A calculation method and system for the dynamic response of a deceleration drive assembly under multi-source excitation

Abstract

The present invention discloses a calculation method and system for the dynamic response of a reduction drive assembly under multi-source excitation, including the following steps: 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 system dynamic model based on the finite element model of the assembly housing and the dynamic equation of the gear transmission system; calculate the dynamic gear meshing force as the mechanical excitation of the system; calculate the radial electromagnetic force of the permanent magnet synchronous motor under no-load and load conditions as the electromagnetic excitation of the system; apply the mechanical excitation and electromagnetic excitation to the gear transmission system, and combine with the dynamic flexibility matrix to calculate the vibration displacement response, velocity response, and acceleration response at each node of the system. The present invention can comprehensively and truly reflect the vibration characteristics of the reduction drive assembly during actual operation.

Description

Technical Field

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

[0002] As a core component of an electric vehicle, the vibration performance of the in-wheel motor reduction drive assembly directly affects the ride comfort of the electric vehicle. The in-wheel motor reduction drive assembly includes two major parts: the in-wheel motor and the planetary reducer. It is a core component of the electric vehicle and also a very important vibration and noise source. In current research on the vibration response analysis of new energy vehicle powertrains, most studies separate the in-wheel motor and the planetary reducer, which cannot well match the test results of the whole vehicle. Moreover, most research objects consider the motor housing and the reducer housing separately, and there is less dynamic research on the integrated structure of the in-wheel motor reduction drive assembly.

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

[0004] Object of the Invention: The object of the present invention is to provide a calculation method for the dynamic response of a reduction drive assembly under multi-source excitation. The present invention can accurately obtain the dynamic response of the reduction drive assembly affected by mechanical excitation and electromagnetic excitation, and comprehensively and truly reflect the vibration characteristics of the reduction 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 reduction drive assembly under multi-source excitation.

[0006] Technical Solution: To achieve the above objects, the present invention discloses a calculation method for the dynamic response of a reduction drive assembly under multi-source excitation, including 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 shafting, extract and analyze to obtain the stiffness matrix and mass matrix of the shafting; then, perform force analysis on the gear pair and bearings in the gear transmission system respectively to obtain the coupled additional stiffness matrix of the gear pair and the bearing additional stiffness matrix in the gear transmission system, and combine the stiffness matrix of the shafting 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 to obtain the dynamic flexibility matrix of the gear transmission system; establish a finite element model of the housing of the in-wheel motor reduction drive assembly, and obtain the overall dynamic model of the system based on the finite element model of the assembly housing and the dynamic equation of the gear transmission system;

[0008] S2. Calculation of the dynamic meshing force of the gear: Construct a slicing algorithm model of the gear based on the basic parameters of the gear pair, calculate the meshing transmission error of the gear pair accumulated from manufacturing errors, pitch cumulative deviation, and torsional deformation factors; conduct a force analysis on the meshing node 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 meshing transmission error of the gear and the dynamic meshing stiffness of the gear pair, which is used as the mechanical excitation of the system.

[0009] S3. Calculation of the radial electromagnetic force of the permanent magnet synchronous motor under no-load and load conditions: Calculate the air-gap magnetic 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. Combine the stator tooth surface area to obtain the radial electromagnetic force of the motor, which is used as the electromagnetic excitation of the system.

[0010] S4. Apply the mechanical excitation to the meshing node of the gear transmission system, and apply the electromagnetic excitation to the surface of the motor electronic iron core; decompose the mechanical excitation and the electromagnetic excitation into forces and torques in 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.

[0011] Optionally, the specific steps of S1 are as follows:

[0012] S11. Establish a full-degree-of-freedom vibration analysis model of the shafting using the lumped parameter method. Consider bending, torsion, axial, and swing vibration modes in the full-degree-of-freedom vibration analysis model, and perform extraction and analysis calculations on the full-degree-of-freedom vibration analysis model of the shafting to obtain the stiffness matrix and mass matrix of the shafting; the stiffness matrix of the shafting includes the axial stiffness matrix, torsional stiffness matrix, and planar bending and swing stiffness matrix. The axial stiffness matrix and torsional stiffness matrix are both in the form of a tridiagonal matrix, and the planar bending and swing stiffness matrix is established according to the Timoshenko beam principle; the mass matrix of the shafting includes the axial mass matrix, torsional mass matrix, and planar bending and swing mass matrix. The axial mass matrix and torsional mass matrix are both diagonal matrices, and the planar bending and swing mass matrix is established according to the Timoshenko beam principle.

[0013] S12. Establish the coupled additional stiffness matrix of the gear pair and the additional stiffness matrix of the bearing, and integrate the coupled additional stiffness matrix of the gear pair and the additional stiffness matrix of the bearing into the stiffness matrix of the shafting to form the overall stiffness matrix of the gear transmission system.

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

[0015]

[0016] Where: xA , x B respectively represent the displacements of the driving wheel A and the driven wheel B in the x-direction; y A , y B respectively represent the displacements of the driving wheel A and the driven wheel B in the y-direction; z A , z B respectively represent the displacements of the driving wheel A and the driven wheel B in the z-direction; respectively represent the rotation angles of the driving wheel A and the driven wheel B; R bA , R bB are respectively the base circle radii of the driving wheel A and the driven wheel B; α n is the normal pressure angle of the gear; α t is the transverse pressure angle of the gear; 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] In the formula: k s represents the normal meshing stiffness of the gear;

[0020] By analyzing the forces on the driving wheel A and the driven wheel B, we get:

[0021]

[0022] In the formula: F Ax , F Ay , F Az are respectively the components of the meshing force of the driving wheel A in the x, y, and z directions, M Ax , M Ay are respectively 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 is the pitch circle radius of the driving wheel; F Bx , F By , F Bz are respectively the components of the meshing force of the driven wheel B in the x, y, and z directions, M Bx , M By are respectively 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 circle radius of the driving wheel;

[0023] Based on the above calculation results, the coupling additional stiffness matrix of the gear pair is established as:

[0024] [K C = [Fp ·[K m ·[D δ

[0025] wherein, [F p is the force application position matrix, obtained by analyzing and calculating the forces on the driving wheel and the driven wheel; [K m is the meshing stiffness matrix, obtained by calculating the normal meshing stiffness of the gear pair; [D δ is the vibration displacement matrix, obtained by calculating the relative extrusion deformation of the gear pair along the meshing line direction during meshing vibration;

[0026] The expression of the bearing additional stiffness matrix K b is as follows:

[0027]

[0028] wherein, F x , F y , F z are respectively the components of the bearing force along the x, y, and z directions, M x and M y are respectively the components of the bearing moment about the x-axis and the y-axis, δ x , δ y , δ z are respectively the relative deformations of the inner and outer rings of the bearing along the three directions of the coordinate system, θ x and θ y are respectively the rotations of the bearing about the x-axis and the y-axis;

[0029] During the actual operation of the bearing, it is assumed that there are n rolling elements in total, and the position angle of the i-th rolling element is The contact load it bears is:

[0030]

[0031] The bearing force balance equation can be obtained as:

[0032]

[0033] wherein, D w , D m respectively represent the diameter of the rolling element in the bearing and the radius of the circumference where 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 is the radius of the circumference of the curvature center of the inner ring of the bearing; r i , r e are respectively the curvature radii of the inner and outer raceways; α0, is the contact angle of the rolling element before and after loading, K n ​is the effective contact stiffness;

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

[0035] S13: Based on the overall stiffness matrix and mass matrix of the gear transmission system, determine the damping matrix of the gear transmission system by specifying the system damping coefficient, finally establish the dynamic equation of the gear transmission system, decouple the dynamic equation of the gear transmission system by means of the principal coordinate transformation, and solve the dynamic flexibility matrix of the gear transmission system;

[0036] Calculate the modal damping of each order by specifying the damping coefficients of each order. The damping coefficients of each order are taken as 0.01 - 0.05. The damping matrix of the gear transmission system is obtained from the modal damping of each order. The calculation expression of the modal damping of each order of the gear transmission system is:

[0037]

[0038] In the formula: ξ 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 mass, P i is the i-th order modal frequency;

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

[0040]

[0041] In the formula: 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 method of principal coordinate transformation, we get:

[0043]

[0044] In the formula, P represents the natural frequency matrix of the system, z represents the physical coordinate after transformation, 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 as follows:

[0046]

[0047] Where: p i is the i-th natural frequency of the system, and ξ i is the i-th 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 equation of the gear transmission system.

[0049] Optionally, the specific steps of S2 are as follows:

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

[0051]

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

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

[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, and f p , f g are the force components at the meshing nodes of the driving gear and the driven gear under the action of the unit normal meshing force respectively;

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

[0058] Fm F(ω) = K m F(ω)·δ

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

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

[0061] S31. Calculation of the radial electromagnetic force of the motor under no-load condition: Under no-load condition, the air-gap magnetic potential of the motor is generated by the permanent magnet. Calculate the air-gap magnetic permeability, expand the radial electromagnetic force of the motor, and obtain the radial electromagnetic force components under no-load condition;

[0062] When the motor is running under 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 rotor of the motor 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, and Λ(θ, t) is the air-gap magnetic permeability;

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

[0066]

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

[0068] Considering the influence of stator slotting, the expression of the air-gap magnetic permeability is:

[0069]

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

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

[0072]

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

[0074]

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

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

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

[0078]

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

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

[0081]

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

[0083] The dynamic meshing force of the gear pair is applied as a system mechanical excitation to the meshing node of the gear transmission system, and the radial electromagnetic force of the motor is applied as an electromagnetic excitation to the surface of the motor electronic iron core. The mechanical excitation and electromagnetic excitation obtained by solving are decomposed into forces and torques in six degrees of freedom, and 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 excitation force array is written in the form of complex exponential, and 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:

[0086]

[0087] Wherein, 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 reduction drive assembly under multi-source excitation, including:

[0089] A dynamic model construction module, used for calculating the dynamic equations of the gear transmission system and the dynamic flexibility matrix. That is, first, establish a full-degree-of-freedom vibration analysis model of the shafting, extract and analyze to obtain the stiffness matrix and mass matrix of the shafting; then, respectively conduct force analysis on the gear pairs and bearings in the gear transmission system to obtain the coupled additional stiffness matrix of the gear pairs and the bearing additional stiffness matrix in the gear transmission system, and combine with the stiffness matrix of the shafting 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 equations 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 based on the finite element model of the assembly housing and the dynamic equations of the gear transmission system, obtain the overall dynamic model of the system;

[0090] A mechanical excitation calculation module, used for calculating the dynamic meshing force of the gears. That is, construct a slicing algorithm model of the gears according to the basic parameters of the gear pairs, calculate the gear meshing transmission error accumulated from the manufacturing error of the gear pairs, the cumulative pitch deviation, and the torsional deformation amount factors; conduct force analysis on the meshing nodes of the gear pairs, and combine with the gear dynamic flexibility to calculate the dynamic meshing stiffness of the gear pairs; calculate the gear dynamic meshing force from the gear meshing transmission error and the dynamic meshing stiffness of the gear pairs, which is used as the mechanical excitation of the system;

[0091] An electromagnetic excitation calculation module, used for calculating the radial electromagnetic force of the permanent magnet synchronous motor under no-load and load conditions. That is, when the three-phase current is balanced, calculate the air-gap magnetic density generated by the stator winding and the permanent magnet, 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 with the stator tooth surface area to obtain the motor radial electromagnetic force, which is used as the electromagnetic excitation of the system;

[0092] A response calculation module, used for loading the mechanical excitation to the meshing nodes of the gear transmission system and loading the electromagnetic excitation to the surface of the motor electronic iron core; decompose the mechanical excitation and the electromagnetic excitation into forces and torques in six degrees of freedom, and combine 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.

[0093] Optionally, in the kinetic model construction module, the lumped parameter method is first used to establish a full-degree-of-freedom vibration analysis model of the shafting. In the full-degree-of-freedom vibration analysis model, bending, torsion, axial, and wobbling vibration modes are considered, and the full-degree-of-freedom vibration analysis model of the shafting is extracted and analyzed to obtain the stiffness matrix and mass matrix of the shafting; the stiffness matrix of the shafting includes an axial stiffness matrix, a torsional stiffness matrix, and a planar bending and wobbling stiffness matrix. The axial stiffness matrix and the torsional stiffness matrix are both in the form of a tridiagonal matrix, and the planar bending and wobbling stiffness matrix is established based on the Timoshenko beam principle; the mass matrix of the shafting includes an axial mass matrix, a torsional mass matrix, and a planar bending and wobbling mass matrix. The axial mass matrix and the torsional mass matrix are both diagonal matrices, and the planar bending and wobbling mass matrix is established based on the Timoshenko beam principle;

[0094] The coupled additional stiffness matrix of the gear pair and the bearing additional stiffness matrix are established, and the coupled additional stiffness matrix of the gear pair and the bearing additional stiffness matrix are integrated into the stiffness matrix of the shafting to form the overall stiffness matrix of the gear transmission system;

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

[0096]

[0097] In the formula: x A 、x B respectively represent the displacements of the driving wheel A and the driven wheel B in the x direction; y A 、y B respectively represent the displacements of the driving wheel A and the driven wheel B in the y direction; z A 、z B respectively represent the displacements of the driving wheel A and the driven wheel B in the z direction; respectively represent the angles turned by 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 normal pressure angle of the gear; α t is the transverse pressure angle of the gear; 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] In the formula: k s represents the normal meshing stiffness of the gear;

[0101] By analyzing the forces on the driving wheel A and the driven wheel B, we get:

[0102]

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

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

[0105] [K C = [F p ·[K m ·[D δ

[0106] In the formula, [F p is the force position matrix, which is obtained by analyzing and calculating the forces on the driving wheel and the driven wheel; [K m is the meshing stiffness matrix, which is obtained by calculating the normal meshing stiffness of the gear pair; [D δ is the vibration displacement matrix, which is obtained by calculating the relative extrusion deformation of the gear pair along the meshing line direction during the meshing vibration;

[0107] The expression of the bearing additional stiffness matrix K b is:

[0108]

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

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

[0111]

[0112] The bearing force balance equation can be obtained as:

[0113]

[0114] In the formula, D w 、D m respectively represent the diameter of the rolling element in the bearing and the radius of the circumference where 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 x-axis direction; R i is the radius of the circumference of the curvature center of the bearing inner ring; r i 、r e are the curvature radii of the inner and outer ring raceways respectively; α0, are the contact angles before and after the rolling element is loaded, and K n is the effective contact stiffness;

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

[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 specifying the system damping coefficient. Finally, the dynamic equation of the gear transmission system is established, and the dynamic equation of the gear transmission system is decoupled by means of the principal coordinate transformation, and the dynamic flexibility matrix of the gear transmission system is solved;

[0117] By specifying the damping coefficients of each order, the modal damping of each order is calculated. The damping coefficients of each order are taken as 0.01 - 0.05. The damping matrix of the gear transmission system is obtained from the modal damping of each order. The calculation expression of the modal damping of each order of the gear transmission system is:

[0118]

[0119] In the formula: ξ 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 mass, 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 measured point displacement, velocity, and acceleration vibration response results;

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

[0124]

[0125] Where, P represents the natural frequency matrix of the system, z represents the physical coordinates after transformation, 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 an overall dynamic model of the system is obtained based on the finite element model of the assembly housing and the dynamic equation of the gear transmission system.

[0130] Optionally, in the mechanical excitation calculation module, it is first necessary to determine the macroscopic parameters of the gear pair, the design load, and the loading conditions. The macroscopic parameters include the number of teeth, module, pressure angle, and helix angle of the gear, and the loading conditions include the input speed and torque of the gear pair; a slicing algorithm model is constructed, and the deformation amount δ of each slice is adjusted in real time according to the relationship between the loading and the design load on each slice i , and the gear meshing transmission error δ is the accumulation of the deformations of each slice. The calculation expression of the gear meshing transmission error δ is:

[0131]

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

[0133] The dynamic meshing stiffness of the gear pair represents the change and fluctuation of the stiffness during the gear meshing process, and is calculated from the dynamic flexibility of the driving gear and the driven gear at the tooth surface meshing;

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

[0135]

[0136] In the formula, 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 gear and the driven gear under the action of the unit normal meshing force respectively;

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

[0138] F m (ω) = K m (ω)·δ

[0139] In the formula: 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 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;

[0141] When the motor is running under 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 rotor of the motor 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] In the formula, F(θ, t) is the magnetic potential distribution function, and Λ(θ, t) is the air-gap magnetic permeability;

[0144] Under no-load conditions, the air-gap magnetic potential of the motor is generated by the permanent magnet, and the expression of the permanent magnet magnetic potential distribution function is:

[0145]

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

[0147] Considering the influence of stator slotting, the expression of air-gap permeability is:

[0148]

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

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

[0151]

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

[0153]

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

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

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

[0157]

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

[0159] The radial electromagnetic force per unit area under the load condition of the motor 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. The mechanical excitation and electromagnetic excitation obtained by solving are decomposed into forces and torques in six degrees of freedom, and the expression is:

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

[0163] Write the exciting force array after conversion in the form of complex exponential. Combine the dynamic flexibility matrix R(ω) of the gear transmission system to calculate the vibration displacement response, velocity response, and acceleration response at each node of the system as follows:

[0164]

[0165] In the formula, 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 remarkable advantages: The present invention establishes a full-degree-of-freedom vibration analysis model of the gear transmission system considering the additional stiffness of gear meshing and the additional stiffness of bearings, and combines the finite element condensation model of the housing to establish the dynamic model of the whole system; Considering the electromagnetic force generation mechanism under different working conditions, the electromagnetic force under no-load and load conditions is analyzed and calculated respectively; Fully consider the two main excitation sources that cause vibration and noise in the hub motor reduction drive assembly system: the mechanical excitation of the gear transmission system and the electromagnetic excitation of the hub drive motor; Thus, accurately obtain 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 reflect the vibration characteristics of the reduction drive assembly during actual operation. Brief Description of the Drawings

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

[0168] Figure 2 is the structural schematic diagram 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 is the frequency domain diagram of the dynamic meshing stiffness of the gear pair in the present invention;

[0171] Figure 5 is the time domain diagram of the radial electromagnetic force in the present invention. Detailed Embodiment

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

[0173] Embodiment 1

[0174] As Figure 2 shown, the schematic diagram of the hub motor reduction drive assembly to which the present invention is applied mainly consists 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 internal gear ring 6, a sun gear 7, a planetary gear 8, a planetary carrier 9, and a spline 10.

[0175] As Figure 1 shown, the present invention discloses a calculation method for the dynamic response of a reduction drive assembly under multi-source excitation, including 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 shafting, extract and analyze it to obtain the stiffness matrix and mass matrix of the shafting; then, analyze the forces on the gear pairs and bearings in the gear transmission system respectively to obtain the coupled additional stiffness matrix of the gear pairs and the bearing additional stiffness matrix in the gear transmission system, and combine the stiffness matrix of the shafting 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 finite element model of the assembly housing and the dynamic equation of the gear transmission system;

[0177] S1 specifically includes the following steps:

[0178] S11. Use the lumped parameter method to establish a full-degree-of-freedom vibration analysis model of the shafting. Consider bending, torsion, axial, and sway vibration modes in the full-degree-of-freedom vibration analysis model, and extract and analyze the full-degree-of-freedom vibration analysis model of the shafting to obtain the stiffness matrix and mass matrix of the shafting; the stiffness matrix of the shafting includes an axial stiffness matrix, a torsional stiffness matrix, and a planar bending and sway stiffness matrix. Both the axial stiffness matrix and the torsional stiffness matrix are in the form of a tridiagonal matrix, and the planar bending and sway stiffness matrix is established according to the Timoshenko beam principle; the mass matrix of the shafting includes an axial mass matrix, a torsional mass matrix, and a planar bending and sway mass matrix. Both the axial mass matrix and the torsional mass matrix are diagonal matrices, and the planar bending and sway mass matrix is established according to the Timoshenko beam principle;

[0179] S12. Establish the coupled additional stiffness matrix of the gear pair and the bearing additional stiffness matrix, and integrate the coupled additional stiffness matrix of the gear pair and the bearing additional stiffness matrix into the stiffness matrix of the shafting to form the 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 coupling additional stiffness of the gear pair and the additional stiffness of the bearing is particularly considered. By integrating the coupling additional stiffness matrix of the gear pair and the additional stiffness matrix of the bearing into the stiffness matrix of the shafting, the 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 the planetary gear transmission system

[0183]

[0184]

[0185] From the basic parameters shown in Table 1, the relative extrusion deformation of the gear pair along the meshing line direction during meshing vibration can be calculated as:

[0186]

[0187] In the formula: x A 、x B respectively represent the displacements of the driving wheel A and the driven wheel B along the x direction; y A 、y B respectively represent the displacements of the driving wheel A and the driven wheel B along the y direction; z A 、z B respectively represent the displacements of the driving wheel A and the driven wheel B along the z direction; respectively represent the angles rotated by 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 normal pressure angle of the gear; α t is the transverse pressure angle of the gear; 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] In the formula: k s represents the normal meshing stiffness of the gear;

[0191] By analyzing the forces on the driving wheel A and the driven wheel B, it can be known that:

[0192]

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

[0194] The coupled additional stiffness matrix of the gear pair is established from the above calculation results as follows:

[0195] [K C = [F p · [K m · [D δ

[0196] In the formula, [F p is the force position matrix, which is obtained by analyzing and calculating the forces on the driving wheel and the driven wheel; [K m is the meshing stiffness matrix, which is obtained by calculating the normal meshing stiffness of the gear pair; [D δ is the vibration displacement matrix, which is obtained by calculating the relative extrusion deformation of the gear pair along the meshing line direction during the meshing vibration;

[0197] The expression of the bearing additional stiffness matrix K b is as follows:

[0198]

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

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

[0201]

[0202] The bearing force balance equation can be obtained as:

[0203]

[0204] In the formula, D w , D m respectively represent the diameter of the rolling element in the bearing and the radius of the circumference where 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 is the radius of the circumference of the curvature center of the inner ring of the bearing; r i , r e are the curvature radii of the inner and outer ring raceways respectively; α0, are the contact angles before and after the rolling element is loaded, and K n is the effective contact stiffness;

[0205] The bearing additional stiffness matrix can be solved from the calculated bearing force balance equation;

[0206] Attach the gear pair coupling additional stiffness matrix to the overall stiffness matrix of the gear transmission system according to the corresponding nodes on the gear transmission system, and attach the calculated bearing additional stiffness matrix to the overall stiffness matrix of the gear transmission system according to the corresponding nodes on the gear transmission system to obtain the overall stiffness matrix of the gear transmission system;

[0207] S13. Based on the overall stiffness matrix and mass matrix of the gear transmission system, determine the damping matrix of the gear transmission system by specifying the system damping coefficient. Finally, establish the dynamic equation of the gear transmission system, decouple the dynamic equation of the gear transmission system by means of principal coordinate transformation, and solve the dynamic flexibility matrix of the gear transmission system;

[0208] The damping matrix of the gear transmission system is generally determined by the measured damping coefficients of each order. Considering the lack of tests during the design stage of the transmission system, calculate the modal damping of each order by specifying 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 from the modal damping of each order;

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

[0210]

[0211] In the formula: ξi 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 mass, 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 points;

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

[0216]

[0217] Where, P represents the natural frequency matrix of the system, z represents the physical coordinates after transformation, 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. 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 equation of the gear transmission system;

[0222] Establish a finite element model of the hub motor reduction drive assembly housing, perform dynamic condensation of the coupling nodes on the finite element model of the assembly housing to obtain the dynamically condensed finite element model of the housing, and the overall dynamic model of the system can be obtained based on the dynamically condensed finite element model of the housing and the dynamic equation of the gear transmission system.

[0223] S2. Calculation of Gear Dynamic Meshing Force: Construct a slicing algorithm model of the gear based on the basic parameters of the gear pair, and calculate the gear meshing transmission error accumulated from the manufacturing error of the gear pair, the cumulative pitch deviation, and the torsional deformation factor; conduct a force analysis on the meshing node of the gear pair, and calculate the dynamic meshing stiffness of the gear pair in combination with the gear dynamic flexibility; calculate the gear dynamic meshing force from the gear meshing transmission error and the dynamic meshing stiffness of the gear pair, which is used 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 macroscopic parameters of the gear pair, the design load, and the loading conditions. The macroscopic parameters include the number of teeth, module, pressure angle, and helix angle of the gear, and the loading conditions include the input speed and torque of the gear pair; construct a slicing algorithm model, and adjust the deformation amount δ 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 accumulation of the deformations of each slice. The calculation expression of the gear meshing transmission error δ is:

[0226]

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

[0228] In this example, taking the meshing of the sun gear and the planet gear as an example, the calculation results of the gear transmission error obtained through the established slicing algorithm model at each sub-step are as Figure 3 shown.

[0229] S22. Calculation of Gear Pair Dynamic Meshing Stiffness: The gear pair dynamic meshing stiffness represents the change and fluctuation of the stiffness during the gear meshing process, and is calculated from the dynamic flexibilities of the driving gear and the driven gear at the tooth surface meshing;

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

[0231]

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

[0233] In this example, also taking the meshing of the sun gear and the planet gear as an example, the calculated gear pair dynamic meshing stiffness is as Figure 4 shown.

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

[0235] F m (ω) = K m (ω)·δ

[0236] In the formula: 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: When the three-phase currents are balanced, the air-gap magnetic density generated by the stator winding and the permanent magnet is calculated. According to the Maxwell stress tensor method, 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 is calculated, that is, the radial electromagnetic force per unit area. Combining with the stator tooth surface area, the radial electromagnetic force of the motor is obtained as the electromagnetic excitation of the system;

[0238] In the hub motor reduction drive assembly to which the present invention is applied, the hub motor is a 32-pole 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 under different conditions are shown in Table 2.

[0239] Table 2 Calculation conditions of electromagnetic excitation

[0240]

[0241] S3 specifically includes the following steps:

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

[0243] When the motor is running under 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 rotor of the motor 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] In the formula, F(θ, t) is the magnetic potential distribution function, and Λ(θ, t) is the air-gap magnetic permeability;

[0246] Under no-load conditions, the air-gap magnetic potential of the motor is generated by the permanent magnet. The expression of the permanent magnet magnetic potential distribution function is obtained as follows:

[0247]

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

[0249] Considering the influence of stator slotting, the expression of air-gap permeability is as follows:

[0250]

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

[0252] Substituting into the formula and calculating, the expression of the air-gap magnetic density b m (θ, t) is:

[0253]

[0254] Furthermore, the radial electromagnetic force density P r (θ, t) is expressed as follows:

[0255]

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

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

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

[0259]

[0260] In the formula: is the angle between the axis of the winding magnetic field and the permanent magnet magnetic field, v is the harmonic order of the winding magnetic field, B v is the average value of the air-gap magnetic density for each harmonic order;

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

[0262]

[0263] In this example, the calculated radial electromagnetic force of the motor under the conditions of a rotational speed of 1000 rpm and a torque of 160 Nm is as Figure 5as shown

[0264] S4. Apply mechanical excitation to the meshing node of the gear transmission system, and apply electromagnetic excitation to the surface of the motor electronic iron core; decompose the mechanical excitation and electromagnetic excitation into forces and torques in six degrees of freedom, and combine 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] Take the dynamic meshing force of the gear pair as the mechanical excitation of the system and apply it to the meshing node of the gear transmission system, take the radial electromagnetic force of the motor as the electromagnetic excitation and apply it to the surface of the motor electronic iron core, and decompose the obtained mechanical excitation and electromagnetic excitation into forces and torques in 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] Write the converted exciting force array in the form of complex exponential, and combine with the dynamic flexibility matrix R(ω) of the gear transmission system to calculate the vibration displacement response, velocity response and acceleration response at each node of the system as:

[0269]

[0270] In the formula, 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 comprehensively 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 meshing 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 received by 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 the housing surface to vibrate and radiate noise externally, affecting the overall performance of the system.

[0272] Embodiment 2

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

[0274] The dynamic model construction module is used for calculating the dynamic equations of the gear transmission system and the dynamic flexibility matrix. That is, first, a full-degree-of-freedom vibration analysis model of the shafting is established, and the stiffness matrix and mass matrix of the shafting are obtained through extraction and analysis calculations. Then, the force analysis of the gear pairs and bearings in the gear transmission system is carried out respectively to obtain the coupled additional stiffness matrix of the gear pairs and the bearing additional stiffness matrix in the gear transmission system. Combining with the stiffness matrix of the shafting, the overall stiffness matrix of the gear transmission system is obtained. 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 finite element model of the assembly housing and the dynamic equations of the gear transmission system. The specific steps of the dynamic model construction module execute step S1 of a calculation method for the dynamic response of the reduction drive assembly under multi-source excitation in Embodiment 1.

[0275] The mechanical excitation calculation module is used for calculating the dynamic meshing force of the gears. That is, a slice algorithm model of the gears is constructed according to the basic parameters of the gear pairs, and the meshing transmission error of the gears caused by the cumulative manufacturing error, pitch cumulative deviation and torsional deformation of the gear pairs is calculated. The force analysis of the meshing nodes of the gear pairs is carried out, and the dynamic meshing stiffness of the gear pairs is calculated in combination with the dynamic flexibility of the gears. The dynamic meshing force of the gears is calculated from the meshing transmission error of the gears and the dynamic meshing stiffness of the gear pairs, which is used as the mechanical excitation of the system. The specific steps of the mechanical excitation calculation module execute step S2 of a calculation method for the dynamic response of the reduction drive assembly under multi-source excitation in Embodiment 1.

[0276] The electromagnetic excitation calculation module is used for calculating the radial electromagnetic force of the permanent magnet synchronous motor under no-load and load conditions. That is, when the three-phase current is balanced, the air-gap magnetic density generated by the stator winding and the permanent magnet is calculated, and 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 is calculated according to the Maxwell stress tensor method, that is, the radial electromagnetic force per unit area. Combining with the stator tooth surface area, the radial electromagnetic force of the motor is obtained, which is used as the electromagnetic excitation of the system. The specific steps of the electromagnetic excitation calculation module execute step S3 of a calculation method for the dynamic response of the reduction drive assembly under multi-source excitation in Embodiment 1.

[0277] The response calculation module is used for loading the mechanical excitation to the meshing nodes of the gear transmission system and loading the electromagnetic excitation to the surface of the motor electronic iron core; decomposing the mechanical excitation and the electromagnetic excitation into forces and torques in six degrees of freedom, and combining 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. The specific steps of the response calculation module execute step S4 of a calculation method for the dynamic response of the reduction drive assembly under multi-source excitation in Embodiment 1.

Claims

1. A calculation method for the dynamic response of a deceleration drive assembly under multi-source excitation, characterized in that It includes the following steps: 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 shafting, and perform extraction and analysis calculations to obtain the stiffness matrix and mass matrix of the shafting; then, perform force analysis on the gear pairs and bearings in the gear transmission system respectively to obtain the coupled additional stiffness matrix of the gear pairs and the bearing additional stiffness matrix in the gear transmission system, and combine the stiffness matrix of the shafting 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 finite element model of the assembly housing and the dynamic equation of the gear transmission system; S2. Calculation of the dynamic meshing force of the gears: Construct a slicing algorithm model of the gears according to the basic parameters of the gear pairs, and calculate the gear meshing transmission error accumulated by the manufacturing error of the gear pairs, the cumulative pitch deviation and the torsional deformation amount factors; perform force analysis on the meshing nodes of the gear pairs, and calculate the dynamic meshing stiffness of the gear pairs in combination with the gear dynamic flexibility; calculate the gear dynamic meshing force from the gear meshing transmission error and the dynamic meshing stiffness of the gear pairs, which is used as the mechanical excitation of the system; S3. Calculation of the radial electromagnetic force of the permanent magnet synchronous motor under no-load and load conditions: Calculate the air-gap magnetic 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 motor radial electromagnetic force, which is used as the electromagnetic excitation of the system; S4. Load the mechanical excitation to the meshing nodes of the gear transmission system, and load the electromagnetic excitation to the surface of the motor electronic iron core; decompose the mechanical excitation and the electromagnetic excitation into forces and torques in six degrees of freedom, and combine 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 calculation method for the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 1, wherein The specific steps of S1 include the following: S11. Use the lumped parameter method to establish a full-degree-of-freedom vibration analysis model of the shafting. Consider bending, torsion, axial and swing vibration modes in the full-degree-of-freedom vibration analysis model, and perform extraction and analysis calculations on the full-degree-of-freedom vibration analysis model of the shafting to obtain the stiffness matrix and mass matrix of the shafting; the stiffness matrix of the shafting includes the axial stiffness matrix, the torsional stiffness matrix and the plane bending and swing stiffness matrix. The axial stiffness matrix and the torsional stiffness matrix are both in the form of tridiagonal matrices, and the plane bending and swing stiffness matrix is established according to the Timoshenko beam principle; the mass matrix of the shafting includes the axial mass matrix, the torsional mass matrix and the plane bending and swing mass matrix. The axial mass matrix and the torsional mass matrix are both diagonal matrices, and the plane bending and swing mass matrix is established according to the Timoshenko beam principle; S12. Establish the coupled additional stiffness matrix of the gear pair and the additional stiffness matrix of the bearing, integrate the coupled additional stiffness matrix of the gear pair and the additional stiffness matrix of the bearing into the stiffness matrix of the shafting to form the overall stiffness matrix of the gear transmission system; The relative squeezing deformation of the gear pair along the meshing line direction during meshing vibration is: ， Wherein: and respectively represent the displacements of the driving wheel A and the driven wheel B in the x direction; and respectively represent the displacements of the driving wheel A and the driven wheel B in the y direction; and respectively represent the displacements of the driving wheel A and the driven wheel B in the z direction; and respectively represent the angles turned by the driving wheel A and the driven wheel B; and are respectively the base circle radii of the driving wheel A and the driven wheel B; is the normal pressure angle of the gear; is the transverse pressure angle of the gear; is the helix angle; The normal meshing force between the driving gear A and the driven gear B is: ， In the formula: represents the normal meshing stiffness of the gear; By analyzing the forces on the driving gear A and the driven gear B, we get: ， In the formula: , , are the components of the meshing force of the driving wheel A in the x, y, and z directions respectively, , are the torque components of the meshing force of the driving wheel A about the x and y axes respectively, is the torque component of the meshing force of the driving wheel A about the z axis, is the pitch circle radius of the driving wheel; , , are the components of the meshing force of the driven wheel B in the x, y, and z directions respectively, , are the torque components of the meshing force of the driven wheel B about the x and y axes respectively, is the torque component of the meshing force of the driven wheel B about the z axis, is the pitch circle radius of the driven wheel; Based on the above calculation results, the coupled additional stiffness matrix of the gear pair is established as: ， In the formula, is the force position matrix, which is obtained by analyzing and calculating the forces on the driving wheel and the driven wheel; is the meshing stiffness matrix, which is obtained by calculating the normal meshing stiffness of the gear pair; is the vibration displacement matrix, which is obtained by calculating the relative extrusion deformation of the gear pair along the meshing line direction during the meshing vibration; Bearing additional stiffness matrix The expression is as follows: ， In the formula, , , are the components of the bearing force in the x, y, and z directions respectively, and are the components of the bearing moment about the x-axis and y-axis respectively, , , are the relative deformations of the bearing inner ring and outer ring in the three directions of the coordinate system respectively, and are the angles of rotation of the bearing about the x-axis and y-axis respectively; During the actual operation of the bearing, assuming there are a total of n rolling elements, the position angle of the th rolling element is : ， The bearing force balance equation can be obtained as: ， In the formula, and respectively represent the diameter of the rolling element in the bearing and the radius of the circumference where the rolling element is located; is the th angle between the line connecting the center of the rolling element and the origin of the coordinate system and the positive direction of the x-axis; is the radius of the circumference of the curvature center of the inner ring of the bearing; and are the curvature radii of the inner and outer ring raceways respectively; and are the contact angles before and after the rolling element is loaded, is the effective contact stiffness; The additional stiffness matrix of the bearing can be solved from the calculated bearing force balance equation; Attach the coupled additional stiffness matrix of the gear pair to the overall stiffness matrix of the gear transmission system according to the corresponding nodes on the gear transmission system, and attach the calculated additional stiffness matrix of the bearing to the overall stiffness matrix of the gear transmission system according to the corresponding nodes on the gear transmission system to obtain the overall stiffness matrix of the gear transmission system; S13: Based on the overall stiffness matrix and mass matrix of the gear transmission system, determine the damping matrix of the gear transmission system by specifying the system damping coefficient, finally establish the dynamic equation of the gear transmission system, decouple the dynamic equation of the gear transmission system by means of the principal coordinate transformation, and solve for the dynamic flexibility matrix of the gear transmission system; Calculate the modal damping of each order by specifying the damping coefficients of each order. The damping coefficients of each order are taken as 0.01 - 0.

05. The damping matrix of the gear transmission system is obtained from the modal damping of each order. The calculation expression of the modal damping of each order of the gear transmission system is: ， Where: is the -th order modal damping matrix, is the -th order modal damping, is the -th order critical damping, is the -th order mass, is the -th order modal frequency; The dynamic equation of the gear transmission system is: ， In the formula: is the mass matrix of the gear transmission system, is the damping matrix of the gear transmission system, is the stiffness matrix of the gear transmission system, is the dynamic excitation matrix, , , respectively represent the vibration response results of the displacement, velocity and acceleration of the measuring point; Using the method of principal coordinate transformation, we get: ， In the formula, represents the natural frequency matrix of the system, z represents the physical coordinates after transformation, is the th modal mass of the system, is the th modal damping of the system, is the th modal stiffness of the system; The dynamic flexibility matrix of the gear transmission system is: ， In the formula: is the th natural frequency of the system, is the th 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 equation of the gear transmission system.

3. A calculation method for the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 2, characterized in that The specific steps of S2 are as follows: S21. Calculation of gear meshing transmission error: First, it is necessary to determine the macroscopic parameters of the gear pair, the design load, and the loaded conditions. The macroscopic parameters include the number of teeth, module, pressure angle, and helix angle of the gears. The loaded conditions include the input speed and torque of the gear pair. Build a slicing algorithm model and adjust the deformation amount of each slice in real time according to the relationship between the load on each slice and the design load. , the gear meshing transmission error is the cumulative deformation of each slice. The calculation expression of the gear meshing transmission error is as follows: ， Wherein: is the deformation amount on each slice, is the gear meshing transmission error, is the number of slices; S22. Calculation of the dynamic meshing stiffness of the gear pair: The dynamic meshing stiffness of the gear pair represents the change and fluctuation of the stiffness during the gear meshing process, and is calculated from the dynamic flexibility of the driving gear and the driven gear at the tooth surface meshing; The calculation expression of the dynamic meshing stiffness of the gear pair is: ， In the formula, is the dynamic flexibility matrix of the gear transmission system, , are the force components at the meshing nodes of the driving and driven wheels under the action of the unit normal meshing force, respectively; S23. Calculation of the dynamic meshing force of the gear pair: Based on the dynamic meshing stiffness of the gear pair and the gear meshing transmission error, calculate the dynamic meshing force of the gear pair during the gear meshing process. The calculation expression of the dynamic meshing force of the gear pair is: ， Wherein: is the dynamic meshing force of the gear pair, is the dynamic meshing stiffness of the gear pair, is the transmission error of gear meshing.

4. A calculation method for the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 3, characterized in that The specific steps of S3 are as follows: S31. Calculation of the 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. Calculate the air-gap magnetic permeability, and expand the radial electromagnetic force of the motor to obtain the radial electromagnetic force components under no-load condition; When the motor runs without load, the magnetic field provided by the permanent magnet enters the stator part of the motor through the air gap and then enters the rotor of the motor through the air gap to form a closed loop, and the air gap magnetic density of the motor is obtained It is: ， wherein, is the magnetomotive force distribution function, is the air-gap magnetic permeability; is the mechanical angle of the rotor; The air-gap magnetic potential of the motor under no-load condition is generated by the permanent magnet, and the expression of the magnetic potential distribution function of the permanent magnet is obtained as: ， In the formula, is the harmonic order, is the harmonic amplitude, is the harmonic angular velocity; Considering the influence of stator slotting, the expression of the air-gap magnetic permeability is: ， In the formula, is the amplitude of the average air-gap permeability, is the amplitude of the th air-gap permeability caused by stator slotting, is the number of stator slots, is the mechanical angle of the rotor; Substitute into the formula to calculate the air-gap magnetic density of the motor under no-load conditions The expression is as follows: ， Obtain the radial electromagnetic force density of the motor stator core The expression is as follows: ， In the formula, is the vacuum permeability, is the angular frequency of the current, is the number of rotor pole pairs; S32. Calculation of the radial electromagnetic force of the motor under load condition: Under the load condition of the motor, the permanent magnet and the armature winding act together to generate the air-gap magnetic field, and calculate the radial electromagnetic force density of the motor under load condition; Under the motor load condition, the permanent magnet and the armature winding act together to generate an air-gap magnetic field. When current passes through the winding, the air-gap magnetic density distribution generated by the armature winding is as follows: ， Where: is the angle between the winding and the magnetic field axis of the permanent magnet, is the harmonic order of the winding magnetic field, is the average 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. A calculation method for the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 4, characterized in that The specific steps of S4 are as follows: Apply the dynamic meshing force of the gear pair as the system mechanical excitation to the meshing node of the gear transmission system, and apply the radial electromagnetic force of the motor as the electromagnetic excitation to the surface of the motor electronic iron core. Decompose the obtained mechanical excitation and electromagnetic excitation into forces and torques in six degrees of freedom. The expression is: ， Write the converted exciting force array in the form of complex exponential, and combine it with the dynamic flexibility matrix of the gear transmission system , and the vibration displacement response, velocity response, and acceleration response at each node of the system are calculated as follows: ， In the formula, is the vibration displacement response of the system node, is the vibration velocity response of the system node, 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 Including: A dynamic model construction module for calculating the dynamic equation and dynamic flexibility matrix of the gear transmission system. That is, first establish a full-degree-of-freedom vibration analysis model of the shafting, extract and analyze to obtain the stiffness matrix and mass matrix of the shafting; then perform force analysis on the gear pair and bearings in the gear transmission system respectively to obtain the coupled additional stiffness matrix of the gear pair and the bearing additional stiffness matrix in the gear transmission system, and combine the stiffness matrix of the shafting 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 system dynamic model based on the finite element model of the assembly housing and the dynamic equation of the gear transmission system; A mechanical excitation calculation module for calculating the dynamic meshing force of the gear. That is, construct a slicing algorithm model of the gear 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 pitch cumulative deviation and the torsional deformation amount factor; perform force analysis on the meshing node of the gear pair, and calculate the dynamic meshing stiffness of the gear pair in combination with the gear dynamic flexibility; calculate the gear dynamic meshing force from the gear meshing transmission error and the dynamic meshing stiffness of the gear pair as the mechanical excitation of the system; An electromagnetic excitation calculation module for calculating the radial electromagnetic force of the permanent magnet synchronous motor under no-load and load conditions. That is, calculate the air-gap magnetic 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; A response calculation module for applying the mechanical excitation to the meshing node of the gear transmission system and applying the electromagnetic excitation to the surface of the motor electronic iron core; decomposing the mechanical excitation and electromagnetic excitation into forces and torques in six degrees of freedom, and combining 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.

7. A calculation system for the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 6, characterized in that In the kinetic model construction module, the lumped parameter method is first used to establish a full-degree-of-freedom vibration analysis model of the shafting. In the full-degree-of-freedom vibration analysis model, bending, torsion, axial, and wobbling vibration modes are considered, and the full-degree-of-freedom vibration analysis model of the shafting is extracted and analyzed to obtain the stiffness matrix and mass matrix of the shafting. The stiffness matrix of the shafting includes an axial stiffness matrix, a torsional stiffness matrix, and a planar bending and wobbling stiffness matrix. The axial stiffness matrix and the torsional stiffness matrix are both in the form of a tridiagonal matrix, and the planar bending and wobbling stiffness matrix is established according to the Timoshenko beam principle. The mass matrix of the shafting includes an axial mass matrix, a torsional mass matrix, and a planar bending and wobbling mass matrix. The axial mass matrix and the torsional mass matrix are both diagonal matrices, and the planar bending and wobbling mass matrix is established according to the Timoshenko beam principle. The coupled additional stiffness matrix of the gear pair and the bearing additional stiffness matrix are established, and the coupled additional stiffness matrix of the gear pair and the bearing additional stiffness matrix are integrated into the stiffness matrix of the shafting to form the overall stiffness matrix of the gear transmission system. The relative extrusion deformation of the gear pair along the meshing line direction during meshing vibration is: , where: and respectively represent the displacements of the driving wheel A and the driven wheel B in the x direction; and respectively represent the displacements of the driving wheel A and the driven wheel B in the y direction; and respectively represent the displacements of the driving wheel A and the driven wheel B in the z direction; and respectively represent the angles of rotation of the driving wheel A and the driven wheel B; and are respectively the base circle radii of the driving wheel A and the driven wheel B; is the normal pressure angle of the gear; is the transverse pressure angle of the gear; is the helix angle; The normal meshing force between the driving gear A and the driven gear B is: ， In the formula: represents the normal meshing stiffness of the gear; By analyzing the forces on the driving gear A and the driven gear B, it is obtained that: ， Where: , , are the components of the meshing force of the driving wheel A in the x, y, and z directions respectively, , are the torque components of the meshing force of the driving wheel A about the x and y axes respectively, is the torque component of the meshing force of the driving wheel A about the z axis, is the pitch circle radius of the driving wheel; , , are the components of the meshing force of the driven wheel B in the x, y, and z directions respectively, , are the torque components of the meshing force of the driven wheel B about the x and y axes respectively, is the torque component of the meshing force of the driven wheel B about the z axis, is the pitch circle radius of the driven wheel; Based on the above calculation results, the coupled additional stiffness matrix of the gear pair is established as: ， In the formula, is the force position matrix, which is obtained by analyzing and calculating the forces on the driving wheel and the driven wheel; is the meshing stiffness matrix, which is obtained by calculating the normal meshing stiffness of the gear pair; is the vibration displacement matrix, which is obtained by calculating the relative extrusion deformation of the gear pair along the meshing line direction during the meshing vibration; Bearing additional stiffness matrix The expression is as follows: ， In the formula, , , are the components of the bearing force in the x, y, and z directions respectively, and are the components of the bearing moment about the x-axis and the y-axis respectively, , , are the relative deformations of the inner and outer rings of the bearing in the three directions of the coordinate system respectively, and are the angles of rotation of the bearing about the x-axis and the y-axis respectively; During the actual operation of the bearing, assuming there are a total of n rolling elements, the position angle of the th rolling element is : ， The bearing force balance equation can be obtained as: ， Wherein, and respectively represent the diameter of the rolling element and the radius of the circumference where the rolling element is located in the bearing; is the th angle between the line connecting the center of the th rolling element and the origin of the coordinate system and the positive direction of the x-axis; is the radius of the circumference of the curvature center of the inner ring of the bearing; and are the curvature radii of the inner and outer ring raceways respectively; and are the contact angles before and after the rolling element is loaded, is the effective contact stiffness; The bearing additional stiffness matrix can be solved from the calculated bearing force balance equation. The coupled additional stiffness matrix of the gear pair is attached to the overall stiffness matrix of the gear transmission system according to the corresponding nodes on the gear transmission system, and the calculated bearing additional stiffness matrix is attached to the overall stiffness matrix of the gear transmission system according to the corresponding nodes on the gear transmission system to obtain the overall stiffness matrix of the gear transmission system. 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 specifying the system damping coefficient. Finally, the dynamic equation of the gear transmission system is established, and the dynamic equation of the gear transmission system is decoupled by means of the principal coordinate transformation, and the dynamic flexibility matrix of the gear transmission system is solved. By specifying the damping coefficients of each order, the modal damping of each order is calculated. The damping coefficients of each order are taken as 0.01 - 0.

05. The damping matrix of the gear transmission system is obtained from the modal damping of each order. The calculation expression of the modal damping of each order of the gear transmission system is: ， In the formula: is the -th order modal damping matrix, is the -th order modal damping, is the -th order critical damping, is the -th order mass, is the -th order modal frequency; The dynamic equation of the gear transmission system is: ， In the formula: is the mass matrix of the gear transmission system, is the damping matrix of the gear transmission system, is the stiffness matrix of the gear transmission system, is the dynamic excitation matrix, , , respectively represent the vibration response results of the displacement, velocity, and acceleration of the measurement point; Using the method of principal coordinate transformation, it is obtained that: ， In the formula, represents the natural frequency matrix of the system, z represents the physical coordinates after transformation, is the th-order modal mass of the system, is the th-order modal damping of the system, is the th-order modal stiffness of the system; The dynamic flexibility matrix of the gear transmission system is: ， In the formula: is the th natural frequency of the system, is the th 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 equation of the gear transmission system.

8. A 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, it is first necessary to determine the macroscopic parameters of the gear pair, the design load, and the loaded conditions. The macroscopic parameters include the number of teeth, module, pressure angle, and helix angle of the gear, and the loaded conditions include the input speed and torque of the gear pair. A slicing algorithm model is constructed, and the deformation amount of each slice is adjusted in real time according to the relationship between the load and the design load on each slice. , the gear meshing transmission error is the accumulation of the deformations of each slice. The calculation expression of the gear meshing transmission error is as follows: ， In the formula: is the deformation amount on each slice, is the gear meshing transmission error, is the number of slices; The dynamic meshing stiffness of the gear pair represents the change and fluctuation of the stiffness during the gear meshing process, and is calculated from the dynamic flexibility of the driving gear and the driven gear at the tooth surface meshing. The calculation expression of the dynamic meshing stiffness of the gear pair is: ， In the formula, is the dynamic flexibility matrix of the gear transmission system, , are the force components at the meshing nodes of the driving gear and the driven gear respectively under the action of the unit normal meshing force; S23. Calculation of the dynamic meshing force of the gear pair: Based on the dynamic meshing stiffness of the gear pair and the gear meshing transmission error, the dynamic meshing force of the gear pair during the gear meshing process is calculated. The calculation expression of the dynamic meshing force of the gear pair is: ， In the formula: is the dynamic meshing force of the gear pair, is the dynamic meshing stiffness of the gear pair, is the transmission error of gear meshing.

9. The calculation system for the dynamic response of a deceleration drive assembly under multi-source excitation according to claim 8, wherein 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 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 without load, the magnetic field provided by the permanent magnet enters the stator part of the motor through the air gap and then enters the rotor of the motor through the air gap to form a closed loop, and the air-gap magnetic density of the motor is obtained. It is: ， In the formula, is the magnetic potential distribution function, is the air-gap magnetic permeability; Under no-load conditions, the air-gap magnetic potential of the motor is generated by the permanent magnet, and the expression of the magnetic potential distribution function of the permanent magnet is obtained as: ， In the formula, is the harmonic order,[ is the harmonic amplitude,[ is the angular velocity of the harmonic; Considering the influence of stator slotting, the expression of the air-gap permeability is: ， In the formula, is the amplitude of the average air-gap permeability, is the amplitude of the th air-gap permeability caused by stator slotting, is the number of stator slots, is the mechanical angle of the rotor; Substitute into the formula to calculate the air-gap magnetic density of the motor under no-load conditions The expression is as follows: ， Obtain the radial electromagnetic force density of the motor stator core The expression is as follows: ， In the formula, is the vacuum permeability, is the current angular frequency, is the number of rotor pole pairs; Under the load conditions of the motor, the permanent magnet and the armature winding act together to generate the air-gap magnetic field, and the radial electromagnetic force density under the load conditions of the motor is calculated; Under the load conditions of the motor, the permanent magnet and the armature winding act together to generate the air-gap magnetic field. When current passes through the winding, the air-gap magnetic density distribution generated by the armature winding is: ， Wherein: is the angle between the winding and the magnetic field axis of the permanent magnet, is the harmonic order of the winding magnetic field, is the average air-gap magnetic flux density at each harmonic order; The radial electromagnetic force per unit area under the load conditions of the motor is calculated as: 。 10. A 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 applied as the system mechanical excitation to the meshing node of the gear transmission system, and the radial electromagnetic force of the motor is applied as the electromagnetic excitation to the surface of the motor iron core. The mechanical excitation and electromagnetic excitation obtained by solving are decomposed into forces and torques in six degrees of freedom, and the expression is: ， Write the converted exciting force array in the form of complex exponential, and combine it with the dynamic flexibility matrix of the gear transmission system , and the vibration displacement response, velocity response and acceleration response at each node of the system are calculated as follows: ， In the formula, is the vibration displacement response of the system node, is the vibration velocity response of the system node, is the vibration acceleration response of the system node.

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