain response analysis), allowing for intuitive acquisition of system parameters such as eigenvalues ​​and transfer functions, providing a mathematical foundation for stability assessment, vibration mode identification, and active control strategy design for electric drive systems.

[0086] Step 240 - 2 : Select characteristic reference quantities for the physical parameters in the state-space equation, and convert the physical parameters into dimensionless quantities based on the characteristic reference quantities to obtain the dimensionless state-space equation.

[0087] Physical parameters refer to quantities with actual physical meaning in state-space equations, such as time parameters (representing the time the system operates), displacement parameters (representing the position change of components), and coefficients such as mass, damping, and stiffness involved in the equations. These parameters all have specific physical units. Characteristic reference quantities are benchmark quantities used for dimensionless transformation and may include at least: a characteristic time reference quantity, which represents the typical time scale in the system and is usually selected from the periodicity of the system itself, such as the period of a gear meshing cycle or the period of the electromagnetic force change in a motor; a characteristic displacement reference quantity, which is used to measure the reference displacement of the system's vibration amplitude and is generally taken as the maximum displacement of a component during vibration, such as the maximum displacement of a gear along the meshing line during meshing; a dimensionless quantity is a unitless value obtained by dividing a physical parameter by its corresponding characteristic reference quantity. It reflects the proportional relationship between the physical parameter and the characteristic reference quantity and is independent of a specific unit system. A dimensionless state-space equation is an equation obtained by converting all physical parameters in the original state-space equation into dimensionless quantities. In this case, the matrices and vectors in the equation are dimensionless, which facilitates universal dynamic analysis and comparison between different systems.

[0088] For the embodiments of the present disclosure, when processing state-space equations, one can first select appropriate characteristic reference quantities for the physical parameters in the equation (such as time and displacement), such as determining a characteristic time reference quantity (which can be understood as a representative length of time in the system, such as the time it takes for a gear to complete a meshing) and a characteristic displacement reference quantity (such as the maximum displacement that a gear can reach when vibrating). Then, using these characteristic reference quantities as a benchmark, all physical parameters that originally had actual units are converted into unitless values. For example, dividing the actual time by the characteristic time reference quantity yields dimensionless time; dividing the actual displacement by the characteristic displacement reference quantity yields dimensionless displacement. Through such a conversion, the original state-space equation becomes a dimensionless state-space equation, and the various parameters in the equation no longer have specific physical units, but instead become relative numerical relationships.

[0089] By nondimensionalizing the state-space equations, on the one hand, the state-space equations are no longer restricted by specific system parameters. Regardless of the specifications of the gearbox or the housing materials, they can be analyzed in a unified form, making it easier to compare the dynamic characteristics of different systems. On the other hand, nondimensionalization can avoid calculation problems caused by large differences in parameter units, making the numerical solution process more stable and efficient. In addition, the parameters in the dimensionless equations can more directly reflect the essential characteristics of the system. For example, the vibration frequency and damping level of the system can be more intuitively seen.

[0090] Step 240-3: Based on the nonlinear characteristics of the rigid-flexible coupling dynamic model, the time-varying parameters in the state-space equation are divided into multiple linear intervals according to different working conditions. In each linear interval, a linear solution is performed based on the dimensionless state-space equation to obtain multivariate time-domain data.

[0091] In specific application scenarios, due to the nonlinear characteristics of rigid-flexible coupling dynamic models (such as the variation of gear mesh stiffness with load and the nonlinearity of housing flexible deformation), it is necessary to divide the time-varying parameters in the state-space equations (i.e., time-varying parameters such as time-varying mesh stiffness and nonlinear damping) into multiple linear intervals according to different operating conditions (such as changes in motor speed and load torque). Within each linear interval, the time-varying parameters can be approximately regarded as constant values. Then, a linear solution is performed based on the dimensionless state-space equations to obtain the variation data of multiple variables in the system (such as gear tangential displacement, housing vibration velocity, bearing load, etc.) in the time dimension, that is, multivariable time domain data. This processing can transform complex nonlinear problems into multiple linear problems to be solved, facilitating engineering applications.

[0092] By dividing the linear interval and solving the dimensionless equations, the nonlinear solution problem of the rigid-flexible coupling model can be effectively solved. On the one hand, by linearizing the time-varying parameters piecewise, mature linear system solution methods can be used in each interval to improve computational efficiency and stability, and avoid the convergence difficulties of directly solving nonlinear equations; on the other hand, multivariable time domain data can fully reflect the dynamic response of the system under different working conditions. For example, the fluctuation of dynamic load over time during gear meshing and the real-time change of housing vibration amplitude can be obtained, providing detailed time domain data support for system vibration noise analysis and component fatigue life assessment. In addition, this method takes into account both model accuracy and engineering practicality, and can be closer to the actual operating conditions of the electric drive system.

[0093] Step 250: Using the electromagnetic excitation in the excitation characteristic parameters as input energy, combined with the gear meshing dynamic load parameters and multivariate time domain data, calculate the transmission efficiency value of the vibration energy among the motor, gears, bearings and housing components through the principle of energy conservation.

[0094] For the embodiments of the present disclosure, the energy provided by the electromagnetic excitation of the motor can be first regarded as the total input energy of the system, and then the energy consumed or transmitted during the gear meshing process can be determined with the help of the dynamic load parameters of the gear meshing, such as the tangential meshing force, the axial meshing force, etc. At the same time, the multivariate time domain data, such as the displacement and velocity changes of each component over time, are used to calculate the changes in kinetic energy and potential energy of each component during the vibration process. Finally, according to the principle of conservation of energy, the input energy is compared with the energy transferred and consumed between the components to obtain the transmission efficiency value of the vibration energy between different components, thereby evaluating the energy transfer between the components of the electric drive system.

[0095] Accordingly, when calculating the transmission efficiency of vibration energy among the motor, gears, bearings, and housing components using the principle of conservation of energy, step 250 of the embodiment may include the following steps: Step 250 - 1 : Calculate the motor input energy during the running time based on the tangential electromagnetic force, axial electromagnetic force, and torque fluctuation in the excitation characteristic parameters.

[0096] In the disclosed embodiments, when calculating the motor input energy during the motor's operating time based on the tangential electromagnetic force, axial electromagnetic force, and torque ripple in the excitation characteristic parameters, these three types of electromagnetic excitations can be multiplied by the corresponding speed parameters, and then the total energy can be obtained by integrating and summing. The calculation method can be to integrate and sum the product of the tangential electromagnetic force and the tangential velocity, the product of the axial electromagnetic force and the axial velocity, and the product of the torque ripple and the motor's angular velocity to obtain the motor input energy. Specifically, the tangential electromagnetic force is the force along the tangential direction of the motor during operation. It is multiplied by the tangential velocity of the motor rotor to obtain the tangential power; the axial electromagnetic force is the force along the motor axis. It is multiplied by the rotor axial velocity to obtain the axial power; the torque ripple is the periodic variation of the motor's electromagnetic torque. It is multiplied by the motor angular velocity to obtain the power in the torsional direction. By integrating and summing the powers in these three directions during the motor's operating time, the total input energy of the motor during that time period can be obtained. This calculation method takes into account the energy input of the motor's electromagnetic excitation in multiple directions.

[0097] Among them, the motor input energy is the total energy obtained by the motor from the electromagnetic excitation during operation. It is obtained by integrating and summing the products of the electromagnetic excitation in each direction and the corresponding speed parameters. It is an important indicator to measure the motor energy input; the tangential speed is the movement speed of the motor rotor in the tangential direction of the circle. Multiplying it with the tangential electromagnetic force can obtain the energy input rate in the tangential direction; the axial speed is the movement speed of the motor rotor in the axial direction. The product of the axial electromagnetic force and the axial speed reflects the energy input in the axial direction; the motor angular velocity is the angular velocity of the motor rotor rotation. The torque fluctuation is multiplied by the angular velocity to obtain the energy input power in the torsional direction.

[0098] Calculating the motor input energy by multiplying and integrating the multi-directional electromagnetic excitation and the speed parameter can comprehensively and accurately reflect the energy input characteristics of the motor during actual operation. The tangential electromagnetic force, axial electromagnetic force, and torque fluctuation correspond to the electromagnetic excitation of the motor in different dimensions, and the multiplication and integration of the corresponding speed parameters cover the energy transfer of the motor in multiple directions such as rotation, axial displacement, and torsional vibration. This calculation method can avoid the one-sidedness of only considering energy input in a single direction, and can more realistically reflect the energy input state of the motor under complex working conditions, thereby providing accurate basic data for the subsequent analysis of the energy transfer efficiency between components such as the motor, gears, bearings, and housing in the electric drive system, which helps to evaluate the energy utilization efficiency of the system and the energy loss of each component.

[0099] Step 250 - 2 : Calculate the shell vibration energy based on the multivariate time domain data.

[0100] For the embodiment of the present disclosure, when calculating the vibration energy of the shell based on multivariate time domain data, the shell condensation stiffness matrix, displacement vector, damping matrix and velocity vector can be comprehensively considered, and the sum of elastic potential energy and damping energy consumption can be obtained by integration. Specifically, the shell will generate elastic potential energy due to elastic deformation during the vibration process, which is related to the displacement and condensation stiffness of various parts of the shell. The greater the stiffness and the greater the displacement, the more elastic potential energy is stored; at the same time, the shell material and structural damping will consume vibration energy, and the damping energy consumption is related to the vibration speed and the damping matrix. The faster the speed and the greater the damping, the more energy is consumed. By using the changes in the shell displacement and velocity over time in the multivariate time domain data, combined with the condensation stiffness matrix and the damping matrix, the two parts of energy are calculated separately and then summed up to obtain the total energy of the shell during the vibration process.

[0101] Among them, the shell displacement vector is a vector that describes the position change of each node of the shell during the vibration process, reflecting the deformation state of the shell; the shell velocity vector is a vector representation of the vibration velocity of each node of the shell, which can be combined with the damping matrix to calculate the damping energy consumption; the elastic potential energy is the energy stored in the shell due to elastic deformation, which is related to the displacement and stiffness. The greater the deformation and the higher the stiffness, the greater the potential energy; the damping energy consumption is the energy loss caused by internal friction of the material and structural damping when the shell vibrates, which is related to the vibration velocity and damping coefficient.

[0102] By combining multivariate time-domain data with shell parameters to calculate vibration energy, the energy loss and storage characteristics of the shell under dynamic loads can be accurately quantified. The elastic potential energy calculation reflects the elastic deformation capacity of the shell structure, while the damping energy calculation reflects the attenuation effect of the shell on vibration. The combination of the two can comprehensively evaluate the vibration energy characteristics of the shell. This provides key data for noise control of electric drive systems, that is, areas with high elastic potential energy may produce larger vibration amplitudes, and areas with low damping energy consumption need to optimize damping characteristics to reduce vibration. In addition, this calculation method takes into account the condensation parameters of the shell flexibility model. While ensuring calculation efficiency, it can ensure the accuracy of energy analysis and help identify the weak links of the shell and areas where vibration energy is concentrated.

[0103] Step 250 - 3 : Calculate the gear received energy based on the tangential meshing force and the axial meshing force in the gear meshing dynamic load parameters, and the gear displacement in the multivariate time domain data.

[0104] Among them, the tangential meshing force is the dynamic force acting along the tangential direction of the circumference when the gear pair is meshing. It is the main force driving the gear to rotate, and its magnitude and direction will change with the gear meshing process; the axial meshing force is the dynamic force acting along the axial direction when the gear pair is meshing. It is generated by factors such as the helix angle of the helical gear, which will cause the gear to be subjected to force in the axial direction; the gear displacement is the position change of the gear during the vibration process, including tangential displacement and axial displacement, which reflects the motion state of the gear; the gear received energy is the energy received by the gear through the meshing force during the vibration process, and is an important indicator for evaluating the energy input and working state of the gear.

[0105] For the embodiment of the present disclosure, the tangential meshing force acts as a driving force along the tangential direction of the circumference when the gears are meshing, which will push the gears to rotate, while the axial meshing force acts along the axial direction, causing the gears to move axially. These two forces do work on the gears during the gear vibration process, and the amount of work is determined by the product of the force and the displacement of the gear in the corresponding direction. In specific calculations, the tangential displacement and axial displacement changes of the gears at different times can be obtained through multivariate time domain data, and then the tangential meshing force at each moment is multiplied by the tangential displacement, and the axial meshing force is multiplied by the axial displacement to obtain the amount of work done by the two forces at that moment. The work done at all moments in the entire vibration process is then integrated and accumulated to finally obtain the total energy received by the gears during the vibration process, that is, the energy received by the gears.

[0106] Calculating the gear received energy by multiplying the meshing force and the gear displacement can accurately quantify the energy the gear receives from the motor and other components during the meshing process. The tangential meshing force and the axial meshing force are the main dynamic loads in the meshing process of the gear pair. The product integral of these two forces and the gear displacement directly reflects the amount of work done by these two types of forces on the gear, and thus reflects the amount of energy received by the gear. This calculation method takes into account the force and displacement of the gear in both the tangential and axial directions, and comprehensively reflects the energy reception status of the gear. The obtained gear received energy can be used to analyze the energy input of the gear under different working conditions, providing important data support for evaluating the gear's workload, fatigue life, and optimizing gear design, which helps to improve the reliability and efficiency of the gear system.

[0107] Step 250 - 4 : Calculate the bearing received energy based on the tangential meshing force and the axial meshing force in the gear meshing dynamic load parameters, and the bearing displacement in the multivariate time domain data.

[0108] Among them, bearing displacement is the deformation of the bearing when it is subjected to load, such as the relative displacement between the inner ring and the outer ring, which reflects the actual response of the bearing support stiffness; bearing received energy is the energy received by the bearing due to resisting deformation in the process of supporting the gear system. It is generated by the coupling effect of load and displacement and is an important indicator for evaluating the bearing's load-bearing capacity.

[0109] For the disclosed embodiments, the tangential and axial meshing forces generated during gear meshing can be determined. These forces are transmitted to the bearings via the gear shafts, acting as tangential and axial dynamic loads on the bearings. Next, bearing displacement data, such as radial and axial deformation, is obtained at different times. Since the bearing support stiffness matrix indicates the bearing's ability to resist deformation, at each moment, the bearing displacement is multiplied by the corresponding parameter in the stiffness matrix to obtain the magnitude of the bearing support force at that moment. The entire vibration process is then integrated over time, and the work done by the bearing support force at each moment is accumulated. This allows the calculation of the total energy received by the bearing from supporting the gear system during the vibration process. The tangential and axial dynamic loads transmitted to the bearings via the gear shafts are key input parameters for determining the bearing support force and calculating the energy received by the bearings in subsequent calculations. These loads cause radial and axial displacements in the bearings. Combined with the bearing support stiffness matrix, the bearing support force at different moments can be calculated from the displacements. By multiplying the support force by the displacement and integrating it over time, the total energy received by the bearing during the vibration process can be quantified, thereby evaluating the bearing's load-bearing condition and energy loss characteristics.

[0110] This process fully considers the coupling between the bearing stiffness characteristics and the actual displacement, thereby enabling the quantitative calculation of the energy input when the load is transmitted through the bearing. By calculating the bearing received energy by multiplying the bearing support stiffness matrix and the displacement, the energy loss and load-bearing characteristics of the bearing in the electric drive system can be accurately evaluated. When the tangential and axial meshing forces are transmitted to the bearing through the gear shaft, the stiffness of the bearing will affect its deformation, which in turn affects the load transfer efficiency. By calculating the bearing received energy, the stress state of the bearing under different working conditions can be identified, such as the energy concentration area caused by high-frequency vibration of the bearing during high-speed operation, or the additional energy loss caused by the axial displacement of the bearing under heavy load conditions.

[0111] Step 250 - 5 : Calculate the transmission efficiency of vibration energy among the motor, gears, bearings, and housing components based on the motor input energy, housing vibration energy, gear receiving energy, and bearing receiving energy.

[0112] Specifically, as a possible implementation manner, the ratio of the housing vibration energy to the motor input energy can be determined as the transmission efficiency value of the vibration energy from the motor to the housing.

[0113] This step, through energy ratio calculation, provides a direct assessment of the efficiency of the motor's vibration energy transfer to the housing in the electric drive system. A high efficiency value indicates that the motor's vibration energy easily excites housing vibration through the drive train, potentially increasing housing radiated noise. A low efficiency value indicates that significant energy loss occurs during transmission through intermediate components, resulting in relatively weak housing vibration. This analysis can inform system vibration reduction design, for example, by optimizing gear mesh stiffness or bearing damping to reduce the energy transfer efficiency to the housing, thereby reducing housing vibration noise.

[0114] As another possible implementation, the ratio of the energy received by the gear to the energy input by the motor can be determined as the transmission efficiency value of the vibration energy from the motor to the gear.

[0115] This efficiency calculation assesses the gear system's ability to absorb motor energy. Low efficiency may indicate high gear meshing losses (such as shock caused by meshing errors) or insufficient drive train stiffness, resulting in significant energy losses during the motor-to-gear transfer process. High efficiency indicates the gears are effectively receiving motor energy and transferring it to subsequent components. This analysis helps optimize gear parameters (such as module and pressure angle) to improve energy transfer efficiency and reduce the risk of gear fatigue damage.

[0116] As another possible implementation, the ratio of the energy received by the bearing to the energy received by the gear can be determined as the transmission efficiency value of the vibration energy from the gear to the bearing.

[0117] The transmission efficiency of vibration energy from gears to bearings can be used to assess the extent of bearing energy loss. A high efficiency indicates that a high amount of gear energy is being transferred to the bearing, potentially leading to bearing overload or heating. A low efficiency indicates that the bearing's damping or stiffness characteristics are optimized, effectively dissipating energy. This analysis provides a reference for bearing selection and lubrication design, such as selecting high-damping bearings to reduce energy transmission efficiency and minimize bearing fatigue wear.

[0118] As another possible implementation, the ratio of the housing vibration energy to the bearing received energy may be determined as the transmission efficiency value of the vibration energy from the bearing to the housing.

[0119] This efficiency calculation identifies the energy source strength of housing vibration. A high efficiency indicates that the bearing transfers a large amount of energy to the housing, making the housing prone to resonance or high-frequency vibration. A low efficiency indicates that the bearing is blocking energy transfer, resulting in minimal housing vibration. This analysis can help optimize bearing support stiffness or housing structure, cut off energy transfer paths, and reduce the level of housing vibration and noise radiation.

[0120] Step 260 : Compare the values ​​of the transmission efficiency of the vibration energy between the components, and select a key noise transmission path of the vehicle electric drive system from the multiple transmission paths based on the comparison result.

[0121] Among them, the vibration energy transfer efficiency value refers to the ratio of the vibration energy received by the target component to the input energy of the source component in a certain energy transfer path, which is used to measure the efficiency of energy transfer between components; the transfer path is the transmission route of vibration energy between the various components of the electric drive system, such as motor → gear, gear → bearing, bearing → housing, etc.; the key noise transfer path is the energy transfer path in the electric drive system with a high vibration energy transfer efficiency value, which plays a major role in the generation and propagation of system noise.

[0122] In the disclosed embodiments, by comparing the vibration energy transfer efficiency values ​​between various components, such as the motor to housing, the motor to the gear, the gear to the bearing, and the bearing to the housing, key noise transmission paths can be screened out from the multiple energy transmission paths of the vehicle electric drive system. Specifically, the higher the transmission efficiency value of a path, the lower the transmission loss of vibration energy on that path, and the easier it is for energy to be transmitted through that path and excite component vibration, thereby generating noise. Therefore, among the multiple transmission paths, the paths with higher transmission efficiency values ​​are the key noise transmission paths, and these paths are the main channels for noise generation and propagation in the electric drive system.

[0123] By quantifying the vibration energy transfer efficiency between components and comparing their magnitudes to screen key noise transfer paths, it's possible to precisely locate the energy transfer paths that contribute most to noise in the electric drive system. This provides clear targets for noise control in the electric drive system, allowing for the implementation of appropriate vibration and noise reduction measures for these key noise transfer paths. For example, optimizing gear mesh parameters to reduce energy transfer efficiency from the motor to the gears, or improving bearing support structures to reduce energy transfer from the bearing to the housing, effectively reducing system noise and improving the vehicle's NVH (noise, vibration, and harshness) performance.

[0124] Suppose that in a certain automotive electric drive system, the calculated vibration energy transfer efficiency values ​​for each transmission path are as follows: 35% for motor-to-housing, 60% for motor-to-gear, 45% for gear-to-bearing, and 50% for bearing-to-housing. Comparing these efficiency values ​​reveals that the motor-to-gear transmission efficiency (60%) is the highest, followed by the bearing-to-housing transmission efficiency (50%), the gear-to-bearing transmission efficiency (45%), and the motor-to-housing transmission efficiency (35%). Therefore, based on a comparison of these transmission efficiencies with a preset efficiency threshold (e.g., 49%), the motor-to-gear and bearing-to-housing transmission paths can be identified as critical noise transmission paths. This means that the motor's vibration energy is transferred more to the gears, while the bearings transfer more energy to the housing, thereby stimulating gear and housing vibrations and generating noise. For these two critical paths, measures such as optimizing gear meshing accuracy to reduce the motor-to-gear transmission efficiency or increasing bearing damping to reduce bearing-to-housing transmission efficiency can be taken to reduce system noise.

[0125] In specific application scenarios, as an optimization solution, after identifying the critical noise transmission paths in an automotive electric drive system, structural parameter optimization can be performed on components along these paths (such as gears, bearings, and housings). This can be achieved by adjusting the gear module, bearing stiffness, or housing wall thickness. After optimization, the rigid-flexible coupling dynamics model is reconstructed based on the new parameters, the state-space equations are solved again, and the transmission efficiency is calculated. The optimization results are verified by comparing the efficiency values ​​before and after optimization until the vibration energy transmission efficiency of the critical path is reduced to the preset target value (for example, from 60% to 30%). This process achieves targeted control of the noise transmission path through a closed-loop "analysis-optimization-verification" process.

[0126] Accordingly, the steps of the embodiment may also include: optimizing the structural parameters of components on the key noise transmission path; reconstructing the rigid-flexible coupling dynamic model based on the optimized structural parameters, and repeating the steps of solving the state-space equations and calculating the transfer efficiency value to verify the optimization effect until the transfer efficiency value corresponding to the vibration energy in the key noise transmission path is reduced to a preset target value.

[0127] This critical path-based structural parameter optimization method can precisely reduce noise radiation from electric drive systems. Through iterative optimization and verification, the effectiveness of optimization measures is ensured. This prevents system performance degradation (e.g., insufficient gear strength) caused by blindly modifying component parameters. Furthermore, quantitative efficiency verification provides a direct reflection of optimization results, ensuring that noise control objectives are achieved. For example, if the critical path is "bearing → housing," increasing bearing damping or modifying the housing rib layout can significantly reduce energy transfer efficiency, thereby reducing housing vibration noise and improving vehicle NVH performance.

[0128] In summary, the technical solution of the present application can effectively solve the problems of insufficient accuracy of single physical field modeling and low efficiency of solving strong nonlinear systems in the existing technology through multi-physics field coupling modeling and efficient solution. Specifically, the finite element simulation is used to solve the characteristic parameters of the electromagnetic excitation of the motor, and the helical gear coupling vibration equation group is established in combination with the dynamic model of the gear system, which can fully consider the interaction between the electromagnetic excitation and the bending-torsion-axial coupling vibration of the gear; the motor, gear, bearing and housing models are coupled to form a rigid-flexible coupling dynamic model, and the mechanical transfer path modeling is realized through the bearing stiffness matrix and the housing contraction matrix, which can accurately reflect the reaction of the housing flexible support to the system vibration and make up for the defects of the traditional simplified model in the characterization of multi-field coupling and flexible influence; through state space equation transformation, dimensionless and piecewise linear method solution, the problem of poor convergence of strong nonlinear system calculation can be solved, and the accurate calculation of multivariable time domain data can be achieved; based on the excitation parameters, meshing load and time domain data, the energy transfer efficiency is calculated, and the key noise path between the motor-gear-bearing-housing can be quantitatively located. Combined with the optimization iterative process, a complete technical path from modeling analysis to optimization verification can be provided for NVH issues such as high-frequency howling under high-speed conditions, so that noise optimization design has a reliable theoretical basis and quantitative support.

[0129] Further, as Figure 1 and Figure 2 The specific implementation of the method shown in this embodiment provides a vibration analysis device for a vehicle electric drive system, such as Figure 3 As shown, the device includes: an analysis module 31 , a coupling module 32 , a first calculation module 33 , and a second calculation module 34 .

[0130] An analysis module 31 can be used to analyze excitation characteristic parameters and gear meshing dynamic load parameters based on the established motor electromagnetic excitation model and gear system dynamics model; The coupling module 32 can be used to use the excitation characteristic parameters and the gear meshing dynamic load parameters as the mechanical excitation of the gear system, and couple the motor electromagnetic excitation model, the gear system dynamic model, the bearing rigidity model, and the housing flexibility model to form a rigid-flexible coupling dynamic model; The first calculation module 33 can be used to convert the rigid-flexible coupling dynamic model into a state-space equation, solve the state-space equation through dimensionless transformation and piecewise linear method, and obtain multivariate time-domain data; The second calculation module 34 can be used to calculate the transmission efficiency of vibration energy between the motor, gears, bearings and housing components based on the excitation characteristic parameters, gear meshing dynamic load parameters and multivariate time domain data, and locate the key noise transmission paths of the vehicle electric drive system according to the size of the transmission efficiency value.

[0131] In some embodiments of the present application, the analysis module 31 can be specifically used to simulate the electromagnetic excitation model of the motor using finite element simulation software to solve the excitation characteristic parameters including tangential electromagnetic force, axial electromagnetic force and torque fluctuation; based on the gear system dynamics model, a group of helical gear coupling vibration equations with multiple pairs of gear pairs, multiple gears and tangential, axial and torsional degrees of freedom is established; based on the helical gear coupling vibration equations, the gear meshing dynamic load parameters including the tangential dynamic meshing force of the gear pair, the axial dynamic meshing force, the torsional vibration load spectrum during multi-gear meshing and the load change data are calculated.

[0132] In some embodiments of the present application, the coupling module 32 can be specifically used to establish a bearing support stiffness matrix corresponding to the bearing rigidity model, and to perform condensation processing on the shell flexibility model to obtain a shell mass matrix, a shell damping matrix and a shell condensation stiffness matrix; based on the bearing support stiffness matrix and the shell condensation stiffness matrix, the gear system dynamics model and the shell flexibility model are connected to establish a mechanical transmission path between the gear system and the shell; the excitation characteristic parameters and the gear meshing dynamic load parameters are substituted into the gear system dynamics model to realize the coupling of the motor electromagnetic excitation model and the gear system dynamics model; the output excitation of the motor electromagnetic excitation model and the gear meshing intrinsic excitation are integrated, and the shell mass matrix, the shell damping matrix and the shell condensation stiffness matrix are combined to construct a rigid-flexible coupling dynamics equation corresponding to the rigid-flexible coupling dynamics model, wherein the output excitation is obtained by electromagnetic mechanical energy conversion of the motor electromagnetic excitation model, and the gear meshing intrinsic excitation is calculated based on the meshing characteristics of the gear pair in the gear system dynamics model.

[0133] In some embodiments of the present application, the first calculation module 33 can be specifically used to convert the rigid-flexible coupling dynamic equation corresponding to the rigid-flexible coupling dynamic model from a second-order differential equation to a first-order state space equation group by defining a state vector containing the system displacement and velocity; select characteristic reference quantities for the physical parameters in the state space equation, and convert the physical parameters into dimensionless quantities based on the characteristic reference quantities to obtain the dimensionless state space equation, where the physical parameters include at least time parameters and displacement parameters, and the characteristic reference quantities include at least characteristic time reference quantities and characteristic displacement reference quantities; based on the nonlinear characteristics of the rigid-flexible coupling dynamic model, the time-varying parameters in the state space equation are divided into multiple linear intervals according to different working conditions, and in each linear interval, a linear solution is performed based on the dimensionless state space equation to obtain multivariate time domain data.

[0134] In some embodiments of the present application, the second calculation module 34 can be specifically used to use the electromagnetic excitation in the excitation characteristic parameters as input energy, combine the gear meshing dynamic load parameters and multivariate time domain data, and calculate the transmission efficiency values ​​of vibration energy between the motor, gears, bearings and housing components through the principle of conservation of energy; compare the sizes of the corresponding transmission efficiency values ​​of the vibration energy between the components, and screen the key noise transmission paths of the vehicle electric drive system from multiple transmission paths based on the comparison results.

[0135] In some embodiments of the present application, when calculating the transmission efficiency values ​​of vibration energy among the motor, gears, bearings and housing components by the principle of conservation of energy, the second calculation module 34 can be specifically used to calculate the motor input energy of the motor during the running time based on the tangential electromagnetic force, axial electromagnetic force and torque fluctuation in the excitation characteristic parameters; calculate the housing vibration energy based on multivariate time domain data; calculate the gear receiving energy based on the tangential meshing force and axial meshing force in the gear meshing dynamic load parameters, and the gear displacement in the multivariate time domain data; calculate the bearing receiving energy based on the tangential meshing force and axial meshing force in the gear meshing dynamic load parameters, and the bearing displacement in the multivariate time domain data; calculate the transmission efficiency values ​​of vibration energy among the motor, gears, bearings and housing components based on the motor input energy, housing vibration energy, gear receiving energy and bearing receiving energy.

[0136] In some embodiments of the present application, Figure 4 As shown, the device further includes: an optimization module 35; Optimization module 35 can be used to optimize the structural parameters of components on the key noise transmission path; based on the optimized structural parameters, the rigid-flexible coupling dynamic model is reconstructed, and the steps of solving the state-space equations and calculating the transfer efficiency value are repeated to verify the optimization effect until the transfer efficiency value corresponding to the vibration energy in the key noise transmission path is reduced to a preset target value.

[0137] It should be noted that for other corresponding descriptions of the functional units involved in the vibration analysis device for a vehicle electric drive system provided in this embodiment, reference can be made to Figure 1 and Figure 2 The corresponding description in will not be repeated here.

[0138] Based on the above Figure 1 and Figure 2 The method shown in FIG. 1 is a method for performing the above-mentioned operation. Accordingly, this embodiment further provides a storage medium on which a computer program is stored. When the program is executed by a processor, the above-mentioned Figure 1 and Figure 2 The vibration analysis method of the vehicle electric drive system is shown.

[0139] Based on this understanding, the technical solution of the present application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, USB flash drive, mobile hard disk, etc.), and includes a number of instructions for enabling an electronic device (which can be a personal computer, server, or network device, etc.) to execute the methods of various implementation scenarios of the present application.

[0140] Based on the above Figure 1 and Figure 2 The method shown, and Figure 3 and Figure 4 In order to achieve the above-mentioned purpose, the embodiment of the present application further provides an electronic device, which can be a personal computer, a tablet computer, a server, or other network equipment, etc. The device includes a storage medium and a processor; the storage medium is used to store a computer program; the processor is used to execute the computer program to achieve the above-mentioned Figure 1 and Figure 2 The vibration analysis method of the vehicle electric drive system is shown.

[0141] Optionally, the physical device may also include a user interface, a network interface, a camera, a radio frequency (RF) circuit, a sensor, an audio circuit, a Wi-Fi module, and the like. The user interface may include a display screen and an input unit such as a keyboard. Optional user interfaces may also include a USB interface and a card reader interface. Optionally, the network interface may include a standard wired interface or a wireless interface (such as a Wi-Fi interface).

[0142] Those skilled in the art will understand that the above-mentioned physical device structure provided in this embodiment does not constitute a limitation on the physical device, and may include more or fewer components, or a combination of certain components, or different component arrangements.

[0143] The storage medium may also include an operating system and a network communication module. The operating system is a program that manages the hardware and software resources of the physical device, supporting the execution of information processing programs and other software and / or programs. The network communication module is used to enable communication between components within the storage medium, as well as with other hardware and software within the physical information processing device.

[0144] Through the description of the above implementation methods, those skilled in the art can clearly understand that the present application can be implemented by means of software plus a necessary general hardware platform, or by hardware.

[0145] The embodiment of the present invention can effectively solve the problems of insufficient accuracy of single physical field modeling and low efficiency of solving strong nonlinear systems in the prior art through multi-physical field coupling modeling and efficient solution. Specifically, finite element simulation is used to solve the characteristic parameters of the electromagnetic excitation of the motor, and the helical gear coupling vibration equation group is established in combination with the gear system dynamics model, which can fully consider the interaction between electromagnetic excitation and gear bending-torsion-axial coupling vibration; the motor, gear, bearing and housing models are coupled to form a rigid-flexible coupling dynamics model, and the mechanical transfer path modeling is realized through the bearing stiffness matrix and the housing contraction matrix, which can accurately reflect the reaction of the housing flexible support to the system vibration and make up for the defects of the traditional simplified model in the characterization of multi-field coupling and flexible influence; through state space equation transformation, dimensionless and piecewise linear method solution, the problem of poor computational convergence of strong nonlinear systems can be solved, and accurate calculation of multivariable time domain data can be achieved; based on the excitation parameters, meshing load and time domain data, the energy transfer efficiency is calculated, and the key noise path between the motor-gear-bearing-housing can be quantitatively located. Combined with the optimization iterative process, a complete technical path from modeling analysis to optimization verification can be provided for NVH issues such as high-frequency howling under high-speed conditions, so that noise optimization design has a reliable theoretical basis and quantitative support.

[0146] Those skilled in the art will understand that the accompanying drawings are only schematic diagrams of a preferred implementation scenario, and the modules or processes in the accompanying drawings are not necessarily required to implement the present application. Those skilled in the art will understand that the modules in the devices in the implementation scenario can be distributed in the devices of the implementation scenario according to the implementation scenario description, or can be changed accordingly and located in one or more devices different from the implementation scenario. The modules of the above-mentioned implementation scenario can be combined into one module, or can be further split into multiple sub-modules.

[0147] The serial numbers of the above application are for descriptive purposes only and do not represent the advantages or disadvantages of the implementation scenarios. The above disclosure only discloses several specific implementation scenarios of the present application, but the present application is not limited thereto. Any changes that can be conceived by those skilled in the art should fall within the scope of protection of the present application.

Claims

1. A vibration analysis method for a vehicle electric drive system, characterized in that: include; Based on the established motor electromagnetic excitation model and gear system dynamics model, the excitation characteristic parameters and gear meshing dynamic load parameters are analyzed; The excitation characteristic parameters and the gear meshing dynamic load parameters are used as mechanical excitations of the gear system, and the motor electromagnetic excitation model, the gear system dynamics model, the bearing rigidity model, and the housing flexibility model are coupled to form a rigid-flexible coupling dynamics model; Converting the rigid-flexible coupling dynamic model into a state-space equation, solving the state-space equation by dimensionless transformation and piecewise linear method to obtain multivariate time-domain data; Based on the excitation characteristic parameters, the gear meshing dynamic load parameters and the multivariate time domain data, the transmission efficiency values ​​of the vibration energy among the motor, gears, bearings and housing components are calculated, and the key noise transmission paths of the vehicle electric drive system are located according to the size of the transmission efficiency values.

2. The method according to claim 1, characterized in that The motor electromagnetic excitation model and gear system dynamics model are created to analyze the excitation characteristic parameters and the gear meshing dynamic load parameters, including: Finite element simulation software is used to simulate the motor electromagnetic excitation model and solve the excitation characteristic parameters including tangential electromagnetic force, axial electromagnetic force and torque fluctuation; Based on the dynamic model of the gear system, a set of coupled vibration equations for helical gears with multiple pairs of gear pairs, multiple gears and three degrees of freedom in tangential, axial and torsional directions is established. Based on the coupled vibration equations for the helical gears, the gear meshing dynamic load parameters, including the tangential dynamic meshing force and axial dynamic meshing force of the gear pairs, the torsional vibration load spectrum during multi-gear meshing and the load change data, are calculated.

3. The method according to claim 1, characterized in that The excitation characteristic parameters and the gear meshing dynamic load parameters are used as mechanical excitations of the gear system, and the motor electromagnetic excitation model, the gear system dynamics model, the bearing rigidity model, and the housing flexibility model are coupled to form a rigid-flexible coupling dynamics model, including: Establish the bearing support stiffness matrix corresponding to the bearing rigidity model, and perform condensation processing on the shell flexibility model to obtain the shell mass matrix, shell damping matrix and shell condensation stiffness matrix; Based on the bearing support stiffness matrix and the housing condensation stiffness matrix, the gear system dynamics model and the housing flexibility model are connected to establish a mechanical transmission path between the gear system and the housing; Substituting the excitation characteristic parameters and the gear meshing dynamic load parameters into the gear system dynamics model to achieve coupling between the motor electromagnetic excitation model and the gear system dynamics model; The output excitation of the motor electromagnetic excitation model and the gear meshing intrinsic excitation are integrated, and the shell mass matrix, the shell damping matrix and the shell condensation stiffness matrix are combined to construct a rigid-flexible coupling dynamic equation corresponding to the rigid-flexible coupling dynamic model, wherein the output excitation is obtained by electromagnetic mechanical energy conversion of the motor electromagnetic excitation model, and the gear meshing intrinsic excitation is calculated based on the meshing characteristics of the gear pair in the gear system dynamic model.

4. The method according to claim 1, wherein The rigid-flexible coupling dynamic model is converted into a state-space equation, and the state-space equation is solved by dimensionless transformation and piecewise linear method to obtain multivariate time-domain data, including: By defining a state vector including the displacement and velocity of the system, the rigid-flexible coupling dynamic equation corresponding to the rigid-flexible coupling dynamic model is transformed from a second-order differential equation to a first-order state space equation system; Selecting characteristic reference quantities for physical parameters in the state-space equation, and converting the physical parameters into dimensionless quantities based on the characteristic reference quantities to obtain a dimensionless state-space equation, wherein the physical parameters include at least a time parameter and a displacement parameter, and the characteristic reference quantities include at least a characteristic time reference quantity and a characteristic displacement reference quantity; Based on the nonlinear characteristics of the rigid-flexible coupling dynamic model, the time-varying parameters in the state-space equation are divided into multiple linear intervals according to different working conditions. Within each linear interval, a linear solution is performed based on the dimensionless state-space equation to obtain multivariate time-domain data.

5. The method according to claim 1, wherein Based on the excitation characteristic parameters, the gear meshing dynamic load parameters, and the multivariate time domain data, the transmission efficiency values ​​of the vibration energy among the motor, gears, bearings, and housing components are calculated, and according to the magnitude of the transmission efficiency values, the key noise transmission paths of the vehicle electric drive system are located, including: Using the electromagnetic excitation in the excitation characteristic parameters as input energy, combined with the gear meshing dynamic load parameters and the multivariate time domain data, the transmission efficiency value of the vibration energy among the motor, gears, bearings and housing components is calculated according to the principle of energy conservation; The vibration energies between the components corresponding to the transmission efficiency values ​​are compared, and based on the comparison results, a key noise transmission path of the vehicle electric drive system is screened from the multiple transmission paths.

6. The method according to claim 5, characterized in that The calculation of the transmission efficiency of vibration energy among the motor, gears, bearings and housing components by the energy conservation principle includes: Calculating the motor input energy during the running time of the motor based on the tangential electromagnetic force, the axial electromagnetic force and the torque fluctuation in the excitation characteristic parameters; calculating the shell vibration energy based on the multivariate time domain data; Calculating the gear received energy based on the tangential meshing force and the axial meshing force in the gear meshing dynamic load parameters and the gear displacement in the multivariate time domain data; Calculating bearing received energy based on the tangential meshing force and the axial meshing force in the gear meshing dynamic load parameters and the bearing displacement in the multivariate time domain data; The transmission efficiency values ​​of the vibration energy among the motor, gear, bearing and housing components are calculated based on the motor input energy, the housing vibration energy, the gear receiving energy and the bearing receiving energy.

7. The method according to any one of claims 1 to 6, characterized in that The method further comprises: Optimize structural parameters of components on key noise transmission paths; The rigid-flexible coupling dynamic model is reconstructed based on the optimized structural parameters, and the steps of solving the state-space equations and calculating the transfer efficiency value are repeated to verify the optimization effect until the transfer efficiency value corresponding to the vibration energy in the critical noise transmission path is reduced to the preset target value.

8. A vibration analysis device for a vehicle electric drive system, characterized in that: include; An analysis module is used to analyze the excitation characteristic parameters and gear meshing dynamic load parameters based on the established motor electromagnetic excitation model and gear system dynamics model; a coupling module, configured to use the excitation characteristic parameters and the gear meshing dynamic load parameters as mechanical excitations of the gear system, and couple the motor electromagnetic excitation model, the gear system dynamics model, the bearing rigidity model, and the housing flexibility model to form a rigid-flexible coupling dynamics model; A first computing module is configured to convert the rigid-flexible coupling dynamics model into a state-space equation, solve the state-space equation by dimensionless transformation and piecewise linear method, and obtain multivariate time-domain data; The second calculation module is used to calculate the transmission efficiency value of vibration energy among the motor, gears, bearings and housing components based on the excitation characteristic parameters, the gear meshing dynamic load parameters and the multivariate time domain data, and locate the key noise transmission path of the vehicle electric drive system according to the size of the transmission efficiency value.

9. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

10. An electronic device comprising a storage medium, a processor, and a computer program stored in the storage medium and executable on the processor, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 7 is implemented.

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