Vibration analysis methods, devices, media and equipment for automotive electric drive systems

Abstract

This application discloses a vibration analysis method, apparatus, medium, and equipment for an automotive electric drive system, relating to the field of electronic digital data processing technology. The method includes: analyzing excitation characteristics and gear meshing dynamic load parameters based on a dynamic model of the motor's electromagnetic excitation and gear system; using these as mechanical excitation to couple a model of the motor, gears, bearings, and housing to form a rigid-flexible coupled dynamic model; transforming this model into state-space equations; obtaining multivariable time-domain data through dimensionless transformation and piecewise linear methods; and then calculating the transmission efficiency of vibration energy among the motor, gears, bearings, and housing components based on the excitation characteristic parameters, gear meshing dynamic load parameters, and multivariable time-domain data. The key noise transmission paths of the automotive electric drive system are then located based on the magnitude of the transmission efficiency values. This application effectively solves NVH problems such as high-frequency howling under high-speed operating conditions by comprehensively analyzing the system's vibration characteristics.

Description

Technical Field

[0001] This application relates to the field of electrical digital data processing technology, and in particular to a vibration analysis method, apparatus, medium and equipment for an automotive electric drive system. Background Technology

[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 evolving rapidly towards higher speeds and greater integration. Unlike traditional internal combustion engine drive systems, electric drive systems lack the masking effect of engine noise, making issues such as motor electromagnetic noise and gear meshing order noise increasingly prominent. Especially at high speeds, the system's dynamic response frequency enters the range of human hearing sensitivity, and high-frequency howling noise is particularly prominent during acceleration or under load, severely impacting the vehicle's NVH (noise, vibration, and harshness) performance. Simultaneously, the internal coupling of electric drive systems is significantly enhanced, involving the coordinated action of multiple components such as the motor, reducer, and controller. Its dynamic characteristics require comprehensive consideration of the coupling effects of multiple physical fields, including electromagnetic excitation, mechanical excitation, and structural deformation, which places higher demands on the vibration analysis of electric drive systems.

[0003] For vibration and noise issues in electric drive systems, existing technologies mainly employ single-physics 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, failing to fully consider the influence of electromagnetic excitation from the motor; other solutions, while considering electromagnetic excitation, have shortcomings in handling the bending-torsional-shaft 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 methods often face problems such as low computational efficiency and poor convergence for strongly nonlinear, multivariable coupled dynamic systems, making it difficult to accurately calculate the multivariable vibration characteristics of electric drive systems. Therefore, existing technologies cannot comprehensively and accurately analyze the vibration characteristics of electric drive systems, resulting in a lack of reliable theoretical basis for optimized design to address noise issues and making it difficult to effectively solve NVH problems such as high-frequency howling under high-speed operating conditions. Summary of the Invention

[0004] In view of this, this application provides a vibration analysis method, device, medium and equipment for automotive electric drive systems, 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 this application, a vibration analysis method for an automotive electric drive system is provided, comprising:

[0006] Based on the created electromagnetic excitation model of the motor and the dynamic model of the gear system, the excitation characteristic parameters and the dynamic load parameters of gear meshing are analyzed.

[0007] The excitation characteristic parameters and the gear meshing dynamic load parameters are used as the mechanical excitation of the gear system. The electromagnetic excitation model of the motor, the dynamic model of the gear system, the rigid model of the bearing, and the flexible model of the housing are coupled to form a rigid-flexible coupled dynamic model.

[0008] The rigid-flexible coupling dynamic model is transformed into a state-space equation, and the state-space equation is solved by dimensionless transformation and piecewise linear method to obtain multivariable time-domain data.

[0009] Based on the excitation characteristic parameters, the gear meshing dynamic load parameters, and the multivariate time-domain data, the transmission efficiency value of vibration energy between the motor, gears, bearings, and housing components is calculated, and the key noise transmission path of the vehicle electric drive system is located according to the magnitude of the transmission efficiency value.

[0010] According to a second aspect of this application, a vibration analysis device for an automotive electric drive system is provided, comprising:

[0011] The analysis module is used to analyze the excitation characteristic parameters and gear meshing dynamic load parameters based on the created motor electromagnetic excitation model and gear system dynamic model.

[0012] The coupling module is used to use the excitation characteristic parameters and the gear meshing dynamic load parameters as mechanical excitations for the gear system, and to couple the motor electromagnetic excitation model, the gear system dynamic model, the bearing rigid model and the housing flexible model to form a rigid-flexible coupled dynamic model.

[0013] The first calculation module is used to transform 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 multivariable time-domain data.

[0014] The second calculation module is used to calculate the transmission efficiency value of vibration energy between 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 to locate the key noise transmission path of the vehicle electric drive system according to the magnitude of the transmission efficiency value.

[0015] According to a third aspect of this application, a storage medium is provided that stores a computer program thereon, which, when executed by a processor, implements the vibration analysis method for the above-described vehicle electric drive system.

[0016] According to a fourth aspect of this application, an electronic device is provided, including a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor, wherein the processor executes the program to implement the vibration analysis method for the above-described vehicle electric drive system.

[0017] By employing the aforementioned technical solutions, the vibration analysis method, apparatus, medium, and equipment for automotive electric drive systems provided in this application effectively address the problems of insufficient accuracy and low solution efficiency in existing single-physics modeling through multi-physics coupled modeling and efficient solution methods. Specifically, by analyzing excitation characteristic parameters and meshing dynamic load parameters based on the motor electromagnetic excitation model and gear system dynamic model, the interaction between electromagnetic excitation and gear coupled vibration can be comprehensively considered; by coupling the motor, gear, bearing, and housing models to form a rigid-flexible coupled dynamic model, the influence of the housing's flexible support on system vibration can be accurately reflected, compensating for the deficiencies of traditional simplified models in multi-physics coupled analysis and characterization of the housing's flexible influence; through state-space equation transformation, dimensionlessization, and piecewise linear solution, the problem of poor convergence in strongly nonlinear systems can be solved, and the solution efficiency of multivariable coupled systems can be improved, enabling accurate calculation of multivariable time-domain data such as vibration displacement and velocity; by calculating energy transfer efficiency and locating key noise paths based on multi-source data, quantitative basis for noise optimization can be provided, and NVH problems such as high-frequency howling under high-speed conditions can be specifically addressed, making the optimization design for noise problems more theoretically supported.

[0018] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0019] Figure 1 A schematic flowchart of a vibration analysis method for an automotive electric drive system provided in an embodiment of this application is shown.

[0020] Figure 2 A flowchart illustrating a vibration analysis method for an automotive electric drive system according to another embodiment of this application is shown.

[0021] Figure 3 This paper shows a schematic diagram of the structure of a vibration analysis device for an automotive electric drive system provided in an embodiment of this application;

[0022] Figure 4 A schematic diagram of the structure of another vibration analysis device for an automotive electric drive system provided in an embodiment of this application is shown. Detailed Implementation

[0023] The present application will be described in detail below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in the embodiments of the present application can be combined with each other.

[0024] To address the aforementioned technical problems, embodiments of the present invention provide a vibration analysis method for automotive electric drive systems, such as... Figure 1 As shown, the method includes:

[0025] Step 110: Based on the created electromagnetic excitation model of the motor and the dynamic model of the gear system, analyze the excitation characteristic parameters and the dynamic load parameters of gear meshing.

[0026] Among them, the motor electromagnetic excitation model is a mathematical model used to describe the tangential electromagnetic force, axial electromagnetic force, and torque fluctuation generated by the electromagnetic effect during motor operation. The electromagnetic excitation characteristics can be solved by finite element simulation based on the motor electromagnetic excitation model. The gear system dynamic model is a dynamic model considering the bending-torsional-shaft coupling vibration of helical gear pairs, 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 system of differential equations. The excitation characteristic parameters are the key parameters characterizing the motor electromagnetic excitation, including tangential electromagnetic force, axial electromagnetic force, and torque fluctuation. The gear meshing dynamic load parameters are parameters describing the dynamic load during gear meshing, including tangential / axial dynamic meshing force, torsional vibration load spectrum, and load change data.

[0027] In this embodiment, an electromagnetic excitation model of the motor and a dynamic model of the gear system can be constructed first. Then, excitation characteristic parameters such as tangential electromagnetic force, axial electromagnetic force, and torque fluctuation can be solved from the electromagnetic excitation model of the motor. Simultaneously, from the helical gear coupled vibration equation set established by the gear system dynamic model, which includes multiple pairs of gears, multiple gears, and helical gears with tangential, axial, and torsional degrees of freedom, the dynamic load parameters of gear meshing, such as the tangential dynamic meshing force, axial dynamic meshing force, and torsional vibration load spectrum and load change data during multi-gear meshing, can be solved. Among them, the helical gear coupled vibration equation set refers to a differential equation set containing tangential, axial, and torsional degrees of freedom, which reflects the dynamic load characteristics of the helical gear pair meshing process by coupling vibrations in three directions through the mass matrix, damping matrix, and stiffness matrix.

[0028] By analyzing the excitation characteristic parameters and gear meshing dynamic load parameters, we can comprehensively obtain specific data on the electromagnetic excitation of the motor and the dynamic load of gear meshing in the electric drive system. This provides accurate excitation input for the subsequent construction of a rigid-flexible coupling dynamic model, enabling the model to more realistically reflect the dynamic characteristics of the electric drive system and providing a reliable basis for the analysis and optimization of system vibration and noise problems.

[0029] Step 120: Using the excitation characteristic parameters and gear meshing dynamic load parameters as the mechanical excitation of the gear system, couple the motor electromagnetic excitation model, the gear system dynamic model, the bearing rigid model, and the housing flexible model to form a rigid-flexible coupled dynamic model.

[0030] Among them, the bearing rigid model is a model established with stiffness as the core, based on the relationship between bearing displacement deformation and external load. It is used to characterize the bearing's support characteristics, determine the bearing support stiffness matrix, and reflect the bearing's support effect on the vibration of the gear system. The shell flexible model is a model obtained by condensing the shell using the finite element substructure analysis method. It includes the shell mass matrix, shell damping matrix, and shell condensed stiffness matrix. It is used to describe the flexible vibration characteristics of the shell and reflect the influence of shell flexibility on system vibration. The rigid-flexible coupling dynamic model is a model formed by coupling the motor electromagnetic excitation model, gear system dynamic model (rigid component), bearing rigid model, and shell flexible model (flexible component) through a mechanical transmission path. It can comprehensively consider the interaction between rigid and flexible components in the system and accurately reflect the dynamic characteristics of the electric drive system.

[0031] In the embodiments of this disclosure, the excitation characteristic parameters such as tangential electromagnetic force, axial electromagnetic force, and torque fluctuation obtained from the electromagnetic excitation model of the motor, and the gear meshing dynamic load parameters such as tangential dynamic meshing force, axial dynamic meshing force, torsional vibration load spectrum and variation data obtained from the dynamic model of the gear system, can be used as the input excitation of the gear system. The electromagnetic excitation model of the motor, the dynamic model of the gear system, the bearing rigid model established with stiffness as the core, and the shell flexible model obtained by condensation processing using the finite element substructure analysis method are connected and combined in a certain way to construct a rigid-flexible coupling dynamic model that considers both rigid and flexible components.

[0032] By coupling multi-source excitation parameters with multi-component models, accurate modeling of the multi-physics, multi-degree-of-freedom vibration characteristics of electric drive systems can be achieved. On the one hand, the introduction of excitation characteristic parameters and gear meshing dynamic load parameters ensures that the synergistic effect of motor electromagnetic excitation and gear meshing excitation can be accurately reflected. On the other hand, the coupling of the bearing rigid model and the shell flexible model enables the rigid-flexible coupling dynamic model to consider the reaction effect of the shell flexible support on the system vibration, making up for the shortcomings of traditional simplified models in dealing with rigid-flexible coupling problems. This ensures the accuracy of the rigid-flexible coupling dynamic model in reproducing the actual working state of the electric drive system, providing a more reliable model foundation for subsequent system vibration response analysis, energy transfer efficiency calculation, and noise path localization.

[0033] Step 130: Transform the rigid-flexible coupling dynamic model into a state-space equation, solve the state-space equation using dimensionless transformation and piecewise linear method, and obtain multivariable time-domain data.

[0034] Among them, the state-space equations are a set of first-order differential equations established based on modern control theory, with the system state vector (such as displacement and velocity) as variables; dimensionless transformation introduces characteristic reference quantities (such as nominal displacement scale and nominal time scale) to transform physical parameters into dimensionless quantities, eliminating the influence of dimensional differences on the calculation; the piecewise linear method is used to divide the nonlinear characteristics of time-varying parameters (such as gear meshing stiffness) into multiple linear intervals according to the working conditions, and uses the linear system solution method in each interval to achieve an approximate solution to the nonlinear problem; multivariate time-domain data are the time-dimensional variation data of each state variable of the system (such as tangential / axial vibration displacement, velocity, torsional angular displacement, etc.) obtained by solving the state-space equations, which are used to describe the dynamic response process of the system.

[0035] In this embodiment of the present disclosure, the second-order differential equation corresponding to the rigid-flexible coupling dynamic model, which includes components such as motors, gears, bearings, and housings, can be transformed into a first-order state-space equation by defining a state vector containing 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 transformed 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 (such as the time-varying meshing stiffness of gears) in the state-space equation are divided into multiple linear intervals according to different working conditions. The dimensionless state-space equation is solved linearly in each interval to obtain multivariate time-domain data of the system's state variables (such as vibration displacement and velocity) changing with time.

[0036] Transforming the rigid-flexible coupled dynamic model into state-space equations and solving them using dimensionless methods and piecewise linear methods can effectively solve 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 electric drive systems, providing an efficient and accurate method for obtaining multivariable time-domain data such as vibration displacement and velocity of various system components. This lays a data foundation for subsequent vibration energy transfer efficiency analysis and key noise transmission path location, making the analysis of vibration and noise problems in electric drive systems more accurate and reliable.

[0037] Step 140: Based on the excitation characteristic parameters, gear meshing dynamic load parameters and multivariate time-domain data, calculate the transmission efficiency value of vibration energy between the motor, gear, bearing and housing components, and locate the key noise transmission path of the vehicle electric drive system according to the magnitude of the transmission efficiency value.

[0038] Among them, the transmission efficiency value is the ratio of vibration energy transmission between various components in the vehicle electric drive system. For example, the efficiency from motor to gear is the ratio of energy received by the gear to energy input to the motor. It is used to quantitatively evaluate the energy transmission efficiency in the system and provide a quantitative basis for noise path localization. The key noise transmission path is the path with high energy transmission efficiency selected based on the transmission efficiency value. For example, the high-efficiency sub-path in "motor → gear → bearing → housing" is the main channel for noise generation and propagation in the electric drive system and provides a target for structural optimization.

[0039] In the embodiments of this 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 velocity in the multivariable time domain data, the motor input energy, gear received energy, bearing received energy and housing vibration energy are calculated by integration. Then, the transmission efficiency value between each component is obtained by the energy ratio. Finally, the noise transmission path with high energy transmission efficiency is selected based on the efficiency value.

[0040] By fusing multi-source data to calculate energy transfer efficiency, quantitative analysis of noise paths in electric drive systems can be achieved. On the one hand, combining excitation parameters and meshing load parameters ensures the integrity of electromagnetic excitation and gear meshing excitation in energy calculations. On the other hand, using multivariate time-domain data to accurately characterize the vibration response of each component makes the transfer efficiency calculation closer to actual operating conditions. By comparing efficiency values ​​to pinpoint key noise paths, clear targets can be provided for noise optimization, avoiding the blindness of traditional trial-and-error methods and improving the efficiency and accuracy of solving NVH problems in electric drive systems.

[0041] In summary, the vibration analysis method for automotive electric drive systems provided by this invention effectively solves the problems of insufficient accuracy and low solution efficiency of single-physics modeling in existing technologies through multi-physics coupled modeling and efficient solution methods. Specifically, by analyzing the excitation characteristic parameters and meshing dynamic load parameters based on the motor electromagnetic excitation model and the gear system dynamic model, the interaction between electromagnetic excitation and gear coupled vibration can be comprehensively considered; by coupling the motor, gear, bearing, and housing models to form a rigid-flexible coupled dynamic model, the influence of the housing flexible support on system vibration can be accurately reflected, making up for the deficiencies of traditional simplified models in multi-physics coupled analysis and characterization of the influence of housing flexibility; by transforming state-space equations, dimensionlessization, and piecewise linear methods, the problem of poor convergence in the calculation of strongly nonlinear systems can be solved, and the solution efficiency of multivariable coupled systems can be improved, achieving accurate calculation of multivariable time-domain data such as vibration displacement and velocity; by calculating energy transfer efficiency and locating key noise paths based on multi-source data, quantitative basis for noise optimization can be provided, and NVH problems such as high-frequency howling under high-speed conditions can be specifically solved, making the optimization design for noise problems more theoretically supported.

[0042] Furthermore, as a refinement and extension of the specific implementation of the above embodiments, and to fully illustrate the implementation of this embodiment, this embodiment also provides another vibration analysis method for automotive electric drive systems, such as... Figure 2 As shown, the method includes:

[0043] Step 210: Use finite element simulation software to simulate the electromagnetic excitation model of the motor and solve for the excitation characteristic parameters including tangential electromagnetic force, axial electromagnetic force and torque fluctuation.

[0044] In this embodiment, finite element simulation software is used to simulate the constructed electromagnetic excitation model of the motor, thereby solving for the excitation characteristic parameters covering tangential electromagnetic force, axial electromagnetic force, and torque fluctuation. Specifically, the tangential electromagnetic force density is first calculated using the Maxwell stress tensor method, and then multiplied by the area of ​​action to obtain the tangential electromagnetic force. Next, the axial electromagnetic force is obtained based on parameters such as electromagnetic power, motor speed, and core length. Then, the electromagnetic torque is calculated by integrating the tangential electromagnetic force along the circumference, and the torque fluctuation is obtained by combining the non-sinusoidal distribution characteristics of the permanent magnet magnetic field obtained from the simulation. Finally, the tangential electromagnetic force, axial electromagnetic force, and torque fluctuation are determined as the excitation characteristic parameters.

[0045] Accordingly, as one possible implementation, step 210 may include the following steps:

[0046] Step 210-1: Simulate the electromagnetic excitation model of the motor using finite element simulation software. Calculate the tangential electromagnetic force density using the Maxwell stress tensor method and multiply it by the area of ​​action to obtain the tangential electromagnetic force.

[0047] Among them, finite element simulation software is a software that performs numerical calculations by discretizing the model into a finite number of elements. It can be used to simulate the electromagnetic field distribution and electromagnetic force calculation in the electromagnetic excitation model of a motor. Maxwell's 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 the calculation space. It is suitable for calculating the electromagnetic force in the air gap of a motor. Tangential electromagnetic force density is the tangential electromagnetic force per unit area. It is an intermediate calculation result of Maxwell's stress tensor method and needs to be combined with the area of ​​action to further solve for the total amount of tangential electromagnetic force. The area of ​​action is the area of ​​the stator and rotor surfaces or air gap region where the tangential electromagnetic force acts in the electromagnetic excitation model of the motor. It is determined by finite element mesh generation and is used to convert the electromagnetic force density into the actual force. Tangential electromagnetic force is the force generated by electromagnetic effects in the tangential direction when the motor is running.

[0048] In the embodiments of this disclosure, when simulating the electromagnetic excitation model of the motor using finite element simulation software, the tangential electromagnetic force density acting on the stator and rotor surfaces of the motor in the air gap can be calculated using the Maxwell stress tensor method. This tangential electromagnetic force density is then multiplied by the corresponding area of ​​action to obtain the specific value of the tangential electromagnetic force. This method, based on electromagnetic field theory, transforms the complex electromagnetic interactions inside the motor into stress tensor calculations, and through finite element discretization, achieves an accurate solution for the tangential electromagnetic force.

[0049] The Maxwell stress tensor method combined with finite element simulation is used to calculate the tangential electromagnetic force. This method fully considers the nonlinear characteristics of the air gap magnetic field distribution of the motor and the influence of the stator and rotor structures. Compared with traditional simplified algorithms, it can more accurately reflect the dynamic changes of electromagnetic force under different operating conditions. This step provides accurate tangential excitation input for subsequent vibration analysis of the electric drive system, enabling the model to more realistically simulate the impact of motor electromagnetic excitation on the gear system and housing vibration. This effectively improves the accuracy of multiphysics coupling analysis and lays a reliable foundation for locating the root causes of noise and vibration problems.

[0050] Step 210-2: Based on the electromagnetic power, motor speed and core length parameters, the axial electromagnetic force is obtained.

[0051] Among them, electromagnetic power is the power of electromagnetic energy conversion during motor operation, which is equal to the product of electromagnetic torque and motor angular velocity, and is measured in watts (W). It is a key parameter characterizing the energy conversion efficiency of the motor and is used to establish the mathematical relationship between electromagnetic force and rotational speed. Motor speed is the rotational speed of the motor rotor per unit time, usually measured in revolutions per minute (r / min). It directly affects the rotational frequency of the magnetic field 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 dimension of the stator or rotor core of the motor, which affects the distribution range and magnetic flux density of the axial magnetic field. It is a geometric parameter characterizing the structural features of the motor in the calculation of axial electromagnetic force and is used to correct the magnetic field area. Axial electromagnetic force is the force along the motor axis generated by the interaction of electromagnetic fields during motor operation. It may cause axial movement of the motor shaft or changes in the axial load of the bearings, and is an important excitation source causing axial vibration of the electric drive system.

[0052] In the embodiments of this disclosure, when calculating the axial electromagnetic force based on electromagnetic power, motor speed, and core length parameters, the electromagnetic torque can first be obtained by combining the relationship that electromagnetic power equals the product of electromagnetic torque and motor angular velocity with motor speed. Then, considering the influence of core length on the distribution range of the axial magnetic field, an axial electromagnetic force calculation model incorporating electromagnetic power, motor speed, and core length is established using electromagnetic theory, and the axial electromagnetic force is then calculated. 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 action of the axial magnetic field. All three factors participate in the quantitative calculation of the axial electromagnetic force, and the specific value of the axial electromagnetic force is finally obtained through mathematical modeling.

[0053] 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 during actual motor operation can be 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 change in axial magnetic pull of the motor under different speed conditions, providing a key input for the calculation of bearing support force in the subsequent rigid-flexible coupled dynamic model. This enables the model to more realistically simulate the impact of motor axial vibration on the gear system and housing, improves the accuracy of multi-physics coupling analysis of electric drive systems, and provides a reliable theoretical basis for the control of axial vibration noise.

[0054] 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 from the simulation.

[0055] Circular integration refers to integrating the tangential electromagnetic force over the entire circumference of the air gap between the stator and rotor of the motor. This is used to calculate the resultant torque of the tangential electromagnetic force about the shaft center at each point, i.e., the electromagnetic torque. It is a method for converting force into torque. The electromagnetic torque is the torque that drives the motor rotor to rotate, obtained by circular integration of the tangential electromagnetic force, and its unit is... The size and stability of the magnetic field directly affect the power output and vibration characteristics of the motor. The non-sinusoidal distribution of the magnetic field of the permanent magnet means 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 and arrangement of the magnetic poles, which will lead to electromagnetic torque fluctuations. Torque fluctuations are the periodic fluctuations of electromagnetic torque caused by the change of rotor position during motor operation. They are usually characterized by fluctuation amplitude and frequency and are one of the important causes of motor vibration and noise, especially under high-speed conditions.

[0056] In this embodiment, the electromagnetic torque is calculated by integrating the tangential electromagnetic force along the circumferential direction. This is then combined with the simulated non-sinusoidal distribution characteristics of the permanent magnet magnetic field to obtain the torque fluctuation. Specifically, the distribution of the tangential electromagnetic force on the circumference of the air gap between the motor stator and rotor is not uniform and constant. The resultant torque, i.e., the electromagnetic torque, over the entire circumference needs to be obtained through integration. Furthermore, the permanent magnet magnetic field, due to its material properties and structural design, is not an ideal sinusoidal distribution. This non-sinusoidal characteristic causes periodic fluctuations in the electromagnetic torque during motor rotation. By simulating and analyzing the magnetic field distribution and incorporating this characteristic, the amplitude and frequency characteristics of the torque fluctuation can be accurately calculated.

[0057] By calculating the electromagnetic torque through integration 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, neglecting the influence of actual non-sinusoidal characteristics on torque. This step, however, 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 a more accurate torsional excitation input for subsequent vibration analysis of the electric drive system. In particular, for noise problems such as high-frequency howling caused by torque fluctuations, accurate quantification can be performed at the excitation source level, providing a reliable basis for the formulation of noise control strategies.

[0058] Step 210-4: Determine the tangential electromagnetic force, axial electromagnetic force, and torque fluctuation as excitation characteristic parameters.

[0059] 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 characteristic in the axial direction of the motor, and the torque fluctuation quantifies the dynamic change of torque caused by the non-sinusoidal distribution of the magnetic field. Together, the three constitute the core parameter system describing the electromagnetic excitation of the motor.

[0060] Defining tangential electromagnetic force, axial electromagnetic force, and torque fluctuation as excitation characteristic parameters comprehensively covers the multi-dimensional characteristics of motor electromagnetic excitation, providing standardized excitation inputs for the dynamic analysis of electric drive systems. This step, by integrating the tangential and axial force components and torque fluctuation parameters during motor operation, avoids the limitations of traditional single-parameter analysis. It allows subsequent rigid-flexible coupled dynamic models to simultaneously consider the effects of motor electromagnetic excitation in different directions, as well as the influence of torque fluctuation on the torsional vibration of the gear system. This improves the completeness and accuracy of system vibration characteristic analysis, providing multi-dimensional quantitative basis for noise source identification and optimized design.

[0061] Step 220: Based on the gear system dynamics model, establish a set of helical gear coupled vibration equations with multiple gear pairs, multiple gear positions, and three degrees of freedom (tangential, axial, and torsional). Based on the set of helical gear coupled vibration equations, calculate the gear meshing dynamic load parameters, which include the tangential dynamic meshing force, axial dynamic meshing force, torsional vibration load spectrum and load change data during multi-gear meshing.

[0062] In this embodiment of the disclosure, a set of coupled vibration equations for helical gears with multiple gear pairs, multiple gear positions, and three degrees of freedom (tangential, axial, and torsional) can be established based on the gear system dynamics model. Specifically, based on the gear system dynamics model, considering the working conditions of multiple gear pairs transmission and multiple gear switching, a set of coupled vibration equations reflecting the vibration characteristics in the three directions (tangential, axial, and torsional) of the helical gears is established. By comprehensively considering the influence of electromagnetic excitation from the motor, internal excitation from the helical gears, and multi-stage transmission, the set of equations is solved to obtain the tangential dynamic meshing force and axial dynamic meshing force of the gear pairs. Then, the torsional vibration load spectrum and load variation data are calculated using the base circle radius of the gears and the load-bearing torque, and finally, the dynamic load parameters of gear meshing are determined.

[0063] In one possible implementation of this disclosure, step 220, which involves calculating the dynamic load parameters of gear meshing based on the helical gear coupling vibration equations, may include the following steps:

[0064] Step 220-1: Based on the helical gear coupled vibration equation set, establish the dynamic equation that includes vibration characteristics in the tangential, axial and torsional directions.

[0065] Among them, the tangential vibration characteristic is the translational vibration of the gear in the circumferential tangential direction, caused by the tangential dynamic meshing force, corresponding to the displacement variable in the y-direction in the dynamic equation, which affects the smoothness of gear rotation; the axial vibration characteristic is the translational vibration of the gear along the axis, caused by the axial dynamic meshing force and the axial component force generated by the helical gear helix angle, corresponding to the displacement variable in the z-direction, which 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, caused by the torque and torque fluctuation generated by the tangential force through the base circle radius, corresponding to the angular displacement variable θ, which is the main factor causing the torsional vibration noise of the gear pair.

[0066] In the embodiments of this disclosure, based on the existing set of coupled vibration equations for multiple pairs of gears, multiple gear positions, and helical gears with three degrees of freedom, the displacements of the gear pairs in the tangential (translational vibration), axial (translational vibration), and torsional (rotational vibration) directions are used as variables. The inertial force, damping force, and elastic force of vibration in each direction are described by the mass matrix, damping matrix, and stiffness matrix, thereby establishing a dynamic equation considering the three-directional coupling effect.

[0067] By establishing a three-degree-of-freedom coupled dynamic equation, 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, it can more accurately reflect the bending-torsional-axial 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 be coupled with the flexible housing model. This multi-dimensional coupled modeling provides a theoretical basis for the accurate solution of gear meshing dynamic load parameters, enabling the calculated tangential / axial dynamic meshing force and torsional vibration load to more realistically reflect the stress state of the gear system under complex working conditions, laying a key foundation for subsequent rigid-flexible coupled dynamic analysis.

[0068] Step 220-2: Taking into account the electromagnetic excitation of the motor, the internal excitation of the helical gear, and the influence of multi-stage transmission, the dynamic equation is solved to obtain the tangential dynamic meshing force and axial dynamic meshing force of the gear pair.

[0069] Among them, the electromagnetic excitation of the motor refers to the tangential electromagnetic force, axial electromagnetic force, and torque fluctuation generated by the interaction of electromagnetic fields during motor operation. This serves as the external excitation input to the dynamic equations, affecting the vibration characteristics of the gear pair. The internal excitation of the helical gear is the excitation generated during helical gear transmission by factors such as time-varying meshing stiffness, gear manufacturing errors, and meshing impact. This is the intrinsic cause of the dynamic meshing force fluctuation of the gear pair and needs to be reflected in the dynamic equations through the stiffness matrix and time-varying parameters. The influence of multi-stage transmission refers to the impact of the transmission ratio, load distribution, and shaft stiffness of each gear pair on 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 stiffness matrix in the dynamic equation. The tangential dynamic meshing force is the dynamic force along the circumferential tangential direction during the meshing process of the gear pair. It is generated by the combined action of the tangential electromagnetic force of the motor, the tangential component force of the helical gear meshing, and the time-varying stiffness excitation. It can affect the rotational smoothness of the gear. The axial dynamic meshing force is the dynamic force along the axial direction during the meshing process of the gear pair. It is determined by the axial electromagnetic force of the motor, the axial component force generated by the helix angle of the helical gear, and the bearing support stiffness. It can affect the axial load of the bearing and the vibration of the housing.

[0070] In the embodiments of this disclosure, based on the established dynamic equations of helical gear coupled vibration including tangential, axial, and torsional three degrees of freedom, the tangential electromagnetic force, axial electromagnetic force, and torque fluctuation in the electromagnetic excitation of the motor are taken as external excitation inputs. At the same time, the internal excitations such as the time-varying meshing stiffness and error excitation of the helical gear, 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 by numerical methods (such as the Runge-Kutta method) to finally obtain the dynamic meshing force of the gear pair in the tangential and axial directions that varies with time.

[0071] By solving the dynamic equations through multi-source excitation coupling, accurate calculation of the dynamic load on gear pairs can be achieved. The introduction of electromagnetic excitation from the motor enables the model to reflect the influence of electromagnetic force fluctuations on gear meshing. The consideration of internal excitation of the helical gears ensures that the effects of time-varying meshing stiffness, manufacturing errors, and other factors on the dynamic meshing force are accurately characterized, while the inclusion of the influence of multi-stage transmission guarantees the rationality of load distribution across multiple gear pairs. The obtained tangential / axial dynamic meshing forces can realistically reflect the gear stress state of the electric drive system under complex operating conditions, providing crucial data support for gear strength verification, bearing life calculation, and system vibration and noise analysis, effectively improving the reliability and optimization accuracy of electric drive system design.

[0072] Step 220-3: Calculate the torsional vibration load using the base circle radius of the gear and the load torque, and obtain the torsional vibration load spectrum and load change data during multi-gear meshing.

[0073] Among them, the gear base circle radius is the radius of the gear's base circle, one of the basic geometric parameters of the gear, used to calculate the gear's tooth profile and meshing characteristics. In torsional vibration load calculation, it is used to convert torque into tangential force. The bearing torque is the torque borne by the gear during transmission, obtained by distributing the motor output torque through multiple transmission stages, reflecting the load magnitude of the gear pair under actual working conditions. The torsional vibration load is the dynamic load borne by the gear in the torsional direction, generated by the tangential force through the base circle radius. Its fluctuation will cause torsional vibration of the gear, which is one of the important factors leading to vibration and noise in the gear system. Multi-gear meshing refers to the meshing state of the gear transmission system at different gears. Different gears correspond to different transmission ratios and torque distributions, and the torsional vibration load will change with the gear position. The torsional vibration load spectrum is the frequency-amplitude distribution spectrum obtained after performing a Fourier transform on the torsional vibration load, used to analyze the frequency components of the torsional vibration load and the magnitude of each frequency component. The load change data is the data of the torsional vibration load changing over time, recording the load value at different times, used to describe the dynamic change process of the load.

[0074] In this embodiment of the present disclosure, the tangential force during gear meshing can be determined by multiplying the load torque by the base circle radius, based on the known base circle radius of the gear. Then, by combining the multi-gear transmission ratio and the torque distribution relationship under each gear, the torsional vibration load during meshing at different gear positions can be calculated. By performing a Fourier transform on the torsional vibration load, its spectral characteristics are obtained, and the load variation over time is recorded, thereby acquiring the torsional vibration load spectrum and load variation data.

[0075] Calculating torsional vibration loads by combining the base circle radius and the load-bearing torque can accurately reflect the torsional stress state of the gear pair under different gear positions. The base circle radius, as a fundamental geometric parameter of the gear, directly affects the conversion of torque into tangential force; the load-bearing torque reflects the magnitude of the load under actual operating conditions. The torsional vibration load calculated by combining these two parameters can realistically reflect the load variations during multi-gear meshing. 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 sources of the gear system; the load variation data provides quantitative support for gear strength design and system dynamic characteristic analysis, helping to improve the operational reliability of the electric drive system under multi-gear conditions.

[0076] Step 220-4: Determine the tangential dynamic meshing force, axial dynamic meshing force, torsional vibration load spectrum, and load change data of the gear pair as the gear meshing dynamic load parameters.

[0077] Among them, the tangential dynamic meshing force reflects the dynamic force along the tangential direction when the gear pair meshes, the axial dynamic meshing force reflects the load characteristics in the axial direction, the torsional vibration load spectrum quantifies the frequency components of the torsional load, and the load change data records the dynamic change of the load over time in each gear position. Together, these four constitute the core parameter system for describing the dynamic load of gear meshing.

[0078] By defining the tangential dynamic meshing force, axial dynamic meshing force, torsional vibration load spectrum, and load variation data of the gear pair as the dynamic load parameters for gear meshing, this method comprehensively covers the multi-dimensional load characteristics during gear meshing, providing standardized load inputs for the dynamic analysis of electric drive systems. This step, by integrating the force components in the tangential and axial directions and the load spectrum and variation data in the torsional direction of the gear pair, avoids the limitations of traditional single-parameter analysis. It allows 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 load during multi-gear switching. This improves the completeness and accuracy of the system vibration characteristic analysis, providing multi-dimensional quantitative basis for gear strength verification, bearing life calculation, and noise source identification.

[0079] Step 230: Using the excitation characteristic parameters and gear meshing dynamic load parameters as the mechanical excitation of the gear system, couple the motor electromagnetic excitation model, the gear system dynamic model, the bearing rigid model, and the housing flexible model to form a rigid-flexible coupled dynamic model.

[0080] In this embodiment, the excitation characteristic parameters such as tangential electromagnetic force, axial electromagnetic force, and torque fluctuation obtained from 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 load change data obtained from the gear system dynamic model, can be used as mechanical excitation sources and input into the corresponding models respectively. By considering the force transmission relationship between the motor and gear, the support constraint between the gear and bearing, and the rigid-flexible coupling effect between the bearing and the housing, the dynamic equations of each model are combined to establish a multi-physics field coupled dynamic equation that includes motor electromagnetic excitation, gear system vibration, bearing rigid support, and housing flexible deformation, thereby forming a rigid-flexible coupled dynamic model that can comprehensively reflect the dynamic interaction of rigid and flexible components of the electric drive system. This model can realize the coupled analysis of the dynamic characteristics of key components such as motor, gear, shaft, bearing, and housing, covering multi-degree-of-freedom vibration variables in the tangential, axial, and torsional directions of the gear system, providing a more accurate model basis for the vibration and noise analysis of the electric drive system.

[0081] Accordingly, step 230 may include the following steps:

[0082] Step 230-1: Establish the bearing support stiffness matrix corresponding to the bearing rigid model, and perform condensation processing on the shell flexible model to obtain the shell mass matrix, shell damping matrix and shell condensation stiffness matrix.

[0083] In this embodiment of the disclosure, a bearing rigidity model with stiffness as its core can be established based on the relationship between bearing displacement deformation and external loads. A bearing support stiffness matrix characterizing the bearing's support properties can then be determined based on this model. Specifically, by analyzing the displacement deformation of the bearing under radial, axial, and other external loads, a mathematical relationship between load and displacement can be established using Hooke's Law (stress is proportional to strain), thus constructing a bearing rigidity model with stiffness as its core. This model simplifies the bearing into a support element with specific stiffness parameters. Stiffness values ​​of the bearing in different directions are obtained through experimental testing or theoretical calculations, thereby forming a stiffness matrix characterizing the bearing's support properties and describing its ability to resist deformation in each degree of freedom.

[0084] Meanwhile, the finite element substructure analysis method can be used to condense the shell flexible model, obtaining the shell mass matrix, shell damping matrix, and condensed stiffness matrix to describe the shell's flexible vibration characteristics. 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, 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 condensation can significantly reduce the model's degrees of freedom while ensuring computational accuracy, efficiently describing the shell's flexible vibration characteristics and providing parameter support for the shell's flexible deformation in rigid-flexible coupled dynamic models.

[0085] Among them, bearing displacement deformation refers to the radial, axial, or angular displacement deformation of the bearing when subjected to external loads. Its magnitude is proportional to the load and is a fundamental parameter for establishing the bearing rigid model. The bearing rigid model simplifies the bearing into a mechanical model with specific stiffness properties, ignoring the complex internal structure of the bearing and describing its support characteristics with stiffness as the core, and 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 torsional), characterizing the bearing's ability to resist deformation in different directions, and is used to describe support constraints in the 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. This can reduce the model's degrees of freedom and improve computational efficiency. The flexible shell model is a dynamic model that considers the elastic deformation of the shell structure and is used to describe the flexible characteristics of the shell under vibration loads, which is different from the rigid model that ignores deformation. The condensation process is the process of reducing the order of the high-order finite element model to a low-order model through modal truncation or static condensation, retaining the main vibration modes to ensure computational accuracy. The shell mass matrix is ​​a matrix that characterizes the mass distribution of the shell, describing the inertial forces in the dynamic equations, and is obtained through finite element discretization. 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 condensed shell stiffness matrix is ​​a matrix that characterizes the elastic stiffness of the shell after condensation, used to describe the relationship between the flexible deformation of the shell and the load, retaining key stiffness characteristics.

[0086] By establishing a bearing rigidity model and determining the bearing support stiffness matrix, a quantitative description of the bearing support characteristics can be achieved, enabling the model to accurately reflect the rigid support effect of the bearing under different loads and providing reliable boundary conditions for gear system vibration analysis. Using the finite element substructure analysis method to condense the shell model can reduce model complexity while preserving key vibration characteristics of the shell, thus improving the computational efficiency of the rigid-flexible coupled dynamic model.

[0087] Step 230-2: Based on the bearing support stiffness matrix and the housing condensation stiffness matrix, connect the gear system dynamic model and the housing flexibility model to establish the mechanical transmission path between the gear system and the housing.

[0088] Among them, the mechanical transmission path refers to the path through which the vibration of the gear system is transmitted to the housing via the bearing, and at the same time the flexible reaction force of the housing is fed back to the gear system. It is constructed by the bearing support stiffness matrix and the housing condensation stiffness matrix, and is a mechanical bridge connecting the gear system and the housing, which can realize the bidirectional transmission of vibration between the two.

[0089] In this embodiment of the disclosure, the dynamic model of the gear system and the flexible model of the shell are connected based on the bearing support stiffness matrix and the shell condensation stiffness matrix. Essentially, this constructs a mechanical bridge for the transmission of gear system vibration 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 gear meshing will be transformed into a force on the shell through the bearing support stiffness matrix, while the flexible response characteristics of the shell are quantified by the shell condensation 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 bidirectional transmission of vibration between the two and forming a complete mechanical transmission path.

[0090] By implementing mechanical coupling between the gear system and the housing through the bearing support stiffness matrix, the accuracy and completeness of the rigid-flexible coupling dynamic model can be significantly improved. Firstly, the coordination between the bearing support stiffness matrix and the housing condensed stiffness matrix ensures the accuracy of the vibration transmission path, allowing for precise quantification of the excitation of the gear system's vibration on the housing and the reaction of the housing's flexibility on the gear system. Secondly, combining the condensed mass matrix and damping matrix of the housing provides a reliable parameter basis for subsequent construction of the rigid-flexible coupling dynamic equations, improving the accuracy of the entire electric drive system's rigid-flexible coupling dynamic model. Thirdly, this connection method considers the coupling effects between multiple components, enabling the model to more realistically reflect the dynamic characteristics of the electric drive system, providing effective theoretical support for analyzing system vibration and noise issues, and contributing to the optimization of the electric drive system's NVH performance.

[0091] Step 230-3: Substitute the excitation characteristic parameters and gear meshing dynamic load parameters into the gear system dynamic model to achieve coupling between the motor electromagnetic excitation model and the gear system dynamic model.

[0092] The excitation characteristic parameters, derived from the motor's electromagnetic excitation model, 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 generate tangential, axial, and torsional vibrations. The gear meshing dynamic load parameters, such as tangential meshing force and axial meshing force, are endogenous excitations calculated based on the meshing characteristics of the gear pair in the gear system dynamic model. These parameters quantify the dynamic loads during gear meshing. Both are used as mechanical excitation inputs to the gear system dynamic model. The motor's electromagnetic energy is then converted into the mechanical vibration energy of the gear system through electromagnetic force and torque, creating a linkage between the motor's electromagnetic excitation and the gear system's vibration response, thus achieving dynamic coupling between the two models.

[0093] The effects of this coupling method are mainly reflected in three aspects: First, it realizes the precise correlation between energy and mechanical transmission between the motor and gear system, enabling the model to truly reflect the transformation process of "electromagnetic excitation-mechanical vibration" in the electric drive system, overcoming the defect of traditional models that separate the connection between the motor and gear system; Second, by integrating external electromagnetic excitation and internal gear meshing excitation, it can comprehensively capture the composite vibration causes of the gear system, improve the accuracy of the dynamic model in representing the vibration characteristics of the system, and provide a reliable basis for analyzing high-frequency howling and other noise problems 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.

[0094] Step 230-4: Integrate the output excitation of the motor electromagnetic excitation model with the intrinsic excitation of gear meshing, and combine the shell mass matrix, shell damping matrix and shell condensation stiffness matrix to construct the rigid-flexible coupling dynamic equations corresponding to the rigid-flexible coupling dynamic model.

[0095] The output excitation is obtained by electromagnetic mechanical energy conversion from the motor electromagnetic excitation model, and the gear meshing endogenous excitation is calculated based on the meshing characteristics of the gear pair in the gear system dynamics model.

[0096] In this embodiment of the disclosure, the mechanical excitation (i.e., output excitation) generated by the electromagnetic excitation of the motor through energy conversion can be coupled with the endogenous excitation generated during the meshing of the gear pair due to time-varying stiffness and other characteristics. Then, the mass, damping, and condensation stiffness parameters of the flexible housing model are introduced to establish a multi-physics simultaneous equation. Specifically, the electromagnetic excitation is transmitted to the gear system through the motor shaft, driving the tangential, axial, and torsional vibrations of the gears. The endogenous excitation of gear meshing further enhances the dynamic load effect, while the mass, damping, and stiffness characteristics of the housing are coupled with the gear system through the bearing support stiffness matrix to form a rigid-flexible coupling dynamic equation including the motor, gear, bearing, and housing, thereby realizing a mathematical description of the dynamic interaction of multiple components of the electric drive system.

[0097] By integrating multi-source excitation with shell flexibility parameters to construct rigid-flexible coupled 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 gear meshing endogenous excitation 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 shell elastic deformation to system 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 under multiple degrees of freedom, such as gear tangential displacement and shell axial vibration acceleration, providing a quantitative basis for system vibration noise source identification, component strength verification, and optimized design.

[0098] Step 240: Transform the rigid-flexible coupling dynamic model into a state-space equation, solve the state-space equation using dimensionless transformation and piecewise linear method, and obtain multivariable time-domain data.

[0099] For embodiments of this disclosure, step 240 may include the following steps:

[0100] Step 240-1: By defining a state vector containing the system displacement and velocity, the rigid-flexible coupling dynamic equations corresponding to the rigid-flexible coupling dynamic model are transformed from second-order differential equations into a first-order state-space equation set.

[0101] In the embodiments of this disclosure, the displacement variables (such as gear tangential displacement and shell axial deformation) and their first derivatives (velocities) in the rigid-flexible coupling dynamic model can be combined into a state vector, and then the second-order differential equation can be reconstructed into a system of first-order equations using matrix operations.

[0102] State-space transformation can improve the solution efficiency and applicability of rigid-flexible coupled dynamic models. First-order state-space equations are more suitable for iterative solutions using numerical integration algorithms (such as the Runge-Kutta method), significantly reducing computational load compared to second-order differential equations, and are particularly suitable for transient response analysis of complex multi-degree-of-freedom systems. 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 the intuitive acquisition of system eigenvalues, transfer functions, and other parameters, providing a mathematical foundation for stability assessment, vibration mode identification, and active control strategy design of electric drive systems.

[0103] Step 240-2: Select characteristic reference quantities for the physical parameters in the state-space equations, and transform the physical parameters into dimensionless quantities based on the characteristic reference quantities to obtain the dimensionless state-space equations.

[0104] Physical parameters refer to quantities with actual physical meaning in the state-space equations, such as time parameters (representing the system's operating time), displacement parameters (representing the positional changes of components), and coefficients related to mass, damping, and stiffness in the equations. These parameters all have specific physical units. Characteristic reference quantities are reference quantities used for dimensionless transformation. They can include at least: characteristic time reference quantities, representing typical time scales in the system, usually selected based on the periodicity of the system itself, such as the period of one gear meshing or the period of change of electromagnetic force in a motor; characteristic displacement reference quantities, used to measure the reference displacement of the system's vibration amplitude, generally taking the maximum displacement that a component may produce during vibration, such as the maximum displacement of a gear along the meshing line during meshing; dimensionless quantities are unitless values ​​obtained by dividing physical parameters by their corresponding characteristic reference quantities. They reflect the proportional relationship between physical parameters and characteristic reference quantities and do not depend on a specific unit system; dimensionless state-space equations are equations obtained by converting all physical parameters in the original state-space equations into dimensionless quantities. At this point, the matrices and vectors in the equations are dimensionless, making it easier to perform universal dynamic analysis and comparisons between different systems.

[0105] In the embodiments of this disclosure, when processing the state-space equations, suitable characteristic reference quantities can be selected for the physical parameters (such as time and displacement) in the equations. For example, a characteristic time reference quantity (which can be understood as a representative time length in the system, such as the time it takes for a gear to complete one meshing) and a characteristic displacement reference quantity (such as the maximum displacement that a gear can reach when vibrating) can be determined. Then, based on these characteristic reference quantities, the physical parameters that originally had actual units are transformed into dimensionless values. For example, dividing the actual time by the characteristic time reference quantity yields a dimensionless time; dividing the actual time by the characteristic displacement reference quantity yields a dimensionless displacement. Through this transformation, the original state-space equations become dimensionless state-space equations, and the parameters in the equations no longer have specific physical units, but become relative numerical relationships.

[0106] By making the state-space equations dimensionless, on the one hand, the equations are no longer limited by specific system parameters. Regardless of the size of the gearbox or the material of the housing, a unified form can be used for analysis, facilitating comparisons of the dynamic characteristics of different systems. On the other hand, dimensionlessness avoids computational problems caused by large differences in parameter units, making the numerical solution process more stable and efficient. Furthermore, the parameters in the dimensionless equations more directly reflect the essential characteristics of the system; for example, the system's vibration frequency and damping degree can be more intuitively observed.

[0107] 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, the state-space equation is solved linearly based on the dimensionless state-space equation to obtain multivariable time-domain data.

[0108] In specific application scenarios, due to the nonlinear characteristics of rigid-flexible coupling dynamic models (such as the nonlinearity of gear meshing stiffness with load and shell flexible deformation), it is necessary to divide the time-varying parameters (i.e., time-varying parameters, such as time-varying meshing stiffness and nonlinear damping) in the state-space equations 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 approximated as constant values. Then, linear solutions are performed based on the dimensionless state-space equations to obtain the time-domain variation data of multiple variables in the system (such as gear tangential displacement, shell vibration velocity, bearing load, etc.), i.e., multivariable time-domain data. This approach transforms complex nonlinear problems into solving multiple linear problems, facilitating engineering applications.

[0109] By partitioning the time-varying parameters into linear intervals and solving the equations dimensionlessly, the challenge of solving nonlinear problems in rigid-flexible coupling models can be effectively addressed. On one hand, piecewise linearization of the time-varying parameters allows for the use of mature linear system solution methods within each interval, improving computational efficiency and stability while avoiding the convergence difficulties associated with directly solving nonlinear equations. On the other hand, multivariate time-domain data comprehensively reflects the dynamic response of the system under different operating conditions. For example, it can acquire data on the fluctuations of dynamic loads over time during gear meshing and the real-time changes in the vibration amplitude of the housing, providing detailed time-domain data support for system vibration and noise analysis and component fatigue life assessment. Furthermore, this method balances model accuracy with engineering practicality, more closely reflecting the actual operating conditions of electric drive systems.

[0110] Step 250: Using the electromagnetic excitation in the excitation characteristic parameters as the input energy, and combining the gear meshing dynamic load parameters and multivariate time-domain data, calculate the transmission efficiency value of vibration energy between the motor, gear, bearing and housing components through the principle of energy conservation.

[0111] In this embodiment of the disclosure, the energy provided by the electromagnetic excitation of the motor can be taken as the total input energy of the system. Then, using dynamic load parameters of gear meshing, such as tangential meshing force and axial meshing force, the energy consumed or transmitted during gear meshing can be determined. Simultaneously, using multivariate time-domain data, such as the displacement and velocity changes of each component over time, the changes in kinetic and potential energy of each component during vibration can be calculated. Finally, according to the principle of energy conservation, the input energy is compared with the energy transmitted and consumed between components to obtain the energy transmission efficiency value between different components, thereby evaluating the energy transmission between components of the electric drive system.

[0112] Accordingly, when calculating the transmission efficiency of vibration energy among the motor, gears, bearings, and housing components using the principle of energy conservation, step 250 of the embodiment may include the following steps:

[0113] Step 250-1: Based on the tangential electromagnetic force, axial electromagnetic force, and torque fluctuation in the excitation characteristic parameters, calculate the motor input energy during the motor's operation time.

[0114] In this embodiment of the present disclosure, when calculating the motor input energy during motor operation based on the tangential electromagnetic force, axial electromagnetic force, and torque fluctuation in the excitation characteristic parameters, these three types of electromagnetic excitation can be multiplied by their corresponding speed parameters, and then the total energy can be obtained by integration and summation. The calculation method can be to integrate and sum the products of the tangential electromagnetic force and tangential velocity, the axial electromagnetic force and axial velocity, and the torque fluctuation and motor 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; multiplying it by the tangential velocity of the motor rotor yields the tangential power. The axial electromagnetic force is the force along the motor axis; multiplying it by the axial velocity of the rotor yields the axial power. The torque fluctuation is the periodic change in the motor's electromagnetic torque; multiplying it by the motor angular velocity yields the torsional power. Integrating and summing the powers in these three directions over the motor operation time yields the total input energy of the motor during that time period. This calculation method considers the energy input of the motor's electromagnetic excitation in multiple directions.

[0115] Among them, the motor input energy is the total energy obtained by the motor from electromagnetic excitation during operation. It is obtained by integrating and summing the products of electromagnetic excitation in each direction and the corresponding speed parameters, and is an important indicator for measuring the motor's energy input. The tangential velocity is the speed of the motor rotor in the tangential direction of the circumference. Multiplying it by the tangential electromagnetic force yields the energy input rate in the tangential direction. The axial velocity is the speed of the motor rotor in the axial direction. The product of the axial electromagnetic force and the axial velocity reflects the energy input in the axial direction. The motor angular velocity is the angular velocity of the motor rotor. Multiplying the torque fluctuation by the angular velocity yields the energy input power in the torsional direction.

[0116] Calculating motor input energy by integrating the product of multi-directional electromagnetic excitation and speed parameters provides a comprehensive and accurate reflection of the motor's energy input characteristics during actual operation. Tangential electromagnetic force, axial electromagnetic force, and torque fluctuation correspond to electromagnetic excitations in different dimensions of the motor, and their product integrals with the corresponding speed parameters encompass energy transfer in multiple directions, including rotation, axial displacement, and torsional vibration. This calculation method avoids the limitations of considering only a single direction of energy input, more realistically reflecting the motor's energy input state under complex operating conditions. This provides accurate foundational data for subsequent analysis of energy transfer efficiency among components such as the motor, gears, bearings, and housing in the electric drive system, aiding in the evaluation of the system's energy utilization efficiency and the energy losses of each component.

[0117] Step 250-2: Calculate the shell vibration energy based on multivariable time-domain data.

[0118] In the embodiments of this disclosure, when calculating the vibration energy of the shell based on multivariate time-domain data, the shell's condensation stiffness matrix, displacement vector, damping matrix, and velocity vector can be comprehensively considered, and the sum of elastic potential energy and damping energy dissipation can be obtained through integration. Specifically, during vibration, the shell generates elastic potential energy due to elastic deformation, 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 consume vibration energy. Damping energy dissipation is related to the vibration velocity and the damping matrix; the faster the velocity and the greater the damping, the more energy is consumed. By utilizing the changes in shell displacement and velocity over time in the multivariate time-domain data, combined with the condensation stiffness matrix and damping matrix, these two parts of energy are calculated separately and then summed to obtain the total energy of the shell during vibration.

[0119] Among them, the shell displacement vector is a vector describing the positional changes of each node of the shell during vibration, 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 dissipation; the elastic potential energy is the energy stored in the shell due to elastic deformation, which is related to displacement and stiffness. The greater the deformation and the higher the stiffness, the greater the potential energy; the damping energy dissipation is the energy loss caused by internal friction of the material and structural damping during shell vibration, which is related to vibration velocity and damping coefficient.

[0120] 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. Elastic potential energy calculation reflects the elastic deformation capacity of the shell structure, while damping energy dissipation calculation reflects the shell's vibration attenuation effect. Combining these two methods allows for a comprehensive assessment of the shell's vibration energy characteristics. This provides crucial data for noise control in electric drive systems; regions with high elastic potential energy may generate larger vibration amplitudes, while areas with low damping energy dissipation require optimization of damping characteristics to reduce vibration. Furthermore, this calculation method considers the condensation parameters of the shell's flexible model, ensuring both computational efficiency and accuracy in energy analysis, and aiding in the identification of weak points in the shell and areas of concentrated vibration energy.

[0121] Step 250-3: Calculate the energy received by the gear based on the tangential meshing force and axial meshing force in the dynamic load parameters of gear meshing, as well as the gear displacement in the multivariable time domain data.

[0122] Among them, tangential meshing force is the dynamic force along the circumferential tangential direction when the gear pair meshes, which is the main force driving the gear rotation. Its magnitude and direction change with the gear meshing process; axial meshing force is the dynamic force along the axial direction when the gear pair meshes, which is generated by factors such as the helix angle of the helical gear, and will cause the gear to be subjected to force in the axial direction; gear displacement is the positional change of the gear during vibration, including tangential displacement and axial displacement, which reflects the motion state of the gear; gear received energy is the energy received by the gear through the work done by the meshing force during vibration, which is an important indicator for evaluating the gear's energy input and working state.

[0123] In this embodiment of the disclosure, the tangential meshing force, acting as the driving force along the circumferential tangential direction during gear meshing, drives the gear to rotate, while the axial meshing force acts along the axial direction, causing the gear to move axially. These two forces do work on the gear during vibration, and the magnitude of the work is determined by the product of the force and the gear's displacement in the corresponding direction. Specifically, the tangential and axial displacement changes of the gear at different times can be obtained first through multivariate time-domain data. Then, the tangential meshing force is multiplied by the tangential displacement at each time point, and the axial meshing force is multiplied by the axial displacement to obtain the work done by the two forces at that time point. Finally, the work done at all times during the entire vibration process is integrated and accumulated to obtain the total energy received by the gear during vibration, i.e., the energy received by the gear.

[0124] Calculating the energy received by a gear by integrating the product of meshing force and gear displacement allows for accurate quantification of the energy acquired by the gear from the motor and other components during meshing. Tangential and axial meshing forces, as the main dynamic loads during gear meshing, directly reflect the amount of work done on the gear by integrating their product with gear displacement, thus indicating the magnitude of the energy received by the gear. This calculation method considers the force and displacement of the gear in both tangential and axial directions, comprehensively reflecting the gear's energy reception status. The obtained gear received energy allows for analysis of the gear's energy input under different operating conditions, providing crucial data support for evaluating gear workload, fatigue life, and optimizing gear design, ultimately contributing to improved reliability and efficiency of gear systems.

[0125] Step 250-4: Calculate the energy received by the bearing based on the tangential meshing force and axial meshing force in the dynamic load parameters of gear meshing, as well as the bearing displacement in the multivariable time domain data.

[0126] Among them, bearing displacement is the amount of deformation generated by the bearing when it is subjected to load, such as the relative displacement between the inner and outer rings, which reflects the actual response of the bearing support stiffness; bearing received energy is the energy received by the bearing in the process of supporting the gear system due to resisting deformation, which is generated by the coupling effect of load and displacement, and is an important indicator for evaluating the bearing load capacity.

[0127] In this embodiment, the tangential and axial meshing forces generated during gear meshing are first identified. These forces are transmitted to the bearing through the gear shaft, becoming tangential and axial dynamic loads acting on the bearing. Next, the bearing displacement data at different times, such as radial and axial deformation, is acquired. Since the bearing support stiffness matrix indicates the bearing's resistance to deformation, the bearing displacement is multiplied by the corresponding parameter in the stiffness matrix at each time step to obtain the bearing support force at that moment. Then, the entire vibration process is integrated over time, and the work done by the bearing support force at each moment is summed up, thus calculating the total energy received by the bearing during vibration due to the support gear system. The tangential and axial dynamic loads transmitted to the bearing through the gear shaft are key input parameters for determining the bearing support force and calculating the energy received by the bearing in subsequent calculations. These loads cause radial and axial displacements in the bearing. Combined with the bearing support stiffness matrix, the bearing support force at different times can be calculated from the displacement. Then, by multiplying the support force by the displacement and integrating over time, the total energy received by the bearing during vibration can be quantified, thereby evaluating the bearing's load-bearing state and energy loss characteristics.

[0128] This process fully considers the coupling effect between bearing stiffness characteristics and actual displacement, thus enabling the quantitative calculation of energy input when load is transmitted through the bearing. By calculating the energy received by the bearing through the integral of the product of the bearing support stiffness matrix and displacement, the energy loss and load-bearing characteristics of the bearing in the electric drive system can be accurately assessed. When tangential and axial meshing forces are transmitted to the bearing through the gear shaft, the bearing stiffness affects its deformation, which in turn affects the load transmission efficiency. By calculating the energy received by the bearing, the stress state of the bearing under different operating 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.

[0129] Step 250-5: Calculate the transmission efficiency of vibration energy between the motor, gears, bearings, and other components of the housing based on the input energy of the motor, the vibration energy of the housing, the energy received by the gears, and the energy received by the bearings.

[0130] Specifically, as one possible implementation, the ratio of the shell vibration energy to the motor input energy can be determined as the transmission efficiency value of vibration energy from the motor to the shell.

[0131] This step, through energy ratio calculation, provides a direct assessment of the efficiency of energy transfer from motor vibration to the housing in an electric drive system. A high efficiency value indicates that the motor vibration energy easily excites housing vibration through the transmission chain, potentially leading to increased radiated noise from the housing. Conversely, a low efficiency value indicates significant energy loss during transmission through intermediate components, resulting in relatively weaker housing vibration. This analysis can provide a basis for system vibration reduction design, such as reducing energy transfer efficiency to the housing by optimizing gear meshing stiffness or bearing damping, thereby reducing housing vibration noise.

[0132] As another possible implementation, the ratio of energy received by the gear to energy input to the motor can be determined as the efficiency value of vibration energy transmission from the motor to the gear.

[0133] This efficiency calculation assesses the gear system's ability to receive energy from the motor. Low efficiency may indicate high gear meshing losses (such as impacts caused by meshing errors) or insufficient transmission chain stiffness, resulting in significant energy loss during transmission from the motor to the gears. High efficiency, on the other hand, indicates that the gears can effectively receive energy from the motor and transfer it to subsequent components. This analysis helps optimize gear parameters (such as module and pressure angle), improve energy transfer efficiency, and reduce the risk of gear fatigue damage.

[0134] As another possible implementation, the ratio of energy received by the bearing to energy received by the gear can be determined as the transmission efficiency of vibration energy from the gear to the bearing.

[0135] The energy transfer efficiency from gears to bearings can be used to assess the degree of energy loss in bearings. High efficiency indicates that more energy is transferred from the gears to the bearings, which may lead to bearing overload or overheating. 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 choosing high-damping bearings to reduce energy transfer efficiency and decrease bearing fatigue wear.

[0136] As another possible implementation, the ratio of the shell vibration energy to the energy received by the bearing can be determined as the transmission efficiency value of vibration energy from the bearing to the shell.

[0137] This efficiency calculation identifies the intensity of the energy source causing the shell vibration. High efficiency indicates that the bearing transfers a large amount of energy to the shell, making the shell prone to resonance or high-frequency vibration. Low efficiency indicates that the bearing obstructs energy transfer, resulting in less shell vibration. This analysis helps optimize bearing support stiffness or shell structure, cuts off energy transfer paths, and reduces the level of shell vibration noise radiation.

[0138] Step 260: Compare the magnitudes of the vibration energy transmission efficiency values ​​between each component, and based on the comparison results, select the key noise transmission path of the vehicle electric drive system from multiple transmission paths.

[0139] 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 energy transfer efficiency between components; the transfer path is the route of vibration energy transfer between various components of the electric drive system, such as motor → gear, gear → bearing, bearing → housing, etc.; the critical 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.

[0140] In this embodiment of the disclosure, by comparing the vibration energy transfer efficiency values ​​between various components such as the motor to the housing, the motor to the gears, the gears to the bearings, and the bearings to the housing, key noise transmission paths can be selected from multiple energy transfer paths in the vehicle electric drive system. Specifically, a path with a higher transfer efficiency value means that the vibration energy transfer loss is smaller along that path, and energy is more easily transferred through that path to excite component vibration, thereby generating noise. Therefore, among multiple transmission paths, the paths with higher transfer 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.

[0141] By quantifying and comparing the vibration energy transfer efficiency between components, key noise transmission paths can be screened, allowing for precise identification of energy transfer paths that significantly contribute to noise in electric drive systems. This provides a clear target for noise control in electric drive systems, enabling the implementation of corresponding vibration reduction and noise reduction measures for key noise transmission paths. Examples include optimizing gear meshing 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. This more effectively reduces system noise and improves the vehicle's NVH (noise, vibration, and harshness) performance.

[0142] Suppose that in a certain vehicle electric drive system, the calculated vibration energy transfer efficiency values ​​for each transmission path are as follows: motor to housing: 35%; motor to gear: 60%; gear to bearing: 45%; bearing to housing: 50%. Comparing these efficiency values, the motor to gear transmission efficiency (60%) is the highest, followed by bearing to housing (50%), gear to bearing (45%), and motor to housing (35%). Therefore, based on the comparison of transmission efficiency 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 a significant amount of vibration energy from the motor is transferred to the gears, and the bearing transfers a considerable amount of energy to the housing, thus exciting gear and housing vibrations and generating noise. For these two critical paths, measures such as optimizing gear meshing precision to reduce the energy transfer efficiency from motor to gear, or increasing bearing damping to reduce the energy transfer from bearing to housing, can be taken to reduce system noise.

[0143] In specific application scenarios, as an optimization approach, after identifying the critical noise transmission paths in an automotive electric drive system, structural parameters of components along these paths (such as gears, bearings, and housings) can be optimized. This includes adjusting gear module, bearing stiffness, or housing wall thickness. After optimization, a rigid-flexible coupling dynamic model is reconstructed based on the new parameters. The state-space equations are then solved again, and the transmission efficiency is calculated. The optimization effect is verified by comparing the efficiency values ​​before and after optimization, until the vibration energy transmission efficiency of the critical path is reduced to a preset target value (e.g., from 60% to 30%). This process, through a closed-loop "analysis-optimization-verification" workflow, achieves directional control of the noise transmission path.

[0144] Accordingly, the implementation steps 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 equation and calculating the transmission efficiency value to verify the optimization effect until the transmission efficiency value corresponding to the vibration energy on the key noise transmission path is reduced to the preset target value.

[0145] 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 the optimization measures can be ensured: on the one hand, it avoids performance degradation caused by blindly modifying component parameters (such as insufficient gear strength); on the other hand, quantified efficiency value verification can intuitively reflect the optimization effect, ensuring the achievement of noise control targets. For example, if the critical path is "bearing → housing", increasing bearing damping or changing the housing rib layout can significantly reduce energy transfer efficiency, thereby reducing housing vibration noise and improving vehicle NVH performance.

[0146] In summary, the technical solution of this application, through multi-physics coupled modeling and efficient solution, effectively solves the problems of insufficient accuracy in single-physics modeling and low solution efficiency in strongly nonlinear systems in existing technologies. Specifically, by using finite element simulation to solve the characteristic parameters of the motor's electromagnetic excitation, and combining the gear system dynamic model to establish a set of helical gear coupled vibration equations, the interaction between electromagnetic excitation and gear bending-torsional-axial coupled vibration can be comprehensively considered. The motor, gear, bearing, and housing models are coupled to form a rigid-flexible coupled dynamic model. The mechanical transmission path is modeled through the bearing stiffness matrix and the housing condensation matrix, which can accurately reflect the reaction of the flexible support of the housing on the system vibration, making up for the defects of traditional simplified models in multi-field coupling and flexible influence characterization. By transforming the state-space equations, dimensionlessization, and piecewise linear solution, the problem of poor convergence in the calculation of strongly 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 can be calculated, and the key noise path between the motor, gear, bearing, and housing can be quantitatively located. By combining the optimization and iteration process, a complete technical path from modeling and analysis to optimization and verification can be provided for NVH problems such as high-frequency howling under high-speed operating conditions, so that noise optimization design has a reliable theoretical basis and quantitative support.

[0147] Furthermore, as Figure 1 and Figure 2 The specific implementation of the method shown in this embodiment provides a vibration analysis device for an automotive 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.

[0148] Analysis module 31 can be used to analyze excitation characteristic parameters and gear meshing dynamic load parameters based on the created motor electromagnetic excitation model and gear system dynamic model;

[0149] The coupling module 32 can be used to use the excitation characteristic parameters and gear meshing dynamic load parameters as mechanical excitation of the gear system, and to couple the motor electromagnetic excitation model, gear system dynamic model, bearing rigid model and housing flexible model to form a rigid-flexible coupled dynamic model.

[0150] The first calculation module 33 can be used to transform 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 multivariable time-domain data.

[0151] The second calculation module 34 can be used to calculate the transmission efficiency value of vibration energy between the motor, gears, bearings and housing components based on excitation characteristic parameters, gear meshing dynamic load parameters and multivariate time domain data, and locate the key noise transmission path of the vehicle electric drive system according to the magnitude of the transmission efficiency value.

[0152] In some embodiments of this application, the analysis module 31 can be specifically used to simulate the electromagnetic excitation model of the motor using finite element simulation software, solve for the excitation characteristic parameters including tangential electromagnetic force, axial electromagnetic force and torque fluctuation; based on the gear system dynamic model, establish a set of helical gear coupled vibration equations with multiple gear pairs, multiple gears and including tangential, axial and torsional three degrees of freedom, and calculate 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 and load change data when meshing in multiple gears based on the set of helical gear coupled vibration equations.

[0153] In some embodiments of this application, the coupling module 32 can be specifically used to establish the bearing support stiffness matrix corresponding to the bearing rigid model, and to perform condensation processing on the shell flexible model to obtain the shell mass matrix, shell damping matrix, and shell condensation stiffness matrix; based on the bearing support stiffness matrix and the shell condensation stiffness matrix, the gear system dynamic model and the shell flexible model are connected to establish the mechanical transmission path between the gear system and the shell; the excitation characteristic parameters and gear meshing dynamic load parameters are substituted into the gear system dynamic model to realize the coupling between the motor electromagnetic excitation model and the gear system dynamic model; the output excitation of the motor electromagnetic excitation model and the gear meshing intrinsic excitation are integrated, and combined with the shell mass matrix, shell damping matrix, and shell condensation stiffness matrix, the rigid-flexible coupling dynamic equation corresponding to the rigid-flexible coupling dynamic model is constructed, wherein the output excitation is obtained by the motor electromagnetic excitation model through electromagnetic mechanical energy conversion, and the gear meshing intrinsic excitation is calculated based on the meshing characteristics of the gear pair in the gear system dynamic model.

[0154] In some embodiments of this application, the first calculation module 33 can be specifically used to transform the rigid-flexible coupling dynamic equations corresponding to the rigid-flexible coupling dynamic model from second-order differential equations into a first-order state-space equation set by defining a state vector containing system displacement and velocity; select characteristic reference quantities for the physical parameters in the state-space equations, and transform the physical parameters into dimensionless quantities based on the characteristic reference quantities to obtain dimensionless state-space equations. 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 equations are divided into multiple linear intervals according to different working conditions, and linear solutions are performed based on the dimensionless state-space equations in each linear interval to obtain multivariable time-domain data.

[0155] In some embodiments of this application, the second calculation module 34 can be specifically used to use electromagnetic excitation in the excitation characteristic parameters as input energy, combined with gear meshing dynamic load parameters and multivariate time-domain data, to calculate the transmission efficiency value of vibration energy between the motor, gear, bearing and housing components through the principle of energy conservation; compare the magnitude of the transmission efficiency value corresponding to the vibration energy between each component, and screen the key noise transmission path of the vehicle electric drive system from multiple transmission paths based on the comparison results.

[0156] In some embodiments of this application, when calculating the transmission efficiency of vibration energy among the motor, gears, bearings, and housing components using the principle of energy conservation, the second calculation module 34 can specifically be used to calculate the motor input energy during operation 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 received energy based on the tangential meshing force, axial meshing force in the gear meshing dynamic load parameters, and the gear displacement in the multivariate time-domain data; calculate the bearing received energy based on the tangential meshing force, axial meshing force in the gear meshing dynamic load parameters, and the bearing displacement in the multivariate time-domain data; and 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 received energy, and bearing received energy.

[0157] In some embodiments of this application, such as Figure 4 As shown, the device also includes: an optimization module 35;

[0158] The optimization module 35 can be used to optimize the structural parameters of components on the critical 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 equation and calculating the transmission efficiency value are repeated to verify the optimization effect until the transmission efficiency value corresponding to the vibration energy under the critical noise transmission path is reduced to the preset target value.

[0159] It should be noted that other corresponding descriptions of the functional units involved in the vibration analysis device for an automotive electric drive system provided in this embodiment can be found in [reference needed]. Figure 1 and Figure 2 The corresponding descriptions in [the document] will not be repeated here.

[0160] Based on the above, Figure 1 and Figure 2 Accordingly, this embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the above-described method. Figure 1 and Figure 2 The vibration analysis method for the vehicle electric drive system is shown.

[0161] Based on this understanding, the technical solution of this application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as CD-ROM, USB flash drive, mobile hard drive, etc.) and includes several instructions to cause an electronic device (such as personal computer, server, or network device, etc.) to execute the methods of various implementation scenarios of this application.

[0162] Based on the above, Figure 1 and Figure 2 The method shown, and Figure 3 and Figure 4 To achieve the above objectives, the present application also provides an electronic device, specifically a personal computer, tablet computer, server, or other network device, as shown in the virtual device embodiment. This device includes a storage medium and a processor; the storage medium stores a computer program; the processor executes the computer program to achieve the above-described objectives. Figure 1 and Figure 2 The vibration analysis method for the vehicle electric drive system is shown.

[0163] Optionally, the aforementioned physical devices may also include a user interface, a network interface, a camera, radio frequency (RF) circuitry, sensors, audio circuitry, a Wi-Fi module, etc. The user interface may include a display screen, input units such as a keyboard, etc., and optional user interfaces may also include USB interfaces, card reader interfaces, etc. The network interface may optionally include standard wired interfaces, wireless interfaces (such as Wi-Fi interfaces), etc.

[0164] Those skilled in the art will understand that the physical device structure provided in this embodiment does not constitute a limitation on the physical device, and may include more or fewer components, or combine certain components, or have different component arrangements.

[0165] 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 aforementioned physical device, supporting the operation of information processing programs and other software and / or programs. The network communication module is used to enable communication between the various components within the storage medium, as well as communication with other hardware and software in the information processing physical device.

[0166] Through the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary general-purpose hardware platform, or it can be implemented by hardware.

[0167] This invention effectively solves the problems of insufficient accuracy in single-physics modeling and low solution efficiency in strongly nonlinear systems in existing technologies by using multi-physics coupled modeling and efficient solution. Specifically, it uses finite element simulation to solve the characteristic parameters of the motor's electromagnetic excitation, and establishes a set of coupled vibration equations for helical gears by combining the dynamic model of the gear system. This comprehensively considers the interaction between electromagnetic excitation and the bending-torsional-axial coupled vibration of the gears. The motor, gear, bearing, and housing models are coupled to form a rigid-flexible coupled dynamic model. The mechanical transmission path is modeled by the bearing stiffness matrix and the housing condensation matrix, which can accurately reflect the reaction of the flexible support of the housing on the system vibration, making up for the shortcomings of traditional simplified models in multi-field coupling and the characterization of flexible effects. By transforming the state-space equations, dimensionlessizing them, and solving them using piecewise linear methods, the problem of poor convergence in the calculation of strongly 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, and housing can be quantitatively located. By combining the optimization and iteration process, a complete technical path from modeling and analysis to optimization and verification can be provided for NVH problems such as high-frequency howling under high-speed operating conditions, so that noise optimization design has a reliable theoretical basis and quantitative support.

[0168] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing this application. Those skilled in the art will understand that the modules in the apparatus of the embodiment can be distributed within the apparatus of the embodiment as described, or can be modified to be located in one or more apparatuses different from this embodiment. The modules of the above-described embodiment can be combined into one module, or further divided into multiple sub-modules.

[0169] The serial numbers in this application are for descriptive purposes only and do not represent the superiority or inferiority of any particular implementation scenario. The above disclosures are merely a few specific implementation scenarios of this application; however, this application is not limited thereto, and any variations conceived by those skilled in the art should fall within the protection scope of this application.

Claims

1. A vibration analysis method for an automotive electric drive system, characterized in that, include; Based on the created electromagnetic excitation model of the motor and the dynamic model of the gear system, the excitation characteristic parameters and the dynamic load parameters of gear meshing are analyzed. The excitation characteristic parameters and the gear meshing dynamic load parameters are used as the mechanical excitation of the gear system. The electromagnetic excitation model of the motor, the dynamic model of the gear system, the rigid bearing model, and the flexible housing model are coupled to form a rigid-flexible coupled dynamic model. This includes: establishing the bearing support stiffness matrix corresponding to the rigid bearing model; and performing a condensation process on the flexible housing model to obtain the housing mass matrix, housing damping matrix, and condensed housing stiffness matrix. Based on the bearing support stiffness matrix and the condensed housing stiffness matrix, the dynamic model of the gear system and the flexible housing model are connected to establish the mechanical transmission between the gear system and the housing. The path involves substituting the excitation characteristic parameters and the gear meshing dynamic load parameters into the gear system dynamic model to achieve coupling between the motor electromagnetic excitation model and the gear system dynamic model; integrating the output excitation of the motor electromagnetic excitation model with the gear meshing intrinsic excitation, and combining the shell mass matrix, the shell damping matrix, and the shell condensation stiffness matrix to construct the rigid-flexible coupling dynamic equations corresponding to the rigid-flexible coupling dynamic model, wherein the output excitation is obtained by the motor electromagnetic excitation model through electromagnetic mechanical energy conversion, and the gear meshing intrinsic excitation is calculated based on the meshing characteristics of the gear pair in the gear system dynamic model; The rigid-flexible coupling dynamic model is transformed into a state-space equation, and the state-space equation is solved by dimensionless transformation and piecewise linear method to obtain multivariable time-domain data. Based on the excitation characteristic parameters, the gear meshing dynamic load parameters, and the multivariate time-domain data, the transmission efficiency value of vibration energy between the motor, gears, bearings, and housing components is calculated, and the key noise transmission path of the vehicle electric drive system is located according to the magnitude of the transmission efficiency value.

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

3. The method according to claim 1, characterized in that, The rigid-flexible coupling dynamic model is transformed into a state-space equation. The state-space equation is then solved using dimensionless transformation and piecewise linear methods to obtain multivariable time-domain data, including: By defining a state vector that includes system displacement and velocity, the rigid-flexible coupling dynamic equations corresponding to the rigid-flexible coupling dynamic model are transformed from second-order differential equations into a set of first-order state-space equations. For the physical parameters in the state-space equation, characteristic reference quantities are selected, and the physical parameters are transformed into dimensionless quantities based on the characteristic reference quantities to obtain the dimensionless state-space equation. 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. In each linear interval, the dimensionless state-space equation is solved linearly to obtain multivariable time-domain data.

4. The method according to claim 1, characterized in that, Based on the excitation characteristic parameters, the gear meshing dynamic load parameters, and the multivariate time-domain data, the transmission efficiency value of vibration energy between the motor, gears, bearings, and housing components is calculated. The key noise transmission paths of the vehicle electric drive system are located based on the magnitude of the transmission efficiency value, including: Using the electromagnetic excitation in the excitation characteristic parameters as the input energy, and combining the gear meshing dynamic load parameters with the multivariable time-domain data, the transmission efficiency value of vibration energy between the motor, gear, bearing and housing components is calculated by the principle of energy conservation. By comparing the magnitudes of the vibration energy between each component and the corresponding transmission efficiency values, the key noise transmission path of the vehicle electric drive system is selected from multiple transmission paths based on the comparison results.

5. The method according to claim 4, characterized in that, The calculation of the transmission efficiency of vibration energy between the motor, gears, bearings, and housing components using the principle of energy conservation includes: Based on the tangential electromagnetic force, axial electromagnetic force, and torque fluctuation in the excitation characteristic parameters, the motor input energy during the running time is calculated. Calculate the shell vibration energy based on the multivariable time-domain data; The energy received by the gear is calculated based on the tangential meshing force and axial meshing force in the gear meshing dynamic load parameters, and the gear displacement in the multivariable time domain data. The energy received by the bearing is calculated based on the tangential meshing force and axial meshing force in the gear meshing dynamic load parameters, and the bearing displacement in the multivariable time domain data. Based on the input energy of the motor, the vibration energy of the housing, the energy received by the gear, and the energy received by the bearing, the transmission efficiency value of vibration energy between the motor, gear, bearing, and housing components is calculated.

6. The method according to any one of claims 1 to 5, characterized in that, The method further includes: Optimize the structural parameters of components along key noise transmission paths; Based on the optimized structural parameters, the rigid-flexible coupling dynamic model is reconstructed, and the steps of solving the state space equation and calculating the transmission efficiency value are repeated to verify the optimization effect until the transmission efficiency value corresponding to the vibration energy under the key noise transmission path is reduced to the preset target value.

7. A vibration analysis device for an automotive electric drive system, characterized in that, include; The analysis module is used to analyze the excitation characteristic parameters and gear meshing dynamic load parameters based on the created motor electromagnetic excitation model and gear system dynamic model. The coupling module is used to couple the excitation characteristic parameters and the gear meshing dynamic load parameters as mechanical excitations for the gear system, and to couple the motor electromagnetic excitation model, the gear system dynamic model, the bearing rigid model, and the housing flexible model to form a rigid-flexible coupled dynamic model. This includes: establishing the bearing support stiffness matrix corresponding to the bearing rigid model; and performing a condensation process on the housing flexible model to obtain the housing mass matrix, housing damping matrix, and housing condensed stiffness matrix; based on the bearing support stiffness matrix and the housing condensed stiffness matrix, connecting the gear system dynamic model and the housing flexible model to establish a coupling between the gear system and the housing. Mechanical transmission path; Substitute the excitation characteristic parameters and the gear meshing dynamic load parameters into the gear system dynamic model to achieve coupling between the motor electromagnetic excitation model and the gear system dynamic model; Integrate the output excitation of the motor electromagnetic excitation model and the gear meshing intrinsic excitation, and combine the shell mass matrix, the shell damping matrix and the shell condensation stiffness matrix to construct the rigid-flexible coupling dynamic equation corresponding to the rigid-flexible coupling dynamic model, wherein the output excitation is obtained by the motor electromagnetic excitation model through electromagnetic mechanical energy conversion, and the gear meshing intrinsic excitation is calculated based on the meshing characteristics of the gear pair in the gear system dynamic model; The first calculation module is used to transform 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 multivariable time-domain data. The second calculation module is used to calculate the transmission efficiency value of vibration energy between 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 to locate the key noise transmission path of the vehicle electric drive system according to the magnitude of the transmission efficiency value.

8. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 6.

9. An electronic device, comprising a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 6.

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