Method for optimizing design parameters of transmission gear in electric drive system

Abstract

The invention relates to the field of motor and gear transmission systems, in particular to a method for optimizing design parameters of a transmission gear in an electric drive system.The method includes the steps that firstly, a two-dimensional finite element model of a permanent magnet synchronous motor is established, rotor stepped skewed slots and material magnetic saturation characteristics are accurately simulated, and an external characteristic MAP is generated; then calculating electromagnetic force density based on a Maxwell stress tensor method, mapping the electromagnetic force density to a multi-body dynamic model to construct a transverse coupling model, extracting an ECE reduced-order model based on a permanent magnet synchronous motor two-dimensional finite element model, forming a torsional vibration model in combination with a control algorithm, integrating a rigid-flexible coupling mechanical system, and establishing an electromechanical-rigid-flexible coupling model; and finally, through sensitivity analysis and a response surface model, with vibration acceleration and torsion amplitude as targets and gear strength as constraints, a Pareto optimal solution is solved by adopting a genetic algorithm, electromechanical coupling simulation precision is greatly improved, system vibration is effectively reduced, gear transmission reliability is enhanced, and the method is suitable for design of a high-dynamic-performance electric drive system.

Description

Technical Field

[0001] This invention relates to the field of motors and gear transmission systems, and more specifically to a method for optimizing the design parameters of transmission gears in an electric drive system. Background Technology

[0002] As a crucial branch of new energy commercial vehicles, pure electric vehicles rely heavily on their electric drive systems, which are core components directly impacting vehicle performance and reliability. Electric drive systems have evolved from initially separate structures to integrated designs, ultimately developing into the mainstream three-in-one electric drive assembly that combines the drive motor, transmission system, and control system. This integrated powertrain directly couples the drive motor and transmission system, eliminating traditional couplings. The motor shaft serves directly as the input shaft for the transmission system, and the drive motor and transmission system are housed in a single enclosure.

[0003] In the early design and optimization of electric drive systems, traditional methods primarily employ a split-structure design and optimization approach, where the drive motor and gears in the transmission system are designed separately. During the design process, the relationship between the drive motor and gear designs is solely based on operating conditions and loading conditions. While this approach may meet requirements in the initial strength and stiffness design stages, it becomes insufficient in the later stages of optimizing vibration and noise dynamic characteristics because it fails to consider the coupling effect between the electromagnetic field and the transmission system. In other words, in optimizing the dynamic characteristics of electric drive systems, traditional design methods primarily analyze the motor and gear transmission system separately, neglecting the coupling effect of electromagnetic fields, electromagnetic force waves, and dynamic excitation from mechanical bearings on the dynamic characteristics of the housing. This approach has at least the following two technical shortcomings:

[0004] 1. Existing methods for optimizing the dynamic characteristics of electric drive systems mainly adopt a split-structure design, with motor design and gear design carried out separately. They do not consider the coupling effect of electromagnetic field and transmission system, and cannot fully reflect the actual dynamic performance of the system.

[0005] 2. Existing gear design methods do not consider design optimization in the multibody system-level model of the gearbox, lack a comprehensive understanding of the overall dynamic characteristics of the system, and make it difficult to achieve effective control of vibration and noise.

[0006] To date, several patent documents have disclosed technical solutions for addressing the problems of coupled modeling of torsional and lateral vibrations in the electromagnetic-mechanical systems of electric drive systems, as well as the optimization of macroscopic and profile parameters of gears, aiming to specifically solve the deep-seated problems of traditional methods. However, in practice, these technical solutions have been found to have many shortcomings:

[0007] For example, patent document CN114912203A discloses a dynamic simulation analysis method for an electric drive system. This method includes calculating the dynamic meshing stiffness of the gear pair, the dynamic meshing force of the i-th harmonic of the gear pair, the r-th natural frequency and mode shape of the system, determining the harmonic order of the largest vibration acceleration response under each excitation, determining the rotational speed and natural frequency of the electric drive system at the location of the largest vibration acceleration response under each excitation, comparing and analyzing the portion occupying the main strain energy, comparing and analyzing the resonance position and amplitude of the system's ODS mode shape at the natural frequencies of each resonance peak, identifying the resonance position, and identifying the order and natural frequency occupying the main radiated sound power. However, this method still has shortcomings in the analysis of the system's natural frequencies and mode shapes, making it difficult to accurately identify the resonance position and the corresponding order and natural frequency, and thus unable to accurately evaluate the dynamic performance of the system.

[0008] Patent document CN118445935A discloses a method for controlling gear noise in a motor reducer. This method includes establishing and optimizing a dynamic analysis model of a flexible support gear system based on a mesh model of the reducer housing structure and a dynamic model of the gear system. The method then performs gear meshing analysis on this model to determine the initial design values ​​of the micro-parameters of the flexible support gear system. Next, it performs tolerance analysis on these initial design values, determines the range of micro-parameters based on the tolerance analysis results, evaluates the range of micro-parameters, and determines the nominal design values ​​and tolerances of the micro-parameters based on the evaluation results. However, when technicians use this method to optimize the entire system in practice, they find that the accuracy and computational efficiency of the model are low when establishing the mesh model of the reducer housing structure and the dynamic model of the gear system, making it difficult to meet actual design requirements.

[0009] Therefore, as drive motors develop towards wider speed ranges, higher speeds, and lighter weights, the challenges and problems faced by integrated electric drive systems in optimizing their dynamic characteristics will become increasingly severe. If the dynamic performance of an integrated electric drive system under electromechanical coupling conditions is not fully understood during the design phase, once put into use, the system's vibration and noise can easily become uncontrollable, and fatigue failure due to vibration may even affect the system's reliability. Therefore, during the electric drive system design phase, it is urgent to propose a system dynamic characteristic optimization method based on the electromechanical coupling dynamic model of the integrated electric drive system to control system vibration, extend system lifespan, and improve operational reliability. Summary of the Invention

[0010] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for optimizing the design parameters of transmission gears in electric drive systems. This method establishes a two-dimensional finite element model of a permanent magnet synchronous motor (PMSM) to accurately simulate the rotor's stepped skewed slots and the material's magnetic saturation characteristics, generating an external characteristic map (MAP). Then, based on Maxwell's stress tensor method, the electromagnetic force density is calculated and mapped to a multibody dynamics model to construct a transverse coupling model. An ECE (Electromechanical Coefficient of Performance) model is extracted from the PMSM's two-dimensional finite element model and combined with a control algorithm to form a torsional vibration model. The rigid-flexible coupled mechanical system is integrated to establish an electromechanical-rigid-flexible coupling model. Through sensitivity analysis and response surface modeling, with vibration acceleration and torsional vibration amplitude as objectives and gear strength as constraints, a genetic algorithm is used to solve for the Pareto optimal solution. This invention improves the accuracy of electromechanical coupling simulation, effectively reduces system vibration, enhances gear transmission reliability, and is suitable for the design of high-dynamic-performance electric drive systems.

[0011] The objective of this invention is achieved through the following approach:

[0012] A method for optimizing the design parameters of transmission gears in an electric drive system includes the following steps:

[0013] 1) Based on the electric drive system to be optimized, a rigid-flexible coupling model of the electric drive system is established using a rigid-flexible coupling method. The rigid-flexible coupling model of the electric drive system can accurately reproduce the mechanical transmission behavior of the electric drive system in the subsequent electromechanical coupling simulation process.

[0014] 2) Obtain the electromagnetic force density map of the permanent magnet synchronous motor in the electric drive system to be optimized, and map the electromagnetic force density map to the rigid-flexible coupling model of the electric drive system to form an electromechanical lateral coupling model;

[0015] 3) By using field-circuit coupling, the permanent magnet synchronous motor in the electric drive system to be optimized is modeled to form a torsional vibration model of the permanent magnet synchronous motor, which is used to accurately simulate the dynamic torque response of the motor under the action of the motor control algorithm in the subsequent electromechanical coupling simulation process.

[0016] 4) Combine the torsional vibration model of the permanent magnet synchronous motor with the electromechanical lateral coupling model obtained in step 2) to form a lateral-torsional vibration coupling model of the electric drive system;

[0017] 5) The response surface model obtained by fitting the lateral-torsional vibration coupling model of the electric drive system is used as the main function to be optimized, and the design parameters of the transmission gear in the electric drive system are used as optimization parameters. An optimization framework is constructed with the vibration acceleration of the housing measuring point and the torsional vibration amplitude of the output shaft as the optimization objectives and the gear strength as the constraint condition.

[0018] 6) Based on the optimization framework, a genetic algorithm is used to solve the Pareto front solution set, and the gear parameter values ​​that can make the overall performance of the electric drive system optimal are selected as the design parameters of the transmission gears in the electric drive system.

[0019] Preferably, in step 1), the establishment of the rigid-flexible coupling model of the electric drive system includes:

[0020] 1-1) Generate finite element mesh models of each component based on the three-dimensional models of each component of the electric drive system;

[0021] 1-2) Import the finite element mesh models of each component into the finite element software Abaqus to generate modally reduced flexible body models of each component of the electric drive system.

[0022] 1-3) In the multibody dynamics software Simpack, the modal-reduced flexible body models of each component of the electric drive system are assembled together to form a rigid-flexible coupling model of the electric drive system.

[0023] Preferably, in step 2), the establishment of the electromechanical lateral coupling model includes:

[0024] 2-1) Using the finite element model and MAP diagram of the permanent magnet synchronous motor, the speed is scanned according to the load torque under typical operating conditions to obtain the radial and tangential electromagnetic force densities between the stator and rotor of the permanent magnet synchronous motor under typical load conditions, forming the electromagnetic force density diagram of the permanent magnet synchronous motor, which is used for the lateral vibration coupling of the electric drive system.

[0025] 2-2) The electromagnetic force density map is mapped to the rigid-flexible coupling model of the electric drive system in the multibody dynamics software to form an electromechanical transverse coupling model.

[0026] Preferably, in step 3), the establishment of the torsional vibration model of the permanent magnet synchronous motor includes:

[0027] 3-1) Extracting a reduced-order ECE model of the permanent magnet synchronous motor based on the finite element model;

[0028] 3-2) The forward and reverse lookup tables in the reduced-order ECE model of the motor are used as the motor body model and coupled with the motor control algorithm to realize the field-circuit coupling between the motor and the control system, forming the torsional vibration model of the permanent magnet synchronous motor.

[0029] Preferably, in step 4), the lateral-torsional vibration coupling model of the electric drive system uses the motor rotor speed and torque as coupling quantities.

[0030] Preferably, in step 5), the construction of the optimization framework specifically includes:

[0031] 5-1) Determine the influence weight of each design parameter of the transmission gear in the electric drive system to be designed on the optimization objective through sensitivity analysis, form a sensitivity matrix of the optimization objective with respect to the design parameters, and select the design parameters that have a great influence on the optimization objective;

[0032] 5-2) The design parameters that have a significant impact on the optimization objective, selected in step 5-1), are used as optimization parameters. Based on the transverse-torsional vibration coupling model obtained in step 4), stratified sampling is performed to obtain several sample points, forming a design point dataset.

[0033] 5-3) Vibration acceleration measurement points are arranged near the bearing hole seat of the housing, and the amplitude of vibration acceleration at the measurement points and the torsional vibration of the output shaft under typical working conditions are used as the dynamic response. A batch of dynamic simulation calculations are performed on several sample points in the design point dataset to obtain DOE simulation results, which are used as optimization targets for optimizing the dynamic characteristics of electric drive.

[0034] 5-4) A response surface model for dynamic simulation is constructed using model fitting methods to predict the model response at different design points;

[0035] 5-5) Using the vibration acceleration of the shell measuring point and the torsional vibration amplitude of the output shaft as optimization objectives, and ensuring the tooth surface contact strength and tooth root bending strength as constraints, a multi-objective optimization solution is set up in combination with the response surface model.

[0036] Preferably, in step 5-1), the mathematical expression for each element in the sensitivity matrix of the optimization objective with respect to the design parameters is as follows:

[0037]

[0038] S i,j ∈S m×n fi i ∈fi m×1 x j ∈x n×1

[0039] In the formula, x j For design parameters, f i To optimize the objective, S i,j Let Δx be the sensitivity of the i-th optimization objective to the j-th design parameter, where m is the number of optimization objectives, n is the number of design parameters, and S is the sensitivity matrix; j Δf represents the change in design parameters. i To optimize the change in the objective, f i Regarding x j The partial derivative of .

[0040] Preferably, in step 5-4), the mathematical expression of the response surface model is as follows:

[0041]

[0042] In the formula, Y is the response surface function, α0 is a constant, and α i To optimize parameter x i The first-order coefficient, α ii To optimize parameter x i The quadratic coefficient, α ij For different optimization parameters x i x j The coefficient of the product term, x i For the i-th optimization parameter, x j Let ε be the j-th optimization parameter, ε be the error term, and n be the number of optimization parameters.

[0043] Preferably, in step 6), the method for obtaining the design parameters of the transmission gears in the electric drive system includes:

[0044] 6-1) Use a genetic algorithm to obtain the Pareto front solution set;

[0045] 6-2) Using the ideal point method, calculate the Euclidean distance between the Pareto solution and the ideal point to form the Pareto front solution set;

[0046] 6-3) Select the solution closest to the ideal point from the Pareto front solution set as the optimal equilibrium solution;

[0047] 6-4) The optimal equilibrium solution is used as the design parameter for the transmission gear in the electric drive system.

[0048] Preferably, in step 6-2), the Euclidean distance between the Pareto solution and the ideal point is calculated according to the following formula:

[0049]

[0050] In the formula, d(x) is the Euclidean distance between the Pareto solution and the ideal point. For the ideal value of the i-th optimization objective, Let f be the normalization range, x be a vector of decision variables for any Pareto solution, and f be the range of normalization variables. i (x) represents the value of the i-th objective function at the Pareto solution x, and m is the number of optimization objectives. Let be the maximum value of the i-th objective function. Let be the minimum value of the i-th objective function.

[0051] The beneficial effects of this invention include the following:

[0052] 1. This invention is essentially a method for optimizing transmission gear design parameters considering the characteristics of motor drive (or, a method for optimizing transmission gear design parameters considering electromechanical coupling vibration characteristics). Based on the electromagnetic field finite element simulation software Maxwell, a two-dimensional finite element model of a permanent magnet synchronous motor is established. The ECE degradation model is extracted through parameter scanning, and a modally reduced flexible body model is established in combination with the multibody dynamics software Simpack. This realizes the coupled modeling of torsional vibration and lateral vibration of the electromagnetic-mechanical system, overcomes the shortcomings of traditional split design that does not consider the coupling effect of electromagnetic field and transmission system, and fully reflects the actual dynamic performance of the system.

[0053] 2. In the gear design process, the macroscopic parameters and modification parameters of the gear are set as variables. A rigid-flexible coupled dynamic model is established by using the multibody dynamics software Simpack, which realizes the optimization of the dynamic characteristics of the gearbox multibody system, effectively controls the vibration and noise of the system, and improves the operational reliability of the system.

[0054] 3. This invention uses the Latin hypercube sampling method for parameter scanning optimization, combined with the Kriging model fitting method, to establish a reduced-order response surface model of the motor finite element model, which improves the accuracy of the system's natural frequency and mode shape analysis, and accurately identifies the resonance location and the corresponding order and natural frequency.

[0055] 4. This invention achieves intelligent optimization design of the system by arranging vibration acceleration measurement points near the bearing bore seat of the housing and using a genetic algorithm for multi-objective parameter optimization, thereby improving computational efficiency and optimization accuracy;

[0056] 5. This invention uses a unidirectional coupling method to handle the lateral vibration of the motor stator and a bidirectional coupling method to handle the torsional vibration, thereby achieving reasonable coupling of the system and improving the accuracy and reliability of the model.

[0057] 6. This invention ensures the accuracy of electromagnetic force density calculation by using a five-layer dense mesh in the air gap region and setting the electric cycle step size; it adopts an ECE reduced-order model (forward / reverse lookup table) and modal reduction technology to reduce the model's degrees of freedom to an appropriate position while retaining key dynamic characteristics. Compared with the computational efficiency of traditional 3D models, this invention has greatly improved the efficiency and effectively overcomes the defect of "difficulty in balancing model accuracy and computational efficiency", providing an efficient and accurate simulation foundation for subsequent optimization.

[0058] 7. This invention constructs a closed-loop optimization framework of "parameter screening - multi-objective constraints - global optimization". Through sensitivity analysis, it accurately identifies the key influencing factors of gear macroscopic parameters (module, helix angle, etc.) and profile parameters (tooth profile, involute slope, etc.), avoiding blind optimization. With vibration acceleration and torsional vibration amplitude as core objectives, combined with tooth surface contact / tooth root bending strength constraints, a genetic algorithm is used to solve the Pareto front, achieving synergistic optimization of "vibration control and strength assurance," solving the industry pain point of "difficulty in balancing vibration noise and reliability" in traditional design.

[0059] Definitions:

[0060] MPC: Multi-Point Constraint.

[0061] DoE: Design of Experiments, which is the combination of a finite number of discrete parameters, each group being called a design point. Attached Figure Description

[0062] Figure 1 This is a flowchart illustrating an embodiment of the present invention;

[0063] Figure 2 This is a flowchart of the genetic algorithm optimization algorithm in this invention;

[0064] Figure 3 This is a schematic diagram of the two-dimensional finite element model structure of the permanent magnet synchronous motor in this embodiment of the invention;

[0065] Figure 4 This refers to the electromagnetic force density between the stator and rotor of the permanent magnet synchronous motor in this embodiment of the invention.

[0066] Figure 5 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0067] like Figures 1 to 5 As shown, a method for optimizing the design parameters of transmission gears in an electric drive system includes the following steps:

[0068] 1) Based on the electric drive system to be optimized, a rigid-flexible coupling model of the electric drive system is established using a rigid-flexible coupling method. The rigid-flexible coupling model of the electric drive system can accurately reproduce the mechanical transmission behavior of the electric drive system in the subsequent electromechanical coupling simulation process.

[0069] 1-1) Based on the three-dimensional models of each component of the electric drive system, generate finite element mesh models of each component (e.g., housing assembly, motor stator, motor rotor, drive shaft, gear blank, etc.);

[0070] 1-2) Import the finite element mesh models of each component into the finite element software Abaqus to generate modally reduced flexible body models of each component of the electric drive system.

[0071] In this embodiment, the finite element mesh models of each component are used as flexible body mesh models. After being imported into the finite element software Abaqus, MPC multi-point constraint relationships are established between the feature surfaces of the components and the corresponding feature master nodes, while retaining the degrees of freedom of the MPC master nodes.

[0072] Then, the mode shapes of each flexible body mesh model are calculated separately, and the mass, damping, and stiffness matrices of each mode are extracted to obtain the corresponding modally reduced flexible body model.

[0073] 1-3) In the multibody dynamics software Simpack, the modal-reduced flexible body models of each component of the electric drive system are assembled together to form a rigid-flexible coupling model of the electric drive system.

[0074] For example, in the multibody dynamics software Simpack, based on the relative motion relationships between the components during the actual operation of the electric drive system, constraint relationships are established between the coupling nodes of the modal reduced flexible body model of each component (i.e., constraint relationships are established through the MPC master node).

[0075] In fact, building a rigid-flexible coupling model of an electric drive system in the multibody dynamics software Simpack also includes simulating the bearing support stiffness and gear meshing stiffness using the lumped parameter force element algorithm built into Simpack.

[0076] In other words, the formation of a rigid-flexible coupling model for an electric drive system requires setting macroscopic gear parameters (such as gear module, number of teeth, tooth width, displacement coefficient, helix angle, and pressure angle) and gear profile parameters (such as tooth profile angle, tooth profile bulge, involute bulge, and involute angle) as variables in the gear meshing force element to achieve parameterization. This behavior of parameterizing transmission gear design parameters in multibody dynamics software falls under gear meshing stiffness and is part of the multibody dynamics calculation task.

[0077] Of course, other multibody dynamics software such as Recurdyn and Ansys Motion can also be used to complete this multibody dynamics calculation task (i.e., given the rotational speed and load torque excitation, obtain the torsional and lateral vibration acceleration of the response component or response point, etc.). Their modeling methods are all based on modal condensation theory and multibody dynamics theory.

[0078] 2) Obtain the electromagnetic force density map of the permanent magnet synchronous motor in the electric drive system to be optimized, and map the electromagnetic force density map to the rigid-flexible coupling model of the electric drive system to form an electromechanical lateral coupling model;

[0079] 2-1) Using the finite element model and MAP diagram of the permanent magnet synchronous motor, the speed is scanned according to the load torque under typical operating conditions to obtain the radial and tangential electromagnetic force densities between the stator and rotor of the permanent magnet synchronous motor under typical load conditions, forming the electromagnetic force density diagram of the permanent magnet synchronous motor, which is used for the lateral vibration coupling of the electric drive system.

[0080] In this embodiment, the method of establishing the finite element model of the permanent magnet synchronous motor includes defining the material properties, rotor stepped skew slot characteristics, simulation parameters and boundary conditions of the permanent magnet synchronous motor in the electromagnetic field finite element simulation software Ansys Maxwell, and then adding three-phase current excitation to establish a finite element model (two-dimensional) of the permanent magnet synchronous motor. This permanent magnet synchronous motor is used as a drive motor in the electric drive system to be designed.

[0081] The method for obtaining the MAP (Motor External Characteristic Map) of the permanent magnet synchronous motor includes: performing parameter scanning on the operating parameters of the finite element model of the permanent magnet synchronous motor to obtain the relationship between the efficiency of the permanent magnet synchronous motor and the load torque, speed, and current power angle, thereby obtaining the MAP of the external characteristics of the permanent magnet synchronous motor. This allows for the determination of the parameters of the three-phase current excitation of the permanent magnet synchronous motor based on the load demand torque and speed. Note that the three-phase current excitation is used to establish the mapping relationship between the operating load and the current excitation.

[0082] In this embodiment, the method for obtaining the electromagnetic force density map of the permanent magnet synchronous motor specifically includes:

[0083] 2-1-1) Determine the current parameters

[0084] Based on the load torque under typical motor operating conditions and combined with the MAP diagram of the motor's external characteristics, the current amplitude and current angle in the finite element model of the permanent magnet synchronous motor are determined.

[0085] 2-1-2) Obtaining the air gap magnetic density cloud map

[0086] Under given current amplitude and current power angle excitation, equally spaced sampling points are defined within the speed variation range of the permanent magnet synchronous motor. The speed parameters are scanned, and the radial and tangential air gap magnetic flux density of the permanent magnet synchronous motor at each speed sampling point is obtained through finite element simulation.

[0087] Under a given operating condition (load, speed) sampling point, based on the finite element model of the permanent magnet synchronous motor, the analysis time step is defined in the electromagnetic field finite element simulation software Ansys Maxwell, and a time domain simulation of one electric cycle is completed. The radial and tangential magnetic flux density vectors of the stator and rotor air gap at each time step are output to form the air gap magnetic flux density cloud map of the permanent magnet synchronous motor.

[0088] Note that in this embodiment, since the calculation cycle of the motor finite element model is one electrical cycle (which is 1 / p of the rotor rotation mechanical cycle, where p is the number of rotor pole pairs), the time axis needs to be extended to one mechanical cycle.

[0089] 2-1-3) Using Maxwell's stress tensor method, the air gap magnetic density map is converted into the electromagnetic force density map of the permanent magnet synchronous motor.

[0090] For example, based on Maxwell's stress tensor method, and combined with the radial and tangential air gap magnetic flux density data of the permanent magnet synchronous motor at each speed sampling point obtained in step 3-2), the radial and tangential electromagnetic force density between the stator and rotor of the permanent magnet synchronous motor at each speed sampling point is calculated according to the following formula (i.e., electromagnetic force density function), thus forming the electromagnetic force density map of the permanent magnet synchronous motor:

[0091]

[0092] In the formula, σ is the radial electromagnetic force density between the stator and rotor, μ0 is the free magnetic permeability, and B r For radial air gap magnetic flux density, B t τ is the tangential air gap magnetic flux density, and τ is the tangential electromagnetic force density between the stator and rotor.

[0093] 2-2) Map the electromagnetic force density map to the rigid-flexible coupling model of the electric drive system to form an electromechanical transverse coupling model, specifically including:

[0094] 2-2-1) Based on the proportional relationship between rotor angle and time at a given speed, the electromagnetic force density of the permanent magnet synchronous motor is used to establish the mapping relationship between electromagnetic force density and rotor time-varying angle and stator spatial angle.

[0095] 2-2-2) Import the radial and tangential electromagnetic force density maps of the permanent magnet synchronous motor into multibody dynamics software (such as Simpack, Ansys Motion, etc.), and define the mapping relationship of electromagnetic force density with respect to rotor time-varying angle and stator spatial angle as the input function of force element 112 in "motor interface";

[0096] 2-2-3) Select the node set on the stator tooth surface of the motor in the rigid-flexible coupling model of the electric drive system as the mapping object. According to the input function of force element No. 112 of the "motor interface", the corresponding radial and tangential electromagnetic forces are mapped onto each node in the node set to form an electromechanical transverse coupling model.

[0097]

[0098] In the formula, F node θ represents the electromagnetic force exerted on the node of the stator tooth surface. rotor For the time-varying angle of the rotor, Let be the stator space angle, n be the rotor speed, and f(x,y,z) be the mapping function of force element 112 in the "motor interface".

[0099] In essence, this involves mapping the electromagnetic force density to the forces acting on the stator tooth surface nodes in the rigid-flexible coupling model of the electric drive system (i.e., mapping the electromagnetic force density to the forces acting on the stator tooth surface nodes in the rigid-flexible coupling model of the electric drive system), thus forming an electromechanical lateral coupling model.

[0100] It should be noted that the lateral vibration here adopts a unidirectional coupling method. This is because the lateral vibration displacement of the motor stator is a small deformation, which has little impact on the motor magnetic circuit. Therefore, the lateral vibration adopts a unidirectional coupling method.

[0101] In summary, in this embodiment, the obtained electromagnetic force density is as follows: Figure 4 As shown, for a given load torque and a given speed, it is a function of time and stator spatial angle. The electromagnetic force density at any speed is obtained by interpolation of the results from nearby sampling points, thus obtaining the electromagnetic force density between the stator and rotor of the permanent magnet synchronous motor under typical load conditions across the entire speed range.

[0102] Essentially, it utilizes the finite element model and MAP diagram of the permanent magnet synchronous motor to perform parameter scanning on the speed based on the load torque under typical operating conditions. This yields the radial and tangential electromagnetic force densities between the stator and rotor of the permanent magnet synchronous motor under typical load conditions, forming an electromagnetic force density diagram of the permanent magnet synchronous motor. This electromagnetic force density diagram includes the radial and tangential electromagnetic force density diagrams of the permanent magnet synchronous motor.

[0103] 3) By using field-circuit coupling, the permanent magnet synchronous motor in the electric drive system to be optimized is modeled to form a torsional vibration model of the permanent magnet synchronous motor, which is used to accurately simulate the dynamic torque response of the motor under the action of the motor control algorithm in the subsequent electromechanical coupling simulation process.

[0104] 3-1) Extracting the reduced-order ECE model of the permanent magnet synchronous motor based on the finite element model (i.e., performing parameter scanning on the finite element model of the permanent magnet synchronous motor and organizing its calculation results into a lookup table, which is the reduced-order ECE model of the motor).

[0105] 3-1-1) In the electromagnetic field finite element simulation software Ansys Maxwell, add external circuit excitation to the three-phase windings in the finite element model of the permanent magnet synchronous motor, and define parameter scanning of current and rotor angle in the external circuit.

[0106] The scanning parameters include current amplitude and rotor angle (its scanning range is 60 electrical degrees);

[0107] Specifically, current scanning is defined as the dq-axis current scanning at equal intervals in the four quadrants, and then the scanning parameters of the three-phase current are obtained through coordinate transformation;

[0108] Regarding the range of rotor angle scanning, due to the symmetry of the three-phase current, in order to reduce computational costs, only 60 degrees of electrical angle can be scanned, and then the complete electrical cycle can be reconstructed in the order of A, -B, C, -A, B, -C. In fact, for parameter scanning of rotor angle, it should ideally scan 360 degrees of electrical angle, i.e., one electrical cycle. However, due to the symmetry of the three-phase current, only 60 degrees of electrical angle is scanned (mainly for the purpose of saving computational costs). By following the order of A / -B / C / -A / B / -C, the response of the complete 360 ​​degrees of electrical angle can be reconstructed.

[0109] 3-1-2) Based on the scanning parameters obtained in step 3-1-1), perform parameter scanning to obtain the motor output torque and the quadrature and direct axis flux linkages. Extract the positive lookup table (three-dimensional matrix table) of the motor output torque and the quadrature and direct axis flux linkages with respect to the quadrature and direct axis currents and rotor angles from the calculation results.

[0110] This embodiment contains three such tables:

[0111] The first table is a three-dimensional lookup table of motor output torque in terms of quadrature-axis current, direct-axis current, and rotor angle. In this table, the dependent variable is motor output torque, and the independent variables are quadrature-axis current, direct-axis current, and rotor angle.

[0112] The second table is a three-dimensional lookup table of the motor's quadrature-axis flux linkage with respect to quadrature-axis current, direct-axis current, and rotor angle. In this table, the dependent variable is the motor's quadrature-axis flux linkage, and the independent variables are quadrature-axis current, direct-axis current, and rotor angle.

[0113] The third table is a three-dimensional lookup table of the motor's direct-axis flux linkage with respect to the quadrature-axis current, direct-axis current, and rotor angle. In this table, the dependent variable is the motor's direct-axis flux linkage, and the independent variables are the quadrature-axis current, direct-axis current, and rotor angle.

[0114] In practical applications, interpolation fitting can be used to obtain the direct-axis current, quadrature-axis current, output torque at any rotor angle, quadrature-axis flux linkage, and direct-axis flux linkage.

[0115] 3-1-3) Based on the forward lookup tables of motor output torque and AC and DC axis flux linkages with respect to AC and DC axis currents and rotor angle, a reverse lookup table of AC and DC axis currents with respect to motor output torque and AC and DC axis flux linkages is generated. The forward and reverse lookup tables are then combined to obtain the reduced-order ECE model of the motor.

[0116] 3-2) In Simulink, the forward and reverse lookup tables in the reduced-order ECE model of the motor are used as the motor body model and coupled with the motor control algorithm. For example, the motor body model is coupled with conventional motor control algorithms such as vector control, maximum torque-to-current ratio control, and field weakening control to achieve field-circuit coupling between the motor and the control system, forming a torsional vibration model of the permanent magnet synchronous motor.

[0117] 4) Combine the torsional vibration model of the permanent magnet synchronous motor with the electromechanical lateral coupling model obtained in step 2) to form a lateral-torsional vibration coupling model of the electric drive system:

[0118] In this embodiment, torsional vibration is achieved through real-time, bidirectional coupling. For example, the electromechanical lateral coupling model obtained in step 2) and the torsional vibration model of the permanent magnet synchronous motor obtained in step 3) use the motor rotor speed and torque as coupling quantities, which are updated in real time with the simulation step size to achieve coupling of the torsional vibration of the motor and the transmission system. Specifically, this includes:

[0119] 4-1) In the multibody dynamics software Simpack, the output shaft speed and position angle of the electromechanical transverse coupling model are used as the output of the mechanical system, and the input torque of the motor rotor is used as the input of the mechanical system. The torque force element is applied between the motor shaft and the inertial coordinate system.

[0120] 4-2) In Simulink, the output torque of the torsional vibration model of the permanent magnet synchronous motor is used as the output of the electrical system, and the speed and position angle feedback of the control system are used as the input of the electrical system.

[0121] 4-3) In the multibody dynamics software Simpack, start the co-simulation. The solver starts on the computer port and waits for Simulink to connect.

[0122] 4-4) In Simulink, the mechanical system in the multibody dynamics software Simpack is connected to the electrical system as a SIMAT module, and the inputs and outputs of the two are connected accordingly;

[0123] 4-5) Define the co-simulation sampling frequency and end time.

[0124] 5) The response surface model obtained by fitting the lateral-torsional vibration coupling model of the electric drive system is used as the main function to be optimized, and the design parameters of the transmission gear in the electric drive system are used as optimization parameters to construct an optimization framework with vibration acceleration and torsional vibration amplitude as optimization objectives and gear strength as constraint condition.

[0125] In this step, the logic for obtaining the principal function to be optimized is as follows: First, a sensitivity analysis is performed (the sample size for sensitivity analysis is much smaller than that for DOE), removing parameter dimensions with low sensitivity; for parameter dimensions with high sensitivity, stratified sampling (Latin hypercube) is designed, and DOE simulation batch processing is performed based on the sample point set obtained from the stratified sampling. Based on the DOE results, a response surface model is fitted as the principal function to be optimized. For example:

[0126] 5-1) Sensitivity analysis is used to determine the influence weight of each design parameter of the transmission gear in the electric drive system to be designed on the optimization objective, forming a sensitivity matrix of the optimization objective with respect to the design parameters. This allows for the selection of design parameters that have a greater impact on the optimization objective, thereby reducing the number of parameter sampling points with less influence (or removing parameter dimensions with low sensitivity and selecting parameter dimensions with high sensitivity), thus reducing computation time and saving computational costs.

[0127] 5-1-1) Through sensitivity analysis, the sensitivity of each optimization objective to each design parameter is obtained, i.e., the sensitivity matrix. The mathematical expression of each element in the sensitivity matrix S is as follows:

[0128]

[0129] S i,j ∈S m×n f i ∈f m×1 x j ∈x n×1

[0130] In the formula, x j For design parameters (i.e., the design parameters of the transmission gears in the electric drive system to be designed, including macroscopic parameters and profile parameters, such as gear macroscopic parameters: gear module, number of teeth, tooth width, displacement coefficient, helix angle, pressure angle, and gear profile parameters: tooth profile angle, tooth profile camber, involute camber, involute angle), f i To optimize the target (i.e., the amplitude of the vibration acceleration at the measuring point and the amplitude of the torsional vibration of the output shaft), S i,j Let Δx be the sensitivity of the i-th optimization objective to the j-th design parameter, where m is the number of optimization objectives, n is the number of design parameters, and S is the sensitivity matrix; j Δf represents the change in design parameters. i To optimize the change in the objective, f i Regarding x j The partial derivative;

[0131] 5-1-2) For each optimization objective, retain the design parameters with high sensitivity. The specific screening process includes:

[0132] For a given optimization objective, the absolute values ​​of the sensitivity of each design parameter are sorted from high to low. The ratio of the absolute value of the sensitivity of the next design parameter to the absolute value of the sensitivity of the previous design parameter is calculated. If the ratio is less than a threshold (the specific value can be adjusted according to the actual situation, for example, the threshold can be 70%), then the next design parameter and all subsequent design parameters are discarded.

[0133] 5-2) The design parameters that have a greater impact on the optimization objective selected in step 5-1) are used as optimization parameters. Based on the transverse-torsional vibration coupling model obtained in step 4), hierarchical sampling (such as Latin hypercube sampling, optimal predictive meta-model adaptive sampling, weight factor sampling) is performed to obtain a number of sample points and form a design point dataset.

[0134] For example, based on the transverse-torsional vibration coupling model, under the DOE module of Simpack, the Latin hypercube sampling method is adopted. For the parameter dimension with high sensitivity, the (Latin hypercube) stratified sampling is designed. Based on the sample point set obtained by stratified sampling, the parameter scan of the gear macro parameters and modification parameters is set (that is, according to the data in the "design point dataset", the parameter scan of the gear macro parameters and modification parameters is performed).

[0135] 5-3) Arrange vibration acceleration measurement points near the bearing housing (measurement points can be arranged only at the bearing housing with the greatest vibration, or one measurement point can be arranged at each bearing housing). Using the amplitude of vibration acceleration at the measurement points and the torsional vibration of the output shaft under typical working conditions as the dynamic response, perform batch dynamic simulation calculations on several sample points in the design point dataset (this can be set in the DOE module of Simpack to automatically perform batch dynamic simulations). Obtain the DOE simulation results as the optimization target for optimizing the dynamic characteristics of the electric drive.

[0136] 5-4) A response surface model for dynamic simulation is constructed using the model fitting method to predict the model response at different design points.

[0137] This embodiment uses model fitting methods such as multinomial regression, Kriging, radial basis function, and artificial neural network to construct a mathematical model with a computational cost far lower than the original model, but which can approximate its input-output relationship. This model is the response surface model for dynamic simulation, used to predict the model response at different design points.

[0138] The mathematical expression for the response surface model is as follows:

[0139]

[0140] In the formula, Y is the response surface function, α0 is a constant, and α iTo optimize the first-order coefficients of the parameters (i.e., gear macroscopic parameters: gear module, number of teeth, tooth width, modification coefficient, helix angle, pressure angle, and gear profile parameters: tooth profile angle, tooth profile bulge, involute bulge, and involute angle), α ii To optimize the quadratic coefficients of the parameters, α ij x represents the coefficient of the product term for different optimization parameters. i x j For different optimization parameters, ε is the error term, and n is the number of optimization parameters;

[0141] 5-5) Using the vibration acceleration at the shell measuring point and the torsional vibration amplitude of the output shaft as optimization objectives, and ensuring the tooth surface contact strength and tooth root bending strength as constraints, a multi-objective optimization solution is set up in conjunction with the response surface model, specifically including:

[0142] 5-5-1) The amplitude of vibration acceleration at the measuring point and the amplitude of torsional vibration of the output shaft are used as optimization targets:

[0143]

[0144] In the formula, f i (x) represents the i-th optimization objective, Acc sensori Let AngleAcc be the vibration acceleration amplitude at the i-th measuring point. outputshaft This refers to the torsional vibration amplitude of the output shaft.

[0145] 5-5-2) The constraint condition is to ensure the contact strength of the tooth surface and the bending strength of the tooth root:

[0146]

[0147] In the formula, c j (x) represents the j-th constraint, σ gear i Let τ be the tooth surface contact stress of the i-th pair of gears. gear i Let σ be the bending stress at the tooth root of the i-th gear pair. Hp,gear i Let τ be the allowable tooth surface contact stress of the i-th pair of gears. Fp,geari Let be the allowable tooth root bending stress of the i-th pair of gears.

[0148] 6) Based on the optimization framework, a genetic algorithm is used to solve the Pareto front solution set, and the gear parameter values ​​(i.e. optimization parameters) that can make the overall performance of the electric drive system optimal are selected as the design parameters of the transmission gears in the electric drive system.

[0149] 6-1) Use a genetic algorithm to obtain the Pareto front solution set;

[0150] 6-2) Using the ideal point method, that is, defining ideal points (the theoretical optimal value of each objective) and negative ideal points (the worst value of each objective), the Euclidean distance between the Pareto solution and the ideal point is calculated to form the Pareto front solution set;

[0151] In this embodiment, the Euclidean distance between the Pareto solution and the ideal point is calculated using the following formula:

[0152]

[0153] In the formula, d(x) is the Euclidean distance between the Pareto solution and the ideal point. For the ideal value of the i-th optimization objective, Let f be the normalization range, x be a vector of decision variables for any Pareto solution, and f be the range of normalization variables. i (x) represents the value of the i-th objective function at the Pareto solution x, and m is the number of optimization objectives. Let be the maximum value of the i-th objective function. Let be the minimum value of the i-th objective function;

[0154] 6-3) Select the solution closest to the ideal point (i.e., the gear parameter value that obviously makes the overall performance of the electric drive system optimal) from the Pareto front solution set as the best balance solution;

[0155] 6-4) The optimal equilibrium solution is used as the design parameter for the transmission gear in the electric drive system.

[0156] Comparative experiments have verified that, because this invention fully considers the coupling effect of electromagnetic field and transmission system, and designs the motor and gear in a common system, it can comprehensively reflect the actual dynamic performance of the system. Compared with existing methods for optimizing the dynamic characteristics of electric drive systems, it can more effectively control the vibration and noise generated during system operation.

[0157] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications made to the present invention by those skilled in the art without departing from the spirit of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for optimizing the design parameters of transmission gears in an electric drive system, characterized in that, Includes the following steps: 1) Based on the electric drive system to be optimized, a rigid-flexible coupling model of the electric drive system is established using a rigid-flexible coupling method. The rigid-flexible coupling model of the electric drive system can accurately reproduce the mechanical transmission behavior of the electric drive system in the subsequent electromechanical coupling simulation process. 2) Obtain the electromagnetic force density map of the permanent magnet synchronous motor in the electric drive system to be optimized, and map the electromagnetic force density map to the rigid-flexible coupling model of the electric drive system to form an electromechanical lateral coupling model; 3) By using field-circuit coupling, the permanent magnet synchronous motor in the electric drive system to be optimized is modeled to form a torsional vibration model of the permanent magnet synchronous motor, which is used to accurately simulate the dynamic torque response of the motor under the action of the motor control algorithm in the subsequent electromechanical coupling simulation process. 4) Combine the torsional vibration model of the permanent magnet synchronous motor with the electromechanical lateral coupling model obtained in step 2) to form a lateral-torsional vibration coupling model of the electric drive system; 5) The response surface model obtained by fitting the lateral-torsional vibration coupling model of the electric drive system is used as the main function to be optimized, and the design parameters of the transmission gear in the electric drive system are used as optimization parameters. An optimization framework is constructed with the vibration acceleration of the housing measuring point and the torsional vibration amplitude of the output shaft as the optimization objectives and the gear strength as the constraint condition. 6) Based on the optimization framework, a genetic algorithm is used to solve the Pareto front solution set, and the gear parameter values ​​that can make the overall performance of the electric drive system optimal are selected as the design parameters of the transmission gears in the electric drive system.

2. The method for optimizing the design parameters of transmission gears in an electric drive system according to claim 1, characterized in that, In step 1), the establishment of the rigid-flexible coupling model of the electric drive system includes: 1-1) Generate finite element mesh models of each component based on the three-dimensional models of each component of the electric drive system; 1-2) Import the finite element mesh models of each component into the finite element software Abaqus to generate modally reduced flexible body models of each component of the electric drive system. 1-3) In the multibody dynamics software Simpack, the modal-reduced flexible body models of each component of the electric drive system are assembled together to form a rigid-flexible coupling model of the electric drive system.

3. The method for optimizing the design parameters of transmission gears in an electric drive system according to claim 1, characterized in that, In step 2), the establishment of the electromechanical lateral coupling model includes: 2-1) Using the finite element model and MAP diagram of the permanent magnet synchronous motor, the speed is scanned according to the load torque under typical operating conditions to obtain the radial and tangential electromagnetic force densities between the stator and rotor of the permanent magnet synchronous motor under typical load conditions, forming the electromagnetic force density diagram of the permanent magnet synchronous motor, which is used for the lateral vibration coupling of the electric drive system. 2-2) The electromagnetic force density map is mapped to the rigid-flexible coupling model of the electric drive system in the multibody dynamics software to form an electromechanical transverse coupling model.

4. The method for optimizing the design parameters of transmission gears in an electric drive system according to claim 1, characterized in that, In step 3), the establishment of the torsional vibration model of the permanent magnet synchronous motor includes: 3-1) Extracting a reduced-order ECE model of the permanent magnet synchronous motor based on the finite element model; 3-2) The forward and reverse lookup tables in the reduced-order ECE model of the motor are used as the motor body model and coupled with the motor control algorithm to realize the field-circuit coupling between the motor and the control system, thus forming the torsional vibration model of the permanent magnet synchronous motor.

5. The method for optimizing the design parameters of transmission gears in an electric drive system according to claim 1, characterized in that, In step 4), the lateral-torsional vibration coupling model of the electric drive system uses the motor rotor speed and torque as coupling quantities.

6. The method for optimizing the design parameters of transmission gears in an electric drive system according to claim 1, characterized in that, In step 5), the construction of the optimization framework specifically includes: 5-1) Determine the influence weight of each design parameter of the transmission gear in the electric drive system to be designed on the optimization objective through sensitivity analysis, form a sensitivity matrix of the optimization objective with respect to the design parameters, and select the design parameters that have a great influence on the optimization objective; 5-2) The design parameters that have a significant impact on the optimization objective, selected in step 5-1), are used as optimization parameters. Based on the transverse-torsional vibration coupling model obtained in step 4), stratified sampling is performed to obtain several sample points, forming a design point dataset. 5-3) Vibration acceleration measurement points are arranged near the bearing hole seat of the housing, and the amplitude of vibration acceleration at the measurement points and the torsional vibration of the output shaft under typical working conditions are used as the dynamic response. A batch of dynamic simulation calculations are performed on several sample points in the design point dataset to obtain DOE simulation results, which are used as optimization targets for optimizing the dynamic characteristics of electric drive. 5-4) A response surface model for dynamic simulation is constructed using model fitting methods to predict the model response at different design points; 5-5) Using the vibration acceleration of the shell measuring point and the torsional vibration amplitude of the output shaft as optimization objectives, and ensuring the tooth surface contact strength and tooth root bending strength as constraints, a multi-objective optimization solution is set up in combination with the response surface model.

7. The method for optimizing the design parameters of transmission gears in an electric drive system according to claim 6, characterized in that, In step 5-1), the mathematical expression for each element in the sensitivity matrix of the optimization objective with respect to the design parameters is as follows: In the formula, x j For design parameters, f i To optimize the objective, S i,j Let Δx be the sensitivity of the i-th optimization objective to the j-th design parameter, where m is the number of optimization objectives, n is the number of design parameters, and S is the sensitivity matrix; j Δf represents the change in design parameters. i To optimize the change in the objective, f i Regarding x j The partial derivative of .

8. The method for optimizing the design parameters of transmission gears in an electric drive system according to claim 6, characterized in that, In step 5-4), the mathematical expression of the response surface model is as follows: In the formula, Y is the response surface function, α0 is a constant, and α i To optimize parameter x i The first-order coefficient, α ii To optimize parameter x i The quadratic coefficient, α ij For different optimization parameters x i x j The coefficient of the product term, x i For the i-th optimization parameter, x j Let ε be the j-th optimization parameter, ε be the error term, and n be the number of optimization parameters.

9. The method for optimizing the design parameters of transmission gears in an electric drive system according to claim 1, characterized in that, In step 6), the methods for obtaining the design parameters of the transmission gears in the electric drive system include: 6-1) Use a genetic algorithm to obtain the Pareto front solution set; 6-2) Using the ideal point method, calculate the Euclidean distance between the Pareto solution and the ideal point to form the Pareto front solution set; 6-3) Select the solution closest to the ideal point from the Pareto front solution set as the optimal equilibrium solution; 6-4) The optimal equilibrium solution is used as the design parameter for the transmission gear in this electric drive system.

10. The method for optimizing the design parameters of transmission gears in an electric drive system according to claim 9, characterized in that, In step 6-2), the Euclidean distance between the Pareto solution and the ideal point is calculated according to the following formula: In the formula, d(x) is the Euclidean distance between the Pareto solution and the ideal point, and f i ideal f is the ideal value for the i-th optimization objective. i max -f i min Let f be the normalization range, x be a vector of decision variables for any Pareto solution, and f be the range of normalization variables. i (x) represents the value of the i-th objective function at the Pareto solution x, m is the number of optimization objectives, and f i max f is the maximum value of the i-th objective function. i min Let be the minimum value of the i-th objective function.

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