Hybrid transmission gear transmission system nonlinear dynamics modeling method

Abstract

The invention discloses a nonlinear dynamic modeling method for a hybrid transmission gear transmission system, which comprises the following specific steps of: (1) establishing a bearing dynamic model, and calculating a bearing supporting force; (2) calculating the dynamic meshing force of the gear; (3) constructing a hybrid transmission gear transmission system kinetic model, and establishing a hybrid transmission gear transmission system kinetic equation; (4) solving the kinetic equation of the hybrid transmission gear transmission system, and obtaining the nonlinear dynamic response of the hybrid transmission gear transmission system; the method has the beneficial effects that the nonlinear dynamic response of the hybrid transmission gear transmission system can be solved, the influence mechanism of the excitation frequency on the equivalent vibration displacement of the hybrid transmission gear transmission system is disclosed, and theoretical support is provided for system parameter design of the hybrid transmission gear transmission system.

Description

Technical Field

[0001] The present invention relates to the technical field of gear dynamics, and in particular to a nonlinear dynamics modeling method for a hybrid transmission gear drive system. Background Art

[0002] Hybrid vehicles, as a means of transportation that combines the advantages of traditional fuel vehicles and electric vehicles, have demonstrated significant advantages in energy conservation, environmental protection, and economy. The hybrid transmission gear drive system exhibits complex operating conditions during operation. Affected by multiple factors such as internal dynamic excitation of the transmission system and external load excitation, the system will exhibit different nonlinear response characteristics, which have a profound impact on the service life and dynamic performance of the system. By deeply analyzing the nonlinear response characteristics of the system and revealing its response laws, it is possible to determine the stable range of the system under operating conditions, thereby providing solid theoretical support for improving system performance, reducing noise, and extending the service life of the structure. However, current research work is still insufficient in nonlinear dynamic modeling under the action of multiple factors, especially the lack of systematic research on hybrid transmission gear drive systems.

[0003] To address the above-mentioned issues, the present invention proposes a nonlinear dynamic modeling method for a hybrid transmission gear transmission system. This method analyzes the structure of the hybrid transmission gear transmission system, establishes a hybrid transmission gear transmission system model, determines the bearing force and the time-varying meshing force of the helical gear pair, constructs a dynamic model of the hybrid transmission gear transmission system, and establishes the dynamic equations of the hybrid transmission gear transmission system. This method can accurately and effectively study the nonlinear dynamic response of the hybrid transmission gear transmission system, fill the relevant technical gaps in the calculation of the nonlinear dynamic response of the hybrid transmission gear transmission system, promote the development of engineering technology, and generate significant social and economic benefits. Summary of the Invention

[0004] In order to overcome the shortcomings of the existing technology and fill the gaps in the relevant technology, the present invention provides a nonlinear dynamic modeling method for a hybrid transmission gear transmission system. The method takes into account multiple factors such as bearing support stiffness, gear time-varying meshing stiffness, tooth side clearance, transmission error, etc., constructs a hybrid transmission gear transmission system dynamic model, establishes the hybrid transmission gear transmission system dynamic equation, and then solves the dynamic equation to obtain the nonlinear dynamic response of the hybrid transmission gear transmission system.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows: a method for nonlinear dynamic modeling of a hybrid transmission gear transmission system, characterized by comprising the following steps:

[0006] Step (1): Construct a bearing dynamics model. The bearing force is the resultant contact force between the bearing rolling element and the inner and outer rings. Its component force F bux 、F buy , according to Hertz contact theory, it can be expressed as:

[0007]

[0008] Among them, F bux 、F buy (u=1,2,3...,12) is the support force of the bearing in the x and y directions, subscripts u=1 and u=2 are the engine input shaft bearings, subscripts u=3 and u=4 are the P1 motor shaft bearings, subscripts u=5 and u=6 are the clutch shaft bearings, subscripts u=7 and u=8 are the differential bearings, subscripts u=9 and u=10 are the motor shaft bearings, and subscripts u=11 and u=12 are the intermediate shaft bearings; γ q (q=1,2,3...,14) is the rolling body rotation angle, and the subscript q represents the number of rolling bodies; γ q (q=1,2,3...,12) is the rolling body angle, γ q (t)=2π(q-1) / N b +r0ωt / (r0+R I ), r0 is the radius of the bearing inner ring, R I is the radius of the bearing outer ring, ω is the angular velocity of the bearing inner ring, N b is the number of rolling elements, t is the bearing working time; q (q=1,2,3...,12) is the deformation of the rolling element and is χ q =(x I -x o )cosγ q +(y I -y o )sinγ q -c,x I is the deformation of the bearing outer ring in the x direction, x0 is the deformation of the bearing inner ring in the x direction, y I is the deformation of the bearing outer ring in the y direction, y0 is the deformation of the bearing inner ring in the y direction, and c is the bearing clearance; K bs is the bearing support stiffness; C bs The damping generated by the deformation of the bearing rolling element; H(χ q ) is the Heaviside function;

[0009] Step (2): Calculate the meshing force of the helical gear pair and the time-varying meshing stiffness of the gear pair, which can be expressed as:

[0010]

[0011] Among them, K mij(ij=12,13,45,67,85) is the time-varying meshing stiffness of the gear pair, subscript ij=12 is the engine gear and P1 motor shaft gear, subscript ij=13 is the engine gear and clutch gear, subscript ij=45 is the clutch gear and differential gear, subscript ij=67 is the P3 motor shaft gear and intermediate shaft gear, subscript ij=85 is the intermediate shaft gear and differential gear; K0 is the mean meshing stiffness; K b is the fluctuation part of meshing stiffness; K e is the meshing stiffness of a single gear tooth; ω m is the meshing frequency; is the initial phase angle; ε α is the contact ratio of the gear pair; t is the gear working time;

[0012] Equivalent meshing displacement S between the engine gear and the P motor shaft gear 12 for:

[0013] S 12 =(x1-x2)sinα n1 +(y1-y2+R1θ1-R2θ2)cosα n1 cosβ1+(z1-z2)cosα n1 sinβ1-e(t) 12 ;

[0014] Among them, x1, y1, z1 are the vibration displacements of the engine gear in the x, y, and z directions; x2, y2, z2 are the vibration displacements of the P1 motor shaft gear in the x, y, and z directions; θ1 is the vibration angular displacement of the engine gear; θ2 is the vibration angular displacement of the P1 motor shaft gear; R1 is the pitch circle radius of the engine gear; R2 is the pitch circle radius of the P1 motor shaft gear; e(t) 12 is the meshing transmission error between the engine gear and the P1 motor shaft gear; α n1 is the pressure angle of the engine gear; β1 is the helix angle of the engine gear;

[0015] Equivalent meshing displacement S of engine gear and clutch gear 13 for:

[0016] S 13 =(x1-x3)sinα n1 +(y1-y3+R1θ1-R3θ3)cosα n1 cosβ1+(z1-z3)cosα n1 sinβ1-e(t) 13 ;

[0017] Where x3, y3, and z3 are the vibration displacements of the clutch gear in the x, y, and z directions; θ3 is the vibration angular displacement of the clutch gear; R3 is the pitch circle radius of the clutch gear 3; and e(t) 13 is the meshing transmission error between the engine gear and the clutch gear;

[0018] Equivalent meshing displacement S of clutch gear and differential gear 45 for:

[0019] S 45 =(x4-x5)sinα n2 +(y4-y5+R4θ4-R5θ5)cosα n4 cosβ4+(z4-z5)cosα n4 sinβ4-e(t) 45 ;

[0020] Where x4, y4, z4 are the vibration displacements of the clutch pinion in the x, y, and z directions; x5, y5, z5 are the vibration displacements of the differential gear in the x, y, and z directions; θ4 is the vibration angular displacement of the clutch pinion; θ5 is the vibration angular displacement of the differential gear; R4 is the pitch circle radius of the clutch pinion; R5 is the pitch circle radius of the differential gear; e(t) 45 is the meshing transmission error between the clutch pinion and the differential gear; α n4 is the pressure angle of the clutch pinion; β4 is the helix angle of the clutch pinion;

[0021] P3 Equivalent meshing displacement S of motor shaft gear and intermediate shaft gear 67 for:

[0022] S 67 =(x6-x7)sinα n6 +(y6-y7+R6θ6-R7θ7)cosα n6 cosβ6+(z6-z7)cosα n6 sinβ6-e(t) 67 ;

[0023] Among them, x6, y6, z6 are the vibration displacements of the P3 motor shaft gear in the x, y, and z directions; x7, y7, z7 are the vibration displacements of the intermediate shaft gear in the x, y, and z directions; θ6 is the vibration angular displacement of the P3 motor shaft gear; θ7 is the vibration angular displacement of the intermediate shaft gear; R6 is the pitch circle radius of the P3 motor shaft gear; R7 is the pitch circle radius of the intermediate shaft gear; e(t) 67 is the meshing transmission error between the P3 motor shaft gear and the intermediate shaft large gear; α n6 is the pressure angle of the P3 motor shaft gear; β6 is the helix angle of the P3 motor shaft gear;

[0024] Equivalent meshing displacement S of the intermediate shaft gear and differential gear 85 for:

[0025] S 85 =(x8-x5)sinα n8 +(y8-y5+R8θ8-R5θ5)cosα n8 cosβ8+(z8-z5)cosα n8 sinβ8-e(t) 85 ;

[0026] Among them, x8, y8, z8 are the vibration displacements of the intermediate shaft pinion in the x, y, and z directions; θ8 is the vibration angular displacement of the intermediate shaft pinion; R8 is the pitch circle radius of the intermediate shaft pinion; e(t) 85 is the meshing transmission error between the intermediate shaft pinion and the differential gear; α n8 is the pressure angle of the intermediate shaft pinion; β8 is the helix angle of the intermediate shaft pinion;

[0027] Meshing force component F of helical gear pair xij 、F yij 、F zij The equivalent vibration displacement S on the meshing line can be ij The nonlinear function f(S ij )express:

[0028]

[0029] Among them, f(S ij )(ij=12,13,45,67,85) is the tooth side clearance function, C mij (ij=12,13,45,67,85) is the meshing damping of the gear pair, is the equivalent meshing speed of the gear pair, subscript ij=12 is the engine gear and P1 motor shaft gear, subscript ij=13 is the engine gear and clutch gear, subscript ij=45 is the clutch pinion and differential gear, subscript ij=67 is the P3 motor shaft gear and intermediate shaft gear, subscript ij=85 is the intermediate shaft pinion and differential gear; α ni (i=1,4,6,8) is the gear pressure angle, β i (i=1, 4, 6, 8) is the gear helix angle, subscript i=1 is the engine gear, i=4 is the clutch pinion, i=6 is the P3 motor shaft gear, and i=8 is the intermediate shaft pinion;

[0030] Step (3): Construct the dynamic model of the hybrid transmission gear drive system, considering the following degrees of freedom:

[0031]

[0032] Among them, x r 、y r 、z r (r=1,2,3...,8) is the vibration displacement of the gear in the x, y, and z directions, θ r (r=1,2,3...,8) is the vibration angular displacement of the gear, subscript r=1 is the engine gear, subscript r=2 is the P1 motor shaft gear, subscript r=3 is the clutch gear, subscript r=4 is the clutch gear, subscript r=5 is the differential gear, subscript r=6 is the P3 motor shaft gear, subscript r=7 is the intermediate shaft gear, and subscript r=8 is the intermediate shaft gear; x bu 、y bu (u=1,2,3...,12) is the vibration displacement of the bearing in the x and y directions, subscripts u=1 and u=2 are the engine input shaft bearings, subscripts u=3 and u=4 are the P1 motor shaft bearings, subscripts u=5 and u=6 are the clutch shaft bearings, subscripts u=7 and u=8 are the differential bearings, subscripts u=9 and u=10 are the motor shaft bearings, and subscripts u=11 and u=12 are the intermediate shaft bearings;

[0033] Taking into account factors such as time-varying meshing stiffness, time-varying support stiffness, static transmission error, tooth side clearance and bearing clearance, the dynamic equation of the hybrid transmission gear transmission system is established:

[0034] The dynamic equation of the engine gear:

[0035]

[0036] Where m1 is the mass of the engine gear; I1 is the moment of inertia of the engine gear; K m12 is the time-varying meshing stiffness of the engine gear and the P1 motor shaft gear; C m12 K is the meshing damping between the engine gear and the P1 motor shaft gear; m13 is the time-varying meshing stiffness of the engine gear and the clutch gear; C m13 is the meshing damping between the engine gear and the clutch gear; f(S 12 ) is the tooth side clearance function of the engine gear and the P1 motor shaft gear pair; f(S 13 ) is the tooth side clearance function of the engine gear and the clutch gear pair; C 1x 、C 1y 、C 1z K is the support damping of the engine gear shaft in the x, y, and z directions; 1x , K 1y , K 1z is the support stiffness of the engine gear shaft in the x, y, and z directions; α n1is the pressure angle of the engine gear; β1 is the helix angle of the engine gear; T1 is the torque of the engine gear;

[0037] Dynamic equations of bearing 1:

[0038]

[0039] Among them, m b1 is the mass of bearing 1; K b1 is the support stiffness of bearing 1; C b1 is the support damping of bearing 1; F b1x is the support force of bearing 1 in the x direction; F b1y is the support force of bearing 1 in the y direction; g is the acceleration due to gravity;

[0040] Dynamic equations of bearing 2:

[0041]

[0042] Among them, m b2 is the mass of bearing 2; K b2 is the support stiffness of bearing 2; C b2 is the support damping of bearing 2; F b2x is the support force of bearing 2 in the x direction; F b2y is the support force of bearing 2 in the y direction;

[0043] The dynamic equation of the P1 motor shaft gear is:

[0044]

[0045] Where m2 is the mass of the P1 motor shaft gear; I2 is the moment of inertia of the P1 motor shaft gear; K m12 is the time-varying meshing stiffness of the engine gear and the P1 motor shaft gear; C m12 is the meshing damping between the engine gear and the P1 motor shaft gear; f(S 12 ) is the tooth backlash function of the engine gear and the P1 motor shaft gear pair; C 2x 、C 2y 、C 2z K is the support damping of the P1 motor shaft in the x, y, and z directions; 2x , K 2y , K 2z is the support stiffness of the P1 motor shaft in the x, y, and z directions; is the pressure angle of the engine gear; β1 is the helix angle of the engine gear; T2 is the torque of the P1 motor shaft gear;

[0046] Bearing 3 dynamic equation:

[0047]

[0048] Among them, m b3 is the mass of bearing 3; K b3 is the support stiffness of bearing 3; C b3 is the support damping of bearing 3; F b3x is the support force of bearing 3 in the x direction; F b3y is the supporting force of bearing 3 in the y direction;

[0049] Bearing 4 dynamic equation:

[0050]

[0051] Among them, m b4 is the mass of bearing 4; K b4 is the support stiffness of bearing 4; C b4 is the support damping of bearing 4; F b4x F is the support force of bearing 4 in the x direction; b4y is the supporting force of bearing 4 in the y direction;

[0052] The dynamic equation of the clutch gear:

[0053]

[0054] Where m3 is the mass of the clutch gear; I3 is the moment of inertia of the clutch gear; K m13 is the time-varying meshing stiffness between the engine gear and the clutch gear; C m13 is the meshing damping between the engine gear and the clutch gear; f(S 13 ) is the tooth side clearance function between the engine gear and the clutch gear; C 3x 、C 3y 、C 3z K is the support damping of the clutch gear shaft in the x, y, and z directions; 3x , K 3y , K 3z C is the support stiffness of the clutch gear shaft in the x, y, and z directions; 34x 、C 34y 、C 34z K is the damping of the connecting shaft between the clutch gear and the clutch pinion; 34x , K 34y , K 34z is the stiffness of the connecting shaft between the clutch gear and the clutch pinion; α n1 is the pressure angle of the engine gear; β1 is the helix angle of the engine gear; T3 is the torque of the clutch gear;

[0055] Dynamic equations of bearing 5:

[0056]

[0057] Among them, m b5 is the mass of bearing 5; K b5 is the support stiffness of bearing 5; C b5 is the support damping of bearing 5; F b5x is the support force of bearing 5 in the x direction; F b5y is the supporting force of bearing 5 in the y direction;

[0058] The dynamic equation of the clutch gear:

[0059]

[0060] Where m4 is the mass of the clutch pinion; I4 is the moment of inertia of the clutch pinion; K m45 is the time-varying meshing stiffness between the clutch pinion and the differential gear; C m45 is the meshing damping between the clutch pinion and the differential gear; f(S 45 ) is the tooth backlash function between the clutch pinion and the differential gear; α n4 is the pressure angle of the clutch pinion; β4 is the helix angle of the clutch pinion; T4 is the torque of the clutch pinion;

[0061] Dynamic equations of bearing 6:

[0062]

[0063] Among them, m b6 is the mass of bearing 6; K b6 is the support stiffness of bearing 6; C b6 is the support damping of bearing 6; F b6x F is the support force of bearing 6 in the x direction; b6y is the supporting force of bearing 6 in the y direction;

[0064] The dynamic equation of the differential gear:

[0065]

[0066] Where m5 is the mass of the differential gear; I5 is the moment of inertia of the differential gear; K m45 is the time-varying meshing stiffness between the clutch pinion and the differential gear; C m45 is the meshing damping between the clutch pinion and the differential gear; f(S 45 ) is the tooth side clearance function between the clutch pinion and the differential gear pair; K m85 is the time-varying meshing stiffness between the intermediate shaft pinion and the differential gear; C m85 is the meshing damping between the intermediate shaft pinion and the differential gear; f(S85 ) is the tooth side clearance function between the intermediate shaft pinion and the differential gear pair; C 5x 、C 5y 、C 5z K is the support damping of the differential gear shaft in the x, y, and z directions; 5x , K 5y , K 5z is the support stiffness of the differential gear shaft in the x, y, and z directions; α n8 is the pressure angle of the intermediate shaft pinion; β8 is the helix angle of the intermediate shaft pinion; T5 is the torque of the differential gear;

[0067] Dynamic equations of bearing 7:

[0068]

[0069] Among them, m b7 is the mass of bearing 7; K b7 is the support stiffness of bearing 7; C b7 is the support damping of bearing 7; F b7x F is the support force of bearing 7 in the x direction; b7y is the supporting force of bearing 7 in the y direction;

[0070] Dynamic equations of bearing 8:

[0071]

[0072] Among them, m b8 is the mass of the bearing 8; K b8 is the support stiffness of bearing 8; C b8 is the support damping of bearing 8; F b8x F is the support force of bearing 8 in the x direction; b8y is the supporting force of the bearing 8 in the y direction;

[0073] The dynamic equation of the P3 motor shaft gear is:

[0074]

[0075] Where m6 is the mass of the P3 motor shaft gear; I6 is the moment of inertia of the P3 motor shaft gear; K m67 is the time-varying meshing stiffness between the P3 motor shaft gear and the intermediate shaft gear; C m67 is the meshing damping between the P3 motor shaft gear and the intermediate shaft gear; f(S 67 ) is the tooth side clearance function between the P3 motor shaft gear and the intermediate shaft large gear pair; C 6x 、C 6y 、C 6z K is the support damping of the P3 motor shaft in the x, y, and z directions;6x , K 6y , K 6z is the support stiffness of the P3 motor shaft in the x, y, and z directions; α n3 is the pressure angle of the P3 motor shaft gear; β3 is the helix angle of the P3 motor shaft gear; T6 is the torque of the P3 motor shaft gear;

[0076] Dynamic equations of bearing 9:

[0077]

[0078] Among them, m b9 is the mass of bearing 9; K b9 is the support stiffness of bearing 9; C b9 is the support damping of bearing 9; F b9x F is the supporting force of bearing 9 in the y direction; b9y is the supporting force of bearing 9 in the y direction;

[0079] Dynamic equation of bearing 10:

[0080]

[0081] Among them, m b10 is the mass of the bearing 10; K b10 is the support stiffness of the bearing 10; C b10 is the support damping of the bearing 10; F bx10 F is the support force of the bearing 10 in the x direction; by10 is the supporting force of the bearing 10 in the y direction;

[0082] Dynamic equation of the intermediate shaft gear:

[0083]

[0084] Where m7 is the mass of the intermediate shaft gear; I7 is the moment of inertia of the intermediate shaft gear; K m67 is the time-varying meshing stiffness between the P3 motor shaft gear and the intermediate shaft gear; C m67 is the meshing damping between the P3 motor shaft gear and the intermediate shaft gear; f(S 67 ) is the tooth side clearance function between the P3 motor shaft gear and the intermediate shaft large gear pair; C 78x 、C 78y 、C 78z K is the damping of the connecting shaft between the intermediate shaft pinion and the intermediate shaft gear; 78x , K 78y , K 78z C is the stiffness of the connecting shaft between the intermediate shaft pinion and the intermediate shaft gear; 7x 、C 7y 、C 7zK is the support damping of the intermediate shaft in the x, y, and z directions; 7x , K 7y , K 7z is the support stiffness of the intermediate shaft in the x, y, and z directions; T7 is the torque of the intermediate shaft gear;

[0085] Dynamic equation of bearing 11:

[0086]

[0087] Among them, m b11 is the mass of the bearing 11; K b11 is the support stiffness of bearing 11; C b11 is the support damping of bearing 11; F bx11 F is the support force of bearing 11 in the x direction; by11 is the supporting force of the bearing 11 in the y direction;

[0088] Dynamic equation of bearing 12:

[0089]

[0090] Among them, m b12 is the mass of the bearing 12; K b12 is the support stiffness of the bearing 12; C b12 is the support damping of bearing 12; F b12x F is the support force of the bearing 12 in the x direction; b12y is the supporting force of the bearing 12 in the y direction;

[0091] Dynamic equation of the intermediate shaft pinion:

[0092]

[0093] Where m8 is the mass of the intermediate shaft pinion; I8 is the moment of inertia of the intermediate shaft pinion; T8 is the torque of the intermediate shaft pinion;

[0094] Step (4): Solve the dynamic equations of the hybrid transmission gear transmission system to obtain the nonlinear dynamic response of the hybrid transmission gear transmission system.

[0095] Compared with the existing technology, the beneficial effect of the present invention is: the beneficial effect is that this method can solve the nonlinear dynamic response of the hybrid transmission gear transmission system, providing strong support for the optimization design of the hybrid transmission gear transmission system, filling the relevant technical gap in the field of nonlinear dynamics of the hybrid transmission gear transmission system, promoting the development of engineering technology, and generating greater social and economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1It is a flow chart of the nonlinear dynamic modeling method of the hybrid transmission gear drive system;

[0097] Figure 2 is the bearing dynamics model;

[0098] Figure 3 It is the dynamic model of the hybrid transmission gear drive system;

[0099] Figure 4 It is the equivalent vibration displacement bifurcation diagram of the engine and P1 motor shaft gear pair;

[0100] Figure 5 This is the time domain diagram of the equivalent vibration displacement of the engine and P1 motor shaft gear pair;

[0101] Figure 6 It is the equivalent vibration displacement phase diagram of the engine and P1 motor shaft gear pair. DETAILED DESCRIPTION

[0102] The embodiments of the present invention are described below with reference to the accompanying drawings. Figure 1 — Figure 6 The specific embodiments of the present invention are described in detail.

[0103] like Figure 1 The figure shows a flow chart of a nonlinear dynamic modeling method for a hybrid transmission gear drive system, which is characterized by comprising the following steps:

[0104] Step (1): Construct the bearing dynamics model as Figure 2 As shown, the bearing force is the resultant force of the contact force between the bearing rolling elements and the inner and outer rings, and its component force F bux 、F buy , according to Hertz contact theory, it can be expressed as:

[0105]

[0106] Among them, F bux 、F buy (u=1,2,3...,12) is the support force of the bearing in the x and y directions, subscripts u=1 and u=2 are the engine input shaft bearings, subscripts u=3 and u=4 are the P1 motor shaft bearings, subscripts u=5 and u=6 are the clutch shaft bearings, subscripts u=7 and u=8 are the differential bearings, subscripts u=9 and u=10 are the motor shaft bearings, and subscripts u=11 and u=12 are the intermediate shaft bearings; γ q (q=1,2,3...,12) is the rolling body angle, γ q (t)=2π(q-1) / N b +r0ωt / (r0+R I ), r0 is the radius of the bearing inner ring, R Iis the radius of the bearing outer ring, ω is the angular velocity of the bearing inner ring, N b is the number of rolling elements, t is the bearing working time; q (q=1,2,3...,12) is the deformation of the rolling element and is χ q =(x I -x o )cosγ q +(y I -y o )sinγ q -c,x I is the deformation of the bearing outer ring in the x direction, x0 is the deformation of the bearing inner ring in the x direction, y I is the deformation of the bearing outer ring in the y direction, y0 is the deformation of the bearing inner ring in the y direction, and c is the bearing clearance; K bs is the bearing support stiffness; C bs The damping generated by the deformation of the bearing rolling element; H(χ q ) is the Heaviside function;

[0107] Step (2): Calculate the meshing force of the helical gear pair and the time-varying meshing stiffness K of the gear pair mij , which can be expressed as:

[0108]

[0109] Among them, K mij (ij=12,13,45,67,85) is the time-varying meshing stiffness of the gear pair, subscript ij=12 is the engine gear and P1 motor shaft gear, subscript ij=13 is the engine gear and clutch gear, subscript ij=45 is the clutch gear and differential gear, subscript ij=67 is the P3 motor shaft gear and intermediate shaft gear, subscript ij=85 is the intermediate shaft gear and differential gear; K0 is the mean meshing stiffness; K b is the fluctuation part of meshing stiffness; K e is the meshing stiffness of a single gear tooth; ω m is the meshing frequency; is the initial phase angle; ε α is the contact ratio of the gear pair; t is the gear working time;

[0110] Equivalent meshing displacement S between the engine gear and the P1 motor shaft gear 12 for:

[0111] S 12 =(x1-x2)sinα n1 +(y1-y2+R1θ1-R2θ2)cosα n1 cosβ1+(z1-z2)cosα n1 sinβ1-e(t)12 ;

[0112] Among them, x1, y1, z1 are the vibration displacements of the engine gear in the x, y, and z directions; x2, y2, z2 are the vibration displacements of the P1 motor shaft gear in the x, y, and z directions; θ1 is the vibration angular displacement of the engine gear; θ2 is the vibration angular displacement of the P1 motor shaft gear; R1 is the pitch circle radius of the engine gear; R2 is the pitch circle radius of the P1 motor shaft gear; e(t) 12 is the meshing transmission error between the engine gear and the P1 motor shaft gear; α n1 is the pressure angle of the engine gear; β1 is the helix angle of the engine gear;

[0113] Equivalent meshing displacement S of engine gear and clutch gear 13 for:

[0114] S 13 =(x1-x3)sinα n1 +(y1-y3+R1θ1-R3θ3)cosα n1 cosβ1+(z1-z3)cosα n1 sinβ1-e(t) 13 ;

[0115] Where x3, y3, and z3 are the vibration displacements of the clutch gear in the x, y, and z directions; θ3 is the vibration angular displacement of the clutch gear; R3 is the pitch circle radius of the clutch gear; and e(t) 13 is the transmission error between the engine gear and the clutch gear;

[0116] Equivalent meshing displacement S of clutch gear and differential gear 45 for:

[0117] S 45 =(x4-x5)sinα n2 +(y4-y5+R4θ4-R5θ5)cosα n4 cosβ4+(z4-z5)cosα n4 sinβ4-e(t) 45 ;

[0118] Where x4, y4, z4 are the vibration displacements of the clutch pinion in the x, y, and z directions; x5, y5, z5 are the vibration displacements of the differential gear in the x, y, and z directions; θ4 is the vibration angular displacement of the clutch pinion; θ5 is the vibration angular displacement of the differential gear; R4 is the pitch circle radius of the clutch pinion; R5 is the pitch circle radius of the differential gear; e(t) 45 is the meshing transmission error between the clutch pinion and the differential gear; α n4is the pressure angle of the clutch pinion; β4 is the helix angle of the clutch pinion;

[0119] P3 Equivalent meshing displacement S of motor shaft gear and intermediate shaft gear 67 for:

[0120] S 67 =(x6-x7)sinα n6 +(y6-y7+R6θ6-R7θ7)cosα n6 cosβ6+(z6-z7)cosα n6 sinβ6-e(t) 67 ;

[0121] Among them, x6, y6, z6 are the vibration displacements of the P3 motor shaft gear in the x, y, and z directions; x7, y7, z7 are the vibration displacements of the intermediate shaft gear in the x, y, and z directions; θ6 is the vibration angular displacement of the P3 motor shaft gear; θ7 is the vibration angular displacement of the intermediate shaft gear; R6 is the pitch circle radius of the P3 motor shaft gear; R7 is the pitch circle radius of the intermediate shaft gear; e(t) 67 is the meshing transmission error between the P3 motor shaft gear and the intermediate shaft large gear; α n6 is the pressure angle of the P3 motor shaft gear; β6 is the helix angle of the P3 motor shaft gear;

[0122] Equivalent meshing displacement S of the intermediate shaft gear and differential gear 85 for:

[0123] S 85 =(x8-x5)sinα n8 +(y8-y5+R8θ8-R5θ5)cosα n8 cosβ8+(z8-z5)cosα n8 sinβ8-e(t) 85 ;

[0124] Among them, x8, y8, z8 are the vibration displacements of the intermediate shaft pinion in the x, y, and z directions; θ8 is the vibration angular displacement of the intermediate shaft pinion; R8 is the pitch circle radius of the intermediate shaft pinion; e(t) 85 is the meshing transmission error between the intermediate shaft pinion and the differential gear; α n8 is the pressure angle of the intermediate shaft pinion; β8 is the helix angle of the intermediate shaft pinion;

[0125] Meshing force component F of helical gear pair xij 、F yij 、F zij The equivalent meshing displacement S on the meshing line can be ij and tooth side clearance function f(S ij )express:

[0126]

[0127] Among them, f(S ij )(ij=12,13,45,67,85) is the tooth side clearance function, C mij (ij=12,13,45,67,85) is the meshing damping of the gear pair, is the equivalent meshing speed of the gear pair, subscript ij=12 is the engine gear and P1 motor shaft gear, subscript ij=13 is the engine gear and clutch gear, subscript ij=45 is the clutch pinion and differential gear, subscript ij=67 is the P3 motor shaft gear and intermediate shaft gear, subscript ij=85 is the intermediate shaft pinion and differential gear; α ni (i=1,4,6,8) is the gear pressure angle, β i (i=1, 4, 6, 8) is the gear helix angle, subscript i=1 is the engine gear, i=4 is the clutch pinion, i=6 is the P3 motor shaft gear, and i=8 is the intermediate shaft pinion;

[0128] Step (3): Construct the dynamic model of the hybrid transmission gear drive system as follows Figure 3 As shown, consider the following degrees of freedom:

[0129]

[0130] Among them, x r 、y r 、z r (r=1,2,3...,8) is the vibration displacement of the gear in the x, y, and z directions, θ r (r=1,2,3...,8) is the vibration angular displacement of the gear, subscript r=1 is the engine gear, subscript r=2 is the P1 motor shaft gear, subscript r=3 is the clutch gear, subscript r=4 is the clutch gear, subscript r=5 is the differential gear, subscript r=6 is the P3 motor shaft gear, subscript r=7 is the intermediate shaft gear, and subscript r=8 is the intermediate shaft gear; x bu 、y bu (u=1,2,3...,12) is the vibration displacement of the bearing in the x and y directions, subscripts u=1 and u=2 are the engine input shaft bearings, subscripts u=3 and u=4 are the P1 motor shaft bearings, subscripts u=5 and u=6 are the clutch shaft bearings, subscripts u=7 and u=8 are the differential bearings, subscripts u=9 and u=10 are the motor shaft bearings, and subscripts u=11 and u=12 are the intermediate shaft bearings;

[0131] Taking into account factors such as time-varying meshing stiffness, time-varying support stiffness, transmission error, tooth side clearance and bearing clearance, the dynamic equation of the hybrid transmission gear transmission system is established:

[0132] The dynamic equation of engine gear 1:

[0133]

[0134] Where m1 is the mass of the engine gear; I1 is the moment of inertia of the engine gear; K m12 is the time-varying meshing stiffness of the engine gear and the P1 motor shaft gear; C m12 K is the meshing damping between the engine gear and the P1 motor shaft gear; m13 is the time-varying meshing stiffness of the engine gear and the clutch gear; C m13 is the meshing damping between the engine gear and the clutch gear; f(S 12 ) is the tooth side clearance function of the engine gear and the P1 motor shaft gear pair; f(S 13 ) is the tooth side clearance function of the engine gear and the clutch gear pair; C 1x 、C 1y 、C 1z K is the support damping of the engine gear shaft in the x, y, and z directions; 1x , K 1y , K 1z is the support stiffness of the engine gear shaft in the x, y, and z directions; α n1 is the pressure angle of engine gear 1; β1 is the helix angle of the engine gear; T1 is the torque of the engine gear;

[0135] Dynamic equations of bearing 1:

[0136]

[0137] Among them, m b1 is the mass of bearing 1; K b1 is the support stiffness of bearing 1; C b1 is the support damping of bearing 1; F b1x is the support force of bearing 1 in the x direction; F b1y is the support force of bearing 1 in the y direction; g is the acceleration due to gravity;

[0138] Dynamic equations of bearing 2:

[0139]

[0140] Among them, m b2 is the mass of bearing 2; K b2 is the support stiffness of bearing 2; C b2 is the support damping of bearing 2; F b2x is the support force of bearing 2 in the x direction; F b2y is the support force of bearing 2 in the y direction;

[0141] The dynamic equation of P1 motor shaft gear 2:

[0142]

[0143] Where m2 is the mass of the P1 motor shaft gear; I2 is the moment of inertia of the P1 motor shaft gear; K m12 is the time-varying meshing stiffness of the engine gear and the P1 motor shaft gear; C m12 is the meshing damping between the engine gear and the P1 motor shaft gear; f(S 12 ) is the tooth backlash function of the engine gear and the P1 motor shaft gear pair; C 2x 、C 2y 、C 2z K is the support damping of the P1 motor shaft in the x, y, and z directions; 2x , K 2y , K 2z is the support stiffness of the P1 motor shaft in the x, y, and z directions; is the pressure angle of the engine gear; β1 is the helix angle of the engine gear; T2 is the torque of the P1 motor shaft gear;

[0144] Bearing 3 dynamic equation:

[0145]

[0146] Among them, m b3 is the mass of bearing 3; K b3 is the support stiffness of bearing 3; C b3 is the support damping of bearing 3; F b3x is the support force of bearing 3 in the x direction; F b3y is the supporting force of bearing 3 in the y direction;

[0147] Bearing 4 dynamic equation:

[0148]

[0149] Among them, m b4 is the mass of bearing 4; K b4 is the support stiffness of bearing 4; C b4 is the support damping of bearing 4; F b4x F is the support force of bearing 4 in the x direction; b4y is the supporting force of bearing 4 in the y direction;

[0150] The dynamic equation of the clutch gear:

[0151]

[0152] Where m3 is the mass of the clutch gear; I3 is the moment of inertia of the clutch gear; K m13 is the time-varying meshing stiffness between the engine gear and the clutch gear; C m13 is the meshing damping between the engine gear and the clutch gear; f(S 13 ) is the tooth side clearance function between the engine gear and the clutch gear pair; C 3x 、C 3y 、C 3z K is the support damping of the clutch gear shaft in the x, y, and z directions; 3x , K 3y , K 3z C is the support stiffness of the clutch gear shaft in the x, y, and z directions; 34x 、C 34y 、C 34z K is the damping of the connecting shaft between the clutch gear and the clutch pinion; 34x , K 34y , K 34z is the stiffness of the connecting shaft between the clutch gear and the clutch pinion; α n1 is the pressure angle of the engine gear; β1 is the helix angle of the engine gear; T3 is the torque of the clutch gear;

[0153] Dynamic equations of bearing 5:

[0154]

[0155] Among them, m b5 is the mass of bearing 5; K b5 is the support stiffness of bearing 5; C b5 is the support damping of bearing 5; F b5x is the support force of bearing 5 in the x direction; F b5y is the supporting force of bearing 5 in the y direction;

[0156] The dynamic equation of the clutch gear 4:

[0157]

[0158] Where m4 is the mass of the clutch gear; I4 is the moment of inertia of the clutch gear; K m45 is the time-varying meshing stiffness between the clutch pinion and the differential gear; C m45 is the meshing damping between the clutch pinion and the differential gear; f(S 45 ) is the tooth backlash function between the clutch pinion and the differential gear; α n4 is the pressure angle of the clutch pinion; β4 is the helix angle of the clutch pinion; T4 is the torque of the clutch pinion;

[0159] Dynamic equations of bearing 6:

[0160]

[0161] Among them, m b6 is the mass of bearing 6; K b6 is the support stiffness of bearing 6; C b6 is the support damping of bearing 6; F b6x F is the support force of bearing 6 in the x direction; b6y is the supporting force of bearing 6 in the y direction;

[0162] Dynamic equation of differential gear 5:

[0163]

[0164] Where m5 is the mass of the differential gear; I5 is the moment of inertia of the differential gear; K m45 is the time-varying meshing stiffness between the clutch pinion and the differential gear; C m45 is the meshing damping between the clutch pinion and the differential gear; f(S 45 ) is the tooth backlash function between the clutch pinion and the differential gear; K m85 is the time-varying meshing stiffness between the intermediate shaft pinion and the differential gear; C m85 is the meshing damping between the intermediate shaft pinion and the differential gear; f(S 85 ) is the tooth side clearance function between the intermediate shaft pinion and the differential gear pair; C 5x 、C 5y 、C 5z K is the support damping of the differential gear shaft in the x, y, and z directions; 5x , K 5y , K 5z is the support stiffness of the differential gear shaft in the x, y, and z directions; α n8 is the pressure angle of the intermediate shaft pinion; β8 is the helix angle of the intermediate shaft pinion; T5 is the torque of the differential gear;

[0165] Dynamic equations of bearing 7:

[0166]

[0167] Among them, m b7 is the mass of bearing 7; K b7 is the support stiffness of bearing 7; C b7 is the support damping of bearing 7; F b7x F is the support force of bearing 7 in the x direction; b7y is the supporting force of bearing 7 in the y direction;

[0168] Dynamic equations of bearing 8:

[0169]

[0170] Among them, m b8 is the mass of the bearing 8; K b8 is the support stiffness of bearing 8; C b8 is the support damping of bearing 8; F b8x F is the support force of bearing 8 in the x direction; b8y is the supporting force of the bearing 8 in the y direction;

[0171] The dynamic equation of P3 motor shaft gear 6:

[0172]

[0173] Where m6 is the mass of the P3 motor shaft gear; I6 is the moment of inertia of the P3 motor shaft gear; K m67 is the time-varying meshing stiffness between the P3 motor shaft gear and the intermediate shaft gear; C m67 is the meshing damping between the P3 motor shaft gear and the intermediate shaft gear; f(S 67 ) is the tooth side clearance function between the P3 motor shaft gear and the intermediate shaft large gear pair; C 6x 、C 6y 、C 6z K is the support damping of the P3 motor shaft in the x, y, and z directions; 6x , K 6y , K 6z is the support stiffness of the P3 motor shaft in the x, y, and z directions; α n3 is the pressure angle of the P3 motor shaft gear; β3 is the helix angle of the P3 motor shaft gear; T6 is the torque of the P3 motor shaft gear;

[0174] Dynamic equations of bearing 9:

[0175]

[0176] Among them, m b9 is the mass of bearing 9; K b9 is the support stiffness of bearing 9; C b9 is the support damping of bearing 9; F b9x F is the supporting force of bearing 9 in the y direction; b9y is the supporting force of bearing 9 in the y direction;

[0177] Dynamic equation of bearing 10:

[0178]

[0179] Among them, m b10 is the mass of the bearing 10; K b10is the support stiffness of the bearing 10; C b10 is the support damping of the bearing 10; F b10x F is the support force of the bearing 10 in the x direction; b10y is the supporting force of the bearing 10 in the y direction;

[0180] Dynamic equation of intermediate shaft gear 7:

[0181]

[0182] Where m7 is the mass of the intermediate shaft gear; I7 is the moment of inertia of the intermediate shaft gear; K m67 is the time-varying meshing stiffness between the P3 motor shaft gear and the intermediate shaft gear; C m67 is the meshing damping between the P3 motor shaft gear and the intermediate shaft gear; f(S 67 ) is the tooth side clearance function between the P3 motor shaft gear and the intermediate shaft large gear pair; C 78x 、C 78y 、C 78z K is the damping of the connecting shaft between the intermediate shaft pinion and the intermediate shaft gear; 78x , K 78y , K 78z C is the stiffness of the connecting shaft between the intermediate shaft pinion and the intermediate shaft gear; 7x 、C 7y 、C 7z K is the support damping of the intermediate shaft in the x, y, and z directions; 7x , K 7y , K 7z is the support stiffness of the intermediate shaft in the x, y, and z directions; T7 is the torque of the intermediate shaft gear;

[0183] Dynamic equation of bearing 11:

[0184]

[0185] Among them, m b11 is the mass of the bearing 11; K b11 is the support stiffness of bearing 11; C b11 is the support damping of bearing 11; F b11x F is the support force of bearing 11 in the x direction; b11y is the supporting force of the bearing 11 in the y direction;

[0186] Dynamic equation of bearing 12:

[0187]

[0188] Among them, m b12 is the mass of the bearing 12; K b12 is the support stiffness of the bearing 12; Cb12 is the support damping of bearing 12; F b12x F is the support force of the bearing 12 in the x direction; b12y is the supporting force of the bearing 12 in the y direction;

[0189] Dynamic equation of intermediate shaft pinion 8:

[0190]

[0191] Where m8 is the mass of the intermediate shaft pinion; I8 is the moment of inertia of the intermediate shaft pinion; T8 is the torque of the intermediate shaft pinion;

[0192] Step (4): Solve the dynamic equations of the hybrid transmission gear transmission system to obtain the nonlinear dynamic response of the hybrid transmission gear transmission system.

[0193] In this example, the nonlinear dynamic response of the hybrid transmission gear system is obtained using the Runge-Kutta method using the aforementioned method. The engine gear and P1 motor shaft gear pair are used as an example, with the dimension-frequency being 0.30. Figure 4 is the gear pair displacement S 12 Bifurcation diagram as the meshing frequency changes, Figure 5 is the gear pair displacement S 12 The time domain diagram changes with time, Figure 6 is the gear pair vibration velocity with vibration displacement S 12 The changing phase diagram shows an amplitude on the time domain diagram and remains stable through the system response. The phase diagram is a closed circle. At this time, the system is in a stable state. The hybrid transmission gear transmission system can improve system performance, reduce noise and increase the service life of the structure in this state.

[0194] The above description is only a preferred embodiment of the invention and does not limit the invention in any way. Any modifications, changes and equivalent changes made to the above embodiments based on the essence of the invention shall still fall within the scope of protection of the technology of the invention.

Claims

1. A nonlinear dynamic modeling method for a hybrid transmission gear drive system, characterized in that: The following steps are involved: Step (1): Construct a bearing dynamics model. The bearing force is the resultant force of the contact force between the bearing rolling element and the inner and outer rings. Its component force F bux 、F buy , according to Hertz contact theory, it can be expressed as: Among them, F bux 、F buy (u=1,2,3...,12) is the support force of the bearing in the x and y directions, subscripts u=1 and u=2 are the engine input shaft bearings, subscripts u=3 and u=4 are the P1 motor shaft bearings, subscripts u=5 and u=6 are the clutch shaft bearings, subscripts u=7 and u=8 are the differential bearings, subscripts u=9 and u=10 are the motor shaft bearings, and subscripts u=11 and u=12 are the intermediate shaft bearings; γ q (q=1,2,3...,14) is the rolling body rotation angle, the subscript q indicates the number of rolling bodies; χ q (q=1,2,3...,14) is the deformation of the rolling element, and the subscript q represents the number of rolling elements; K bs is the bearing support stiffness; C bs is the bearing damping; H(χ q ) is the Heaviside function; Step (2): Calculate the meshing force of the helical gear pair and the time-varying meshing stiffness K of the gear pair mij , which can be expressed as: Among them, K mij (ij=12,13,45,67,85) is the time-varying meshing stiffness of the gear pair, subscript ij=12 is the engine gear and P1 motor shaft gear, subscript ij=13 is the engine gear and clutch gear, subscript ij=45 is the clutch gear and differential gear, subscript ij=67 is the P3 motor shaft gear and intermediate shaft gear, subscript ij=85 is the intermediate shaft gear and differential gear; K0 is the mean meshing stiffness; K b is the fluctuation part of meshing stiffness; K e is the meshing stiffness of a single gear tooth; ω m is the meshing frequency; is the initial phase angle; ε α is the contact ratio of the gear pair; t is the gear working time; Equivalent meshing displacement S between the engine gear and the P1 motor shaft gear 12 for: S 12 =(x1-x2)sinα n1 +(y1-y2+R1θ1-R2θ2)cosα n1 cosβ1+(z1-z2)cosα n1 sinβ1-e(t) 12 ; Among them, x1, y1, z1 are the vibration displacements of the engine gear in the x, y, and z directions; x2, y2, z2 are the vibration displacements of the P1 motor shaft gear in the x, y, and z directions; θ1 is the vibration angular displacement of the engine gear; θ2 is the vibration angular displacement of the P1 motor shaft gear; R1 is the pitch circle radius of the engine gear; R2 is the pitch circle radius of the P1 motor shaft gear; e(t) 12 is the meshing transmission error between the engine gear and the P1 motor shaft gear; α n1 is the pressure angle of the engine gear; β1 is the helix angle of the engine gear; Equivalent meshing displacement S of engine gear and clutch gear 13 for: S 13 =(x1-x3)sinα n1 +(y1-y3+R1θ1-R3θ3)cosα n1 cosβ1+(z1-z3)cosα n1 sinβ1-e(t) 13 ; Where x3, y3, and z3 are the vibration displacements of the clutch gear in the x, y, and z directions; θ3 is the vibration angular displacement of the clutch gear; R3 is the pitch circle radius of the clutch gear; and e(t) 13 is the meshing transmission error between the engine gear and the clutch gear; Equivalent meshing displacement S of clutch gear and differential gear 45 for: S 45 =(x4-x5)sine n2 +(y4-y5+R4θ4-R5θ5)cosα n2 cosβ2+(z4-z5)cosα n2 sinβ2-e(t) 45 ; Where x4, y4, z4 are the vibration displacements of the clutch pinion in the x, y, and z directions; x5, y5, z5 are the vibration displacements of the differential gear in the x, y, and z directions; θ4 is the vibration angular displacement of the clutch pinion; θ5 is the vibration angular displacement of the differential gear; R4 is the pitch circle radius of the clutch pinion; R5 is the pitch circle radius of the differential gear 5; e(t) 45 is the meshing transmission error between the clutch pinion and the differential gear; α n4 is the pressure angle of the clutch pinion; β4 is the helix angle of the clutch pinion; P3 Equivalent meshing displacement S of motor shaft gear and intermediate shaft gear 67 for: S 67 =(x6-x7)sinα n3 +(y6-y7+R6θ6-R7θ7)cosα n3 cosβ3+(z6-z7)cosα n3 sinβ3-e(t) 67 ; Among them, x6, y6, z6 are the vibration displacements of the P3 motor shaft gear in the x, y, and z directions; x7, y7, z7 are the vibration displacements of the intermediate shaft gear in the x, y, and z directions; θ6 is the vibration angular displacement of the P3 motor shaft gear; θ7 is the vibration angular displacement of the intermediate shaft gear; R6 is the pitch circle radius of the P3 motor shaft gear; R7 is the pitch circle radius of the intermediate shaft gear; e(t) 67 is the meshing transmission error between the P3 motor shaft gear and the intermediate shaft large gear; α n6 is the pressure angle of the P3 motor shaft gear; β6 is the helix angle of the P3 motor shaft gear; Equivalent meshing displacement S of the intermediate shaft gear and differential gear 85 for: S 85 =(x8-x5)sinα n8 +(y8-y5+R8θ8-R5θ5)cosα n8 cosβ8+(z8-z5)cosα n8 sinβ8-e(t) 85 ; Among them, x8, y8, z8 are the vibration displacements of the intermediate shaft pinion in the x, y, and z directions; θ8 is the vibration angular displacement of the intermediate shaft pinion; R8 is the pitch circle radius of the intermediate shaft pinion; e(t) 85 is the meshing transmission error between the intermediate shaft pinion and the differential gear; α n8 is the pressure angle of the intermediate shaft pinion; β8 is the helix angle of the intermediate shaft pinion; Meshing force component F of helical gear pair xij 、F yij 、F zij The equivalent meshing displacement S on the meshing line can be ij and tooth side clearance function f(S ij )express: Among them, f(S ij )(ij=12,13,45,67,85) is the tooth side clearance function, C mij (ij=12,13,45,67,85) is the meshing damping of the gear pair, is the equivalent meshing speed of the gear pair, subscript ij=12 is the engine gear and P1 motor shaft gear, subscript ij=13 is the engine gear and clutch gear, subscript ij=45 is the clutch pinion and differential gear, subscript ij=67 is the P3 motor shaft gear and intermediate shaft gear, subscript ij=85 is the intermediate shaft pinion and differential gear; α ni (i=1,4,6,8) is the gear pressure angle, β i (i=1, 4, 6, 8) is the gear helix angle, subscript i=1 is the engine gear, i=4 is the clutch pinion, i=6 is the P3 motor shaft gear, and i=8 is the intermediate shaft pinion; Step (3): Construct the dynamic model of the hybrid transmission gear drive system, considering the following degrees of freedom: Among them, x r 、y r 、z r (r=1,2,3...,8) is the vibration displacement of the gear in the x, y, and z directions, θ r (r=1,2,3...,8) is the vibration angular displacement of the gear, subscript r=1 is the engine gear, subscript r=2 is the P1 motor shaft gear, subscript r=3 is the clutch gear, subscript r=4 is the clutch gear, subscript r=5 is the differential gear, subscript r=6 is the P3 motor shaft gear, subscript r=7 is the intermediate shaft gear, and subscript r=8 is the intermediate shaft gear; x bu 、y bu (u=1,2,3...,12) are the vibration displacements of the bearings in the x and y directions respectively. Subscripts u=1 and u=2 are the engine input shaft bearings, subscripts u=3 and u=4 are the P1 motor shaft bearings, subscripts u=5 and u=6 are the clutch shaft bearings, subscripts u=7 and u=8 are the differential bearings, subscripts u=9 and u=10 are the motor shaft bearings, and subscripts u=11 and u=12 are the intermediate shaft bearings. Taking into account factors such as time-varying meshing stiffness, time-varying support stiffness, transmission error, tooth side clearance and bearing clearance, the dynamic equation of the hybrid transmission gear transmission system is established: The dynamic equation of the engine gear: Where m1 is the mass of the engine gear; I1 is the moment of inertia of the engine gear; K m12 is the time-varying meshing stiffness of the engine gear and the P1 motor shaft gear; C m12 K is the meshing damping between the engine gear and the P1 motor shaft gear; m13 is the time-varying meshing stiffness of the engine gear and the clutch gear; C m13 is the meshing damping between the engine gear and the clutch gear; f(S 12 ) is the tooth side clearance function of the engine gear and the P1 motor shaft gear pair; f(S 13 ) is the tooth side clearance function of the engine gear and the clutch gear pair; C 1x 、C 1y 、C 1z K is the support damping of the engine gear shaft in the x, y, and z directions; 1x , K 1y , K 1z is the support stiffness of the engine gear shaft in the x, y, and z directions; α n1 is the pressure angle of engine gear 1; β1 is the helix angle of the engine gear; T1 is the torque of the engine gear; Dynamic equations of bearing 1: Among them, m b1 is the mass of bearing 1; K b1 is the support stiffness of bearing 1; C b1 is the support damping of bearing 1; F b1x is the support force of bearing 1 in the x direction; F b1y is the support force of bearing 1 in the y direction; g is the acceleration due to gravity; Dynamic equations of bearing 2: Among them, m b2 is the mass of bearing 2; K b2 is the support stiffness of bearing 2; C b2 is the support damping of bearing 2; F b2x is the support force of bearing 2 in the x direction; F b2y is the supporting force of bearing 2 in the y direction; The dynamic equation of the P1 motor shaft gear is: Where m2 is the mass of the P1 motor shaft gear; I2 is the moment of inertia of the P1 motor shaft gear; K m12 is the time-varying meshing stiffness of the engine gear and the P1 motor shaft gear; C m12 is the meshing damping between the engine gear and the P1 motor shaft gear; f(S 12 ) is the tooth side clearance function of the engine gear and the P1 motor shaft gear pair; C 2x 、C 2y 、C 2z K is the support damping of the P1 motor shaft gear shaft in the x, y, and z directions; 2x , K 2y , K 2z is the support stiffness of the P1 motor shaft gear shaft in the x, y, and z directions; n1 is the pressure angle of the engine gear; β1 is the helix angle of the engine gear; T2 is the torque of the P1 motor shaft gear; Bearing 3 dynamic equation: Among them, m b3 is the mass of bearing 3; K b3 is the support stiffness of bearing 3; C b3 is the support damping of bearing 3; F b3x is the support force of bearing 3 in the x direction; F b3y is the supporting force of bearing 3 in the y direction; Bearing 4 dynamic equation: Among them, m b4 is the mass of bearing 4; K b4 is the support stiffness of bearing 4; C b4 is the support damping of bearing 4; F b4x F is the support force of bearing 4 in the x direction; b4y is the supporting force of bearing 4 in the y direction; The dynamic equation of the clutch gear: Where m3 is the mass of the clutch gear; I3 is the moment of inertia of the clutch gear; K m13 is the time-varying meshing stiffness between the engine gear and the clutch gear; C m13 is the meshing damping between the engine gear and the clutch gear; f(S 13 ) is the tooth side clearance function between the engine gear and the clutch gear pair; C 3x 、C 3y 、C 3z K is the support damping of the clutch gear shaft in the x, y, and z directions; 3x , K 3y , K 3z C is the support stiffness of the clutch gear shaft in the x, y, and z directions; 34x 、C 34y 、C 34z is the damping of the clutch gear connecting shaft; K 34x , K 34y , K 34z is the stiffness of the clutch gear connecting shaft; α n1 is the pressure angle of the engine gear; β1 is the helix angle of the engine gear; T3 is the torque of the clutch gear; Dynamic equations of bearing 5: Among them, m b5 is the mass of bearing 5; K b5 is the support stiffness of bearing 5; C b5 is the support damping of bearing 5; F b5x is the support force of bearing 5 in the x direction; F b5y is the supporting force of bearing 5 in the y direction; The dynamic equation of the clutch gear: Where m4 is the mass of the clutch pinion; I4 is the moment of inertia of the clutch pinion; K m45 is the time-varying meshing stiffness between the clutch pinion and the differential gear; C m45 is the meshing damping between the clutch pinion and the differential gear; f(S 45 ) is the tooth side clearance function between the clutch pinion and the differential gear pair; α n4 is the pressure angle of the clutch pinion; β4 is the helix angle of the clutch pinion; T4 is the torque of the clutch pinion; Dynamic equations of bearing 6: Among them, m b6 is the mass of bearing 6; K b6 is the support stiffness of bearing 6; C b6 is the support damping of bearing 6; F b6x F is the support force of bearing 6 in the x direction; b6y is the support force of bearing 6 in the y direction; The dynamic equation of the differential gear: Where m5 is the mass of the differential gear; I5 is the moment of inertia of the differential gear; K m45 is the time-varying meshing stiffness between the clutch pinion and the differential gear; C m45 is the meshing damping between the clutch pinion and the differential gear; f(S 45 ) is the tooth side clearance function between the clutch pinion and the differential gear pair; K m85 is the time-varying meshing stiffness between the intermediate shaft pinion and the differential gear; C m85 is the meshing damping between the intermediate shaft pinion and the differential gear; f(S 85 ) is the tooth side clearance function between the intermediate shaft pinion and the differential gear pair; C 5x 、C 5y 、C 5z K is the support damping of the differential gear shaft in the x, y, and z directions; 5x , K 5y , K 5z is the support stiffness of the differential gear shaft in the x, y, and z directions; α n8 is the pressure angle of the intermediate shaft pinion; β8 is the helix angle of the intermediate shaft pinion; T5 is the torque of the differential gear; Dynamic equations of bearing 7: Among them, m b7 is the mass of bearing 7; K b7 is the support stiffness of bearing 7; C b7 is the support damping of bearing 7; F b7x F is the support force of bearing 7 in the x direction; b7y is the supporting force of bearing 7 in the y direction; Dynamic equations of bearing 8: Among them, m b8 is the mass of the bearing 8; K b8 is the support stiffness of bearing 8; C b8 is the support damping of bearing 8; F b8x F is the support force of bearing 8 in the x direction; b8y is the supporting force of the bearing 8 in the y direction; The dynamic equation of the P3 motor shaft gear is: Where m6 is the mass of the P3 motor shaft gear; I6 is the moment of inertia of the P3 motor shaft gear; K m67 is the time-varying meshing stiffness between the P3 motor shaft gear and the intermediate shaft gear; C m67 is the meshing damping between the P3 motor shaft gear and the intermediate shaft gear; f(S 67 ) is the tooth side clearance function between the P3 motor shaft gear and the intermediate shaft large gear pair; C 6x 、C 6y 、C 6z K is the support damping of the P3 motor gear shaft in the x, y, and z directions; 6x , K 6y , K 6z is the support stiffness of the P3 motor gear shaft in the x, y, and z directions; α n3 is the pressure angle of the P3 motor shaft gear; β3 is the helix angle of the P3 motor shaft gear; T6 is the torque of the P3 motor shaft gear; Dynamic equations of bearing 9: Among them, m b9 is the mass of bearing 9; K b9 is the support stiffness of bearing 9; C b9 is the support damping of bearing 9; F b9x F is the supporting force of bearing 9 in the y direction; b9y is the supporting force of bearing 9 in the y direction; Dynamic equation of bearing 10: Among them, m b10 is the mass of the bearing 10; K b10 is the support stiffness of the bearing 10; C b10 is the support damping of the bearing 10; F bx10 F is the support force of the bearing 10 in the x direction; by10 is the supporting force of the bearing 10 in the y direction; Dynamic equation of the intermediate shaft gear: Where m7 is the mass of the intermediate shaft gear; I7 is the moment of inertia of the intermediate shaft gear; K m67 is the time-varying meshing stiffness between the P3 motor shaft gear and the intermediate shaft gear; C m67 is the meshing damping between the P3 motor shaft gear and the intermediate shaft gear; f(S 67 ) is the tooth side clearance function between the P3 motor shaft gear and the intermediate shaft large gear pair; C 78x 、C 78y 、C 78z K is the damping of the connecting shaft between the intermediate shaft pinion and the intermediate shaft gear; 78x , K 78y , K 78z C is the stiffness of the connecting shaft between the intermediate shaft pinion and the intermediate shaft gear; 7x 、C 7y 、C 7z K is the support damping of the intermediate shaft in the x, y, and z directions; 7x , K 7y , K 7z is the support stiffness of the intermediate shaft in the x, y, and z directions; T7 is the torque of the intermediate shaft gear; Dynamic equation of bearing 11: Among them, m b11 is the mass of the bearing 11; K b11 is the support stiffness of bearing 11; C b11 is the support damping of bearing 11; F bx11 F is the support force of bearing 11 in the x direction; by11 is the supporting force of the bearing 11 in the y direction; Dynamic equation of bearing 12: Among them, m b12 is the mass of the bearing 12; K b12 is the support stiffness of the bearing 12; C b12 is the support damping of bearing 12; F b12x F is the support force of the bearing 12 in the x direction; b12y is the supporting force of the bearing 12 in the y direction; Dynamic equation of the intermediate shaft pinion: Where m8 is the mass of the intermediate shaft pinion; I8 is the moment of inertia of the intermediate shaft pinion; T8 is the torque of the intermediate shaft pinion; Step (4): Solve the dynamic equations of the hybrid transmission gear transmission system to obtain the nonlinear dynamic response of the hybrid transmission gear transmission system.

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