A method for modeling coupled dynamics of an electric vehicle transmission system in a vehicle environment

Abstract

This invention discloses a method for modeling the coupled dynamics of an electric vehicle transmission system in a vehicle environment. The specific steps are as follows: 1) Establishing a dynamic model of the transmission system; 2) Establishing a dynamic model of the vehicle's vertical system; 3) Establishing a road excitation model of the coupled system; 4) Establishing a coupled dynamic model of the vehicle transmission system; 5) Calculating the coupled dynamics of the transmission system. The beneficial effect is that this method considers the influence of low-frequency vehicle vibrations caused by road excitation on the vibration of the transmission system. Simultaneously, the high-frequency vibrations of the gears caused by transmission system excitation will also act on the vehicle, thereby analyzing the dynamic characteristics of the gear transmission system in a vehicle environment. This improves the accuracy of the coupled dynamics analysis of the electric vehicle transmission system and the vehicle's vertical system, providing technical support for the study of coupled dynamics of the electric vehicle transmission system and the vehicle's vertical system, and ultimately improving vehicle performance.

Description

Technical Field

[0001] This invention relates to the field of electric vehicle drive system dynamics, and in particular to a method for modeling coupled dynamics of electric vehicle drive systems in an on-board environment. Background Technology

[0002] my country's new energy vehicle industry is currently experiencing rapid development. Electric vehicles, as a core carrier for carbon emission reduction in the transportation sector, have their transmission system dynamics directly impacting overall vehicle NVH, comfort, component fatigue life, and system reliability. In actual vehicle operation, the electric vehicle transmission system not only withstands high-frequency dynamic torque fluctuations from the motor output but also experiences multiple excitations from various sources, including road surface unevenness, suspension coupling vibration, and time-varying stiffness of gear meshing, resulting in complex electromechanical-structural-road coupled dynamic behavior. A strong nonlinear coupling effect exists between the transmission system and the vehicle system dynamics, causing the vibration of the transmission gears to exhibit significant coupling characteristics, severely affecting transmission system vibration and noise, as well as overall vehicle comfort. Therefore, establishing an accurate and reliable coupled dynamic model of the electric vehicle transmission system under on-board conditions and conducting coupling mechanism analysis is of significant engineering importance for improving the overall performance of electric vehicles.

[0003] However, existing dynamic analysis methods for electric vehicle transmission systems typically simplify the transmission system into an independent torsional vibration model, neglecting the coupling influence of suspension motion and road excitation on the dynamic behavior of the transmission system in the vehicle environment. They also lack a detailed characterization of boundary condition changes, making it difficult for the established dynamic model to truly reflect the vibration characteristics of the transmission system driven by multi-source excitation coupling in the vehicle environment. This results in inaccurate and unreliable nonlinear coupled dynamic analysis results of the transmission system. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a coupled dynamics modeling method for electric vehicle transmission systems in an on-board environment. This method constructs a dynamic model of the electric vehicle gear transmission system, a dynamic model of the vehicle's vertical system, and an external excitation model of the coupled system, and couples these three models to characterize the nonlinear coupling relationship between the transmission system and the vertical motion of the entire vehicle.

[0005] The technical solution adopted by this invention to solve its technical problem is as follows:

[0006] A method for modeling the coupled dynamics of an electric vehicle transmission system in a vehicle environment, characterized by the following steps:

[0007] Step (1): Establishing the dynamic model of the transmission system;

[0008] The dynamic model of the transmission system is as follows:

[0009] ;

[0010] In the formula, m m With J mz These are the mass and moment of inertia of the motor rotor, respectively; m p1 With J p1z These are the mass and moment of inertia of the pinion P1, respectively; m g1 With J g1z These are the mass and moment of inertia of the large gear G1, respectively; m p2 With J p2z These are the mass and moment of inertia of the pinion P2, respectively; m g2 With J g2z The mass and moment of inertia of the large gear G2 are respectively; x m y m z rm These represent the motor rotor's translational vibration along the x-axis, translational vibration along the y-axis, and torsional vibration about the z-axis, respectively; x p1 y p1 z rp1 These represent the translational vibrations of pinion P1 along the x-axis, the translational vibrations along the y-axis, and the torsional vibrations about the z-axis, respectively; x g1 y g1 z rg1 These represent the translational vibrations of the large gear G1 along the x-axis, the translational vibrations along the y-axis, and the torsional vibrations about the z-axis, respectively; x p2 y p2 z rp2 These represent the translational vibrations of pinion P2 along the x-axis, the translational vibrations along the y-axis, and the torsional vibrations about the z-axis, respectively; x g2 y g2 z rg2 These represent the translational vibrations of the large gear G2 along the x-axis, the translational vibrations along the y-axis, and the torsional vibrations about the z-axis, respectively; r This represents the vertical vibration of the unsprung mass at the rear suspension; no dot above the symbol indicates vibration displacement; one dot above the symbol indicates vibration velocity; two dots above the symbol indicate vibration acceleration; k a1x k a1y k a1rz These represent the bending stiffness in the x-direction, bending stiffness in the y-direction, and torsional stiffness about the z-axis of the shaft segment between the motor rotor and pinion P1, respectively; k a2x k a2y k a2rz These represent the bending stiffness in the x-direction, bending stiffness in the y-direction, and torsional stiffness about the z-axis of the shaft segment between the large gear G1 and the small gear P2, respectively; k b1x With k b1y These represent the x-axis and y-axis support stiffness of the left-side bearing of the motor rotor, respectively; k b2x With k b2y These represent the x-axis and y-axis support stiffness of the right-side bearing of the motor rotor, respectively; k b3x With k b3yThese represent the x- and y-direction support stiffness of the left bearing of the large gear G1, respectively; k b4x With k b4y These represent the x- and y-direction support stiffness of the bearing on the right side of pinion P2, respectively; k b5x With k b5y These represent the x- and y-direction support stiffness of the left bearing of the large gear G2, respectively; k b6x With k b6y These represent the x- and y-direction support stiffness of the right-side bearing of the large gear G2, respectively; k m1 With k m2 These are the meshing stiffnesses of the first and second stage gear pairs, respectively; c a1x c a1y c a1rz These are the bending damping in the x-direction, bending damping in the y-direction, and torsional damping about the z-axis of the shaft segment between the motor rotor and pinion P1, respectively; c a2x c a2y c a2rz These are the bending damping in the x-direction, bending damping in the y-direction, and torsional damping about the z-axis of the shaft segment between the large gear G1 and the small gear P2, respectively; c b1x With c b1y These represent the x-axis and y-axis support damping of the left-side bearing of the motor rotor, respectively; c b2x With c b2y These represent the x-axis and y-axis support damping of the right-side bearing of the motor rotor, respectively; c b3x With c b3y These represent the x- and y-direction support damping of the left bearing of the large gear G1; c b4x With c b4y These represent the x-axis and y-axis support damping of the bearing on the right side of pinion P2, respectively; c b5x With c b5y These represent the x- and y-direction support damping of the left bearing of the large gear G2; c b6x With c b6y These represent the x- and y-direction support damping of the right-side bearing of the large gear G2; c m1 With c m2 α1 and β1 are the meshing damping of the first and second stage gear pairs, respectively; α2 and β2 are the pressure angle and helix angle of the first stage helical gear, respectively; F is the pressure angle and helix angle of the second stage helical gear, respectively. rx With F ry These are the components of the radial electromagnetic force of the drive motor in the x and y directions, respectively; T in T is the input torque for driving the motor. load For load torque; ΔT load For load torque fluctuation; δ1 and δ2 are the relative displacements of the first and second stage gear pairs, respectively; r bp1 r bg1 r bp2 r bg2These are the base circle radii of pinion P1, gear G1, pinion P2, and gear G2, respectively.

[0011] Load torque T load for:

[0012] ;

[0013] In the formula, z p1 z g1 z p2 z g2 These are the number of teeth of pinion P1, gear G1, pinion P2, and gear G2, respectively.

[0014] Step (2): Establishment of the vehicle vertical system dynamics model;

[0015] To construct the coupled dynamics of the drivetrain system of a bridge-drive electric vehicle in an on-board environment, the vertical vibration y of the unsprung masses of the left and right front suspensions of the vehicle is considered. fl With y fr Vertical vibration of unsprung mass y r Lateral vibration θ rx Vertical vibration of the spring-loaded mass y r Pitch vibration θ cz and tilting vibration θ cx ;

[0016] The vehicle vertical system dynamics model can be expressed as:

[0017] ;

[0018] In the formula, m c J c with I c These are the vehicle's sprung mass, pitch moment of inertia, and roll moment of inertia, respectively; m fl With m fr These are the unsprung masses of the left and right front suspensions, respectively; m r with I r The unsprung mass (excluding the drivetrain) and roll inertia of the rear suspension; k s1 k s2 k s3 k s4 These refer to the suspension stiffness of the vehicle's left front, right front, left rear, and right rear, respectively; c s1 c s2 c s3 c s4 These are the front left, front right, rear left, and rear right suspension dampings of the vehicle; k w1 k w2 k w3 k w4These refer to the stiffness of the front left, front right, rear left, and rear right wheels of the vehicle; c w1 c w2 c w3 c w4 q1, q2, q3, and q4 represent the damping of the vehicle's left front, right front, left rear, and right rear wheels, respectively; q4 represents the road displacement excitation experienced by the vehicle's left front, right front, left rear, and right rear wheels, respectively; l f With l r These are the distances between the sprung center of gravity and the front and rear overhangs of the vehicle, respectively; c It is half the track width of the left and right wheels; F by The force exerted on the unsprung mass of the rear suspension by the gear transmission system through the bearings can be expressed as:

[0019] ;

[0020] Step (3): Establishment of the road surface excitation model for the coupled system;

[0021] The vertical excitation of the road surface is:

[0022] ;

[0023] In the formula, t represents time; q(t) and Let u be the road surface excitation displacement and velocity, respectively. Integrating the excitation velocity yields the excitation displacement; u is the forward vehicle speed; n q =0.01m -1 , where n is the spatial cutoff frequency; n0 = 0.1m -1 , is the space reference frequency; G q (n0) is the road surface roughness coefficient; ω(t) is white noise with a power intensity of 0.5;

[0024] The road load torque fluctuation excitation is:

[0025] ;

[0026] In the formula, F z R is the normal force at the contact point between the tire and the road surface. e s is the tire radius; s is the distance traveled. The slope represents the road surface excitation.

[0027] Step (4): Establishment of the coupled dynamics model of the vehicle transmission system;

[0028] By coupling the dynamic model of the transmission system with the dynamic model of the vehicle's vertical system, a coupled dynamic model of the on-board transmission system can be established.

[0029] ;

[0030] In the formula, M1 and M2 are the mass matrices of the vehicle's vertical system and transmission system, respectively; 0 7×15 With 0 15×7 These are zero matrices with rows of 7x15 and 15x7 respectively; X1 and X2 are the displacement vectors of the vehicle's vertical system and transmission system, respectively; K 11 With K 22 These are the stiffness matrices for the vehicle's vertical system and transmission system, respectively; K 12 With K 21 C represents the interaction stiffness matrix between the vehicle's vertical system and transmission system. 11 With C 22 These are the damping matrices for the vehicle's vertical system and transmission system, respectively; C 12 With C 21 F1 represents the interaction damping matrix between the vehicle's vertical system and transmission system; F2 and F1 represent the load vectors of the vehicle's vertical system and transmission system, respectively; matrices K and C have the same structural form; detailed expressions of each symbol are as follows:

[0031] ;

[0032] In the formula, the superscript T indicates transpose;

[0033] K 11 Given a 7x7 matrix, the expression k(i, j) in the i-th row and j-th column is shown below, with all other values ​​being 0:

[0034] ;

[0035] K 12 Given a 7x15 matrix, the expression k(i, j) in the i-th row and j-th column is shown below, with all other values ​​being 0:

[0036] ;

[0037] K 21 For K 12 transpose;

[0038] K 22 Given a 15x15 matrix, the expression k(i, j) in the i-th row and j-th column is shown below, with all other values ​​being 0:

[0039] ;

[0040] Step (5): Calculation of coupling dynamics of electric vehicle transmission system in vehicle environment;

[0041] The dynamic model of the vehicle transmission system described in step (4) is programmed and solved using numerical calculation methods. Taking the translational vibration of the transmission system gears as the analysis object, the vibration acceleration under different driving speeds, gear pair meshing stiffness and damping parameters, bearing support stiffness and damping parameters is calculated to analyze the coupled dynamic characteristics of the electric vehicle transmission system in the vehicle environment.

[0042] Compared with existing technologies, this invention can promote the development of coupled dynamics modeling methods for electric vehicle transmission systems, improve the accuracy and reliability of dynamic analysis in complex on-board environments, provide theoretical support for vibration reduction, noise reduction and durability optimization design of electric vehicle transmission systems, overcome the shortcomings of existing technologies, and has significant social and economic benefits. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating the implementation of a coupled dynamics modeling method for an electric vehicle drive system in an on-board environment.

[0044] Figure 2 It is a dynamic model of the transmission system;

[0045] Figure 3 It is a dynamic model of the vehicle's vertical system;

[0046] Figure 4 This is a diagram showing the translational vibration acceleration of the large gear G1 in the electric vehicle transmission system along the y-axis under different vehicle speeds in an on-board environment.

[0047] Figure 5 The diagram shows the translational vibration acceleration response of pinion P1 along the y-direction under different meshing stiffness and damping.

[0048] Figure 6 The graph shows the acceleration response of the pinion P1 along the y-direction during translational vibration under different support stiffness and damping. Detailed Implementation

[0049] Embodiments of the present invention will be described with reference to the accompanying drawings, which will be further described below. Figure 1 — Figure 6 The specific embodiments of the present invention will be described in detail below.

[0050] Reference Figure 1 A method for modeling the coupled dynamics of an electric vehicle transmission system in an on-board environment includes the following steps:

[0051] Step (1): Establishing the dynamic model of the transmission system;

[0052] Reference Figure 2 The dynamic model of the transmission system is as follows:

[0053] ;

[0054] In the formula, m m With J mz These are the mass and moment of inertia of the motor rotor, respectively; m p1 With J p1z These are the mass and moment of inertia of the pinion P1, respectively; m g1 With J g1z These are the mass and moment of inertia of the large gear G1, respectively; m p2 With J p2z These are the mass and moment of inertia of the pinion P2, respectively; m g2 With J g2z The mass and moment of inertia of the large gear G2 are respectively; x m y m z rm These represent the motor rotor's translational vibration along the x-axis, translational vibration along the y-axis, and torsional vibration about the z-axis, respectively; x p1 y p1 z rp1 These represent the translational vibrations of pinion P1 along the x-axis, the translational vibrations along the y-axis, and the torsional vibrations about the z-axis, respectively; x g1 y g1 z rg1 These represent the translational vibrations of the large gear G1 along the x-axis, the translational vibrations along the y-axis, and the torsional vibrations about the z-axis, respectively; x p2 y p2 z rp2 These represent the translational vibrations of pinion P2 along the x-axis, the translational vibrations along the y-axis, and the torsional vibrations about the z-axis, respectively; x g2 y g2 z rg2 These represent the translational vibrations of the large gear G2 along the x-axis, the translational vibrations along the y-axis, and the torsional vibrations about the z-axis, respectively; r This represents the vertical vibration of the unsprung mass at the rear suspension; no dot above the symbol indicates vibration displacement; one dot above the symbol indicates vibration velocity; two dots above the symbol indicate vibration acceleration; k a1x k a1y k a1rz These represent the bending stiffness in the x-direction, bending stiffness in the y-direction, and torsional stiffness about the z-axis of the shaft segment between the motor rotor and pinion P1, respectively; k a2x k a2y k a2rz These represent the bending stiffness in the x-direction, bending stiffness in the y-direction, and torsional stiffness about the z-axis of the shaft segment between the large gear G1 and the small gear P2, respectively; k b1x With k b1y These represent the x-axis and y-axis support stiffness of the left-side bearing of the motor rotor, respectively; k b2x With k b2y These represent the x-axis and y-axis support stiffness of the right-side bearing of the motor rotor, respectively; k b3x With k b3yThese represent the x- and y-direction support stiffness of the left bearing of the large gear G1, respectively; k b4x With k b4y These represent the x- and y-direction support stiffness of the bearing on the right side of pinion P2, respectively; k b5x With k b5y These represent the x- and y-direction support stiffness of the left bearing of the large gear G2, respectively; k b6x With k b6y These represent the x- and y-direction support stiffness of the right-side bearing of the large gear G2, respectively; k m1 With k m2 These are the meshing stiffnesses of the first and second stage gear pairs, respectively; c a1x c a1y c a1rz These are the bending damping in the x-direction, bending damping in the y-direction, and torsional damping about the z-axis of the shaft segment between the motor rotor and pinion P1, respectively; c a2x c a2y c a2rz These are the bending damping in the x-direction, bending damping in the y-direction, and torsional damping about the z-axis of the shaft segment between the large gear G1 and the small gear P2, respectively; c b1x With c b1y These represent the x-axis and y-axis support damping of the left-side bearing of the motor rotor, respectively; c b2x With c b2y These represent the x-axis and y-axis support damping of the right-side bearing of the motor rotor, respectively; c b3x With c b3y These represent the x- and y-direction support damping of the left bearing of the large gear G1; c b4x With c b4y These represent the x-axis and y-axis support damping of the bearing on the right side of pinion P2, respectively; c b5x With c b5y These represent the x- and y-direction support damping of the left bearing of the large gear G2; c b6x With c b6y These represent the x- and y-direction support damping of the right-side bearing of the large gear G2; c m1 With c m2 α1 and β1 are the meshing damping of the first and second stage gear pairs, respectively; α2 and β2 are the pressure angle and helix angle of the first stage helical gear, respectively; F is the pressure angle and helix angle of the second stage helical gear, respectively. rx With F ry These are the components of the radial electromagnetic force of the drive motor in the x and y directions, respectively; T in T is the input torque for driving the motor. load For load torque; ΔT load For load torque fluctuation; δ1 and δ2 are the relative displacements of the first and second stage gear pairs, respectively; r bp1 r bg1 r bp2 r bg2These are the base circle radii of pinion P1, gear G1, pinion P2, and gear G2, respectively.

[0055] Load torque T load for:

[0056] ;

[0057] In the formula, z p1 z g1 z p2 z g2 These are the number of teeth of pinion P1, gear G1, pinion P2, and gear G2, respectively.

[0058] Step (2): Establishment of the vehicle vertical system dynamics model;

[0059] Reference Figure 3 To construct the coupled dynamic relationship of the drivetrain system of a bridge-drive electric vehicle in an on-board environment, the vertical vibration y of the unsprung masses of the left and right front suspensions of the vehicle is considered. fl With y fr Vertical vibration of unsprung mass y r Lateral vibration θ rx Vertical vibration of the spring-loaded mass y r Pitch vibration θ cz and tilting vibration θ cx ;

[0060] The vehicle vertical system dynamics model can be expressed as:

[0061] ;

[0062] In the formula, m c J c with I c These are the vehicle's sprung mass, pitch moment of inertia, and roll moment of inertia, respectively; m fl With m fr These are the unsprung masses of the left and right front suspensions, respectively; m r with I r The unsprung mass (excluding the drivetrain) and roll inertia of the rear suspension; k s1 k s2 k s3 k s4 These refer to the suspension stiffness of the vehicle's left front, right front, left rear, and right rear, respectively; c s1 c s2 c s3 c s4 These are the front left, front right, rear left, and rear right suspension dampings of the vehicle; k w1 k w2 k w3 k w4These refer to the stiffness of the front left, front right, rear left, and rear right wheels of the vehicle; c w1 c w2 c w3 c w4 q1, q2, q3, and q4 represent the damping of the vehicle's left front, right front, left rear, and right rear wheels, respectively; q4 represents the road displacement excitation experienced by the vehicle's left front, right front, left rear, and right rear wheels, respectively; l f With l r These are the distances between the sprung center of gravity and the front and rear overhangs of the vehicle, respectively; c It is half the track width of the left and right wheels; F by The force exerted on the unsprung mass of the rear suspension by the gear transmission system through the bearings can be expressed as:

[0063] ;

[0064] Step (3): Establishment of the road surface excitation model for the coupled system;

[0065] The vertical excitation of the road surface is:

[0066] ;

[0067] In the formula, t represents time; q(t) and These represent the road surface excitation displacement and velocity, respectively; u is the forward vehicle speed; n q =0.01m -1 , where n is the spatial cutoff frequency; n0 = 0.1m -1 , is the space reference frequency; G q (n0) is the road surface roughness coefficient; ω(t) is white noise with a power intensity of 0.5;

[0068] The road load torque fluctuation excitation is:

[0069] ;

[0070] In the formula, F z R is the normal force at the contact point between the tire and the road surface. e s is the tire radius; s is the distance traveled. The slope represents the road surface excitation.

[0071] Step (4): Establishment of the coupled dynamics model of the vehicle transmission system;

[0072] By coupling the dynamic model of the transmission system with the dynamic model of the vehicle's vertical system, a coupled dynamic model of the on-board transmission system can be established.

[0073] ;

[0074] In the formula, M1 and M2 are the mass matrices of the vehicle's vertical system and transmission system, respectively; 0 7×15 With 0 15×7 These are zero matrices with rows of 7x15 and 15x7 respectively; X1 and X2 are the displacement vectors of the vehicle's vertical system and transmission system, respectively; K 11 With K 22 These are the stiffness matrices for the vehicle's vertical system and transmission system, respectively; K 12 With K 21 C represents the interaction stiffness matrix between the vehicle's vertical system and transmission system. 11 With C 22 These are the damping matrices for the vehicle's vertical system and transmission system, respectively; C 12 With C 21 F1 represents the interaction damping matrix between the vehicle's vertical system and transmission system; F2 and F1 represent the load vectors of the vehicle's vertical system and transmission system, respectively; matrices K and C have the same structural form; detailed expressions of each symbol are as follows:

[0075] ;

[0076] In the formula, the superscript T indicates transpose;

[0077] K 11 Given a 7x7 matrix, the expression k(i, j) in the i-th row and j-th column is shown below, with all other values ​​being 0:

[0078] ;

[0079] K 12 Given a 7x15 matrix, the expression k(i, j) in the i-th row and j-th column is shown below, with all other values ​​being 0:

[0080] ;

[0081] K 21 For K 12 transpose;

[0082] K 22 Given a 15x15 matrix, the expression k(i, j) in the i-th row and j-th column is shown below, with all other values ​​being 0:

[0083] ;

[0084] Step (5): Calculation of coupling dynamics of electric vehicle transmission system in vehicle environment;

[0085] The dynamic model of the vehicle transmission system described in step (4) is programmed and solved using numerical calculation methods. Taking the translational vibration of the transmission system gears as the analysis object, the vibration acceleration is calculated under different driving speeds, gear pair meshing stiffness and damping parameters, and bearing support stiffness and damping parameters, as shown below. Figure 4 , Figure 5 , Figure 6 As shown, the coupled dynamic characteristics of the electric vehicle transmission system in a vehicle environment can be analyzed.

[0086] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any modifications, alterations, and equivalent changes made to the above embodiments based on the essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for modeling the coupled dynamics of an electric vehicle transmission system in a vehicle-mounted environment, characterized in that... Includes the following steps: Step (1): Establishing the dynamic model of the transmission system; The dynamic model of the transmission system is as follows: ； In the formula, m m With J mz These are the mass and moment of inertia of the motor rotor, respectively; m p1 With J p1z These are the mass and moment of inertia of the pinion P1, respectively; m g1 With J g1z These are the mass and moment of inertia of the large gear G1, respectively; m p2 With J p2z These are the mass and moment of inertia of the pinion P2, respectively; m g2 With J g2z The mass and moment of inertia of the large gear G2 are respectively; x m y m z rm These represent the motor rotor's translational vibration along the x-axis, translational vibration along the y-axis, and torsional vibration about the z-axis, respectively; x p1 y p1 z rp1 These represent the translational vibrations of pinion P1 along the x-axis, the translational vibrations along the y-axis, and the torsional vibrations about the z-axis, respectively; x g1 y g1 z rg1 These represent the translational vibrations of the large gear G1 along the x-axis, the translational vibrations along the y-axis, and the torsional vibrations about the z-axis, respectively; x p2 y p2 z rp2 These represent the translational vibrations of pinion P2 along the x-axis, the translational vibrations along the y-axis, and the torsional vibrations about the z-axis, respectively; x g2 y g2 z rg2 These represent the translational vibrations of the large gear G2 along the x-axis, the translational vibrations along the y-axis, and the torsional vibrations about the z-axis, respectively; r This represents the vertical vibration of the unsprung mass in the rear suspension; no dot above the symbol indicates vibration displacement; one dot above the symbol indicates vibration velocity; two dots above the symbol indicate vibration acceleration; k a1x k a1y k a1rz These represent the bending stiffness in the x-direction, bending stiffness in the y-direction, and torsional stiffness about the z-axis of the shaft segment between the motor rotor and pinion P1, respectively; k a2x k a2y k a2rz These represent the bending stiffness in the x-direction, bending stiffness in the y-direction, and torsional stiffness about the z-axis of the shaft segment between the large gear G1 and the small gear P2, respectively; k b1x With k b1y These represent the x-axis and y-axis support stiffness of the left-side bearing of the motor rotor, respectively; k b2x With k b2y These represent the x-axis and y-axis support stiffness of the right-side bearing of the motor rotor, respectively; k b3x With k b3y These represent the x- and y-direction support stiffness of the left bearing of the large gear G1, respectively; k b4x With k b4y These represent the x- and y-direction support stiffness of the bearing on the right side of pinion P2, respectively; k b5x With k b5y These represent the x- and y-direction support stiffness of the left bearing of the large gear G2, respectively; k b6x With k b6y These represent the x- and y-direction support stiffness of the right-side bearing of the large gear G2, respectively; k m1 With k m2 These are the meshing stiffnesses of the first and second stage gear pairs, respectively; c a1x c a1y c a1rz These are the bending damping in the x-direction, bending damping in the y-direction, and torsional damping about the z-axis of the shaft segment between the motor rotor and pinion P1, respectively; c a2x c a2y c a2rz These are the bending damping in the x-direction, bending damping in the y-direction, and torsional damping about the z-axis of the shaft segment between the large gear G1 and the small gear P2, respectively; c b1x With c b1y These represent the x-axis and y-axis support damping of the left-side bearing of the motor rotor, respectively; c b2x With c b2y These represent the x-axis and y-axis support damping of the right-side bearing of the motor rotor, respectively; c b3x With c b3y These represent the x- and y-direction support damping of the left bearing of the large gear G1; c b4x With c b4y These represent the x-axis and y-axis support damping of the bearing on the right side of pinion P2, respectively; c b5x With c b5y These represent the x- and y-direction support damping of the left bearing of the large gear G2; c b6x With c b6y These represent the x- and y-direction support damping of the right-side bearing of the large gear G2; c m1 With c m2 α1 and β1 represent the meshing damping of the first and second stage gear pairs, respectively; α1 and β1 represent the pressure angle and helix angle of the first stage helical gear, respectively; α2 and β2 represent the pressure angle and helix angle of the second stage helical gear, respectively; F rx With F ry These are the components of the radial electromagnetic force of the drive motor in the x and y directions, respectively; T in T is the input torque for driving the motor. load For load torque; ΔT load For load torque fluctuation; δ1 and δ2 are the relative displacements of the first and second stage gear pairs, respectively; r bp1 r bg1 r bp2 r bg2 These are the base circle radii of pinion P1, gear G1, pinion P2, and gear G2, respectively. Load torque T load for: ； In the formula, z p1 z g1 z p2 z g2 These are the number of teeth of pinion P1, gear G1, pinion P2, and gear G2, respectively. Step (2): Establishment of the vehicle vertical system dynamics model; To construct the coupled dynamics of the drivetrain system of a bridge-drive electric vehicle in an on-board environment, the vertical vibration y of the unsprung masses of the left and right front suspensions of the vehicle is considered. fl With y fr Vertical vibration of unsprung mass y r Lateral vibration θ rx Vertical vibration of the spring-loaded mass y r Pitch vibration θ cz and tilting vibration θ cx ; The vehicle vertical system dynamics model can be expressed as: ； In the formula, m c J c with I c These are the vehicle's sprung mass, pitch moment of inertia, and roll moment of inertia, respectively; m fl With m fr These are the unsprung masses of the left and right front suspensions, respectively; m r with I r The unsprung mass (excluding the drivetrain) and roll inertia of the rear suspension; k s1 k s2 k s3 k s4 These refer to the suspension stiffness of the vehicle's left front, right front, left rear, and right rear, respectively; c s1 c s2 c s3 c s4 These are the front left, front right, rear left, and rear right suspension dampings of the vehicle; k w1 k w2 k w3 k w4 These refer to the stiffness of the front left, front right, rear left, and rear right wheels of the vehicle; c w1 c w2 c w3 c w4 q1, q2, q3, and q4 represent the damping of the vehicle's left front, right front, left rear, and right rear wheels, respectively; q4 represents the road displacement excitation experienced by the vehicle's left front, right front, left rear, and right rear wheels, respectively; l f With l r These are the distances between the sprung center of gravity and the front and rear overhangs of the vehicle, respectively; c It is half the track width of the left and right wheels; F by The force exerted on the unsprung mass of the rear suspension by the gear transmission system through the bearings can be expressed as: ； Step (3): Establishment of the road surface excitation model for the coupled system; The formula for calculating the vertical excitation of the road surface is: ； In the formula, t represents time; q(t) and These are the road surface excitation displacement and velocity, respectively; u represents the forward speed; n q =0.01m -1 , where n is the spatial cutoff frequency; n0 = 0.1m -1 , is the space reference frequency; G q (n0) is the road surface roughness coefficient; ω(t) is white noise with a power intensity of 0.5; The road load torque fluctuation excitation is: ； In the formula, F z R is the normal force at the contact point between the tire and the road surface. e s is the tire radius; s is the distance traveled. The slope represents the road surface excitation. Step (4): Establishment of the coupled dynamics model of the vehicle transmission system; By coupling the dynamic model of the transmission system with the dynamic model of the vehicle's vertical system, a coupled dynamic model of the on-board transmission system can be established. ； In the formula, M1 and M2 are the mass matrices of the vehicle's vertical system and transmission system, respectively; 0 7×15 With 0 15×7 These are zero matrices with rows of 7x15 and 15x7 respectively; X1 and X2 are the displacement vectors of the vehicle's vertical system and transmission system, respectively; K 11 With K 22 These are the stiffness matrices for the vehicle's vertical system and transmission system, respectively; K 12 With K 21 C represents the interaction stiffness matrix between the vehicle's vertical system and transmission system. 11 With C 22 These are the damping matrices for the vehicle's vertical system and transmission system, respectively; C 12 With C 21 F1 represents the interaction damping matrix between the vehicle's vertical system and transmission system; F2 and F1 represent the load vectors of the vehicle's vertical system and transmission system, respectively; matrices K and C have the same structural form; detailed expressions of each symbol are as follows: ； In the formula, the superscript T indicates transpose; K 11 Given a 7x7 matrix, the expression k(i, j) in the i-th row and j-th column is shown below, with all other values ​​being 0: ； K 12 Given a 7x15 matrix, the expression k(i, j) in the i-th row and j-th column is shown below, with all other values ​​being 0: ； K 21 For K 12 transpose; K 22 Given a 15x15 matrix, the expression k(i, j) in the i-th row and j-th column is shown below, with all other values ​​being 0: ； Step (5): Calculation of coupling dynamics of electric vehicle transmission system in vehicle environment; The dynamic model of the vehicle transmission system described in step (4) is programmed and solved using numerical calculation methods. Taking the translational vibration of the transmission system gears as the analysis object, the vibration acceleration under different driving speeds, gear pair meshing stiffness and damping parameters, bearing support stiffness and damping parameters is calculated to analyze the coupled dynamic characteristics of the electric vehicle transmission system in the vehicle environment.

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