Calculation method and system for dynamic response of deceleration drive assembly under multi-source excitation

Abstract

The invention discloses a calculation method and system for dynamic response of a deceleration drive assembly under multi-source excitation, and the method comprises the following steps: building a kinetic equation of a gear transmission system based on an overall stiffness matrix, a mass matrix and a damping matrix of the gear transmission system, and carrying out the calculation to obtain a dynamic flexibility matrix of the gear transmission system; establishing a hub motor deceleration driving assembly shell finite element model, and obtaining a system overall kinetic model based on the assembly shell finite element model and the gear transmission system kinetic equation; calculating the dynamic meshing force of the gear as the mechanical excitation of the system; calculating the radial electromagnetic force of the permanent magnet synchronous motor under the no-load and load working conditions as the electromagnetic excitation of the system; mechanical excitation and electromagnetic excitation are loaded to the gear transmission system, and vibration displacement response, speed response and acceleration response at each node of the system are calculated in combination with the dynamic flexibility matrix. According to the invention, the vibration characteristics of the deceleration driving assembly in the actual operation process can be comprehensively and truly reflected.

Description

Technical Field

[0001] The present invention belongs to the technical field of dynamic response, and in particular relates to a calculation method and system for the dynamic response of a deceleration drive assembly under multi-source excitation. Background Art

[0002] As the core component of electric vehicles, the vibration performance of the wheel hub motor reduction drive assembly directly affects the driving comfort of electric vehicles. The wheel hub motor reduction drive assembly consists of two major parts: the wheel hub motor and the planetary reducer. It is the core component of electric vehicles and also a very important source of vibration and noise. However, in the current research on the vibration response analysis of the powertrain of new energy vehicles, most of the wheel hub motors and planetary reducers are studied separately, which cannot fit the test results of the whole vehicle well. In addition, most of the research objects are the motor housing and the reducer housing. There are few studies on the dynamics of the integrated structure of the wheel hub motor reduction drive assembly.

[0003] Therefore, it is urgent to solve the above problems. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a method for calculating the dynamic response of a deceleration drive assembly under multi-source excitation. The present invention can accurately obtain the dynamic response of the deceleration drive assembly under the influence of mechanical excitation and electromagnetic excitation, and comprehensively and truly reflect the vibration characteristics of the deceleration drive assembly during actual operation.

[0005] The second object of the present invention is to provide a calculation system for the dynamic response of a deceleration drive assembly under multi-source excitation.

[0006] Technical solution: To achieve the above purpose, the present invention discloses a method for calculating the dynamic response of a deceleration drive assembly under multi-source excitation, comprising the following steps:

[0007] S1. Calculation of the dynamic equation and dynamic flexibility matrix of the gear transmission system: First, establish a full-degree-of-freedom vibration analysis model of the shaft system, extract and analyze the calculation to obtain the stiffness matrix and mass matrix of the shaft system; then perform force analysis on the gear pairs and bearings in the gear transmission system to obtain the gear pair coupling additional stiffness matrix and the bearing additional stiffness matrix in the gear transmission system, and combine the stiffness matrix of the shaft system to obtain the overall stiffness matrix of the gear transmission system; based on the overall stiffness matrix, mass matrix and damping matrix of the gear transmission system, establish the dynamic equation of the gear transmission system and calculate the dynamic flexibility matrix of the gear transmission system; establish a finite element model of the hub motor reduction drive assembly housing, and obtain the overall dynamic model of the system based on the assembly housing finite element model and the dynamic equation of the gear transmission system;

[0008] S2. Calculation of dynamic meshing force of gears: construct a gear slicing algorithm model based on the basic parameters of the gear pair, calculate the gear meshing transmission error obtained by accumulating the manufacturing error of the gear pair, the cumulative deviation of the tooth pitch, and the torsional deformation factor; perform force analysis on the meshing nodes of the gear pair, and calculate the dynamic meshing stiffness of the gear pair in combination with the dynamic flexibility of the gear; calculate the dynamic meshing force of the gear from the gear meshing transmission error and the dynamic meshing stiffness of the gear pair as the mechanical excitation of the system;

[0009] S3. Calculation of radial electromagnetic force of permanent magnet synchronous motor under no-load and load conditions: Calculate the air gap magnetic flux density generated by stator winding and permanent magnet when the three-phase current is balanced. Calculate the radial electromagnetic force density generated by the interaction between stator and rotor in the air gap magnetic field of permanent magnet synchronous motor according to Maxwell stress tensor method, that is, radial electromagnetic force per unit area. Combined with the stator tooth surface area, the radial electromagnetic force of the motor is obtained as the electromagnetic excitation of the system.

[0010] S4. Load mechanical excitation to the meshing node of the gear transmission system, and load electromagnetic excitation to the surface of the motor electronic core; decompose the mechanical excitation and electromagnetic excitation into forces and torques on six degrees of freedom, and combine them with the dynamic flexibility matrix of the gear transmission system to calculate the vibration displacement response, velocity response and acceleration response at each node of the system.

[0011] Optionally, the S1 specifically includes the following steps:

[0012] S11. A full-degree-of-freedom vibration analysis model of the shaft system is established by using the lumped parameter method. The full-degree-of-freedom vibration analysis model includes bending, torsion, axial and swing vibration modes. The full-degree-of-freedom vibration analysis model of the shaft system is extracted and analyzed and calculated to obtain the stiffness matrix and mass matrix of the shaft system. The stiffness matrix of the shaft system includes an axial stiffness matrix, a torsional stiffness matrix and a plane bending and pendulum stiffness matrix. Both the axial stiffness matrix and the torsional stiffness matrix are in the form of tridiagonal matrices. The plane bending and pendulum stiffness matrix is ​​established according to the Timoshenko beam principle. The mass matrix of the shaft system includes an axial mass matrix, a torsional mass matrix and a plane bending and pendulum mass matrix. Both the axial mass matrix and the torsional mass matrix are diagonal matrices. The plane bending and pendulum mass matrix is ​​established according to the Timoshenko beam principle.

[0013] S12, establishing a gear pair coupling additional stiffness matrix and a bearing additional stiffness matrix, integrating the gear pair coupling additional stiffness matrix and the bearing additional stiffness matrix into the stiffness matrix of the shaft system, and forming an overall stiffness matrix of the gear transmission system;

[0014] The relative extrusion deformation of the gear pair along the meshing line during meshing vibration is:

[0015]

[0016] Where: xA 、x B They represent the displacement of the driving wheel A and the driven wheel B along the x direction; y A ,y B They represent the displacement of the driving wheel A and the driven wheel B along the y direction; A 、z B They represent the displacement of the driving wheel A and the driven wheel B along the z direction respectively; Respectively represent the angles of rotation of the driving wheel A and the driven wheel B; R bA , R bB are the base circle radii of the driving wheel A and the driven wheel B respectively; α n is the gear normal pressure angle; α t is the gear end face pressure angle; β is the helix angle;

[0017] The normal meshing force between the driving wheel A and the driven wheel B is:

[0018] F n =k s δ m

[0019] Where: k s It represents the normal meshing stiffness with the gear;

[0020] The force analysis of the driving wheel A and the driven wheel B yields the following results:

[0021]

[0022] Where: F Ax 、F Ay 、F Az are the components of the meshing force of the driving wheel A along the x, y, and z directions, respectively, and M Ax 、M Ay are the torque components of the meshing force of the driving wheel A around the x and y axes, T A is the torque component of the meshing force of the driving wheel A around the z-axis, R A F is the pitch radius of the driving wheel; Bx 、F By 、F Bz are the components of the meshing force of the driven wheel B along the x, y, and z directions, respectively, M Bx 、M By are the torque components of the meshing force of the driven wheel B around the x and y axes, T B is the torque component of the meshing force of the driven wheel B around the z-axis, R B is the pitch radius of the driving wheel;

[0023] The gear pair coupling additional stiffness matrix established by the above calculation results is:

[0024] [K C ]=[Fp ]·[K m ]·[D δ ]

[0025] In the formula, [F p ] is the force position matrix, which is calculated by the force analysis of the driving wheel and the driven wheel; [K m ] is the meshing stiffness matrix, which is calculated from the normal meshing stiffness of the gear pair; [D δ ] is the vibration displacement matrix, which is calculated by the relative extrusion deformation of the gear pair along the meshing line during the meshing vibration process;

[0026] Bearing additional stiffness matrix K b The expression is:

[0027]

[0028] In the formula, F x 、F y 、F z are the components of the bearing force along the x, y, and z directions, respectively, M x With M y are the components of the bearing moment about the x-axis and the y-axis, δ x , δ y , δ z are the relative deformations of the inner and outer rings of the bearing along the three directions of the coordinate system, θ x With θ y are the rotation angles of the bearing around the x-axis and y-axis respectively;

[0029] In the actual operation of the bearing, assuming that there are n rolling elements, the position angle of the i-th rolling element is The contact load it bears for:

[0030]

[0031] The bearing force balance equation is:

[0032]

[0033] Where D w , D m Respectively represent the diameter of the rolling element in the bearing and the radius of the circle on which the rolling element is located; is the angle between the line connecting the center of the i-th rolling element and the origin of the coordinate system and the positive direction of the x-axis; R i r is the radius of the center circle of the inner ring of the bearing; i 、r e are the curvature radii of the inner and outer raceways respectively; α0, K is the contact angle of the rolling element before and after loading. nis the effective contact stiffness;

[0034] The calculated bearing force balance equation can be solved to obtain the bearing additional stiffness matrix; the gear pair coupling additional stiffness matrix is ​​added to the gear transmission system overall stiffness matrix according to its corresponding nodes on the gear transmission system, and the calculated bearing additional stiffness matrix is ​​added to the gear transmission system overall stiffness matrix according to its corresponding nodes on the gear transmission system to obtain the gear transmission system overall stiffness matrix;

[0035] S13: Based on the overall stiffness matrix and mass matrix of the gear transmission system, the damping matrix of the gear transmission system is determined by giving the system damping coefficient, and finally the dynamic equation of the gear transmission system is established. The dynamic equation of the gear transmission system is decoupled with the help of principal coordinate transformation, and the dynamic flexibility matrix of the gear transmission system is solved;

[0036] By giving each order of damping coefficient, the modal damping of each order is calculated. The damping coefficient of each order is 0.01~0.05. The damping matrix of the gear transmission system is obtained by the modal damping of each order. The calculation expression of the modal damping of each order of the gear transmission system is:

[0037]

[0038] Where: i is the i-th order modal damping matrix, c i is the i-th order modal damping, c ci is the i-th order critical damping, M i is the i-th order quality, P i is the i-th order modal frequency;

[0039] The dynamic equation of the gear transmission system is:

[0040]

[0041] Where: M is the mass matrix of the gear transmission system, C is the damping matrix of the gear transmission system, K is the stiffness matrix of the gear transmission system, f is the dynamic excitation matrix, x, Respectively represent the displacement, velocity and acceleration vibration response results of the measuring point;

[0042] Using the principal coordinate transformation method, we get:

[0043]

[0044] In the formula, P represents the natural frequency matrix of the system, z represents the physical coordinate after transformation, and M i is the i-th order modal mass of the system, c i is the i-th order modal damping of the system, K i is the i-th order modal stiffness of the system;

[0045] The dynamic flexibility matrix of the gear transmission system is:

[0046]

[0047] Where: p i is the i-th order natural frequency of the system, ξ i is the i-th order modal damping ratio of the system;

[0048] S14: Establish a finite element model of the hub motor reduction drive assembly housing, and obtain the overall dynamic model of the system based on the finite element model of the assembly housing and the dynamic equations of the gear transmission system.

[0049] Optionally, S2 specifically includes the following steps:

[0050] S21. Calculation of gear meshing transmission error: First, it is necessary to determine the gear pair macro parameters, design load and load conditions. The macro parameters include the number of gear teeth, module, pressure angle and helix angle. The load conditions include the input speed and torque of the gear pair. Construct a slicing algorithm model to adjust the deformation of each slice in real time according to the relationship between the load on each slice and the design load. i , the gear meshing transmission error δ is the cumulative deformation of each slice, and the calculation expression of the gear meshing transmission error δ is:

[0051]

[0052] Where: i is the deformation on each slice, δ is the gear meshing transmission error, and m is the number of slices;

[0053] S22. Calculation of dynamic meshing stiffness of gear pair: The dynamic meshing stiffness of gear pair indicates the change and fluctuation of stiffness during gear meshing, which is calculated from the dynamic flexibility of the driving wheel and the driven wheel at the meshing point of the tooth surface;

[0054] The calculation expression of the dynamic meshing stiffness of the gear pair is:

[0055]

[0056] Where R(ω) is the dynamic flexibility matrix of the gear transmission system, f p 、f g are the force components at the meshing nodes of the driving wheel and the driven wheel under the action of unit normal meshing force;

[0057] S23. Calculation of dynamic meshing force of gear pair: The dynamic meshing force of gear pair during the meshing process is calculated based on the dynamic meshing stiffness of gear pair and the gear meshing transmission error. The calculation expression of the dynamic meshing force of gear pair is:

[0058] Fm (ω)=K m (ω)·δ

[0059] Where: F m (ω) is the dynamic meshing force of the gear pair, K m (ω) is the dynamic meshing stiffness of the gear pair, and δ is the gear meshing transmission error.

[0060] Optionally, S3 specifically includes the following steps:

[0061] S31. Calculation of radial electromagnetic force of the motor under no-load condition: The air gap magnetic potential of the motor under no-load condition is generated by the permanent magnet, and the air gap magnetic permeability is calculated. The radial electromagnetic force of the motor is expanded to obtain the radial electromagnetic force component under no-load condition;

[0062] When the motor is running at no load, the magnetic field provided by the permanent magnet enters the stator part of the motor through the air gap and then enters the motor rotor through the air gap to form a closed loop. The air gap magnetic density b(θ, t) of the motor is obtained as:

[0063] b(θ,t)=F(θ,t)Λ(θ,t)

[0064] Where, F(θ, t) is the magnetic potential distribution function, Λ(θ, t) is the air gap permeability;

[0065] The air gap magnetic potential of the motor under no-load condition is generated by the permanent magnet, and the distribution function expression of the permanent magnet magnetic potential is obtained as follows:

[0066]

[0067] Where μ is the harmonic order, F μ is the harmonic amplitude, ω μ is the harmonic angular velocity;

[0068] Taking into account the influence of stator slotting, the expression of air gap permeability is:

[0069]

[0070] Where Λ0 is the average air gap permeability amplitude, k is the kth air gap permeability amplitude caused by stator slotting, Z is the number of stator slots, and θ is the rotor mechanical angle;

[0071] Substitute the formula to calculate the air gap magnetic density b of the motor under no-load condition: m The expression of (θ, t) is:

[0072]

[0073] Get the radial electromagnetic force density P of the motor stator core r The expression of (θ, t) is:

[0074]

[0075] In the formula, μ0 is the vacuum magnetic permeability, ω is the current angular frequency, and p is the number of rotor pole pairs;

[0076] S32. Calculation of radial electromagnetic force of the motor under load conditions: Under load conditions of the motor, the permanent magnet and the armature winding work together to generate an air gap magnetic field, and the radial electromagnetic force density of the motor under load conditions is calculated;

[0077] Under the load condition of the motor, the permanent magnet and the armature winding work together to generate an air gap magnetic field. When the current passes through the winding, the air gap magnetic density distribution generated by the armature winding is:

[0078]

[0079] Where: is the angle between the winding and the permanent magnet magnetic field axis, v is the harmonic order of the winding magnetic field, B v is the mean value of air gap magnetic flux density at each harmonic order;

[0080] The radial electromagnetic force per unit area under the motor load condition is calculated as:

[0081]

[0082] Optionally, the S4 specifically includes the following steps:

[0083] The dynamic meshing force of the gear pair is loaded as the system mechanical excitation to the meshing node of the gear transmission system, and the radial electromagnetic force of the motor is loaded as the electromagnetic excitation to the surface of the motor electronic core. The mechanical excitation and electromagnetic excitation obtained are decomposed into forces and torques on six degrees of freedom. The expression is:

[0084] F m (ω)=[0··F x (ω)M y (ω)F y (ω)M x (ω)F z (ω)T m (ω)··0] T (6n，1)

[0085] The converted exciting force array is written in the form of complex exponentials. Combined with the dynamic flexibility matrix R(ω) of the gear transmission system, the vibration displacement response, velocity response and acceleration response at each node of the system are calculated as follows:

[0086]

[0087] Where X is the vibration displacement response of the system node, v is the vibration velocity response of the system node, and a is the vibration acceleration response of the system node.

[0088] Based on the same inventive concept, the present invention discloses a calculation system for the dynamic response of a deceleration drive assembly under multi-source excitation, comprising:

[0089] The dynamic model building module is used to calculate the dynamic equations and dynamic flexibility matrix of the gear transmission system. That is, first, a full-degree-of-freedom vibration analysis model of the shaft system is established, and the stiffness matrix and mass matrix of the shaft system are extracted and analyzed and calculated; then, the force analysis of the gear pairs and bearings in the gear transmission system is performed to obtain the gear pair coupling additional stiffness matrix and the bearing additional stiffness matrix in the gear transmission system, and the overall stiffness matrix of the gear transmission system is obtained by combining the stiffness matrix of the shaft system; based on the overall stiffness matrix, mass matrix and damping matrix of the gear transmission system, the dynamic equations of the gear transmission system are established and the dynamic flexibility matrix of the gear transmission system is calculated; a finite element model of the hub motor reduction drive assembly housing is established, and the overall dynamic model of the system is obtained based on the assembly housing finite element model and the dynamic equations of the gear transmission system;

[0090] The mechanical excitation calculation module is used to calculate the dynamic meshing force of the gears. That is, the gear slicing algorithm model is constructed according to the basic parameters of the gear pair, and the gear meshing transmission error obtained by accumulating the manufacturing error of the gear pair, the cumulative deviation of the tooth pitch, and the torsional deformation factor is calculated; the force analysis is performed on the meshing nodes of the gear pair, and the dynamic meshing stiffness of the gear pair is obtained by combining the dynamic flexibility of the gear; the dynamic meshing force of the gear is calculated from the gear meshing transmission error and the dynamic meshing stiffness of the gear pair as the mechanical excitation of the system;

[0091] The electromagnetic excitation calculation module is used to calculate the radial electromagnetic force of the permanent magnet synchronous motor under no-load and load conditions, that is, to calculate the air gap magnetic flux density generated by the stator winding and the permanent magnet when the three-phase current is balanced, and to calculate the radial electromagnetic force density generated by the interaction between the stator and the rotor in the air gap magnetic field of the permanent magnet synchronous motor according to the Maxwell stress tensor method, that is, the radial electromagnetic force per unit area, and to obtain the radial electromagnetic force of the motor in combination with the stator tooth surface area as the electromagnetic excitation of the system;

[0092] The response calculation module is used to load mechanical excitation to the meshing nodes of the gear transmission system and electromagnetic excitation to the surface of the motor electronic core; the mechanical excitation and electromagnetic excitation are decomposed into forces and torques on six degrees of freedom, and combined with the dynamic flexibility matrix of the gear transmission system, the vibration displacement response, velocity response and acceleration response at each node of the system are calculated.

[0093] Optionally, in the dynamic model construction module, a full-degree-of-freedom vibration analysis model of the shaft system is first established by using a lumped parameter method, and the full-degree-of-freedom vibration analysis model is considered to include bending, torsion, axial and swing vibration modes, and the full-degree-of-freedom vibration analysis model of the shaft system is extracted and analyzed and calculated to obtain the stiffness matrix and mass matrix of the shaft system; the stiffness matrix of the shaft system includes an axial stiffness matrix, a torsional stiffness matrix and a plane bending and pendulum stiffness matrix, both of which are in the form of tridiagonal matrices, and the plane bending and pendulum stiffness matrix is ​​established according to the Timoshenko beam principle; the mass matrix of the shaft system includes an axial mass matrix, a torsional mass matrix and a plane bending and pendulum mass matrix, both of which are diagonal matrices, and the plane bending and pendulum mass matrix is ​​established according to the Timoshenko beam principle;

[0094] Establish the gear pair coupling additional stiffness matrix and the bearing additional stiffness matrix, integrate the gear pair coupling additional stiffness matrix and the bearing additional stiffness matrix into the stiffness matrix of the shaft system, and form the overall stiffness matrix of the gear transmission system;

[0095] The relative extrusion deformation of the gear pair along the meshing line during meshing vibration is:

[0096]

[0097] Where: x A 、x B They represent the displacement of the driving wheel A and the driven wheel B along the x direction; y A ,y B They represent the displacement of the driving wheel A and the driven wheel B along the y direction; A 、z B They represent the displacement of the driving wheel A and the driven wheel B along the z direction respectively; Respectively represent the angles of rotation of the driving wheel A and the driven wheel B; R bA , R bB are the base circle radii of the driving wheel A and the driven wheel B respectively; α n is the gear normal pressure angle; α t is the gear end face pressure angle; β is the helix angle;

[0098] The normal meshing force between the driving wheel A and the driven wheel B is:

[0099] F n =k s δ m

[0100] Where: k s It represents the normal meshing stiffness with the gear;

[0101] The force analysis of the driving wheel A and the driven wheel B yields the following results:

[0102]

[0103] Where: F Ax 、F Ay 、F Az are the components of the meshing force of the driving wheel A along the x, y, and z directions, respectively, and M Ax 、M Ay are the torque components of the meshing force of the driving wheel A around the x and y axes, T A is the torque component of the meshing force of the driving wheel A around the z-axis, R A F is the pitch radius of the driving wheel; Bx 、F By 、F Bz are the components of the meshing force of the driven wheel B along the x, y, and z directions, respectively, M Bx 、M By are the torque components of the meshing force of the driven wheel B around the x and y axes, T B is the torque component of the meshing force of the driven wheel B around the z-axis, R B is the pitch radius of the driving wheel;

[0104] The gear pair coupling additional stiffness matrix established by the above calculation results is:

[0105] [K C ]=[F p ]·[K m ]·[D δ ]

[0106] In the formula, [F p ] is the force position matrix, which is calculated by the force analysis of the driving wheel and the driven wheel; [K m ] is the meshing stiffness matrix, which is calculated from the normal meshing stiffness of the gear pair; [D δ ] is the vibration displacement matrix, which is calculated by the relative extrusion deformation of the gear pair along the meshing line during the meshing vibration process;

[0107] Bearing additional stiffness matrix K b The expression is:

[0108]

[0109] In the formula, F x 、F y 、F z are the components of the bearing force along the x, y, and z directions, respectively, M x With M y are the components of the bearing moment about the x-axis and the y-axis, δ x , δ y , δ z are the relative deformations of the inner and outer rings of the bearing along the three directions of the coordinate system, θ xWith θ y are the rotation angles of the bearing around the x-axis and y-axis respectively;

[0110] In the actual operation of the bearing, assuming that there are n rolling elements, the position angle of the i-th rolling element is The contact load it bears for:

[0111]

[0112] The bearing force balance equation is:

[0113]

[0114] Where D w , D m Respectively represent the diameter of the rolling element in the bearing and the radius of the circle on which the rolling element is located; is the angle between the line connecting the center of the i-th rolling element and the origin of the coordinate system and the positive direction of the x-axis; R i r is the radius of the center circle of the inner ring of the bearing; i 、r e are the curvature radii of the inner and outer raceways respectively; α0, K is the contact angle of the rolling element before and after loading. n is the effective contact stiffness;

[0115] The calculated bearing force balance equation can be solved to obtain the bearing additional stiffness matrix; the gear pair coupling additional stiffness matrix is ​​added to the gear transmission system overall stiffness matrix according to its corresponding nodes on the gear transmission system, and the calculated bearing additional stiffness matrix is ​​added to the gear transmission system overall stiffness matrix according to its corresponding nodes on the gear transmission system to obtain the gear transmission system overall stiffness matrix;

[0116] Based on the overall stiffness matrix and mass matrix of the gear transmission system, the damping matrix of the gear transmission system is determined by giving the system damping coefficient, and finally the dynamic equation of the gear transmission system is established. The dynamic equation of the gear transmission system is decoupled with the help of principal coordinate transformation, and the dynamic flexibility matrix of the gear transmission system is solved.

[0117] By giving each order of damping coefficient, the modal damping of each order is calculated. The damping coefficient of each order is 0.01~0.05. The damping matrix of the gear transmission system is obtained by the modal damping of each order. The calculation expression of the modal damping of each order of the gear transmission system is:

[0118]

[0119] Where: i is the i-th order modal damping matrix, c i is the i-th order modal damping, cci is the i-th order critical damping, M i is the i-th order quality, P i is the i-th order modal frequency;

[0120] The dynamic equation of the gear transmission system is:

[0121]

[0122] Where: M is the mass matrix of the gear transmission system, C is the damping matrix of the gear transmission system, K is the stiffness matrix of the gear transmission system, f is the dynamic excitation matrix, x, Respectively represent the displacement, velocity and acceleration vibration response results of the measuring point;

[0123] Using the principal coordinate transformation method, we get:

[0124]

[0125] In the formula, P represents the natural frequency matrix of the system, z represents the physical coordinate after transformation, and M i is the i-th order modal mass of the system, c i is the i-th order modal damping of the system, K i is the i-th order modal stiffness of the system;

[0126] The dynamic flexibility matrix of the gear transmission system is:

[0127]

[0128] Where: p i is the i-th order natural frequency of the system, ξ i is the i-th order modal damping ratio of the system;

[0129] A finite element model of the hub motor reduction drive assembly housing is established, and the overall dynamic model of the system is obtained based on the finite element model of the assembly housing and the dynamic equations of the gear transmission system.

[0130] Optionally, the mechanical excitation calculation module first needs to determine the gear pair macro parameters, design load and load conditions, the macro parameters include the number of gear teeth, module, pressure angle and helix angle, and the load conditions include the input speed and torque of the gear pair; construct a slicing algorithm model, and adjust the deformation amount δ on each slice in real time according to the relationship between the load on each slice and the design load i , the gear meshing transmission error δ is the cumulative deformation of each slice, and the calculation expression of the gear meshing transmission error δ is:

[0131]

[0132] Where: iis the deformation on each slice, δ is the gear meshing transmission error, and m is the number of slices;

[0133] The dynamic meshing stiffness of a gear pair indicates the change and fluctuation of the stiffness during the meshing process of the gears, which is calculated from the dynamic flexibility of the driving wheel and the driven wheel at the meshing point of the tooth surfaces;

[0134] The calculation expression of the dynamic meshing stiffness of the gear pair is:

[0135]

[0136] Where R(ω) is the dynamic flexibility matrix of the gear transmission system, f p 、f g are the force components at the meshing nodes of the driving wheel and the driven wheel under the action of unit normal meshing force;

[0137] S23. Calculation of dynamic meshing force of gear pair: The dynamic meshing force of gear pair during the meshing process is calculated based on the dynamic meshing stiffness of gear pair and the gear meshing transmission error. The calculation expression of the dynamic meshing force of gear pair is:

[0138] F m (ω)=K m (ω)·δ

[0139] Where: F m (ω) is the dynamic meshing force of the gear pair, K m (ω) is the dynamic meshing stiffness of the gear pair, and δ is the gear meshing transmission error.

[0140] Optionally, in the electromagnetic excitation calculation module, the air gap magnetic potential of the motor under no-load condition is generated by the permanent magnet, the air gap magnetic permeability is calculated, the radial electromagnetic force of the motor is expanded, and the radial electromagnetic force component under no-load condition is obtained;

[0141] When the motor is running at no load, the magnetic field provided by the permanent magnet enters the stator part of the motor through the air gap and then enters the motor rotor through the air gap to form a closed loop. The air gap magnetic density b(θ, t) of the motor is obtained as:

[0142] b(θ,t)=F(θ,t)Λ(θ,t)

[0143] Where, F(θ, t) is the magnetic potential distribution function, Λ(θ, t) is the air gap permeability;

[0144] The air gap magnetic potential of the motor under no-load condition is generated by the permanent magnet, and the distribution function expression of the permanent magnet magnetic potential is obtained as follows:

[0145]

[0146] Where μ is the harmonic order, F μ is the harmonic amplitude, ωμ is the harmonic angular velocity;

[0147] Taking into account the influence of stator slotting, the expression of air gap permeability is:

[0148]

[0149] Where Λ0 is the average air gap permeability amplitude, k is the kth air gap permeability amplitude caused by stator slotting, Z is the number of stator slots, and θ is the rotor mechanical angle;

[0150] Substitute the formula to calculate the air gap magnetic density b of the motor under no-load condition: m The expression of (θ, t) is:

[0151]

[0152] Get the radial electromagnetic force density P of the motor stator core r The expression of (θ, t) is:

[0153]

[0154] In the formula, μ0 is the vacuum magnetic permeability, ω is the current angular frequency, and p is the number of rotor pole pairs;

[0155] Under the motor load condition, the permanent magnet and the armature winding work together to generate the air gap magnetic field, and the radial electromagnetic force density under the motor load condition is calculated;

[0156] Under the load condition of the motor, the permanent magnet and the armature winding work together to generate an air gap magnetic field. When the current passes through the winding, the air gap magnetic density distribution generated by the armature winding is:

[0157]

[0158] Where: is the angle between the winding and the permanent magnet magnetic field axis, v is the harmonic order of the winding magnetic field, B v is the mean value of air gap magnetic flux density at each harmonic order;

[0159] The radial electromagnetic force per unit area under the motor load condition is calculated as:

[0160]

[0161] Optionally, in the response calculation module, the dynamic meshing force of the gear pair is loaded as the system mechanical excitation to the meshing node of the gear transmission system, and the radial electromagnetic force of the motor is loaded as the electromagnetic excitation to the surface of the motor electronic core, and the solved mechanical excitation and electromagnetic excitation are decomposed into forces and torques on six degrees of freedom, and the expression is:

[0162] F m(ω)=[0··F x (ω)M y (ω)F y (ω)M x (ω)F z (ω)T m (ω)··0] T (6n，1)

[0163] The converted exciting force array is written in the form of complex exponentials. Combined with the dynamic flexibility matrix R(ω) of the gear transmission system, the vibration displacement response, velocity response and acceleration response at each node of the system are calculated as follows:

[0164]

[0165] Where X is the vibration displacement response of the system node, v is the vibration velocity response of the system node, and a is the vibration acceleration response of the system node.

[0166] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the present invention establishes a full-degree-of-freedom vibration analysis model of the gear transmission system taking into account the additional stiffness of gear meshing and the additional stiffness of the bearing, and establishes a dynamic model of the entire system in combination with the shell finite element condensation model; considering the electromagnetic force generation mechanism under different working conditions, the electromagnetic force under no-load and load conditions is analytically calculated respectively; the two main excitation sources causing the vibration noise of the hub motor reduction drive assembly system are fully considered: the mechanical excitation of the gear transmission system and the electromagnetic excitation of the hub drive motor; thereby accurately obtaining the vibration response of the hub motor reduction drive assembly system under the influence of multiple factors such as gear meshing transmission error, gear dynamic meshing stiffness, and motor radial electromagnetic force, and comprehensively and truly reflecting the vibration characteristics of the reduction drive assembly during actual operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0167] Figure 1 is a flow chart of the present invention;

[0168] Figure 2 It is a schematic diagram of the structure of the hub motor reduction drive assembly in the present invention;

[0169] Figure 3 is the gear meshing transmission error obtained by the slicing algorithm in the present invention;

[0170] Figure 4 It is the frequency domain diagram of the dynamic meshing stiffness of the gear pair in the present invention;

[0171] Figure 5 This is the time domain diagram of the radial electromagnetic force in the present invention. DETAILED DESCRIPTION

[0172] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0173] Example 1

[0174] like Figure 2 As shown, a schematic diagram of a hub motor reduction drive assembly to which the present invention is applied is shown, which is mainly composed of a planetary reducer and a hub motor, and specifically includes a hub 1, a housing 2, a motor stator 3, a motor rotor 4, a motor output shaft 5, an inner gear ring 6, a sun gear 7, a planetary gear 8, a planetary carrier 9 and a spline 10.

[0175] like Figure 1 As shown, the present invention discloses a method for calculating the dynamic response of a deceleration drive assembly under multi-source excitation, comprising the following steps:

[0176] S1. Calculation of the dynamic equation and dynamic flexibility matrix of the gear transmission system: First, establish a full-degree-of-freedom vibration analysis model of the shaft system, extract and analyze the calculation to obtain the stiffness matrix and mass matrix of the shaft system; then perform force analysis on the gear pairs and bearings in the gear transmission system to obtain the gear pair coupling additional stiffness matrix and the bearing additional stiffness matrix in the gear transmission system, and combine the stiffness matrix of the shaft system to obtain the overall stiffness matrix of the gear transmission system; based on the overall stiffness matrix, mass matrix and damping matrix of the gear transmission system, establish the dynamic equation of the gear transmission system and calculate the dynamic flexibility matrix of the gear transmission system; establish a finite element model of the hub motor reduction drive assembly housing, and obtain the overall dynamic model of the system based on the assembly housing finite element model and the dynamic equation of the gear transmission system;

[0177] S1 specifically includes the following steps:

[0178] S11. A full-degree-of-freedom vibration analysis model of the shaft system is established by using the lumped parameter method. The full-degree-of-freedom vibration analysis model includes bending, torsion, axial and swing vibration modes. The full-degree-of-freedom vibration analysis model of the shaft system is extracted and analyzed and calculated to obtain the stiffness matrix and mass matrix of the shaft system. The stiffness matrix of the shaft system includes an axial stiffness matrix, a torsional stiffness matrix and a plane bending and pendulum stiffness matrix. Both the axial stiffness matrix and the torsional stiffness matrix are in the form of tridiagonal matrices. The plane bending and pendulum stiffness matrix is ​​established according to the Timoshenko beam principle. The mass matrix of the shaft system includes an axial mass matrix, a torsional mass matrix and a plane bending and pendulum mass matrix. Both the axial mass matrix and the torsional mass matrix are diagonal matrices. The plane bending and pendulum mass matrix is ​​established according to the Timoshenko beam principle.

[0179] S12, establishing a gear pair coupling additional stiffness matrix and a bearing additional stiffness matrix, integrating the gear pair coupling additional stiffness matrix and the bearing additional stiffness matrix into the stiffness matrix of the shaft system, and forming an overall stiffness matrix of the gear transmission system;

[0180] In the process of establishing the overall stiffness matrix of the gear transmission system, the influence of the additional stiffness of the gear pair coupling and the additional stiffness of the bearing is specially considered. By integrating the additional stiffness matrix of the gear pair coupling and the additional stiffness matrix of the bearing into the stiffness matrix of the shaft system, their influence on the overall stiffness matrix of the gear transmission system is considered.

[0181] The gear transmission system of the hub motor reduction drive assembly to which the present invention is applied is a single-stage planetary gear transmission system, and its basic parameters are shown in Table 1.

[0182] Table 1 Basic parameters of planetary gear transmission system

[0183]

[0184]

[0185] The basic parameters shown in Table 1 can be used to calculate the relative extrusion deformation of the gear pair along the meshing line during the meshing vibration process:

[0186]

[0187] Where: x A 、x B They represent the displacement of the driving wheel A and the driven wheel B along the x direction; y A ,y B They represent the displacement of the driving wheel A and the driven wheel B along the y direction; A 、z B They represent the displacement of the driving wheel A and the driven wheel B along the z direction respectively; Respectively represent the angles of rotation of the driving wheel A and the driven wheel B; R bA , R bB are the base circle radii of the driving wheel A and the driven wheel B respectively; α n is the gear normal pressure angle; α t is the gear end face pressure angle; β is the helix angle;

[0188] The normal meshing force between the driving wheel A and the driven wheel B is:

[0189] F n =k s δ m

[0190] Where: k s It represents the normal meshing stiffness with the gear;

[0191] The force analysis of the driving wheel A and the driven wheel B shows that:

[0192]

[0193] Where: F Ax、F Ay 、F Az are the components of the meshing force of the driving wheel A along the x, y, and z directions, respectively, and M Ax 、M Ay are the torque components of the meshing force of the driving wheel A around the x and y axes, T A is the torque component of the meshing force of the driving wheel A around the z-axis, R A F is the pitch radius of the driving wheel; Bx 、F By 、F Bz are the components of the meshing force of the driven wheel B along the x, y, and z directions, respectively, M Bx 、M By are the torque components of the meshing force of the driven wheel B around the x and y axes, T B is the torque component of the meshing force of the driven wheel B around the z-axis, R B is the pitch radius of the driving wheel;

[0194] The gear pair coupling additional stiffness matrix established by the above calculation results is:

[0195] [K C ]=[F p ]·[K m ]·[D δ ]

[0196] In the formula, [F p ] is the force position matrix, which is calculated by the force analysis of the driving wheel and the driven wheel; [K m ] is the meshing stiffness matrix, which is calculated from the normal meshing stiffness of the gear pair; [D δ ] is the vibration displacement matrix, which is calculated by the relative extrusion deformation of the gear pair along the meshing line during the meshing vibration process;

[0197] Bearing additional stiffness matrix K b The expression is as follows:

[0198]

[0199] In the formula, F x 、F y 、F z are the components of the bearing force along the x, y, and z directions, respectively, M x With M y are the components of the bearing moment about the x-axis and the y-axis, δ x , δ y , δ z are the relative deformations of the inner and outer rings of the bearing along the three directions of the coordinate system, θ x With θ y are the rotation angles of the bearing around the x-axis and y-axis respectively;

[0200] In the actual operation of the bearing, assuming that there are n rolling elements, the position angle of the i-th rolling element is The contact load it bears for:

[0201]

[0202] The bearing force balance equation is:

[0203]

[0204] Where D w , D m Respectively represent the diameter of the rolling element in the bearing and the radius of the circle on which the rolling element is located; is the angle between the line connecting the center of the i-th rolling element and the origin of the coordinate system and the positive direction of the x-axis; R i r is the radius of the center circle of the inner ring of the bearing; i 、r e are the curvature radii of the inner and outer raceways respectively; α0, K is the contact angle of the rolling element before and after loading. n is the effective contact stiffness;

[0205] The bearing force balance equation obtained by calculation can be solved to obtain the bearing additional stiffness matrix;

[0206] The gear pair coupling additional stiffness matrix is ​​added to the gear transmission system overall stiffness matrix according to its corresponding nodes on the gear transmission system, and the calculated bearing additional stiffness matrix is ​​added to the gear transmission system overall stiffness matrix according to its corresponding nodes on the gear transmission system to obtain the gear transmission system overall stiffness matrix;

[0207] S13. Based on the overall stiffness matrix and mass matrix of the gear transmission system, the damping matrix of the gear transmission system is determined by giving the system damping coefficient, and finally the dynamic equation of the gear transmission system is established. The dynamic equation of the gear transmission system is decoupled by means of principal coordinate transformation, and the dynamic flexibility matrix of the gear transmission system is solved;

[0208] The damping matrix of the gear transmission system is generally determined by the damping coefficients of each order measured by the test. Considering the lack of test of the transmission system in the design stage, the damping of each order is calculated by giving the damping coefficients of each order. The damping coefficients of each order are taken as 0.01~0.05, and the damping matrix of the gear transmission system is obtained by the damping of each order.

[0209] The modal damping of the gear transmission system can be calculated by the following formula:

[0210]

[0211] Where:i is the i-th order modal damping matrix, c i is the i-th order modal damping, c ci is the i-th order critical damping, M i is the i-th order quality, P i is the i-th order modal frequency;

[0212] The dynamic equation of the gear transmission system is:

[0213]

[0214] Where: M is the mass matrix of the gear transmission system, C is the damping matrix of the gear transmission system, K is the stiffness matrix of the gear transmission system, f is the dynamic excitation matrix, x, Respectively represent the displacement, velocity and acceleration vibration response results of the measuring point;

[0215] Using the principal coordinate transformation method, we get:

[0216]

[0217] In the formula, P represents the natural frequency matrix of the system, z represents the physical coordinate after transformation, and M i is the i-th order modal mass of the system, c i is the i-th order modal damping of the system, K i is the i-th order modal stiffness of the system;

[0218] The dynamic flexibility matrix of the gear transmission system is:

[0219]

[0220] Where: p i is the i-th order natural frequency of the system, ξ i is the i-th order modal damping ratio of the system;

[0221] S14, establishing a finite element model of the hub motor reduction drive assembly housing, and obtaining an overall dynamic model of the system based on the finite element model of the assembly housing and the dynamic equations of the gear transmission system;

[0222] A finite element model of the hub motor reduction drive assembly shell is established, and the dynamic shrinkage finite element model of the shell is obtained by dynamically shrinking the coupling nodes of the assembly shell finite element model. Based on the dynamic shrinkage finite element model of the shell and the dynamic equations of the gear transmission system, the overall dynamic model of the system can be obtained.

[0223] S2. Calculation of dynamic meshing force of gears: construct a gear slicing algorithm model based on the basic parameters of the gear pair, calculate the gear meshing transmission error obtained by accumulating the manufacturing error of the gear pair, the cumulative deviation of the tooth pitch, and the torsional deformation factor; perform force analysis on the meshing nodes of the gear pair, and calculate the dynamic meshing stiffness of the gear pair in combination with the dynamic flexibility of the gear; calculate the dynamic meshing force of the gear from the gear meshing transmission error and the dynamic meshing stiffness of the gear pair as the mechanical excitation of the system;

[0224] S2 specifically includes the following steps:

[0225] S21. Calculation of gear meshing transmission error: First, it is necessary to determine the gear pair macro parameters, design load and load conditions. The macro parameters include the number of gear teeth, module, pressure angle and helix angle. The load conditions include the input speed and torque of the gear pair. Construct a slicing algorithm model to adjust the deformation of each slice in real time according to the relationship between the load on each slice and the design load. i , the gear meshing transmission error δ is the cumulative deformation of each slice, and the calculation expression of the gear meshing transmission error δ is:

[0226]

[0227] Where: i is the deformation on each slice, δ is the gear meshing transmission error, and m is the number of slices;

[0228] In this example, the meshing of the sun gear and the planetary gear is taken as an example. The calculation results of the gear transmission error at each sub-step are obtained by the established slicing algorithm model, such as Figure 3 shown.

[0229] S22. Calculation of dynamic meshing stiffness of gear pair: The dynamic meshing stiffness of gear pair indicates the change and fluctuation of stiffness during gear meshing, which is calculated from the dynamic flexibility of the driving wheel and the driven wheel at the meshing point of the tooth surface;

[0230] The calculation expression of the dynamic meshing stiffness of the gear pair is:

[0231]

[0232] Where R(ω) is the dynamic flexibility matrix of the gear transmission system, f p 、f g are the force components at the meshing nodes of the driving wheel and the driven wheel under the action of unit normal meshing force;

[0233] In this example, the meshing of the sun gear and the planetary gear is also taken as an example. The dynamic meshing stiffness of the gear pair is calculated as follows: Figure 4 shown.

[0234] S23. Calculation of dynamic meshing force of gear pair: The dynamic meshing force of gear pair during the meshing process is calculated based on the dynamic meshing stiffness of gear pair and the gear meshing transmission error. The calculation expression of the dynamic meshing force of gear pair is:

[0235] F m (ω)=K m (ω)·δ

[0236] Where: F m (ω) is the dynamic meshing force of the gear pair, K m (ω) is the dynamic meshing stiffness of the gear pair, and δ is the gear meshing transmission error.

[0237] S3. Calculate the radial electromagnetic force of the permanent magnet synchronous motor under no-load and load conditions respectively: calculate the air gap magnetic flux density generated by the stator winding and the permanent magnet when the three-phase current is balanced, and calculate the radial electromagnetic force density generated by the interaction between the stator and the rotor in the air gap magnetic field of the permanent magnet synchronous motor according to the Maxwell stress tensor method, that is, the radial electromagnetic force per unit area, and combine the stator tooth surface area to obtain the radial electromagnetic force of the motor as the electromagnetic excitation of the system;

[0238] The hub motor in the hub motor reduction drive assembly to which the present invention is applied is a 32-stage 48-slot permanent magnet synchronous motor. The calculation of the radial electromagnetic force of the motor is carried out under no-load and load conditions. The specific parameters of different working conditions are shown in Table 2.

[0239] Table 2 Electromagnetic excitation calculation conditions

[0240]

[0241] S3 specifically includes the following steps:

[0242] S31. Calculation of radial electromagnetic force of the motor under no-load condition: The air gap magnetic potential of the motor under no-load condition is generated by the permanent magnet, and the air gap magnetic permeability is calculated. The radial electromagnetic force of the motor is expanded to obtain the radial electromagnetic force component under no-load condition;

[0243] When the motor is running at no load, the magnetic field provided by the permanent magnet enters the stator part of the motor through the air gap and then enters the motor rotor through the air gap to form a closed loop. The air gap magnetic density b(θ,t) of the motor is obtained as follows:

[0244] b(θ,t)=F(θ,t)Λ(θ,t)

[0245] Where F(θ,t) is the magnetic potential distribution function, Λ(θ,t) is the air gap permeability;

[0246] The air gap magnetic potential of the motor under no-load condition is generated by the permanent magnet, and the expression of the permanent magnet magnetic potential distribution function is as follows:

[0247]

[0248] Where μ is the harmonic order, F μ is the harmonic amplitude, ω μ is the harmonic angular velocity;

[0249] Taking into account the influence of stator slotting, the expression of air gap permeability is as follows:

[0250]

[0251] Where Λ0 is the average air gap permeability amplitude, k is the kth air gap permeability amplitude caused by stator slotting, Z is the number of stator slots, and θ is the rotor mechanical angle;

[0252] Substitute the formula to calculate the air gap magnetic density b of the motor under no-load condition: m The expression of (θ,t) is:

[0253]

[0254] Then the radial electromagnetic force density P of the motor stator core is obtained r The expression of (θ,t) is as follows:

[0255]

[0256] In the formula, μ0 is the vacuum magnetic permeability, ω is the current angular frequency, and p is the number of rotor pole pairs;

[0257] S32. Calculation of radial electromagnetic force of the motor under load conditions: Under load conditions of the motor, the permanent magnet and the armature winding work together to generate an air gap magnetic field, and the radial electromagnetic force density of the motor under load conditions is calculated;

[0258] Under the load condition of the motor, the permanent magnet and the armature winding work together to generate an air gap magnetic field. When the current passes through the winding, the air gap magnetic density distribution generated by the armature winding is:

[0259]

[0260] Where: is the angle between the winding and the permanent magnet magnetic field axis, v is the harmonic order of the winding magnetic field, B v is the mean value of air gap magnetic flux density at each harmonic order;

[0261] The radial electromagnetic force per unit area under the motor load condition is calculated as:

[0262]

[0263] In this example, the radial electromagnetic force of the motor at a speed of 1000 rpm and a torque of 160 Nm is calculated as follows: Figure 5shown.

[0264] S4. Load mechanical excitation to the meshing node of the gear transmission system, and load electromagnetic excitation to the surface of the motor electronic core; decompose the mechanical excitation and electromagnetic excitation into forces and torques on six degrees of freedom, and combine them with the dynamic flexibility matrix of the gear transmission system to calculate the vibration displacement response, velocity response and acceleration response at each node of the system.

[0265] S4 specifically includes the following steps:

[0266] The dynamic meshing force of the gear pair is loaded as the system mechanical excitation to the meshing node of the gear transmission system, and the radial electromagnetic force of the motor is loaded as the electromagnetic excitation to the surface of the motor electronic core. The solved mechanical excitation and electromagnetic excitation are decomposed into forces and torques on six degrees of freedom, as follows:

[0267] F m (ω)=[0··F x (ω)M y (ω)F y (ω)M x (ω)F z (ω)T m (ω)··0] T (6n，1)

[0268] The converted exciting force array is written in the form of complex exponentials. Combined with the dynamic flexibility matrix R(ω) of the gear transmission system, the vibration displacement response, velocity response and acceleration response at each node of the system are calculated as follows:

[0269]

[0270] Where X is the vibration displacement response of the system node, v is the vibration velocity response of the system node, and a is the vibration acceleration response of the system node.

[0271] In order to fully and truly reflect the vibration characteristics of the drive assembly during actual operation, it is necessary to comprehensively consider the mechanical excitation of the planetary reduction gear transmission system and the electromagnetic excitation of the hub drive motor; the mechanical excitation mainly comes from the dynamic meshing force generated by the planetary gear transmission system during the meshing process due to factors such as transmission error and dynamic meshing stiffness, and the electromagnetic excitation mainly comes from the dynamic radial force and tangential force exerted on the motor stator; due to the action of various dynamic excitations, the system vibrates, and these vibrations are transmitted to the housing through the shaft and bearings, causing vibration on the housing surface and radiating noise to the outside, affecting the overall performance of the system.

[0272] Example 2

[0273] The present invention discloses a calculation system for the dynamic response of a deceleration drive assembly under multi-source excitation, comprising:

[0274] The dynamic model construction module is used for calculating the dynamic equation and dynamic flexibility matrix of the gear transmission system, that is, firstly, establishing the full-degree-of-freedom vibration analysis model of the shaft system, extracting and analyzing and calculating the stiffness matrix and mass matrix of the shaft system; then respectively analyzing the force on the gear pair and the bearing in the gear transmission system to obtain the gear pair coupling additional stiffness matrix and the bearing additional stiffness matrix in the gear transmission system, and combining the stiffness matrix of the shaft system to obtain the overall stiffness matrix of the gear transmission system; based on the overall stiffness matrix, mass matrix and damping matrix of the gear transmission system, the dynamic equation of the gear transmission system is established and the dynamic flexibility matrix of the gear transmission system is calculated; the finite element model of the hub motor reduction drive assembly housing is established, and the overall dynamic model of the system is obtained based on the assembly housing finite element model and the gear transmission system dynamic equation. The specific steps of the dynamic model construction module are to execute step S1 of a calculation method for the dynamic response of a reduction drive assembly under multi-source excitation in Example 1.

[0275] The mechanical excitation calculation module is used to calculate the dynamic meshing force of the gears, that is, to construct a slicing algorithm model of the gears according to the basic parameters of the gear pair, calculate the gear meshing transmission error accumulated by the manufacturing error of the gear pair, the cumulative deviation of the tooth pitch, and the torsional deformation factor; perform force analysis on the meshing nodes of the gear pair, and calculate the dynamic meshing stiffness of the gear pair in combination with the dynamic flexibility of the gear; calculate the dynamic meshing force of the gears from the gear meshing transmission error and the dynamic meshing stiffness of the gear pair as the mechanical excitation of the system. The specific steps of the mechanical excitation calculation module are to execute step S2 of a method for calculating the dynamic response of a reduction drive assembly under multi-source excitation in Example 1.

[0276] The electromagnetic excitation calculation module is used to calculate the radial electromagnetic force of the permanent magnet synchronous motor under no-load and load conditions, that is, to calculate the air gap magnetic flux density generated by the stator winding and the permanent magnet when the three-phase current is balanced, and to calculate the radial electromagnetic force density generated by the interaction between the stator and the rotor in the air gap magnetic field of the permanent magnet synchronous motor according to the Maxwell stress tensor method, that is, the radial electromagnetic force per unit area, and to obtain the motor radial electromagnetic force in combination with the stator tooth surface area as the electromagnetic excitation of the system. The specific steps of the electromagnetic excitation calculation module are to perform step S3 of a calculation method for the dynamic response of a deceleration drive assembly under multi-source excitation in Example 1.

[0277] The response calculation module is used to load mechanical excitation to the meshing nodes of the gear transmission system and electromagnetic excitation to the surface of the motor electronic core; decompose the mechanical excitation and electromagnetic excitation into forces and torques on six degrees of freedom, and calculate the vibration displacement response, velocity response and acceleration response at each node of the system in combination with the dynamic flexibility matrix of the gear transmission system. The specific steps of the response calculation module are executed in step S4 of a method for calculating the dynamic response of a reduction drive assembly under multi-source excitation in Example 1.

Claims

1. A method for calculating the dynamic response of a deceleration drive assembly under multi-source excitation, characterized in that: The steps include: S1. Calculation of the dynamic equation and dynamic flexibility matrix of the gear transmission system: First, establish a full-degree-of-freedom vibration analysis model of the shaft system, extract and analyze the calculation to obtain the stiffness matrix and mass matrix of the shaft system; then perform force analysis on the gear pairs and bearings in the gear transmission system to obtain the gear pair coupling additional stiffness matrix and the bearing additional stiffness matrix in the gear transmission system, and combine the stiffness matrix of the shaft system to obtain the overall stiffness matrix of the gear transmission system; based on the overall stiffness matrix, mass matrix and damping matrix of the gear transmission system, establish the dynamic equation of the gear transmission system and calculate the dynamic flexibility matrix of the gear transmission system; Establish a finite element model of the wheel hub motor reduction drive assembly housing, and obtain the overall dynamic model of the system based on the finite element model of the assembly housing and the dynamic equations of the gear transmission system; S2. Calculation of dynamic meshing force of gears: construct a gear slicing algorithm model based on the basic parameters of the gear pair, calculate the gear meshing transmission error obtained by accumulating the manufacturing error of the gear pair, the cumulative deviation of the tooth pitch, and the torsional deformation factor; perform force analysis on the meshing nodes of the gear pair, and calculate the dynamic meshing stiffness of the gear pair in combination with the dynamic flexibility of the gear; calculate the dynamic meshing force of the gear from the gear meshing transmission error and the dynamic meshing stiffness of the gear pair as the mechanical excitation of the system; S3. Calculation of radial electromagnetic force of permanent magnet synchronous motor under no-load and load conditions: Calculate the air gap magnetic flux density generated by stator winding and permanent magnet when the three-phase current is balanced. Calculate the radial electromagnetic force density generated by the interaction between stator and rotor in the air gap magnetic field of permanent magnet synchronous motor according to Maxwell stress tensor method, that is, radial electromagnetic force per unit area. Combined with the stator tooth surface area, the radial electromagnetic force of the motor is obtained as the electromagnetic excitation of the system. S4. Load mechanical excitation to the meshing node of the gear transmission system, and load electromagnetic excitation to the surface of the motor electronic core; decompose the mechanical excitation and electromagnetic excitation into forces and torques on six degrees of freedom, and combine them with the dynamic flexibility matrix of the gear transmission system to calculate the vibration displacement response, velocity response and acceleration response at each node of the system.

2. The method for calculating the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 1, characterized in that: The S1 specifically includes the following steps: S11. A full-degree-of-freedom vibration analysis model of the shaft system is established by using the lumped parameter method. The full-degree-of-freedom vibration analysis model includes bending, torsion, axial and swing vibration modes. The full-degree-of-freedom vibration analysis model of the shaft system is extracted and analyzed and calculated to obtain the stiffness matrix and mass matrix of the shaft system. The stiffness matrix of the shaft system includes an axial stiffness matrix, a torsional stiffness matrix and a plane bending and pendulum stiffness matrix. Both the axial stiffness matrix and the torsional stiffness matrix are in the form of tridiagonal matrices. The plane bending and pendulum stiffness matrix is ​​established according to the Timoshenko beam principle. The mass matrix of the shaft system includes an axial mass matrix, a torsional mass matrix and a plane bending and pendulum mass matrix. Both the axial mass matrix and the torsional mass matrix are diagonal matrices. The plane bending and pendulum mass matrix is ​​established according to the Timoshenko beam principle. S12, establishing a gear pair coupling additional stiffness matrix and a bearing additional stiffness matrix, integrating the gear pair coupling additional stiffness matrix and the bearing additional stiffness matrix into the stiffness matrix of the shaft system, and forming an overall stiffness matrix of the gear transmission system; The relative extrusion deformation of the gear pair along the meshing line during meshing vibration is: Where: x A 、x B They represent the displacement of the driving wheel A and the driven wheel B along the x direction; y A ,y B They represent the displacement of the driving wheel A and the driven wheel B along the y direction; A 、z B They represent the displacement of the driving wheel A and the driven wheel B along the z direction respectively; Respectively represent the angles of rotation of the driving wheel A and the driven wheel B; R bA , R bB are the base circle radii of the driving wheel A and the driven wheel B respectively; α n is the gear normal pressure angle; α t is the gear end face pressure angle; β is the helix angle; The normal meshing force between the driving wheel A and the driven wheel B is: F n =k s d m Where: k s It represents the normal meshing stiffness with the gear; The force analysis of the driving wheel A and the driven wheel B yields the following results: Where: F Ax 、F Ay 、F Az are the components of the meshing force of the driving wheel A along the x, y, and z directions, respectively, and M Ax 、M Ay are the torque components of the meshing force of the driving wheel A around the x and y axes, T A is the torque component of the meshing force of the driving wheel A around the z-axis, R A F is the pitch radius of the driving wheel; Bx 、F By 、F Bz are the components of the meshing force of the driven wheel B along the x, y, and z directions, respectively, M Bx 、M By are the torque components of the meshing force of the driven wheel B around the x and y axes, T B is the torque component of the meshing force of the driven wheel B around the z-axis, R B is the pitch radius of the driving wheel; The gear pair coupling additional stiffness matrix established by the above calculation results is: [K C ]=[F p ]·[K m ]·[D δ ] In the formula, [F p ] is the force position matrix, which is calculated by the force analysis of the driving wheel and the driven wheel; [K m ] is the meshing stiffness matrix, which is calculated from the normal meshing stiffness of the gear pair; [D δ ] is the vibration displacement matrix, which is calculated by the relative extrusion deformation of the gear pair along the meshing line during the meshing vibration process; Bearing additional stiffness matrix K b The expression is: In the formula, F x 、F y 、F z are the components of the bearing force along the x, y, and z directions, respectively, M x With M y are the components of the bearing moment around the x-axis and the y-axis, δ x , δ y , δ z are the relative deformations of the inner and outer rings of the bearing along the three directions of the coordinate system, θ x With θ y are the rotation angles of the bearing around the x-axis and y-axis respectively; In the actual operation of the bearing, assuming that there are n rolling elements, the position angle of the i-th rolling element is The contact load it bears for: The bearing force balance equation is: Where D w , D m Respectively represent the diameter of the rolling element in the bearing and the radius of the circle on which the rolling element is located; is the angle between the line connecting the center of the i-th rolling element and the origin of the coordinate system and the positive direction of the x-axis; R i r is the radius of the center circle of the inner ring of the bearing; i 、r e are the curvature radii of the inner and outer raceways respectively; α0, K is the contact angle of the rolling element before and after loading. n is the effective contact stiffness; The bearing force balance equation obtained by calculation can be solved to obtain the bearing additional stiffness matrix; The gear pair coupling additional stiffness matrix is ​​added to the gear transmission system overall stiffness matrix according to its corresponding nodes on the gear transmission system, and the calculated bearing additional stiffness matrix is ​​added to the gear transmission system overall stiffness matrix according to its corresponding nodes on the gear transmission system to obtain the gear transmission system overall stiffness matrix; S13: Based on the overall stiffness matrix and mass matrix of the gear transmission system, the damping matrix of the gear transmission system is determined by giving the system damping coefficient, and finally the dynamic equation of the gear transmission system is established. The dynamic equation of the gear transmission system is decoupled with the help of principal coordinate transformation, and the dynamic flexibility matrix of the gear transmission system is solved; By giving each order of damping coefficient, the modal damping of each order is calculated. The damping coefficient of each order is 0.01~0.

05. The damping matrix of the gear transmission system is obtained by the modal damping of each order. The calculation expression of the modal damping of each order of the gear transmission system is: Where: i is the i-th order modal damping matrix, c i is the i-th order modal damping, c ci is the i-th order critical damping, M i is the i-th order quality, P i is the i-th order modal frequency; The dynamic equation of the gear transmission system is: Where: M is the mass matrix of the gear transmission system, C is the damping matrix of the gear transmission system, K is the stiffness matrix of the gear transmission system, f is the dynamic excitation matrix, Respectively represent the displacement, velocity and acceleration vibration response results of the measuring point; Using the principal coordinate transformation method, we get: In the formula, P represents the natural frequency matrix of the system, z represents the physical coordinate after transformation, and M i is the i-th order modal mass of the system, c i is the i-th order modal damping of the system, K i is the i-th order modal stiffness of the system; The dynamic flexibility matrix of the gear transmission system is: Where: p i is the i-th order natural frequency of the system, ξ i is the i-th order modal damping ratio of the system; S14: Establish a finite element model of the hub motor reduction drive assembly housing, and obtain the overall dynamic model of the system based on the finite element model of the assembly housing and the dynamic equations of the gear transmission system.

3. The method for calculating the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 2, characterized in that: The S2 specifically includes the following steps: S21. Calculation of gear meshing transmission error: First, it is necessary to determine the gear pair macro parameters, design load and load conditions. The macro parameters include the number of gear teeth, module, pressure angle and helix angle. The load conditions include the input speed and torque of the gear pair. Construct a slicing algorithm model to adjust the deformation of each slice in real time according to the relationship between the load on each slice and the design load. i , the gear meshing transmission error δ is the cumulative deformation of each slice, and the calculation expression of the gear meshing transmission error δ is: Where: i is the deformation on each slice, δ is the gear meshing transmission error, and m is the number of slices; S22. Calculation of dynamic meshing stiffness of gear pair: The dynamic meshing stiffness of gear pair indicates the change and fluctuation of stiffness during gear meshing, which is calculated from the dynamic flexibility of the driving wheel and the driven wheel at the meshing point of the tooth surface; The calculation expression of the dynamic meshing stiffness of the gear pair is: Where R(ω) is the dynamic flexibility matrix of the gear transmission system, f p 、f g are the force components at the meshing nodes of the driving wheel and the driven wheel under the action of unit normal meshing force; S23. Calculation of dynamic meshing force of gear pair: The dynamic meshing force of gear pair during the meshing process is calculated based on the dynamic meshing stiffness of gear pair and the gear meshing transmission error. The calculation expression of the dynamic meshing force of gear pair is: F m (ω)=K m (ω)·d Where: F m (ω) is the dynamic meshing force of the gear pair, K m (ω) is the dynamic meshing stiffness of the gear pair, and δ is the gear meshing transmission error.

4. The method for calculating the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 3, characterized in that: The S3 specifically includes the following steps: S31. Calculation of radial electromagnetic force of the motor under no-load condition: The air gap magnetic potential of the motor under no-load condition is generated by the permanent magnet, and the air gap magnetic permeability is calculated. The radial electromagnetic force of the motor is expanded to obtain the radial electromagnetic force component under no-load condition; When the motor is running at no load, the magnetic field provided by the permanent magnet enters the stator part of the motor through the air gap and then enters the motor rotor through the air gap to form a closed loop. The air gap magnetic density b(θ,t) of the motor is obtained as: b(θ,t)=F(θ,t)Λ(θ,t) Where F(θ,t) is the magnetic potential distribution function, Λ(θ,t) is the air gap permeability; The air gap magnetic potential of the motor under no-load condition is generated by the permanent magnet, and the distribution function expression of the permanent magnet magnetic potential is obtained as follows: Where μ is the harmonic order, F μ is the harmonic amplitude, ω μ is the harmonic angular velocity; Taking into account the influence of stator slotting, the expression of air gap permeability is: Where Λ0 is the average air gap permeability amplitude, k is the kth air gap permeability amplitude caused by stator slotting, Z is the number of stator slots, and θ is the rotor mechanical angle; Substitute the formula to calculate the air gap magnetic density b of the motor under no-load condition: m The expression of (θ,t) is: Get the radial electromagnetic force density P of the motor stator core r The expression of (θ,t) is: In the formula, μ0 is the vacuum magnetic permeability, ω is the current angular frequency, and p is the number of rotor pole pairs; S32. Calculation of radial electromagnetic force of the motor under load conditions: Under load conditions of the motor, the permanent magnet and the armature winding work together to generate an air gap magnetic field, and the radial electromagnetic force density of the motor under load conditions is calculated; Under the load condition of the motor, the permanent magnet and the armature winding work together to generate an air gap magnetic field. When the current passes through the winding, the air gap magnetic density distribution generated by the armature winding is: Where: is the angle between the winding and the permanent magnet magnetic field axis, v is the harmonic order of the winding magnetic field, B v is the mean value of air gap magnetic flux density at each harmonic order; The radial electromagnetic force per unit area under the motor load condition is calculated as:

5. The method for calculating the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 4, characterized in that: The S4 specifically includes the following steps: The dynamic meshing force of the gear pair is loaded as the system mechanical excitation to the meshing node of the gear transmission system, and the radial electromagnetic force of the motor is loaded as the electromagnetic excitation to the surface of the motor electronic core. The mechanical excitation and electromagnetic excitation obtained are decomposed into forces and torques on six degrees of freedom. The expression is: F m (ω)=[0··F x (oh)M y (ω)F y (oh)M x (ω)F z (ω)T m (ω)··0] T (6n,1) The converted exciting force array is written in the form of complex exponentials. Combined with the dynamic flexibility matrix R(ω) of the gear transmission system, the vibration displacement response, velocity response and acceleration response at each node of the system are calculated as follows: Where X is the vibration displacement response of the system node, v is the vibration velocity response of the system node, and a is the vibration acceleration response of the system node.

6. A calculation system for the dynamic response of a deceleration drive assembly under multi-source excitation, characterized in that: include: The dynamic model building module is used for calculating the dynamic equations and dynamic flexibility matrix of the gear transmission system. That is, firstly, a full-degree-of-freedom vibration analysis model of the shaft system is established, and the stiffness matrix and mass matrix of the shaft system are extracted and analyzed and calculated; then, the force analysis of the gear pairs and bearings in the gear transmission system is performed to obtain the gear pair coupling additional stiffness matrix and the bearing additional stiffness matrix in the gear transmission system, and the overall stiffness matrix of the gear transmission system is obtained by combining the stiffness matrix of the shaft system; based on the overall stiffness matrix, mass matrix and damping matrix of the gear transmission system, the dynamic equations of the gear transmission system are established and the dynamic flexibility matrix of the gear transmission system is calculated; Establish a finite element model of the wheel hub motor reduction drive assembly housing, and obtain the overall dynamic model of the system based on the finite element model of the assembly housing and the dynamic equations of the gear transmission system; The mechanical excitation calculation module is used to calculate the dynamic meshing force of the gears. That is, the gear slicing algorithm model is constructed according to the basic parameters of the gear pair, and the gear meshing transmission error obtained by accumulating the manufacturing error of the gear pair, the cumulative deviation of the tooth pitch, and the torsional deformation factor is calculated; the force analysis is performed on the meshing nodes of the gear pair, and the dynamic meshing stiffness of the gear pair is obtained by combining the dynamic flexibility of the gear; the dynamic meshing force of the gear is calculated from the gear meshing transmission error and the dynamic meshing stiffness of the gear pair as the mechanical excitation of the system; The electromagnetic excitation calculation module is used to calculate the radial electromagnetic force of the permanent magnet synchronous motor under no-load and load conditions, that is, to calculate the air gap magnetic flux density generated by the stator winding and the permanent magnet when the three-phase current is balanced, and to calculate the radial electromagnetic force density generated by the interaction between the stator and the rotor in the air gap magnetic field of the permanent magnet synchronous motor according to the Maxwell stress tensor method, that is, the radial electromagnetic force per unit area, and to obtain the radial electromagnetic force of the motor in combination with the stator tooth surface area as the electromagnetic excitation of the system; The response calculation module is used to load mechanical excitation to the meshing nodes of the gear transmission system and electromagnetic excitation to the surface of the motor electronic core; the mechanical excitation and electromagnetic excitation are decomposed into forces and torques on six degrees of freedom, and combined with the dynamic flexibility matrix of the gear transmission system, the vibration displacement response, velocity response and acceleration response at each node of the system are calculated.

7. The calculation system for the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 6, characterized in that: In the dynamic model construction module, a full-degree-of-freedom vibration analysis model of the shaft system is first established by using a lumped parameter method, and the full-degree-of-freedom vibration analysis model is considered to include bending, torsion, axial and swing vibration modes, and the full-degree-of-freedom vibration analysis model of the shaft system is extracted and analyzed and calculated to obtain the stiffness matrix and mass matrix of the shaft system; the stiffness matrix of the shaft system includes an axial stiffness matrix, a torsional stiffness matrix and a plane bending and pendulum stiffness matrix, both of which are in the form of tridiagonal matrices, and the plane bending and pendulum stiffness matrix is ​​established according to the Timoshenko beam principle; the mass matrix of the shaft system includes an axial mass matrix, a torsional mass matrix and a plane bending and pendulum mass matrix, both of which are diagonal matrices, and the plane bending and pendulum mass matrix is ​​established according to the Timoshenko beam principle; Establish the gear pair coupling additional stiffness matrix and the bearing additional stiffness matrix, integrate the gear pair coupling additional stiffness matrix and the bearing additional stiffness matrix into the stiffness matrix of the shaft system, and form the overall stiffness matrix of the gear transmission system; The relative extrusion deformation of the gear pair along the meshing line during meshing vibration is: Where: x A 、x B They represent the displacement of the driving wheel A and the driven wheel B along the x direction; y A ,y B They represent the displacement of the driving wheel A and the driven wheel B along the y direction; A 、z B They represent the displacement of the driving wheel A and the driven wheel B along the z direction respectively; Respectively represent the angles of rotation of the driving wheel A and the driven wheel B; R bA , R bB are the base circle radii of the driving wheel A and the driven wheel B respectively; α n is the gear normal pressure angle; α t is the gear end face pressure angle; β is the helix angle; The normal meshing force between the driving wheel A and the driven wheel B is: F n =k s d m Where: k s It represents the normal meshing stiffness with the gear; The force analysis of the driving wheel A and the driven wheel B yields the following results: Where: F Ax 、F Ay 、F Az are the components of the meshing force of the driving wheel A along the x, y, and z directions, respectively, and M Ax 、M Ay are the torque components of the meshing force of the driving wheel A around the x and y axes, T A is the torque component of the meshing force of the driving wheel A around the z-axis, R A F is the pitch radius of the driving wheel; Bx 、F By 、F Bz are the components of the meshing force of the driven wheel B along the x, y, and z directions, respectively, M Bx 、M By are the torque components of the meshing force of the driven wheel B around the x and y axes, T B is the torque component of the meshing force of the driven wheel B around the z-axis, R B is the pitch radius of the driving wheel; The gear pair coupling additional stiffness matrix established by the above calculation results is: [K C ]=[F p ]·[K m ]·[D δ ] In the formula, [F p ] is the force position matrix, which is calculated by the force analysis of the driving wheel and the driven wheel; [K m ] is the meshing stiffness matrix, which is calculated from the normal meshing stiffness of the gear pair; [D δ ] is the vibration displacement matrix, which is calculated by the relative extrusion deformation of the gear pair along the meshing line during the meshing vibration process; Bearing additional stiffness matrix K b The expression is: In the formula, F x 、F y 、F z are the components of the bearing force along the x, y, and z directions, respectively, M x With M y are the components of the bearing moment around the x-axis and the y-axis, δ x , δ y , δ z are the relative deformations of the inner and outer rings of the bearing along the three directions of the coordinate system, θ x With θ y are the rotation angles of the bearing around the x-axis and y-axis respectively; In the actual operation of the bearing, assuming that there are n rolling elements, the position angle of the i-th rolling element is The contact load it bears for: The bearing force balance equation is: Where D w , D m They represent the diameter of the rolling element in the bearing and the radius of the circle on which the rolling element is located; is the angle between the line connecting the center of the i-th rolling element and the origin of the coordinate system and the positive direction of the x-axis; R i r is the radius of the center circle of the inner ring of the bearing; i 、r e are the curvature radii of the inner and outer raceways respectively; α0, K is the contact angle of the rolling element before and after loading. n is the effective contact stiffness; The bearing force balance equation obtained by calculation can be solved to obtain the bearing additional stiffness matrix; The gear pair coupling additional stiffness matrix is ​​added to the gear transmission system overall stiffness matrix according to its corresponding nodes on the gear transmission system, and the calculated bearing additional stiffness matrix is ​​added to the gear transmission system overall stiffness matrix according to its corresponding nodes on the gear transmission system to obtain the gear transmission system overall stiffness matrix; Based on the overall stiffness matrix and mass matrix of the gear transmission system, the damping matrix of the gear transmission system is determined by giving the system damping coefficient, and finally the dynamic equation of the gear transmission system is established. The dynamic equation of the gear transmission system is decoupled with the help of principal coordinate transformation, and the dynamic flexibility matrix of the gear transmission system is solved. By giving each order of damping coefficient, the modal damping of each order is calculated. The damping coefficient of each order is 0.01~0.

05. The damping matrix of the gear transmission system is obtained by the modal damping of each order. The calculation expression of the modal damping of each order of the gear transmission system is: Where: i is the i-th order modal damping matrix, c i is the i-th order modal damping, c ci is the i-th order critical damping, M i is the i-th order quality, P i is the i-th order modal frequency; The dynamic equation of the gear transmission system is: Where: M is the mass matrix of the gear transmission system, C is the damping matrix of the gear transmission system, K is the stiffness matrix of the gear transmission system, f is the dynamic excitation matrix, Respectively represent the displacement, velocity and acceleration vibration response results of the measuring point; Using the principal coordinate transformation method, we get: In the formula, P represents the natural frequency matrix of the system, z represents the physical coordinate after transformation, and M i is the i-th order modal mass of the system, c i is the i-th order modal damping of the system, K i is the i-th order modal stiffness of the system; The dynamic flexibility matrix of the gear transmission system is: Where: p i is the i-th order natural frequency of the system, ξ i is the i-th order modal damping ratio of the system; A finite element model of the hub motor reduction drive assembly housing is established, and the overall dynamic model of the system is obtained based on the finite element model of the assembly housing and the dynamic equations of the gear transmission system.

8. The calculation system for the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 7, characterized in that: In the mechanical excitation calculation module, the macro parameters, design load and load conditions of the gear pair need to be determined first. The macro parameters include the number of gear teeth, module, pressure angle and helix angle, and the load conditions include the input speed and torque of the gear pair; a slicing algorithm model is constructed to adjust the deformation amount δ on each slice in real time according to the relationship between the load on each slice and the design load. i , the gear meshing transmission error δ is the cumulative deformation of each slice, and the calculation expression of the gear meshing transmission error δ is: Where: i is the deformation on each slice, δ is the gear meshing transmission error, and m is the number of slices; The dynamic meshing stiffness of a gear pair indicates the change and fluctuation of the stiffness during the meshing process of the gears, which is calculated from the dynamic flexibility of the driving wheel and the driven wheel at the meshing point of the tooth surfaces; The calculation expression of the dynamic meshing stiffness of the gear pair is: Where R(ω) is the dynamic flexibility matrix of the gear transmission system, f p 、f g are the force components at the meshing nodes of the driving wheel and the driven wheel under the action of unit normal meshing force; S23. Calculation of dynamic meshing force of gear pair: The dynamic meshing force of gear pair during the meshing process is calculated based on the dynamic meshing stiffness of gear pair and the gear meshing transmission error. The calculation expression of the dynamic meshing force of gear pair is: F m (ω)=K m (ω)·d Where: F m (ω) is the dynamic meshing force of the gear pair, K m (ω) is the dynamic meshing stiffness of the gear pair, and δ is the gear meshing transmission error.

9. The calculation system for the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 8, characterized in that: In the electromagnetic excitation calculation module, the air gap magnetic potential of the motor is generated by the permanent magnet under no-load conditions, the air gap magnetic permeability is calculated, and the radial electromagnetic force of the motor is expanded to obtain the radial electromagnetic force component under no-load conditions; When the motor is running at no load, the magnetic field provided by the permanent magnet enters the stator part of the motor through the air gap and then enters the motor rotor through the air gap to form a closed loop. The air gap magnetic density b(θ,t) of the motor is obtained as: b(θ,t)=F(θ,t)Λ(θ,) Where F(θ,t) is the magnetic potential distribution function, Λ(θ,t) is the air gap permeability; The air gap magnetic potential of the motor under no-load condition is generated by the permanent magnet, and the distribution function expression of the permanent magnet magnetic potential is obtained as follows: Where μ is the harmonic order, F μ is the harmonic amplitude, ω μ is the harmonic angular velocity; Taking into account the influence of stator slotting, the expression of air gap permeability is: Where Λ0 is the average air gap permeability amplitude, k is the kth air gap permeability amplitude caused by stator slotting, Z is the number of stator slots, and θ is the rotor mechanical angle; Substitute the formula to calculate the air gap magnetic density b of the motor under no-load condition: m The expression of (θ,t) is: Get the radial electromagnetic force density P of the motor stator core r The expression of (θ,t) is: In the formula, μ0 is the vacuum magnetic permeability, ω is the current angular frequency, and p is the number of rotor pole pairs; Under the motor load condition, the permanent magnet and the armature winding work together to generate the air gap magnetic field, and the radial electromagnetic force density under the motor load condition is calculated; Under the load condition of the motor, the permanent magnet and the armature winding work together to generate an air gap magnetic field. When the current passes through the winding, the air gap magnetic density distribution generated by the armature winding is: Where: is the angle between the winding and the permanent magnet magnetic field axis, v is the harmonic order of the winding magnetic field, B v is the mean value of air gap magnetic flux density at each harmonic order; The radial electromagnetic force per unit area under the motor load condition is calculated as:

10. The calculation system for the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 9, characterized in that: In the response calculation module, the dynamic meshing force of the gear pair is loaded as the system mechanical excitation to the meshing node of the gear transmission system, and the radial electromagnetic force of the motor is loaded as the electromagnetic excitation to the surface of the motor electronic core. The mechanical excitation and electromagnetic excitation obtained by the solution are decomposed into forces and torques on six degrees of freedom, and the expression is: F m (ω)=[0··F x (oh)M y (ω)F y (oh)M x (ω)F z (ω)T m (ω)··0] T (6n,1) The converted exciting force array is written in the form of complex exponentials. Combined with the dynamic flexibility matrix R(ω) of the gear transmission system, the vibration displacement response, velocity response and acceleration response at each node of the system are calculated as follows: Where X is the vibration displacement response of the system node, v is the vibration velocity response of the system node, and a is the vibration acceleration response of the system node.

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