Planetary speed change mechanism multi-point support bending-torsion coupling excitation dynamic characteristic estimation method

Abstract

The invention relates to a multi-point support bending-torsion coupling excitation dynamic characteristic estimation method for a planetary speed change mechanism, and belongs to the technical field of planetary gears. The problem that the dynamic load of the multi-point supporting bearing under the actual working condition is difficult to predict and inhibit due to the dynamic coupling effect between the bending-torsional vibration of the transmission shaft and the dynamic load of the multi-point supporting bearing and the dynamic load of the planetary gear set in the prior art is solved. The method comprises the following steps: acquiring various planet wheel component parameters and various bearing parameters of the planetary speed change mechanism; based on each bearing parameter, calculating to obtain the time-varying nonlinear support stiffness of the bearing; establishing a subsystem dynamical model of the planetary speed change mechanism based on the time-varying nonlinear support stiffness of the bearing and the component parameters of each planetary gear; in a given time step, when an inner ring and an outer ring of an intermediate bearing rotate at the same time, the dynamic load fo and the deformation delta o of a planet carrier / bearing seat to the outer ring of the bearing and the dynamic load fi and the deformation delta i of a transmission shaft to the inner ring are calculated, the supporting rigidity and the dynamic response of a system at the current moment are calculated, and dynamic models of subsystems of the planetary speed change mechanism are combined; and a fourth-order Runge-Kutta numerical iteration algorithm is used to solve the dynamic characteristic estimation result, the dynamic response of the planetary speed change mechanism in the next time step is obtained, and loop iteration is carried out until the dynamic characteristic estimation is completed.

Description

Technical Field

[0001] The present invention relates to the technical field of planetary gears, and in particular to a method for estimating dynamic characteristics of multi-point supported bending-torsion coupling excitation of a planetary speed change mechanism. Background Art

[0002] Automatic transmission is a kind of automobile transmission system, which can automatically adjust the speed ratio according to different driving conditions and vehicle speed, so as to improve the fuel economy and driving comfort of the vehicle. Automatic transmission generally adopts planetary gear transmission, which has the advantages of good transmission stability, strong load bearing capacity, long service life, smooth speed change process, and can achieve a wide range of speed ratios, etc. It can meet the high reliability requirements of the vehicle, thus improving the reliability and safety of the vehicle.

[0003] However, in the planetary speed change mechanism, the bending moment of the transmission shaft caused by the dynamic load supported by the multiple rolling bearing elements of the transmission shaft and the torque of the transmission shaft caused by the dynamic meshing force of the planetary gear set directly affect the bending and swing vibrations and torsional vibrations of the transmission shaft; on the other hand, the bending and swing vibrations and torsional vibrations of the transmission shaft respectively change the displacement of the inner rings of each supporting bearing and the meshing displacement of each sun gear-planet gear, thereby affecting the dynamic load of the multi-point support bearings and the meshing force of the dynamic group of planetary gears, that is, there is a dynamic coupling between the bending and torsional vibrations of the transmission shaft and the dynamic loads of the multi-point support bearings and the planetary gear sets, and it is difficult to predict the dynamic characteristics of the planetary speed change mechanism. At present, there is no analysis method for the dynamic characteristics of high power density planetary speed change mechanisms. Summary of the invention

[0004] In view of the above analysis, an embodiment of the present invention aims to provide a method for estimating the dynamic characteristics of multi-point support bending-torsion coupling excitation of a planetary speed change mechanism, so as to solve the problems that the dynamic coupling effect between the bending-torsion vibration of the transmission shaft and the dynamic loads of the multi-point support bearings and the planetary gear set is difficult to accurately model, and there is a lack of effective methods to predict and suppress the dynamic loads of the multi-point support bearings under actual working conditions.

[0005] The purpose of the present invention is mainly achieved through the following technical solutions:

[0006] The present invention provides a method for estimating dynamic characteristics of a planetary speed change mechanism with multi-point support bending-torsion coupling excitation, wherein the planetary speed change mechanism adopts a dual-rotor structure; the method comprises:

[0007] Obtaining parameters of each planetary gear component and each bearing parameter of the planetary speed change mechanism; wherein the parameters of the planetary gear component include: number of teeth, module, pressure angle, mass, Young's modulus and Poisson's ratio; the bearing parameters include: inner diameter, outer diameter, width, roller diameter, stiffness, damping, clearance and Young's modulus;

[0008] Based on the bearing parameters, the time-varying nonlinear support stiffness of the bearing is calculated;

[0009] Based on the time-varying nonlinear support stiffness of the bearing and the parameters of each of the planetary gear components, a subsystem dynamic model of the planetary transmission mechanism is established; wherein the planetary transmission mechanism subsystem includes an input shaft subsystem, a double planetary gear subsystem, an output end transmission shaft subsystem and a compound gear subsystem;

[0010] In a given time step, when the inner and outer rings of the intermediate bearing rotate simultaneously, calculate the dynamic load f of the planet carrier / bearing seat on the outer ring of the bearing o and deformation δ o And the dynamic load f of the transmission shaft on the inner ring i and deformation δ i , and calculate the support stiffness and dynamic response of the system at the current moment, jointly establish the dynamic models of the subsystems of the planetary speed change mechanism, use the fourth-order Runge-Kutta numerical iterative algorithm to solve it, obtain the dynamic response of the planetary speed change mechanism in the next time step, and iterate until the dynamic characteristics estimation is completed.

[0011] Furthermore, the time-varying nonlinear support stiffness of the bearing is calculated using the following formula:

[0012]

[0013] Among them, K n A represents the normal comprehensive contact stiffness between the inner roller and the inner and outer rings of the bearing; n represents the contact factor; N represents the total number of rollers in the bearing; A 0 Indicates the relative distance between the center of curvature of the inner and outer raceways of the bearing before deflection; A j It indicates the relative distance between the center of curvature of the groove after the inner and outer raceways of the jth roller in the bearing are deflected; represents the azimuth angle of the jth roller in the bearing at time t; δ jr It indicates the relative distance along the radial direction between the centers of curvature of the inner and outer ring grooves at the jth roller in the bearing after deflection.

[0014] Furthermore, in the input shaft subsystem of the planetary speed change mechanism, the B1 support bearing is located at the input end; the outer rings of the B2 intermediate bearing and the B3 intermediate bearing support the planetary carrier of the first row of planetary gear train; the outer rings of the B4 intermediate bearing and the B5 intermediate bearing support the planetary carrier of the second row of planetary gear train; the input shaft is the sun gear shaft, which meshes with the planetary gears of the two rows of planetary gear trains, and its meshing force generates meshing force components and torque in the X and Y directions on the input shaft.

[0015] Furthermore, the dynamic equation of the input shaft subsystem is a 5-degree-of-freedom dynamic equation of bending-torsion-pendulum coupling excitation. The 5-degree-of-freedom dynamic equation of the input shaft subsystem of bending-torsion-pendulum coupling excitation is constructed using the following formula:

[0016]

[0017] Among them, q si =[x si ,y si ,θ xsi ,θ ysi ,θ zsi ] represents the 5 degrees of freedom of the input axis; (f xi ,f yi ) represents the input load of the hydraulic torque converter at the front end of the planetary transmission mechanism to the input shaft in the X and Y directions; M θzi Indicates input torque; M si =diag([m si ,m si ,I xsi ,I ysi ,I zsi ]) represents the mass matrix of the sun gear shaft; They represent the support reaction forces of the B1 support bearing, B2 intermediate bearing, B3 intermediate bearing, B4 intermediate bearing and B5 intermediate bearing in the input shaft subsystem in the X and Y directions respectively; Respectively represent the projections of the meshing forces of the first row of planetary gear trains and the second row of planetary gear trains on the input shaft in the X and Y directions; It represents the projection of the dynamic unbalanced force caused by the mass eccentricity of the CH operating part on the input shaft in the X and Y directions; It represents the projection of the dynamic unbalanced moment caused by the mass eccentricity of the CH operating part on the input shaft in the X and Y directions; They represent the coupling force of the CH operating member on the input shaft in the X and Y directions and the torsion direction when combined; a b1 、a b2 、a b3 、a b4 and a b5 Respectively represent the distances from the five bearings to the center of mass of the input shaft; a p1 and a p2 Respectively represent the distances from the first planetary row and the second planetary row to the mass center of the input shaft; a i Indicates the distance between the input load and the center of mass of the shaft; a d1 Indicates the distance between the CH control and the axis mass center; and Respectively represent the torques of the first planetary gear train and the second planetary gear train on the input shaft;

[0018] The support reaction forces of the B1 support bearing, B2 intermediate bearing, B3 intermediate bearing, B4 intermediate bearing and B5 intermediate bearing in the input shaft subsystem in the X and Y directions are respectively calculated based on the time-varying nonlinear support stiffness of the bearing, the displacement of the first row planet carrier, the second row planet carrier and the sun gear shaft in the X and Y directions, and the distance from each bearing on the input shaft to the center of mass of the input shaft.

[0019] Furthermore, in the double planetary gear subsystem of the planetary speed change mechanism, the planet carrier of the first planetary gear train is connected to the inner gear ring of the second planetary gear train, the power is input from the sun gear shaft, and the power is output from the planet carrier of the second planetary gear train;

[0020] For the planet carrier of the first row of planetary gear systems, which supports the planetary gears of the first row of planetary gear systems, the three-degree-of-freedom dynamic equations of its bending-torsion coupling excitation are constructed;

[0021] For the component consisting of the first row of internal gear rings and the second row of planet carriers, which not only meshes with the first row of planetary gear sets but also supports the second row of planetary gear sets, the three-degree-of-freedom dynamic equations of its bending-torsion coupling excitation are constructed;

[0022] For the first row of planetary gears, which mesh with the sun gear and the first row of inner gear ring at the same time, the three-degree-of-freedom dynamic equations of the bending-torsion coupling excitation of each planetary gear are constructed;

[0023] For the second row of internal gear rings, which mesh with the second row of planetary gear sets, the three-degree-of-freedom dynamic equations of its bending-torsion coupling excitation are constructed;

[0024] For the second row of planetary gear sets, which mesh with the sun gear and the second row of inner gear ring at the same time, a three-degree-of-freedom dynamic equation of the bending-torsion coupling excitation of each planetary gear is constructed.

[0025] Furthermore, the following equation is used to construct the dynamic equation of the planet carrier of the first row of planetary gear systems:

[0026]

[0027] in, Represents the three degrees of freedom of the bending-torsion coupling excitation of the planet carrier of the first row of planetary gear systems; represents the mass matrix of the first row of planet carriers; Respectively represent the support reaction forces of the B2 intermediate bearing and the B3 intermediate bearing in the X and Y directions; represents the bearing support force between the first row of planet carriers and the hth planetary gear in the X and Y directions; R c1 Indicates the distance from the center of the planetary gear to the center of the first row of planetary carriers; Indicates the positioning angle of the hth planet gear in the first row of planet carriers; They respectively represent the coupling forces of the CH operating member on the input shaft in the X and Y directions and the torsional direction when combined; represents the coupling force vector between the first row planet carrier and the planetary speed change mechanism when the CR clutch is engaged;

[0028] The bearing support forces of the first row of planet carriers and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear of the first row of planetary gear train, the displacement vector of the first row of planet carriers, the time-varying nonlinear support stiffness of the first row of planetary gear bearings, and the support damping of the first row of planetary gear bearings in the X and Y directions;

[0029] The coupling force vector between the first row planet carrier and the planetary speed change mechanism is calculated based on the displacement vector of the first row planet carrier and the coupling stiffness vector and coupling damping vector of the CR clutch when the CR clutch is engaged; and is set to 0 when the CR clutch is disengaged;

[0030] The following equation is used to construct the dynamic equation of the components consisting of the first row of internal gear rings and the second row of planet carriers:

[0031]

[0032] in, F represents the three degrees of freedom of the bending-torsion coupling excitation of the components consisting of the first row of internal gear rings and the second row of planet carriers; rco ={f xrco ,f yrco ,M θzrco} T represents the output load vector of the components consisting of the first row of internal gear rings and the second row of planet carriers; The mass matrix representing the components of the first row of internal gear rings and the second row of planet carriers; represents the bearing support force between the second row planet carrier and the hth planet gear in the X and Y directions; R c2 Indicates the distance from the center of the second row of planetary gears to the center of the planet carrier; Indicates the base circle radius of the first row of internal gear rings; represents the position angle of the hth planetary gear in the second row; represents the dynamic load between the first row of internal gear rings and the hth planetary gear; Respectively represent the support reaction forces of the B4 intermediate bearing, the B5 intermediate bearing and the B6 support bearing in the X and Y directions; It represents the angular position of the meshing line between the hth planetary gear in the first row and the first row of internal gear ring from the X axis;

[0033] The bearing support forces of the second row planet carrier and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear of the second row planetary gear system, the displacement vector of the second row planet carrier, the time-varying nonlinear support stiffness of the second row planetary gear bearings and the support damping of the second row planetary gear bearings in the X and Y directions;

[0034] The dynamic load between the first row of inner gear rings and each planetary gear is calculated based on the meshing relative displacement between the first row of inner gear rings and each planetary gear, the tooth side clearance between the first row of inner gear rings and each planetary gear, the displacement vector of the first row of inner gear rings, the angular position of the meshing line of each planetary gear and the first row of inner gear rings from the X-axis, the distance from the center of each planetary gear to the center of the first row of inner gear rings, the base circle radius of the first row of inner gear rings, and the meshing stiffness and meshing damping between the first row of inner gear rings and each planetary gear;

[0035] The following formula is used to construct the dynamic equations of each planetary gear of the first row of planetary gear sets:

[0036]

[0037] in, It represents the three degrees of freedom of the bending-torsion coupling excitation of the hth planetary gear in the first row of planetary gear sets; represents the mass matrix of the hth planetary gear in the first row; and They represent the dynamic meshing forces between the first row sun gear and the hth planetary gear and between the first row internal gear and the hth planetary gear respectively; It represents the bearing support force between the first row of planet carriers and the hth planetary gear in the X and Y directions; Indicates the base circle radius of the first row of planetary gears;

[0038] The bearing support forces of the first row planet carrier and each planet gear in the X and Y directions are calculated based on the displacement vectors of each planet gear of the first row planet gear system, the displacement vector of the first row planet carrier, the time-varying nonlinear support stiffness of the first row planet gear bearings, and the support damping of the first row planet gear bearings in the X and Y directions;

[0039] The dynamic meshing force between the first row sun gear and each planetary gear is calculated based on the meshing relative displacement between the first row sun gear and each planetary gear, the tooth side clearance between the first row sun gear and each planetary gear, the displacement vector of the first row sun gear, the angular position of the meshing line of each planetary gear and the first row sun gear from the X-axis, the distance from the center of each planetary gear to the center of the first row sun gear, the base circle radius of the first row sun gear, and the meshing stiffness and meshing damping between the first row sun gear and each planetary gear;

[0040] The dynamic equation of the second row of internal gears is constructed using the following formula:

[0041]

[0042] in, Represents the 3 degrees of freedom of the bending-torsion coupling excitation of the second row of internal gear rings; represents the mass matrix of the second row of internal gear rings; represents the coupling force vector between the second row planet carrier and the planetary speed change mechanism when the CL clutch is engaged; represents the dynamic meshing force between the second row of internal gear rings and the hth planetary gear; Indicates the angular position of the meshing line between the hth planetary gear and the inner gear ring from the X axis; Indicates the base circle radius of the second row of internal gear ring;

[0043] The dynamic equations of each planetary gear of the second row of planetary gear sets are constructed using the following formula:

[0044]

[0045] in, It represents the 3 degrees of freedom of the bending-torsion coupling excitation of the hth planetary gear of the second row of planetary gear sets; represents the mass matrix of the hth planetary gear in the second row; and They represent the dynamic meshing forces between the second row sun gear and the hth planetary gear and between the second row internal gear and the hth planetary gear respectively; represents the bearing support force between the second row planet carrier and the hth planet gear in the X and Y directions; Indicates the base circle radius of the second row of planetary gears;

[0046] The bearing support forces of the second row planet carrier and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear of the second row planetary gear system, the displacement vector of the second row planet carrier, the time-varying nonlinear support stiffness of the second row planetary gear bearings and the support damping of the second row planetary gear bearings in the X and Y directions;

[0047] The dynamic meshing force between the second-row sun gear and each planetary gear is calculated based on the meshing relative displacement between the second-row sun gear and each planetary gear, the tooth side clearance between the second-row sun gear and each planetary gear, the displacement vector of the second-row sun gear, the angular position of the meshing line of each planetary gear and the second-row sun gear from the X-axis, the distance from the center of each planetary gear to the center of the second-row sun gear, the base circle radius of the second-row sun gear, and the meshing stiffness and meshing damping between the second-row sun gear and each planetary gear.

[0048] Furthermore, in the output end transmission shaft subsystem of the planetary speed change mechanism, a B10 support bearing is provided on the output end transmission shaft, a B8 intermediate bearing supports the compound row input gear ring, a B9 intermediate bearing supports the compound row planetary carrier, and the transmission shaft is the sun gear shaft, which meshes with the long planetary gear of the compound row, and its meshing force generates meshing force components and torque in the X and Y directions on the transmission shaft.

[0049] Furthermore, the dynamic equation of the output-end transmission shaft subsystem is a 5-degree-of-freedom dynamic equation of bending-torsion-pendulum coupling excitation. The following formula is used to construct the 5-degree-of-freedom dynamic equation of the output-end transmission shaft subsystem of bending-torsion-pendulum coupling excitation:

[0050]

[0051] Among them, q so =[x so ,y so ,θ xso ,θ yso ,θ zso ] represents the 5 degrees of freedom of the output transmission shaft; M so =diag([m so ,m so ,I xso ,I yso ,I zso ]) represents the mass matrix of the output transmission shaft; F o ={f xo ,f yo ,M θzo} T Represents the external load vector on the output transmission shaft; Respectively represent the support reaction forces of the B8 intermediate bearing, the B9 intermediate bearing and the B10 support bearing in the X and Y directions; It indicates the projection of the dynamic unbalanced force caused by the mass eccentricity of the C2 and C3 operating parts on the output end transmission shaft in the X and Y directions; It indicates the projection of the dynamic unbalanced moment caused by the mass eccentricity of the C2 and C3 operating parts on the output end transmission shaft in the X and Y directions; They respectively represent the coupling force of the C2 operating member / C3 operating member on the output end transmission shaft in the X and Y directions and the torsional direction when the operating member is combined; a b8 、a b9 and a b10 Respectively represent the distances from the B8 intermediate bearing, B9 intermediate bearing and B10 support bearing to the mass center of the output end transmission shaft; a p3 represents the distance from the compound row to the center of mass of the transmission shaft, a d3 Indicates the distance between the C2 control member and the C3 control member and the center of mass of the shaft; It represents the projection of the meshing force of the compound row on the sun gear of the output transmission shaft in the X and Y directions; Indicates the torque of the compound row on the sun gear of the output drive shaft; a o Indicates the distance between the input load and the center of mass of the output transmission shaft;

[0052] The support reaction forces of the B8 intermediate bearing, the B9 intermediate bearing and the B10 support bearing in the output end transmission shaft subsystem in the X and Y directions are calculated based on the time-varying nonlinear support stiffness of the bearings, the displacements of the composite planetary carrier and the output end transmission shaft in the X and Y directions, and the distances from the center of mass of each bearing on the output end transmission shaft to the input shaft.

[0053] Further, in the compound row subsystem of the planetary speed change mechanism, the planet carrier includes a long planetary gear set and a short planetary gear set; wherein the long planetary gear set meshes with the sun gear and the input gear ring to form a row of planetary gear transmission; the short planetary gear set meshes with the long planetary gear set and the floating support ring to form another row of planetary gear transmission; the two rows of planetary gear transmissions form a compact compound planetary gear transmission through the meshing between the long planetary gear set and the short planetary gear set; power is input from the compound row input gear ring and output from the compound row planet carrier;

[0054] For the planet carrier of the compound planetary gear system, which supports both the long planetary gear set and the short planetary gear set, the three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed;

[0055] For the compound row input ring gear, it is coupled with the planet carrier of the second row planetary gear system of the planetary speed change mechanism and meshes with the compound row long planetary gear set, and a 3-DOF dynamic equation of its bending-torsion coupling excitation is constructed;

[0056] For the composite long planetary gear set, which is meshed with the input ring gear, sun gear and short planetary gear set at the same time, the 3-DOF dynamic equation of its bending-torsion coupling excitation is constructed;

[0057] For the composite short planetary gear set, which is meshed with the long planetary gear set and the floating ring gear at the same time, the three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed;

[0058] For the compound row floating ring gear, which is meshed with the compound row planetary gear set, the three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed.

[0059] Furthermore, the following formula is used to construct the dynamic equation of the planet carrier of the compound planetary gear system:

[0060]

[0061] in, Represents the three degrees of freedom of the bending-torsion coupling excitation of the planet carrier of the compound planetary gear system; Represents the mass matrix of the planet carrier of the compound planetary gear system; Respectively represent the support reaction forces of the B7 intermediate bearing, the B8 intermediate bearing and the B9 intermediate bearing in the X and Y directions; It represents the bearing support force of the composite planet carrier and the u-th short planet gear in the X direction and the Y direction; It represents the bearing support force of the composite planet carrier and the u-th long planet gear in the X direction and the Y direction; It represents the coupling force between the planet carrier of the compound planetary gear system and the transmission mechanism case in the X and Y directions and the torsion direction when the C2 operating member / C3 operating member are combined; r c Indicates the distance from the center of the short planetary gear to the center of the planetary carrier; r lc Indicates the distance from the center of the long planet gear to the center of the planet carrier; represents the positioning angle of the uth short planetary gear; represents the positioning angle of the u-th long planet gear;

[0062] The bearing support forces of the composite planet carrier and each short planet gear in the X direction and the Y direction are calculated based on the displacement vector of each short planet gear in the composite row, the support stiffness of the short planet gear bearing in the X direction and the Y direction, the support damping of the short planet gear bearing in the X direction and the Y direction, the distance from the center of the short planet gear to the center of the planet carrier, and the positioning angle of each short planet gear;

[0063] The bearing support forces of the composite planet carrier and each long planet wheel in the X direction and the Y direction are calculated based on the displacement vector of each long planet wheel in the composite row, the support stiffness of the long planet wheel bearing in the X direction and the Y direction, the support damping of the long planet wheel bearing in the X direction and the Y direction, the distance from the center of the long planet wheel to the center of the planet carrier, and the positioning angle of each long planet wheel;

[0064] The support reaction force of the B7 intermediate bearing in the planetary carrier of the compound row planetary gear system in the X and Y directions is calculated based on the time-varying nonlinear support stiffness of the bearing, the displacement of the compound row input gear ring in the X and Y directions, and the support damping of the bearing in the X and Y directions;

[0065] The dynamic equation of the compound row input ring gear is constructed using the following formula:

[0066]

[0067] in, F represents the three degrees of freedom of the bending-torsion coupling excitation of the compound row input gear ring; ro ={f xro ,f yro ,M θzro} T represents the input load vector of the compound row input ring gear; F represents the mass matrix of the compound row input gear ring; rlpu represents the dynamic load of the u-th long planetary gear in the compound row and the input ring gear; ψ rpu Indicates the angular position of the meshing line between the u-th short planet gear in the compound row and the sun gear from the X axis; Indicates the base circle radius of the compound row input gear ring;

[0068] The dynamic load of each long planetary gear of the compound row and the input gear ring is calculated based on the tooth side clearance between the inner gear ring and the corresponding long planetary gear, the displacement vector of the long planetary gear corresponding to the compound row, the angular position of the meshing line of the corresponding long planetary gear and the input gear ring from the X axis, the input gear ring base circle radius, the displacement of the input gear ring in the X direction, the Y direction and the torsional direction, and the displacement of the planet carrier in the torsional direction;

[0069] The dynamic equation of the composite long-row planetary gear set is constructed using the following formula:

[0070]

[0071] in, represents the three degrees of freedom of the bending-torsion coupling excitation of the u-th long planetary gear in the composite row; represents the mass matrix of the u-th long planetary gear in the composite row; F slpu represents the dynamic load of the u-th long planetary gear in the composite row and the sun gear shaft; F rlpu F represents the dynamic load of the u-th long planetary gear in the compound row and the input ring gear; lppu represents the dynamic load of the u-th long planetary gear and the u-th short planetary gear in the compound row; ψ slpu represents the angle between the meshing line of the u-th long planetary gear in the composite row and the sun gear shaft and the X-axis; ψ rlpu represents the angle between the meshing line of the u-th long planetary gear in the compound row and the input ring gear and the X-axis; ψ lppu Indicates the angular position of the meshing line between the u-th long planetary gear and the u-th short planetary gear in the compound row from the X-axis; Indicates the base circle radius of the composite long planet gear;

[0072] The dynamic load of the u-th long planetary gear and the u-th short planetary gear of the compound row is calculated based on the tooth side clearance of the u-th long planetary gear and the u-th short planetary gear, the displacement vector of the u-th long planetary gear, the displacement vector of the u-th short planetary gear, the angular position of the meshing line of the u-th long planetary gear and the u-th short planetary gear from the X-axis, and the base circle radius of the short planetary gear;

[0073] The dynamic equation of the composite short-row planetary gear set is constructed using the following formula:

[0074]

[0075] in, represents the three degrees of freedom of the bending-torsion coupling excitation of the u-th short planetary gear in the composite row; F represents the mass matrix of the u-th short planetary gear in the composite row; frpu represents the dynamic load between the composite floating ring gear and the uth short planetary gear; ψfrpu Indicates the angular position of the meshing line between the composite row floating ring gear and the uth short planetary gear from the X axis; Indicates the base circle radius of the compound short planetary gear;

[0076] The dynamic load between the composite row floating ring gear and the u-th short planet gear is calculated based on the tooth side clearance between the composite row floating ring gear and each short planet gear, the displacement vector of the floating ring gear, the displacement in the torsion direction of the planet carrier, the meshing secondary pressure angle of the floating ring gear-short planet gear, the meshing stiffness and meshing damping between the floating ring gear and each short planet gear, and the base circle radius of the floating ring gear;

[0077] The dynamic equation of the composite floating gear ring is constructed using the following formula:

[0078]

[0079] in, Represents the three degrees of freedom of bending-torsion coupling excitation of the composite row floating gear ring; Represents the mass matrix of the composite row floating gear ring; It represents the coupling force vector between the compound row floating ring gear and the transmission case when the C1 clutch is engaged;

[0080] The coupling force vector between the compound row floating ring gear and the transmission mechanism case when the C1 clutch is engaged is calculated based on the coupling stiffness vector and the coupling damping vector between the compound row floating ring gear and the transmission mechanism case.

[0081] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0082] 1. The present invention establishes a method for estimating the dynamic characteristics of a planetary speed change mechanism with multi-point support bending-torsion coupling excitation, which can simulate and analyze its motion characteristics and transmission performance and optimize the design to improve its working efficiency and transmission stability, thereby reducing the energy consumption and cost of the mechanical system.

[0083] 2. The method of the present invention can more accurately predict the dynamic characteristics of the planetary speed change mechanism by coupling the motion equations of multiple degrees of freedom of each component, while ensuring high calculation efficiency. At the same time, it takes into account the time-varying nonlinear support stiffness characteristics of the rolling bearing, making the model closer to the actual working state and improving the accuracy of the dynamic model.

[0084] 3. The present invention can predict the motion state and transmission characteristics of the mechanism under different working conditions by estimating the dynamic characteristics of the planetary speed change mechanism, thereby providing a reliable reference for the design and optimization of the mechanical system and improving the reliability and service life of the mechanical system.

[0085] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] The drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.

[0087] Figure 1 It is a structural schematic diagram of a planetary speed change mechanism in an embodiment of the present invention;

[0088] Figure 2 It is a flow chart of a method for estimating dynamic characteristics of multi-point support bending-torsion coupling excitation of a planetary speed change mechanism in an embodiment of the present invention;

[0089] Figure 3 Schematic diagram of the geometric dimensions of the ball bearing and the center of curvature of the groove of the raceway before and after deflection in an embodiment of the present invention;

[0090] Figure 4 A schematic diagram of solving a bearing pseudo-dynamics model using the Newton iteration method in an embodiment of the present invention;

[0091] Figure 5 Schematic diagram of the bending, torsion and swing coupling excitation dynamics model of the input shaft of the planetary speed change mechanism in an embodiment of the present invention;

[0092] Figure 6 Schematic diagram of the bending-torsion coupling dynamics model of the first row of planetary gear system in an embodiment of the present invention;

[0093] Figure 7 Schematic diagram of the bending-torsion coupling dynamics model of the second row planetary gear system in an embodiment of the present invention;

[0094] Figure 8 Schematic diagram of the bending-torsion dynamics model of the double planetary gear set at the input end of the planetary speed change mechanism in an embodiment of the present invention;

[0095] Fig. 9 Schematic diagram of the bending-torsion dynamics model of the transmission shaft at the output end of the planetary speed change mechanism in an embodiment of the present invention;

[0096] Fig.10 It is a schematic diagram of the planar dynamics model of the compound planetary gear system in an embodiment of the present invention.

[0097] Reference numerals:

[0098] 1-B1 support bearing; 2-B2 intermediate bearing; 3-B3 intermediate bearing; 4-B4 intermediate bearing; 5-B5 intermediate bearing; 6-B6 support bearing; 7-B7 intermediate bearing; 8-B8 intermediate bearing; 9-B9 intermediate bearing; 10-B10 support bearing; 11-first planetary row; 12-second planetary row; 13-compound row; 14-CH operating member; 15-CR clutch; 16-CL clutch; 17-C1 clutch; 18-C2 operating member; 19-C3 operating member; DETAILED DESCRIPTION

[0099] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0100] A specific embodiment of the present invention discloses a method for estimating dynamic characteristics of a planetary speed change mechanism with multi-point support bending-torsion coupling excitation, such as Figure 1 As shown, the planetary speed change mechanism adopts a dual rotor structure, which can effectively shorten the span of the rotor fulcrum and reduce the weight of the planetary speed change mechanism. The planetary speed change mechanism includes three rows of planetary gear trains (the first planetary row 11, the second planetary row 12 and the compound row 13), three support bearings (B1 support bearing 1, B6 support bearing 6 and B10 support bearing 10) and seven intermediate bearings (B2 intermediate bearing 2, B3 intermediate bearing 3, B4 intermediate bearing 4, B5 intermediate bearing 5, B7 intermediate bearing 7, B8 intermediate bearing 8 and B9 intermediate bearing 9). The outer ring of the support bearing is fixed on the chassis, and the inner ring rotates with the rotor; the outer ring of the intermediate bearing rotates with the planet carrier or the outer rotor, and the inner ring rotates with the rotor; the planetary speed change mechanism also includes components for controlling the operation of the clutch or brake in the speed change mechanism (CH operating member 14, CR clutch 15, CL clutch 16, C1 clutch 17, C2 operating member 18 and C3 operating member 19)

[0101] Specifically, the right end of the transmission mechanism case is the input end of the transmission mechanism, including a 2-row planetary gear transmission system, 2 support bearings, and 4 intermediate bearings; the system power is introduced by the input shaft and output to the left end compound row system through the planetary carrier of the second row of planetary gears; the left end of the transmission mechanism case is the output end of the transmission mechanism, including a 3-row compound planetary gear transmission system, 1 support bearing and 3 intermediate bearings. The power of the planetary transmission mechanism is transmitted through the compound row planetary carrier, and the clutch / brake of different operating parts of the transmission mechanism is controlled by the electronic control hydraulic system, and the splitting or engagement of the friction plate and the steel plate realizes the speed and torque output of different transmission ratios.

[0102] Further, such as Figure 2 As shown, a method for estimating dynamic characteristics of a planetary speed change mechanism with multi-point support bending-torsion coupling excitation includes the following steps S1 to S4:

[0103] Step S1, obtaining parameters of each planetary gear component and each bearing parameter of the planetary speed change mechanism; wherein the planetary gear component parameters include: number of teeth, module, pressure angle, mass, Young's modulus and Poisson's ratio; the bearing parameters include: inner diameter, outer diameter, width, roller diameter, stiffness, damping, clearance and Young's modulus.

[0104] Specifically, the planetary gear components of the planetary transmission mechanism include: a sun gear, which is a fixed or rotating central gear; planetary gears, which are gears that rotate and mesh around the sun gear and are usually mounted on a planet carrier; an inner ring gear, which is a gear that surrounds the planetary gears and is usually fixed to the housing of the transmission; and a planetary carrier, which is a component used to support the planetary gears and allow them to rotate around the sun gear.

[0105] Its parameters include but are not limited to: the number of teeth, which is the number of teeth on the planetary gear, which determines the tooth profile shape and gear ratio of the gear, and has an important influence on the transmission ratio and meshing characteristics; the module, which is a measure of the gear size and is related to the size of the teeth; among them, the larger the module, the higher the gear tooth profile, the stronger the load-bearing capacity, and the larger the volume; the pressure angle, which is the angle of the tooth profile when the gears are meshing, which affects the contact stress and transmission efficiency of the gears; the mass of the gear, which is the weight of the gear, which affects the rotational inertia of the gear, and thus affects the dynamic response and balance of the gear; the Young's modulus of the gear, which is the elastic modulus of the material. For gear materials, the Young's modulus affects its deformation and stress distribution under load; the Poisson's ratio, which is the ratio of lateral contraction of a material when it is subjected to axial tension. For gear materials, the Poisson's ratio affects its dimensional stability under load.

[0106] The inner diameter in the bearing parameters is the diameter of the inner ring of the bearing, which determines the size of the shaft that the bearing can adapt to. The outer diameter is the diameter of the outer ring of the bearing, which determines the size requirements of the bearing installation space; the width is the width of the bearing, which affects the bearing's load-bearing capacity and installation space; the roller diameter is the diameter of the rolling element, which determines the bearing's load-bearing capacity and stiffness; the stiffness is the degree of deformation of the bearing when it is loaded, which determines the bearing's ability to resist deformation; the damping is the friction and energy dissipation characteristics inside the bearing; the clearance is the gap between the rolling element and the inner and outer rings inside the bearing, which affects the running smoothness, noise level and life of the bearing; the Young's modulus is the elastic modulus of the bearing, which affects the deformation and stress distribution of the bearing under load.

[0107] Step S2: Based on the bearing parameters, the time-varying nonlinear support stiffness of the bearing is calculated.

[0108] Specifically, the bearing support stiffness is a necessary parameter for simulating the dynamic characteristics of the system. The existing simulation system assumes the bearing stiffness to be a constant value, such as 1*10 8N / m, which ignores the nonlinear relationship that the bearing stiffness increases with the support load, resulting in inaccurate modeling and prediction of the dynamic characteristics of the multi-point support system of the planetary transmission mechanism. The inner ring of the intermediate bearing supports the shaft, and the outer ring supports the planetary carrier. The inner and outer rings rotate at the same time and bear loads or deformations at the same time, resulting in the bearing's support stiffness for the shaft and the planetary carrier being nonlinear (the greater the load or deformation, the greater the stiffness) and time-varying (the rollers revolve, causing the stiffness to change with time). By integrating the calculated time-varying support stiffness parameters when both the inner and outer rings of the bearing are deformed into the bending-torsion coupling excitation dynamics model of the planetary transmission mechanism, the dynamic characteristics of the system can be more accurately predicted.

[0109] like Figure 3 As shown in the figure, when the bearing is working under load, the generalized deflection displacement of the inner and outer rings in the X, Y and Z directions causes the inner and outer rings to roll to the groove curvature center to change, from which the relative distance A of the groove curvature center before the inner and outer raceways deflect can be obtained. 0 :

[0110] A 0 =(R iw +r iw )-(R ow +r ow ) (1)

[0111] Among them, R iw Indicates the minimum distance from the inner ring groove to the bearing center axis before deflection; R ow Indicates the maximum distance from the outer ring groove to the bearing center axis before deflection; r iw Indicates the radius of curvature of the inner groove; r ow Indicates the radius of curvature of the outer ring groove.

[0112] The relative distance A between the center of curvature of the groove after the inner and outer raceways of the jth roller are deflected j The calculation formula is as follows:

[0113]

[0114] Among them, δ jr and δ jz They represent the relative distances of the inner and outer ring groove curvature centers along the radial and axial directions at the jth roller after deflection, respectively. The calculation formula is as follows:

[0115]

[0116] Among them, δ ix and δ ox Respectively represent the deflection displacement of the inner ring and the outer ring along the X-axis direction; δ iy and δ oy Respectively represent the deflection displacement of the inner ring and the outer ring along the Y axis; δ iz and δ ozRespectively represent the deflection displacement of the inner ring and the outer ring along the Z-axis (i.e. axial direction); φ j represents the azimuth angle of the jth roller relative to the X-axis; r L is the radial clearance of the bearing.

[0117] Further, such as Figure 4 As shown, taking into account the time-varying position distribution of the rolling elements of the rolling bearing and the overall radial deflection displacement of the bearing under load, the following formula is used to calculate the time-varying nonlinear support stiffness of the bearing in the X and Y directions according to the Hertz contact theory:

[0118]

[0119] Among them, K s It represents the normal comprehensive contact stiffness between the inner roller and the inner and outer rings of the bearing; n represents the contact factor, which is set to 10 / 9 for line contact and 3 / 2 for point contact; N represents the total number of rollers in the bearing; A 0 Indicates the relative distance between the center of curvature of the inner and outer raceways of the bearing before deflection; A j It indicates the relative distance between the center of curvature of the groove after the inner and outer raceways of the jth roller in the bearing are deflected; represents the azimuth angle of the jth roller in the bearing at time t; δ jr It indicates the relative distance along the radial direction between the centers of curvature of the inner and outer ring grooves at the jth roller in the bearing after deflection.

[0120] Step S3, based on the time-varying nonlinear support stiffness of the bearing and the parameters of each of the planetary gear components, establish a subsystem dynamic model of the planetary speed change mechanism; wherein the planetary speed change mechanism subsystem includes an input shaft subsystem, a dual planetary gear subsystem, an output end transmission shaft subsystem and a compound gear subsystem.

[0121] Specifically, according to the structure and dynamic relationship of the planetary speed mechanism, a bending-torsion swing model of the planetary speed mechanism transmission shaft and a bending-torsion model of the planetary gear train are established, and the planetary row and the transmission shaft are coupled through the nonlinear time-varying support stiffness of the multi-point support bearing to predict the dynamic response of each component of the planetary speed mechanism system.

[0122] The planetary speed change mechanism includes four subsystems, namely, an input shaft, a double planetary gear, an output end transmission shaft and a compound gear; wherein, there are five multi-point support bearings between the input shaft and the double planetary gear, and there are three multi-point support bearings between the output end transmission shaft and the compound gear; dynamic models of the four subsystems, namely, the input shaft, the double planetary gear, the output end transmission shaft and the compound gear, are established respectively, and the coupling of different system dynamic models is realized by the nonlinear time-varying support stiffness of the multi-point support bearings under different inner and outer ring deflection displacements obtained in step S2.

[0123] Further, such as Figure 5As shown, in the input shaft subsystem of the planetary speed change mechanism, the B1 support bearing 1 is located at the input end; the outer rings of the B2 intermediate bearing 2 and the B3 intermediate bearing 3 support the planetary carrier of the first row of planetary gear trains; the outer rings of the B4 intermediate bearing 4 and the B5 intermediate bearing 5 support the planetary carrier of the second row of planetary gear trains; the input shaft is the sun gear shaft, which meshes with the two rows of planetary gear trains, and its meshing force generates meshing force components and torque in the X and Y directions on the input shaft.

[0124] Specifically, the support bearing is used to support the rotating shaft, bear radial loads, maintain the stable operation of the shaft, and reduce vibration and wear caused by the load. The planet carrier is a component that supports the planetary gears and allows them to rotate around the sun gear. The intermediate bearing is used to transmit power and support the planet carrier to ensure that the planetary gear system can operate smoothly. The input shaft is also called the sun gear shaft, which meshes with the planetary gears of the two rows of planetary gear systems. In the planetary gear system, the sun gear is the central gear that meshes with the planetary gears and transmits power through this meshing. When the input shaft (sun gear shaft) meshes with the planetary gears, a meshing force is generated. This force not only has a component in the axial direction (along the direction of the input shaft), but also has a component in the X and Y directions (i.e., the lateral direction). These components will affect the input shaft, causing the shaft to displace or vibrate in these directions. At the same time, the meshing force will also generate torque, affecting the rotational motion of the input shaft. Each bearing on the input shaft will also generate support force and bending moment in the X and Y directions for the input shaft. At the same time, the dynamic unbalanced force and torque generated by the CH operating member cylinder due to mass eccentricity and deflection also act on the input shaft.

[0125] Furthermore, the dynamic equation of the input shaft subsystem is a 5-DOF dynamic equation of bending-torsion-pendulum coupling excitation. According to Newton's second law, the 5-DOF dynamic equation of the input shaft subsystem of bending-torsion-pendulum coupling excitation is constructed using the following formula:

[0126]

[0127] Among them, q si =[x si ,y si ,θ xsi ,θ ysi ,θ zsi ] represents the 5 degrees of freedom of the input axis; (f xi ,f yi ) represents the input load of the hydraulic torque converter at the front end of the planetary transmission mechanism to the input shaft in the X and Y directions; M θzi Indicates input torque; M si =diag([m si ,m si ,I xsi ,I ysi ,I zsi ]) represents the mass matrix of the sun gear shaft; They represent the support reaction forces of the B1 support bearing, B2 intermediate bearing, B3 intermediate bearing, B4 intermediate bearing and B5 intermediate bearing in the input shaft subsystem in the X and Y directions respectively; Respectively represent the projections of the meshing forces of the first row of planetary gear trains and the second row of planetary gear trains on the input shaft in the X and Y directions; It represents the projection of the dynamic unbalanced force caused by the mass eccentricity of the CH operating part on the input shaft in the X and Y directions; It represents the projection of the dynamic unbalanced moment caused by the mass eccentricity of the CH operating part on the input shaft in the X and Y directions; They represent the coupling force of the CH operating member on the input shaft in the X and Y directions and the torsion direction when combined; a b1 、a b2 、a b3 、a b4 and a b5 Respectively represent the distances from the five bearings to the center of mass of the input shaft; a p1 and a p2 Respectively represent the distances from the first planetary row and the second planetary row to the mass center of the input shaft; a i Indicates the distance between the input load and the center of mass of the shaft; a d1 Indicates the distance between the CH control and the axis mass center; and Respectively represent the torque of the first planetary gear train and the second planetary gear train on the input shaft.

[0128] The support reaction forces of B1 support bearing 1, B2 intermediate bearing 2, B3 intermediate bearing 3, B4 intermediate bearing 4 and B5 intermediate bearing 5 in the input shaft subsystem in the X and Y directions are calculated based on the time-varying nonlinear support stiffness of the bearings, the displacements of the first row planetary carrier, the second row planetary carrier and the sun gear shaft in the X and Y directions, and the distances from the center of mass of each bearing on the input shaft to the input shaft.

[0129] Specifically, the support reaction forces of B1 support bearing 1, B2 intermediate bearing 2, B3 intermediate bearing 3, B4 intermediate bearing 4 and B5 intermediate bearing 5 in the X direction are calculated using the following formula:

[0130]

[0131] in, x si They represent the displacements of the first row planet carrier, the second row planet carrier and the sun gear shaft in the X direction respectively; They represent the support stiffness of B1 support bearing 1, B2 intermediate bearing 2, B3 intermediate bearing 3, B4 intermediate bearing 4 and B5 intermediate bearing 5 in the X direction, respectively, and are calculated using formula (4); They respectively represent the support damping of B1 support bearing 1, B2 intermediate bearing 2, B3 intermediate bearing 3, B4 intermediate bearing 4 and B5 intermediate bearing 5 in the X direction. In this embodiment, the damping ratio is set to a constant value, and the exemplary value is 0.01-0.05.

[0132] Similarly, the support reaction forces of B1 support bearing 1, B2 intermediate bearing 2, B3 intermediate bearing 3, B4 intermediate bearing 4 and B5 intermediate bearing 5 in the Y direction are as follows:

[0133]

[0134] in, y si They represent the displacements of the first row planet carrier, the second row planet carrier and the sun gear axis in the Y direction respectively; They represent the support stiffness of B1 support bearing 1, B2 intermediate bearing 2, B3 intermediate bearing 3, B4 intermediate bearing 4 and B5 intermediate bearing 5 in the Y direction, respectively, and are calculated using formula (4); They respectively represent the support damping of B1 support bearing 1, B2 intermediate bearing 2, B3 intermediate bearing 3, B4 intermediate bearing 4 and B5 intermediate bearing 5 in the Y direction. In this embodiment, the damping ratio is set to a constant value, and the exemplary value is 0.01-0.05.

[0135] When the CH operating member 14 is combined, the coupling force between the first row planet carrier and the sun gear shaft is calculated using the following formula:

[0136]

[0137] in, represents the coupling stiffness vector of the CH operating member 14; represents the coupling damping vector of the CH operating member 14; Represents the displacement vector of the first row of planet carriers.

[0138] When the CH operating member 14 is disengaged, K CH =0, C CH =0.

[0139] Specifically, Figure 6 As shown, the projection of the meshing force of the first row of planetary gears on the input shaft in the X and Y directions and the torque are calculated using the following formula:

[0140]

[0141] Among them, R s Indicates the base circle radius of the sun gear; represents the angular position of the meshing line between the kth planetary gear of the first row of planetary gears and the sun gear from the X axis; is the dynamic load between the sun gear and the kth planet gear of the first row of planetary gears.

[0142] On the other hand, Figure 7 As shown, the projection of the meshing force of the second row of planetary gears on the input shaft in the X and Y directions and the torque are calculated using the following formula:

[0143]

[0144] in, represents the angular position of the meshing line between the kth planetary gear of the second row of planetary gears and the sun gear from the X axis; is the dynamic load between the sun gear and the kth planet gear of the first row of planetary gears.

[0145] It should be noted that the angular position of the meshing line between the kth planetary gear of the first row / second row planetary gear train and the sun gear from the X-axis is calculated as follows: Among them, φ k represents the position angle of the kth planetary gear, α sp is the pressure angle of the sun gear-planet gear meshing;

[0146] The dynamic load between the sun gear and the kth planet gear of the first / second planet gear train is calculated using the following formula:

[0147]

[0148] δ spk =(x si -x pk )cosψ spk +(y si -y pk )sinψ spk +(R s θ zsi +R p θ zpk )-r cpk θ zc cosα sp -e spk

[0149] Among them, δ spk represents the relative displacement between the sun gear and the kth planet gear; b spk represents the tooth side clearance between the sun gear and the kth planet gear; x pk ,y pk ,θ zpk Respectively represent the displacement of the kth planetary gear along the X direction, Y direction and torsion direction; θ zc Represents the displacement of the planet carrier in the torsion direction; r cpkrepresents the distance from the center of the kth planetary gear to the center of the sun gear; e spk It represents the transmission error between the sun gear and the kth planetary gear along the meshing line. Its value is related to the gear tooth profile error, modification and other parameters. spk and c spk represent the meshing stiffness and meshing damping between the sun gear and the kth planetary gear respectively.

[0150] It should be noted that the meshing stiffness between the sun gear and each planetary gear can be considered to be the same in size and amplitude, but there is a phase difference. Therefore, the meshing stiffness of the gear pair is calculated according to the energy method.

[0151] Use the following formula to calculate the meshing damping between the sun gear and each planet gear:

[0152]

[0153] Wherein, ζ represents the meshing damping rate, which is a constant value and is set to 0.07 in this embodiment; m si and m pk They represent the masses of the sun gear shaft and the kth planet gear respectively.

[0154] Further, such as Figure 8 As shown, the dynamic model of the first and second row coupling system at the input end of the planetary transmission mechanism is established. In the double planetary gear subsystem of the planetary transmission mechanism, the planet carrier of the first row planetary gear system is connected to the inner gear ring of the second row planetary gear system, the power is input by the sun gear shaft, and the planet carrier of the second row planetary gear system outputs.

[0155] For the planet carrier of the first row of planetary gear systems, which supports the planetary gears of the first row of planetary gear systems, a three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed.

[0156] Specifically, the planet carrier is the central component of the planetary gear system, supporting the planetary gears and allowing them to rotate around the central sun gear. The planetary gears mesh with the sun gear through their outer edges and are connected to the planet carrier through their inner edges. This design allows the planetary gears to transfer power between the sun gear and the planet carrier.

[0157] It should be noted that when the CR clutch 15 is engaged (i.e., the planetary carrier is locked so that it cannot rotate), the CH operating member 14 and the CL clutch 16 are disengaged (i.e., the power of the input shaft will not be transmitted to the planetary carrier and the brake does not apply additional locking), the planetary carrier is connected to the planetary speed change mechanism housing. At this time, since the planetary carrier is locked, the rotation of the input shaft will cause the planetary gear train to rotate in the opposite direction, and the transmission ratio of the planetary speed change mechanism is negative (i.e., reverse gear); when the CH operating member 14 is engaged (i.e., the power of the input shaft is allowed to be transmitted to the planetary carrier), the CR clutch 15 and the CL clutch 16 are disengaged (i.e., the CR clutch 15 does not lock the planetary carrier and does not apply additional locking), the planetary carrier is connected to the input shaft, and the rotation of the input shaft is directly transmitted to the planetary carrier without increasing or decreasing the speed. At this time, the transmission ratio of the two rows of planetary gear trains on the right end of the planetary speed change mechanism is 1:1 (i.e., forward high gear).

[0158] Furthermore, according to Newton's second law, the following formula is used to construct the three-degree-of-freedom dynamic equation of the bending-torsion coupling excitation of the planet carrier of the first row of planetary gear system:

[0159]

[0160] in, Represents the three degrees of freedom of the bending-torsion coupling excitation of the planet carrier of the first row of planetary gear systems; represents the mass matrix of the first row of planet carriers; Respectively represent the support reaction forces of the B2 intermediate bearing and the B3 intermediate bearing in the X and Y directions; represents the bearing support force between the first row of planet carriers and the hth planetary gear in the X and Y directions; R c1 Indicates the distance from the center of the planetary gear to the center of the first row of planetary carriers; Indicates the positioning angle of the hth planet gear in the first row of planet carriers; They respectively represent the coupling forces of the CH operating member on the input shaft in the X and Y directions and the torsional direction when combined; It represents the coupling force vector between the first row planet carrier and the planetary speed change mechanism when the CR clutch is engaged.

[0161] Furthermore, the bearing support force of the first row of planetary carriers and each planetary gear in the X and Y directions is calculated based on the displacement vectors of each planetary gear of the first row of planetary gear train, the displacement vector of the first row of planetary carriers, the time-varying nonlinear support stiffness of the first row of planetary gear bearings and the support damping of the first row of planetary gear bearings in the X and Y directions.

[0162] Specifically, the bearing support forces of the first row of planet carriers and each planetary gear in the X and Y directions are calculated using the following formula:

[0163]

[0164] in, represents the displacement vector of the hth planetary gear in the first row; They represent the support stiffness of the first row of planetary gear bearings in the X and Y directions, respectively, and are calculated using formula (4); They represent the support damping of the first row of planetary gear bearings in the X direction and the Y direction respectively.

[0165] Furthermore, the coupling force vector between the first row planetary carrier and the planetary speed change mechanism is calculated based on the displacement vector of the first row planetary carrier and the coupling stiffness vector and coupling damping vector of the CR clutch 15 when the CR clutch 15 is engaged; and is set to 0 when the CR clutch 15 is disengaged.

[0166] Specifically, the coupling force vector between the first row planet carrier and the planetary transmission mechanism when the CR clutch 15 is engaged is calculated using the following formula:

[0167]

[0168] in, represents the coupling stiffness vector of the CR clutch 15; represents the coupling damping vector of the CR clutch 15; Represents the displacement vector of the first row of planet carriers.

[0169] When CR clutch 15 is disengaged, K CR =0, C CR =0.

[0170] Furthermore, for the component consisting of the first row of inner gear rings and the second row of planetary carriers, which not only meshes with the first row of planetary gear sets but also supports the second row of planetary gear sets, a three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed.

[0171] Specifically, the component is engaged with the first row of planetary gear sets to transmit power, and at the same time supports the second row of planetary gear sets to provide rotational support for them.

[0172] Further, according to Newton's second law, the following equation is used to construct the dynamic equation of the component consisting of the first row of internal gear rings and the second row of planet carriers:

[0173]

[0174] in, F represents the three degrees of freedom of the bending-torsion coupling excitation of the components consisting of the first row of internal gear rings and the second row of planet carriers; rco ={f xrco ,f yrco ,M θzrco} Trepresents the output load vector of the components consisting of the first row of internal gear rings and the second row of planet carriers; The mass matrix representing the components of the first row of internal gear rings and the second row of planet carriers; represents the bearing support force between the second row planet carrier and the hth planet gear in the X and Y directions; R c2 Indicates the distance from the center of the second row of planetary gears to the center of the planet carrier; Indicates the base circle radius of the first row of internal gear rings; represents the position angle of the hth planetary gear in the second row; represents the dynamic load between the first row of internal gear rings and the hth planetary gear; Respectively represent the support reaction forces of the B4 intermediate bearing, the B5 intermediate bearing and the B6 support bearing in the X and Y directions; It represents the angular position of the meshing line between the hth planetary gear in the first row and the first row of internal gear ring from the X-axis.

[0175] Furthermore, the bearing support forces of the second row planet carrier and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear of the second row planetary gear system, the displacement vector of the second row planet carrier, the time-varying nonlinear support stiffness of the second row planetary gear bearings and the support damping of the second row planetary gear bearings in the X and Y directions.

[0176] Specifically, the bearing support forces of the second row of planet carriers and each planetary gear in the X and Y directions are calculated using the following formula:

[0177]

[0178] in, represents the displacement vector of the hth planetary gear in the second row; They represent the support stiffness of the second row planetary gear bearing in the X direction and the Y direction, respectively, and are calculated using formula (4); They represent the support damping of the second row planetary gear bearings in the x direction and the y direction respectively.

[0179] Furthermore, the dynamic load between the first row of inner gear rings and each planetary gear is calculated based on the relative displacement of the meshing between the first row of inner gear rings and each planetary gear, the tooth side clearance between the first row of inner gear rings and each planetary gear, the displacement vector of the first row of inner gear rings, the angular position of the meshing line of each planetary gear and the first row of inner gear rings from the X-axis, the distance from the center of each planetary gear to the center of the first row of inner gear rings, the base circle radius of the first row of inner gear rings, and the meshing stiffness and meshing damping between the first row of inner gear rings and each planetary gear.

[0180] Specifically, the dynamic load F between the inner ring and the hth planetary gear is calculated using the following formula: rph :

[0181]

[0182] Among them, δ rph represents the relative displacement between the inner gear ring and the hth planetary gear; b rph represents the tooth side clearance between the inner ring gear and the hth planetary gear; x r ,y r ,θ zr Respectively represent the displacement of the inner gear ring along the X direction, Y direction and torsion direction; θ zc Indicates the displacement of the planet carrier in the torsion direction; α rp Indicates the pressure angle of the inner ring gear-planet gear meshing pair; ψ rph It is expressed as the angular position of the meshing line of the hth planetary gear and the inner gear ring from the X axis; r cph Represents the distance from the center of the hth planetary gear to the center of the inner gear ring; R r Indicates the base circle radius of the inner gear ring; e rph represents the transmission error between the inner gear ring and the hth planetary gear along the meshing line; k rph and c rph They represent the meshing stiffness and meshing damping between the hth planetary gear and the inner ring gear respectively.

[0183] It should be noted that the meshing stiffness between the inner ring gear and each planetary gear can be considered to be the same in size and amplitude, but there is a phase difference. The meshing stiffness of the gear pair can be calculated according to the energy method.

[0184] Use the following formula to calculate the meshing damping between the ring gear and each planet gear:

[0185]

[0186] Wherein, ζ represents the meshing damping rate, which is a constant value and is set to 0.07 in this embodiment; m r and m ph represent the masses of the inner ring gear and the hth planetary gear respectively.

[0187] Furthermore, for the first row of planetary gear sets, which mesh with the sun gear and the first row of inner gear rings at the same time, a three-degree-of-freedom dynamic equation of the bending-torsion coupling excitation of each planetary gear is constructed.

[0188] Specifically, the first row of planetary gears consists of multiple planetary gears, which mesh not only with the sun gear but also with the first row of inner gear rings. This double meshing relationship makes the planetary gear set affected by both the sun gear and the inner gear ring during the transmission process, thus exhibiting complex bending-torsion coupling behavior in dynamics.

[0189] Furthermore, the dynamic equations of each planetary gear of the first row of planetary gear sets are constructed using the following formula according to Newton's second law:

[0190]

[0191] in, It represents the three degrees of freedom of the bending-torsion coupling excitation of the hth planetary gear in the first row of planetary gear sets; represents the mass matrix of the hth planetary gear in the first row; and They represent the dynamic meshing forces between the first row sun gear and the hth planetary gear and between the first row internal gear and the hth planetary gear respectively; It represents the bearing support force between the first row of planet carriers and the hth planetary gear in the X and Y directions; Indicates the base circle radius of the first row of planetary gears.

[0192] The bearing support force of the first row of planet carriers and each planet gear in the X and Y directions It is calculated based on the displacement vectors of each planetary gear of the first row of planetary gear train, the displacement vector of the first row of planet carriers, the time-varying nonlinear support stiffness of the first row of planetary gear bearings, and the support damping of the first row of planetary gear bearings in the X and Y directions.

[0193] Specifically, the bearing support forces of the first row of planet carriers and each planetary gear in the X and Y directions are calculated using formula (14):

[0194] Dynamic meshing force between the first row sun gear and each planetary gear It is calculated based on the meshing relative displacement between the first row sun gear and each planetary gear, the tooth side clearance between the first row sun gear and each planetary gear, the displacement vector of the first row sun gear, the angular position of the meshing line of each planetary gear and the first row sun gear from the X-axis, the distance from the center of each planetary gear to the center of the first row sun gear, the base circle radius of the first row sun gear, and the meshing stiffness and meshing damping between the first row sun gear and each planetary gear.

[0195] Specifically, the dynamic meshing force between the first row of sun gears and each planetary gear is calculated using formula (11):

[0196] Furthermore, for the second row of inner gear rings, which mesh with the second row of planetary gear sets, a three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed.

[0197] Specifically, the inner gear ring is a circular ring with teeth inside, which mesh with the outer teeth of the planetary gears. The function of the second row of inner gear rings is to transmit torque and change the transmission ratio. At the same time, its motion state is affected by the meshing with the planetary gears.

[0198] It should be noted that when the CL clutch 16 is engaged (i.e., it will lock the second row of inner gear rings and prevent them from rotating), the CH operating member 14 and the CR clutch 15 are disengaged (i.e., the CH operating member 14 is disengaged, indicating that the power of the input shaft will not be transmitted to the planetary carrier or the sun gear, and the CR clutch 15 is disengaged, indicating that the first row of inner gear rings are not locked and can rotate freely), the second row of inner gear rings are connected to the planetary transmission mechanism housing. At this time, the transmission ratio of the two rows of planetary gear trains at the right end of the planetary transmission mechanism is 1:3.111 (i.e., forward low speed gear). In this case, the rotation of the input shaft is transmitted to the second row of inner gear rings through the first row of planetary gear trains. Since the second row of inner gear rings are locked, they rotate together with the housing, and the rotation speed of the housing is 1 / 3.111 times the speed of the input shaft, i.e., low speed gear, to provide greater torque output, which is suitable for situations requiring greater traction, such as climbing or starting acceleration.

[0199] Furthermore, the dynamic equation of the second row of internal gear rings is constructed using the following formula according to Newton's second law:

[0200]

[0201] in, Represents the 3 degrees of freedom of the bending-torsion coupling excitation of the second row of internal gear rings; represents the mass matrix of the second row of internal gear rings; represents the coupling force vector between the second row planet carrier and the planetary speed change mechanism when the CL clutch is engaged; represents the dynamic meshing force between the second row of internal gear rings and the hth planetary gear; Indicates the angular position of the meshing line between the hth planetary gear and the inner gear ring from the X axis; Indicates the base circle radius of the second row of internal gear rings.

[0202] Specifically, the dynamic meshing force between the second row of internal gear and the hth planetary gear is Calculated using formula (18).

[0203] The coupling force vector between the second row planet carrier and the planetary speed change mechanism when the CL clutch 16 is engaged is calculated using the following formula:

[0204]

[0205] Specifically, represents the coupling stiffness vector of the CL clutch 16; represents the coupling damping vector of the CL clutch 16 .

[0206] When the CL clutch 16 is disengaged, K CL =0, C CL =0.

[0207] Furthermore, for the second row of planetary gear sets, which mesh with the sun gear and the second row of inner gear ring at the same time, a three-degree-of-freedom dynamic equation of the bending-torsion coupling excitation of each planetary gear is constructed.

[0208] Specifically, the second row of planetary gears consists of multiple planetary gears, which are meshed not only with the sun gear but also with the second row of inner gear rings. This double meshing relationship makes the planetary gear set affected by both the sun gear and the inner gear ring during the transmission process, thus exhibiting complex bending-torsion coupling behavior in dynamics.

[0209] Furthermore, the dynamic equation of each planetary gear of the second row of planetary gear sets is constructed using the following formula according to Newton's second law:

[0210]

[0211] in, It represents the 3 degrees of freedom of the bending-torsion coupling excitation of the hth planetary gear of the second row of planetary gear sets; represents the mass matrix of the hth planetary gear in the second row; and They represent the dynamic meshing forces between the second row sun gear and the hth planetary gear and between the second row internal gear and the hth planetary gear respectively; represents the bearing support force between the second row planet carrier and the hth planet gear in the X and Y directions; Indicates the base circle radius of the second row of planetary gears.

[0212] The bearing support force of the second row planet carrier and each planet gear in the X and Y directions It is calculated based on the displacement vectors of the planetary gears of the second row of planetary gear train, the displacement vector of the second row of planet carriers, the time-varying nonlinear support stiffness of the second row of planetary gear bearings, and the support damping of the second row of planetary gear bearings in the X and Y directions.

[0213] Specifically, the bearing support forces of the second row of planet carriers and each planetary gear in the X and Y directions are calculated using formula (14):

[0214] Dynamic meshing force between the second row sun gear and each planetary gear It is calculated based on the meshing relative displacement between the second row sun gear and each planetary gear, the tooth side clearance between the second row sun gear and each planetary gear, the displacement vector of the second row sun gear, the angular position of the meshing line of each planetary gear and the second row sun gear from the X-axis, the distance from the center of each planetary gear to the center of the second row sun gear, the base circle radius of the second row sun gear, and the meshing stiffness and meshing damping between the second row sun gear and each planetary gear.

[0215] Specifically, the dynamic meshing force between the second row sun gear and each planetary gear is calculated using formula (11):

[0216] Further, such as Fig. 9 As shown, in the output end transmission shaft subsystem of the planetary speed change mechanism, a B10 support bearing is arranged on the output end transmission shaft, a B8 intermediate bearing supports the compound row input gear ring, a B9 intermediate bearing supports the compound row planet carrier, and the transmission shaft is the sun gear shaft, which meshes with the long planet gear of the compound row, and its meshing force generates meshing force components and torque in the X and Y directions on the transmission shaft.

[0217] Specifically, in the output end transmission shaft subsystem of the planetary speed change mechanism, the B10 support bearing is used to support the transmission shaft, bear the radial and axial loads from the transmission shaft, and maintain the stability and accuracy of the transmission shaft; the B8 intermediate bearing and the B9 intermediate bearing are used to transmit loads and support the planetary gear system to ensure that the planetary gear system can operate smoothly; the compound row input ring gear is a component in the planetary gear system, which is meshed with the planetary gear and participates in power transmission; the compound row planetary carrier is a component that supports the planetary gear and allows them to rotate around the sun gear; the sun gear shaft is meshed with the planetary gear, and power is transmitted through this meshing. When the sun gear shaft meshes with the long planetary gear of the compound row, a meshing force is generated. This force has components not only in the axial direction (along the direction of the transmission shaft), but also in the X and Y directions (i.e., lateral directions). These components will affect the transmission shaft, causing the shaft to be displaced or vibrated in these directions. At the same time, the meshing force will also generate torque, affecting the rotational motion of the transmission shaft. This torque is the key to the transmission of power by the transmission shaft and determines the output speed and torque of the transmission shaft.

[0218] It should be noted that the dynamic unbalanced force and torque generated by the C2 operating member 18 and the C3 operating member 19 due to mass eccentricity and deflection also act on the transmission shaft.

[0219] Furthermore, the dynamic equation of the output-end transmission shaft subsystem is a 5-degree-of-freedom dynamic equation of bending-torsion-pendulum coupling excitation. The 5-degree-of-freedom dynamic equation of the output-end transmission shaft subsystem of bending-torsion-pendulum coupling excitation is constructed using the following formula according to Newton's second law:

[0220]

[0221] Among them, q so =[x so ,y so ,θ xso ,θ yso ,θ zso ] represents the 5 degrees of freedom of the output transmission shaft; M so =diag([m so ,m so,I xso ,I yso ,I zso ]) represents the mass matrix of the output transmission shaft; F o ={f xo ,f yo ,M θzo} T Represents the external load vector on the output transmission shaft; Respectively represent the support reaction forces of the B8 intermediate bearing, the B9 intermediate bearing and the B10 support bearing in the X and Y directions; It indicates the projection of the dynamic unbalanced force caused by the mass eccentricity of the C2 and C3 operating parts on the output end transmission shaft in the X and Y directions; It indicates the projection of the dynamic unbalanced moment caused by the mass eccentricity of the C2 and C3 operating parts on the output end transmission shaft in the X and Y directions; They respectively represent the coupling force of the C2 operating member / C3 operating member on the output end transmission shaft in the X and Y directions and the torsional direction when the operating member is combined; a b8 、a b9 and a b10 Respectively represent the distances from the B8 intermediate bearing, B9 intermediate bearing and B10 support bearing to the mass center of the output end transmission shaft; a p3 represents the distance from the compound row to the center of mass of the transmission shaft, a d3 Indicates the distance between the C2 control member and the C3 control member and the center of mass of the shaft; It represents the projection of the meshing force of the compound row on the sun gear of the output transmission shaft in the X and Y directions; Indicates the torque of the compound row on the sun gear of the output drive shaft; a o Indicates the distance between the input load and the center of mass of the output drive shaft.

[0222] The support reaction forces of the B8 intermediate bearing, the B9 intermediate bearing and the B10 support bearing in the output end transmission shaft subsystem in the X and Y directions are calculated based on the time-varying nonlinear support stiffness of the bearings, the displacements of the composite planetary carrier and the output end transmission shaft in the X and Y directions, and the distances from the center of mass of each bearing on the output end transmission shaft to the input shaft.

[0223] Specifically, the following formula is used to calculate the support reaction forces of the B8 intermediate bearing, the B9 intermediate bearing and the B10 support bearing in the X direction and the Y direction:

[0224]

[0225] in, x so ,y so represent the displacements of the composite planet carrier and the transmission shaft in the X and Y directions, respectively; They represent the support stiffness of B8 intermediate bearing 8, B9 intermediate bearing 9 and B10 support bearing 10 in the X direction and Y direction respectively, calculated using formula (4); They represent the support damping of the B8 intermediate bearing 8, the B9 intermediate bearing 9 and the B10 support bearing 10 in the X direction and the Y direction respectively. In this embodiment, a constant damping ratio is set, and an exemplary value is 0.01-0.05.

[0226] It should be noted that, in the output end transmission shaft subsystem, when the C2 operating member 18 is engaged (i.e., the relative movement between the sun gear shaft and the planetary transmission mechanism housing is locked so that they can rotate synchronously), the C3 operating member 19 and the C1 clutch 17 are separated, the sun gear shaft is connected to the planetary transmission mechanism housing, and the compound row transmission ratio of the left end of the planetary transmission mechanism is 1:1.442, indicating that the rotation speed of the sun gear shaft is 1.442 times the rotation speed of the housing, which is used for specific driving conditions; when the C3 operating member 19 is engaged (i.e., the relative movement between the sun gear shaft and the compound row planet carrier is locked so that they can rotate synchronously), the C2 operating member 18 and the C1 clutch 17 are separated, the sun gear shaft is connected to the compound row planet carrier, and the compound row transmission ratio of the left end of the planetary transmission mechanism is 1:1, indicating that the rotation speed of the sun gear shaft is the same as the rotation speed of the compound row planet carrier, which is used for high-speed driving.

[0227] When the C2 operating member 18 is engaged, the coupling force of the output drive shaft in the X and Y directions and the torsional direction is calculated using the following formula:

[0228]

[0229] in, represents the coupling stiffness vector of the C2 control member 18; Represents the coupled damping vector of the C2 actuator 18.

[0230] When the C3 operating member 19 is engaged, the coupling force vector of the output drive shaft in the X and Y directions and the torsional direction is calculated using the following formula:

[0231]

[0232] in, represents the coupling stiffness vector of the C3 control member 19; represents the coupling damping vector of the C3 operating member 19; Represents the displacement vector of the compound planet carrier.

[0233] Specifically, the projection of the meshing force of the composite row on the transmission shaft sun gear in the X and Y directions and the torque are calculated using the following formula:

[0234]

[0235] in, represents the base circle radius of the compound sun gear; ψ slpu Indicates Fig.10 The angular position of the meshing line between the u-th long planetary gear of the composite row and the sun gear from the X-axis is calculated as follows: in, Represents the position angle of the u-th long planet gear in the compound row; α slp Indicates the pressure angle of the sun gear-long planet gear meshing; F slpu It represents the dynamic load between the sun gear and the u-th long planet gear, and its calculation formula is:

[0236]

[0237] Among them, δ slpu represents the relative displacement between the composite sun gear and the uth long planet gear; b slpu represents the tooth side clearance between the sun gear and the uth planet gear; x lpu ,y lpu ,θ zlpu represents the displacement of the u-th long planetary gear along the X direction, Y direction and torsion direction; r clpu Indicates the distance from the center of the u-th long planet gear to the center of the sun gear; R s Indicates the base circle radius of the compound sun gear; R lp Indicates the radius of the long planetary gear base circle; e slpu It represents the transmission error between the sun gear and the u-th long planet gear along the meshing line. This value is related to the gear tooth profile error, modification and other parameters; k slpu and c slpu They respectively represent the meshing stiffness and meshing damping between the compound row sun gear and the u-th long planet gear.

[0238] It should be noted that the meshing stiffness between the sun gear and each long planet gear can be considered to be the same in size and amplitude, but there is a phase difference. Therefore, the meshing stiffness of the gear pair is calculated according to the energy method.

[0239] Calculate the meshing damping between the sun gear and each long planet gear using the following formula:

[0240]

[0241] Wherein, ζ is the meshing damping rate, which is a constant value and is set to 0.07 in this embodiment; m so and m lpu They represent the masses of the sun gear shaft and the u-th long planet gear respectively.

[0242] Further, such as Fig.10As shown, in the compound row subsystem of the planetary speed change mechanism, the planet carrier includes a long planetary gear set and a short planetary gear set; wherein the long planetary gear set meshes with the sun gear and the input gear ring to form a row of planetary gear transmission; the short planetary gear set meshes with the long planetary gear set and the floating support ring to form another row of planetary gear transmission; the two rows of planetary gear transmissions form a compact compound planetary gear transmission through the meshing between the long planetary gear set and the short planetary gear set; power is input from the compound row input gear ring and output from the compound row planet carrier.

[0243] Specifically, the compound gear is a Ravigneaux planetary gear mechanism.

[0244] Furthermore, for the planetary carrier of the compound planetary gear system, which supports both the long planetary gear set and the short planetary gear set, a three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed.

[0245] Specifically, the planet carrier of the compound planetary gear system supports all the planetary gears. The planet carrier can rotate around the input shaft or the output shaft, and its movement is affected by the input load and the meshing of the planetary gears.

[0246] Furthermore, the dynamic equation of the planet carrier of the compound planetary gear system is constructed using the following formula according to Newton's second law:

[0247]

[0248] Among them, q Represents the three degrees of freedom of the bending-torsion coupling excitation of the planet carrier of the compound planetary gear system; Represents the mass matrix of the planet carrier of the compound planetary gear system; Respectively represent the support reaction forces of the B7 intermediate bearing, the B8 intermediate bearing and the B9 intermediate bearing in the X and Y directions; It represents the bearing support force of the composite planet carrier and the u-th short planet gear in the X direction and the Y direction; It represents the bearing support force of the composite planet carrier and the u-th long planet gear in the X direction and the Y direction; It represents the coupling force between the planet carrier of the compound planetary gear system and the transmission mechanism case in the X and Y directions and the torsion direction when the C2 operating member / C3 operating member are combined; r c Indicates the distance from the center of the short planetary gear to the center of the planetary carrier; r lc Indicates the distance from the center of the long planet gear to the center of the planet carrier; represents the positioning angle of the uth short planetary gear; Represents the u-th long planet gear positioning angle.

[0249] Furthermore, the bearing support forces of the composite planetary carrier and each short planetary gear in the X and Y directions are calculated based on the displacement vectors of each short planetary gear in the composite row, the support stiffness of the short planetary gear bearings in the X and Y directions, the support damping of the short planetary gear bearings in the X and Y directions, the distance from the center of the short planetary gear to the center of the planetary carrier, and the positioning angles of each short planetary gear.

[0250] Specifically, the bearing support forces of the composite planetary carrier and each short planetary gear in the X direction and the Y direction are calculated using the following formula:

[0251]

[0252] in, represents the displacement vector of the u-th short planet gear in the composite row; They represent the support stiffness of the short planetary gear bearing in the X and Y directions, respectively, and are calculated using formula (4); Respectively represent the support damping of the short planetary gear bearing in the x direction and the y direction; r c Indicates the distance from the center of the short planetary gear to the center of the planet carrier; Represents the positioning angle of the uth short planet gear.

[0253] Furthermore, the bearing support forces of the composite planet carrier and each long planet wheel in the X direction and the Y direction are calculated based on the displacement vector of each long planet wheel of the composite row, the support stiffness of the long planet wheel bearing in the X direction and the Y direction, the support damping of the long planet wheel bearing in the X direction and the Y direction, the distance from the center of the long planet wheel to the center of the planet carrier, and the positioning angle of each long planet wheel.

[0254] Specifically, the bearing support forces of the composite planetary carrier and each long planetary gear in the X direction and the Y direction are calculated using the following formula:

[0255]

[0256] in, represents the displacement vector of the u-th long planet gear in the composite row; They represent the support stiffness of the long planetary wheel bearing in the X direction and the Y direction, respectively, and are calculated using formula (4); Respectively represent the support damping of the long planetary wheel bearing in the x direction and the y direction; r lc Indicates the distance from the center of the long planet gear to the center of the planet carrier; Represents the u-th long planet gear positioning angle.

[0257] Furthermore, the support reaction force of the B7 intermediate bearing in the planetary carrier of the compound planetary gear system in the X and Y directions is calculated based on the time-varying nonlinear support stiffness of the bearing, the displacement of the compound input gear ring in the X and Y directions, and the support damping of the bearing in the X and Y directions.

[0258] Specifically, the support reaction force of the B7 intermediate bearing 7 in the planetary carrier of the composite planetary gear system in the X and Y directions is calculated using the following formula:

[0259]

[0260] in, Respectively represent the displacement of the compound row input gear ring in the X direction and the Y direction; They represent the support stiffness of the intermediate bearing 7 of B7 in the X direction and the Y direction, respectively, and are calculated using formula (4); They represent the support damping of B7 intermediate bearing 7 in the X direction and Y direction respectively.

[0261] When the C2 operating member 18 is engaged, the coupling force vector between the composite planetary carrier and the transmission case is calculated using the following formula:

[0262]

[0263] in, represents the coupling stiffness vector of the C2 control member 18; Represents the coupled damping vector of the C2 actuator 18.

[0264] When the C3 operating member 19 is engaged, the coupling force vector between the composite planetary carrier and the transmission shaft is calculated using the following formula:

[0265]

[0266] in, represents the coupling stiffness vector of the C3 control member 19; represents the coupling damping vector of the C3 operating member 19; Represents the displacement vector of the compound transmission shaft of the transmission mechanism.

[0267] When the C2 operating member 18 is disengaged, K C2 =0, C C2 = 0 when C3 operating member 19 is disengaged K C3 =0, C C3 =0.

[0268] Furthermore, for the compound row input ring gear, it is coupled with the second row planetary gear system planet carrier of the planetary speed change mechanism and meshed with the compound row long planetary gear set, and the three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed.

[0269] Specifically, the movement of the compound row input ring gear is affected by the connection with the planet carrier and the meshing with the long planet gear, and its dynamic equation needs to consider the support force from the connection with the planet carrier and the meshing with the long planet gear, as well as the torque generated by the meshing.

[0270] Furthermore, according to Newton's second law, the dynamic equation of the compound row input gear ring is constructed using the following formula:

[0271]

[0272] in, F represents the three degrees of freedom of the bending-torsion coupling excitation of the compound row input gear ring; ro ={f xro ,f yro ,M θzro} T represents the input load vector of the compound row input ring gear; F represents the mass matrix of the compound row input gear ring; rlpu represents the dynamic load of the u-th long planetary gear in the compound row and the input ring gear; ψ rpu Indicates the angular position of the meshing line between the u-th short planet gear in the compound row and the sun gear from the X axis; Indicates the base circle radius of the compound row input gear ring.

[0273] The dynamic load of each long planetary gear of the compound row and the input ring gear is calculated based on the tooth side clearance between the inner ring gear and the corresponding long planetary gear, the displacement vector of the long planetary gear corresponding to the compound row, the angular position of the meshing line of the corresponding long planetary gear and the input ring gear from the X-axis, the base circle radius of the input ring gear, the displacement of the input ring gear in the X-direction, the Y-direction and the torsional direction, and the displacement of the planet carrier in the torsional direction.

[0274] Specifically, the following formula is used to calculate the dynamic load of each long planetary gear and the input ring gear of the compound row:

[0275]

[0276] in, Represents the coupling stiffness vector between the components consisting of the first row of internal gear rings and the second row of planet carriers at the input end of the planetary transmission mechanism and the composite row of input gear rings at the output end; It represents the coupling damping vector between the components consisting of the first row of internal gear rings and the second row of planet carriers at the input end of the planetary transmission mechanism and the compound row of input gear rings at the output end.

[0277] Use the following formula to calculate the dynamic load F between the uth long planet gear in the compound row and the input ring gear: rlpu :

[0278]

[0279] Among them, δ rlpu represents the relative displacement between the compound row input gear ring and the uth long planetary gear; b rlpu represents the tooth side clearance between the inner gear ring and the u-th long planet gear; x r ,y r ,θzr Represents the displacement of the input gear ring along the X direction, Y direction and torsion direction; θ zc Indicates the displacement of the planet carrier in the torsion direction; α rlp Indicates the pressure angle of the meshing pair between the input ring gear and the long planet gear; ψ rlpu represents the angular position of the meshing line between the uth long planetary gear and the input ring gear from the X axis; r clpu Represents the distance from the center of the u-th long planetary gear to the center of the input ring gear; R r Indicates the input gear ring base circle radius; e rlpu represents the transmission error between the input ring gear and the uth long planetary gear along the meshing line; k rlpu 、c rlpu represent the meshing stiffness and meshing damping between the input ring gear and the u-th long planet gear respectively.

[0280] It should be noted that the meshing stiffness between the input ring gear and each long planet gear can be considered to be the same in size and amplitude, but there is a phase difference. Therefore, the meshing stiffness of the gear pair can be calculated according to the energy method.

[0281] Calculate the meshing damping between the input ring gear and each long planet gear using the following formula:

[0282]

[0283] Wherein, ζ represents the meshing damping rate, which is a constant value and is set to 0.07 in this embodiment; m r and m lpu They represent the masses of the input ring gear and the u-th long planet gear respectively.

[0284] Furthermore, for the composite long planetary gear set, which is meshed with the input ring gear, the sun gear and the short planetary gear set at the same time, the three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed.

[0285] Specifically, the compound long planetary gear set meshes with the input ring gear, so that the input ring gear transmits power to the long planetary gears; the compound long planetary gears mesh with the sun gear, so that the sun gear can affect the rotation speed and direction of the long planetary gears; the long planetary gear set meshes with the short planetary gear set, forming the second stage transmission of the compound planetary gear system.

[0286] Further, according to Newton's second law, the dynamic equation of the composite long-row planetary gear set is constructed using the following formula:

[0287]

[0288] in, represents the three degrees of freedom of the bending-torsion coupling excitation of the u-th long planetary gear in the composite row; represents the mass matrix of the u-th long planetary gear in the composite row; Fslpu represents the dynamic load of the u-th long planetary gear in the composite row and the sun gear shaft; F rlpu F represents the dynamic load of the u-th long planetary gear in the compound row and the input ring gear; lppu represents the dynamic load of the u-th long planetary gear and the u-th short planetary gear in the compound row; ψ slpu represents the angle between the meshing line of the u-th long planetary gear in the composite row and the sun gear shaft and the X-axis; ψ rlpu represents the angle between the meshing line of the u-th long planetary gear in the compound row and the input ring gear and the X-axis; ψ llpu Indicates the angular position of the meshing line between the u-th long planetary gear and the u-th short planetary gear in the compound row from the X-axis; Indicates the base radius of the composite long planet gear.

[0289] The dynamic load of the u-th long planet gear and the u-th short planet gear in the compound row is calculated based on the tooth side clearance between the u-th long planet gear and the u-th short planet gear, the displacement vector of the u-th long planet gear, the displacement vector of the u-th short planet gear, the angular position of the meshing line of the u-th long planet gear and the u-th short planet gear from the X-axis, and the base circle radius of the short planet gear.

[0290] Specifically, the dynamic load F of the u-th long planetary gear and the u-th short planetary gear in the compound row is calculated using the following formula: lppu :

[0291]

[0292] Among them, δ lppu represents the relative displacement between the u-th long planetary gear and the u-th short planetary gear; b lppu represents the tooth side clearance between the u-th long planet gear and the u-th short planet gear; x pu ,y pu ,θ zpu Respectively represent the displacement of the u-th short planetary gear along the X direction, Y direction and torsion direction; θ zc Indicates the displacement of the planet carrier in the torsion direction; α lppu represents the pressure angle of the u-th long planet gear-short planet gear meshing pair; represents the angular position of the meshing line between the uth long planet gear and the kth short planet gear from the X axis; r cpu Represents the distance from the center of the u-th short planetary gear to the center of the inner gear ring; R p e is the base circle radius of the short planet gear; lppu represents the transmission error between the u-th long planetary gear and the u-th short planetary gear along the meshing line; k lppu 、c lppu Respectively represent the meshing stiffness and meshing damping between each pair of long planetary gears and short planetary gears; γ p Indicates the positioning angle of the short planetary gear.

[0293] It should be noted that the meshing stiffness size and amplitude between each pair of long planetary gears and short planetary gears can be considered to be the same, but there is a phase difference. Therefore, the meshing stiffness of the gear pair can be calculated according to the energy method.

[0294] Calculate the meshing damping between each pair of long and short planet gears using the following formula:

[0295]

[0296] Wherein, ζ represents the meshing damping rate, which is a constant value and is set to 0.07 in this embodiment; m lpu , m pu They represent the masses of the u-th long planet gear and the u-th short planet gear respectively.

[0297] Furthermore, for the compound short planetary gear set, which is meshed with the long planetary gear set and the floating ring gear at the same time, the three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed.

[0298] Specifically, each short planetary gear in the compound short planetary gear set is meshed with the corresponding long planetary gear to transmit power between the planet carrier and the floating ring gear; the short planetary gear is meshed with the floating ring gear to transmit power between the floating ring gear and the short planetary gear. After the power is transmitted to the short planetary gear set through the long planetary gear set, it is transmitted to other parts of the system through the meshing of the short planetary gear and the floating ring gear, so that the compound planetary gear system can achieve a variety of transmission ratios and power distribution.

[0299] Further, according to Newton's second law, the dynamic equation of the composite short-row planetary gear set is constructed using the following formula:

[0300]

[0301] in, represents the three degrees of freedom of the bending-torsion coupling excitation of the u-th short planetary gear in the composite row; F represents the mass matrix of the u-th short planetary gear in the composite row; frpu represents the dynamic load between the composite floating ring gear and the uth short planetary gear; ψ frpu Indicates the angular position of the meshing line between the composite row floating ring gear and the uth short planetary gear from the X axis; Indicates the base radius of the compound row short planet gear.

[0302] Furthermore, the dynamic load between the compound row floating ring gear and the u-th short planetary gear is calculated based on the tooth side clearance between the compound row floating ring gear and each short planetary gear, the displacement vector of the floating ring gear, the displacement in the torsion direction of the planet carrier, the floating ring gear-short planetary gear meshing secondary pressure angle, the meshing stiffness and meshing damping between the floating ring gear and each short planetary gear, and the base circle radius of the floating ring gear.

[0303] Specifically, the dynamic load F between the composite floating ring gear and the uth short planetary gear is calculated using the following formula: frpu :

[0304]

[0305] Among them, δ frpu represents the relative displacement of the meshing between the composite floating gear ring and the uth short planetary gear; b frpu represents the tooth side clearance between the composite row floating ring gear and the uth short planetary gear; x fr ,y fr ,θ zfr Respectively represent the displacement of the floating gear ring along the X direction, Y direction and torsional direction; θ zc Indicates the displacement of the planet carrier in the torsion direction; α frp represents the meshing pressure angle of floating ring gear-short planet gear; ψ frpu represents the angular position of the meshing line between the floating ring gear and the uth short planetary gear from the X axis; r cpu Represents the distance from the center of the u-th short planetary gear to the center of the floating ring gear; R fr Indicates the base circle radius of the floating gear ring; e frpu represents the transmission error between the floating gear ring and the uth short planetary gear along the meshing line; k frpu and c frpu They represent the meshing stiffness and meshing damping between the composite row floating ring gear and the u-th short planetary gear respectively.

[0306] It should be noted that the meshing stiffness between the input ring gear and each short planetary gear can be considered to be the same in size and amplitude, but there is a phase difference. Therefore, the meshing stiffness of the gear pair can be calculated according to the energy method.

[0307] Use the following formula to calculate the mesh damping between the input ring gear and each short planet gear:

[0308]

[0309] Wherein, ζ is the meshing damping rate, which is a constant value and is set to 0.07 in this embodiment; m fr and m pu Represent the masses of the floating ring gear and the uth short planetary gear respectively

[0310] Furthermore, for the compound row floating ring gear, which is meshed with the compound row planetary gear set, a three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed.

[0311] Specifically, the floating ring gear is a peripheral gear in the compound planetary gear system, meshing with the long planet gear and the short planet gear in the planetary gear set, and is floating relative to the planet carrier, that is, its position can be adjusted to adapt to different load and speed conditions. The floating ring gear meshes with the short planet gear, and the short planet gear meshes with the long planet gear. This relationship enables the floating ring gear to receive power from the planetary gear set and output the power according to the configuration of the system.

[0312] Furthermore, according to Newton's second law, the dynamic equation of the composite row floating gear ring is constructed using the following formula:

[0313]

[0314] in, Represents the three degrees of freedom of bending-torsion coupling excitation of the composite row floating gear ring; Represents the mass matrix of the composite row floating gear ring; Represents the coupling force vector between the compound row floating ring gear and the transmission case when the C1 clutch is engaged.

[0315] The coupling force vector between the compound row floating ring gear and the transmission mechanism case when the C1 clutch is engaged is calculated based on the coupling stiffness vector and the coupling damping vector between the compound row floating ring gear and the transmission mechanism case.

[0316] Specifically, when the C1 clutch 17 is engaged, and the C3 operating member 19 and the C2 operating member 18 are disengaged, the compound row floating ring gear is connected to the planetary transmission mechanism housing, that is, the floating ring gear is locked, and the power is directly transmitted from the input ring gear to the planetary carrier through the long planetary gear and the short planetary gear. At this time, the transmission ratio of the compound row at the left end of the planetary transmission mechanism is 1:2.065.

[0317] Use the following formula to calculate the coupling force vector between the compound row floating gear ring and the transmission case when the C1 clutch is engaged.

[0318]

[0319] in, represents the coupling stiffness vector of the C1 clutch 17; represents the coupling damping vector of the C1 clutch 17 .

[0320] When the C1 clutch 17 is disengaged, K C1 =0, C C1 =0.

[0321] Step S4: within a given time step, when the inner and outer rings of the intermediate bearing rotate simultaneously, calculate the dynamic load f of the planet carrier / bearing seat on the outer ring of the bearing o and deformation δ o And the dynamic load f of the transmission shaft on the inner ring i and deformation δ i , and calculate the support stiffness and dynamic response of the system at the current moment, jointly establish the dynamic models of the subsystems of the planetary speed change mechanism, use the fourth-order Runge-Kutta numerical iterative algorithm to solve it, obtain the dynamic response of the planetary speed change mechanism in the next time step, and iterate until the dynamic characteristics estimation is completed.

[0322] Specifically, set the initial time t of the differential equation 0 The initial vibration displacement q of the system 0 and the initial vibration velocity of the system =0, estimate the static load on each support bearing according to the weight of each component, and use formula (4) in step S2 to obtain the initial support stiffness K of each bearing b0 The numerical integration step length Δt is set, and the dynamic model of each subsystem of the planetary transmission mechanism in step S3 is brought into the time-varying support stiffness of the bearing at the last iteration, and the dynamic response of the system at the current moment is calculated until the simulation cutoff moment is reached, so as to realize the simulation and prediction of the dynamic characteristics of the bending-torsion coupling excitation of the multi-point support components of the planetary transmission mechanism.

[0323] In summary, the method for estimating dynamic characteristics of multi-point support bending-torsion coupling excitation of a planetary speed change mechanism according to the embodiment of the present invention has the following beneficial effects:

[0324] 1. The present invention establishes a method for estimating the dynamic characteristics of a planetary speed change mechanism with multi-point support bending-torsion coupling excitation, which can simulate and analyze its motion characteristics and transmission performance and optimize the design to improve its working efficiency and transmission stability, thereby reducing the energy consumption and cost of the mechanical system.

[0325] 2. The method of the present invention can more accurately predict the dynamic characteristics of the planetary speed change mechanism by coupling the motion equations of multiple degrees of freedom of each component, while ensuring high calculation efficiency. At the same time, it takes into account the time-varying nonlinear support stiffness characteristics of the rolling bearing, making the model closer to the actual working state and improving the accuracy of the dynamic model.

[0326] 3. The present invention can predict the motion state and transmission characteristics of the mechanism under different working conditions by estimating the dynamic characteristics of the planetary speed change mechanism, thereby providing a reliable reference for the design and optimization of the mechanical system and improving the reliability and service life of the mechanical system.

[0327] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for estimating dynamic characteristics of multi-point support bending-torsion coupling excitation of a planetary speed change mechanism, characterized in that: The planetary speed change mechanism adopts a dual-rotor structure; the method comprises: Obtaining parameters of each planetary gear component and each bearing parameter of the planetary speed change mechanism; wherein the parameters of the planetary gear component include: number of teeth, module, pressure angle, mass, Young's modulus and Poisson's ratio; the bearing parameters include: inner diameter, outer diameter, width, roller diameter, stiffness, damping, clearance and Young's modulus; Based on the bearing parameters, the time-varying nonlinear support stiffness of the bearing is calculated; Based on the time-varying nonlinear support stiffness of the bearing and the parameters of each of the planetary gear components, a subsystem dynamic model of the planetary transmission mechanism is established; wherein the planetary transmission mechanism subsystem includes an input shaft subsystem, a double planetary gear subsystem, an output end transmission shaft subsystem and a compound gear subsystem; In a given time step, when the inner and outer rings of the intermediate bearing rotate simultaneously, calculate the dynamic load f of the planet carrier / bearing seat on the outer ring of the bearing o and deformation δ o And the dynamic load f of the transmission shaft on the inner ring i and deformation δ i , and calculate the support stiffness and dynamic response of the system at the current moment, jointly establish the dynamic models of the subsystems of the planetary speed change mechanism, use the fourth-order Runge-Kutta numerical iterative algorithm to solve it, obtain the dynamic response of the planetary speed change mechanism in the next time step, and iterate until the dynamic characteristics estimation is completed.

2. The method according to claim 1, characterized in that: The time-varying nonlinear support stiffness of the bearing is calculated using the following equation: Among them, K n It represents the normal comprehensive contact stiffness between the inner roller and the inner and outer rings of the bearing; n represents the contact factor; N represents the total number of rollers in the bearing; A0 represents the relative distance between the center of curvature of the groove before the inner and outer raceways of the bearing are deflected; A j It indicates the relative distance between the center of curvature of the groove after the inner and outer raceways of the jth roller in the bearing are deflected; represents the azimuth angle of the jth roller in the bearing at time t; δ jr It indicates the relative distance along the radial direction between the centers of curvature of the inner and outer ring grooves at the jth roller in the bearing after deflection.

3. The method according to claim 2, characterized in that: In the input shaft subsystem of the planetary speed change mechanism, the B1 support bearing is located at the input end; the outer rings of the B2 intermediate bearing and the B3 intermediate bearing support the planetary carrier of the first row of planetary gear trains; the outer rings of the B4 intermediate bearing and the B5 intermediate bearing support the planetary carrier of the second row of planetary gear trains; the input shaft is the sun gear shaft, which meshes with the planetary gears of the two rows of planetary gear trains, and its meshing force generates meshing force components and torque in the X and Y directions on the input shaft.

4. The method according to claim 3, characterized in that: The dynamic equation of the input shaft subsystem is a 5-DOF dynamic equation of bending-torsion-pendulum coupling excitation. The following formula is used to construct the 5-DOF dynamic equation of the input shaft subsystem of bending-torsion-pendulum coupling excitation: Among them, q si =[x si ,y si ,θ xsi ,θ ysi ,θ zsi ] represents the 5 degrees of freedom of the input axis; (f xi , f yi ) represents the input load of the hydraulic torque converter at the front end of the planetary transmission mechanism to the input shaft in the X and Y directions; M θzi Indicates input torque; M si =diag([m si , m si , I xsi , I ysi , I zsi ]) represents the mass matrix of the sun gear shaft; They represent the support reaction forces of the B1 support bearing, B2 intermediate bearing, B3 intermediate bearing, B4 intermediate bearing and B5 intermediate bearing in the input shaft subsystem in the X and Y directions respectively; Respectively represent the projections of the meshing forces of the first row of planetary gear trains and the second row of planetary gear trains on the input shaft in the X and Y directions; It represents the projection of the dynamic unbalanced force caused by the mass eccentricity of the CH operating part on the input shaft in the X and Y directions; It represents the projection of the dynamic unbalanced moment caused by the mass eccentricity of the CH operating part on the input shaft in the X and Y directions; They represent the coupling force of the CH operating member on the input shaft in the X and Y directions and the torsion direction when combined; a b1 、a b2 、a b3 、a b4 and a b5 Respectively represent the distances from the five bearings to the center of mass of the input shaft; a p1 and a p2 Respectively represent the distances from the first planetary row and the second planetary row to the mass center of the input shaft; a i Indicates the distance between the input load and the center of mass of the shaft; a d1 Indicates the distance between the CH control and the axis mass center; and Respectively represent the torques of the first planetary gear train and the second planetary gear train on the input shaft; The support reaction forces of the B1 support bearing, B2 intermediate bearing, B3 intermediate bearing, B4 intermediate bearing and B5 intermediate bearing in the input shaft subsystem in the X and Y directions are respectively calculated based on the time-varying nonlinear support stiffness of the bearing, the displacement of the first row planet carrier, the second row planet carrier and the sun gear shaft in the X and Y directions, and the distance from each bearing on the input shaft to the center of mass of the input shaft.

5. The method according to claim 2, characterized in that: In the double planetary gear subsystem of the planetary speed change mechanism, the planet carrier of the first planetary gear train is connected to the inner gear ring of the second planetary gear train, the power is input from the sun gear shaft, and the power is output from the planet carrier of the second planetary gear train; For the planet carrier of the first row of planetary gear systems, which supports the planetary gears of the first row of planetary gear systems, the three-degree-of-freedom dynamic equations of its bending-torsion coupling excitation are constructed; For the component consisting of the first row of internal gear rings and the second row of planet carriers, which not only meshes with the first row of planetary gear sets but also supports the second row of planetary gear sets, the three-degree-of-freedom dynamic equations of its bending-torsion coupling excitation are constructed; For the first row of planetary gears, which mesh with the sun gear and the first row of inner gear ring at the same time, the three-degree-of-freedom dynamic equations of the bending-torsion coupling excitation of each planetary gear are constructed; For the second row of internal gear rings, which mesh with the second row of planetary gear sets, the three-degree-of-freedom dynamic equations of its bending-torsion coupling excitation are constructed; For the second row of planetary gear sets, which mesh with the sun gear and the second row of inner gear ring at the same time, a three-degree-of-freedom dynamic equation of the bending-torsion coupling excitation of each planetary gear is constructed.

6. The method according to claim 5, characterized in that: The dynamic equation of the planet carrier of the first row of planetary gear system is constructed using the following formula: in, Represents the three degrees of freedom of the bending-torsion coupling excitation of the planet carrier of the first row of planetary gear systems; represents the mass matrix of the first row of planet carriers; Respectively represent the support reaction forces of the B2 intermediate bearing and the B3 intermediate bearing in the X and Y directions; represents the bearing support force between the first row of planet carriers and the hth planetary gear in the X and Y directions; R c1 Indicates the distance from the center of the planetary gear to the center of the first row of planetary carriers; Indicates the positioning angle of the hth planet gear in the first row of planet carriers; They respectively represent the coupling forces of the CH operating member on the input shaft in the X and Y directions and the torsional direction when combined; represents the coupling force vector between the first row planet carrier and the planetary speed change mechanism when the CR clutch is engaged; The bearing support forces of the first row of planet carriers and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear of the first row of planetary gear train, the displacement vector of the first row of planet carriers, the time-varying nonlinear support stiffness of the first row of planetary gear bearings, and the support damping of the first row of planetary gear bearings in the X and Y directions; The coupling force vector between the first row planet carrier and the planetary speed change mechanism is calculated based on the displacement vector of the first row planet carrier and the coupling stiffness vector and coupling damping vector of the CR clutch when the CR clutch is engaged; and is set to 0 when the CR clutch is disengaged; The following equation is used to construct the dynamic equation of the components consisting of the first row of internal gear rings and the second row of planet carriers: in, F represents the three degrees of freedom of the bending-torsion coupling excitation of the components consisting of the first row of internal gear rings and the second row of planet carriers; rco ={f xrco ,f yrco ,M θzrco } T represents the output load vector of the components consisting of the first row of internal gear rings and the second row of planet carriers; The mass matrix representing the components of the first row of internal gear rings and the second row of planet carriers; represents the bearing support force between the second row planet carrier and the hth planet gear in the X and Y directions; R c2 Indicates the distance from the center of the second row of planetary gears to the center of the planet carrier; Indicates the base circle radius of the first row of internal gear rings; represents the position angle of the hth planetary gear in the second row; represents the dynamic load between the first row of internal gear rings and the hth planetary gear; Respectively represent the support reaction forces of the B4 intermediate bearing, the B5 intermediate bearing and the B6 support bearing in the X and Y directions; It represents the angular position of the meshing line between the hth planetary gear in the first row and the first row of internal gear ring from the X axis; The bearing support forces of the second row planet carrier and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear of the second row planetary gear system, the displacement vector of the second row planet carrier, the time-varying nonlinear support stiffness of the second row planetary gear bearings and the support damping of the second row planetary gear bearings in the X and Y directions; The dynamic load between the first row of inner gear rings and each planetary gear is calculated based on the meshing relative displacement between the first row of inner gear rings and each planetary gear, the tooth side clearance between the first row of inner gear rings and each planetary gear, the displacement vector of the first row of inner gear rings, the angular position of the meshing line of each planetary gear and the first row of inner gear rings from the X-axis, the distance from the center of each planetary gear to the center of the first row of inner gear rings, the base circle radius of the first row of inner gear rings, and the meshing stiffness and meshing damping between the first row of inner gear rings and each planetary gear; The following formula is used to construct the dynamic equations of each planetary gear of the first row of planetary gear sets: in, It represents the three degrees of freedom of the bending-torsion coupling excitation of the hth planetary gear in the first row of planetary gear sets; represents the mass matrix of the hth planetary gear in the first row; and They represent the dynamic meshing forces between the first row sun gear and the hth planetary gear and between the first row internal gear and the hth planetary gear respectively; It represents the bearing support force between the first row of planet carriers and the hth planetary gear in the X and Y directions; Indicates the base circle radius of the first row of planetary gears; The bearing support forces of the first row planet carrier and each planet gear in the X and Y directions are calculated based on the displacement vectors of each planet gear of the first row planet gear system, the displacement vector of the first row planet carrier, the time-varying nonlinear support stiffness of the first row planet gear bearings, and the support damping of the first row planet gear bearings in the X and Y directions; The dynamic meshing force between the first row sun gear and each planetary gear is calculated based on the meshing relative displacement between the first row sun gear and each planetary gear, the tooth side clearance between the first row sun gear and each planetary gear, the displacement vector of the first row sun gear, the angular position of the meshing line of each planetary gear and the first row sun gear from the X-axis, the distance from the center of each planetary gear to the center of the first row sun gear, the base circle radius of the first row sun gear, and the meshing stiffness and meshing damping between the first row sun gear and each planetary gear; The dynamic equation of the second row of internal gears is constructed using the following formula: in, Represents the 3 degrees of freedom of the bending-torsion coupling excitation of the second row of internal gear rings; represents the mass matrix of the second row of internal gear rings; represents the coupling force vector between the second row planet carrier and the planetary speed change mechanism when the CL clutch is engaged; represents the dynamic meshing force between the second row of internal gear rings and the hth planetary gear; Indicates the angular position of the meshing line between the hth planetary gear and the inner gear ring from the X axis; Indicates the base circle radius of the second row of internal gear ring; The dynamic equations of each planetary gear of the second row of planetary gear sets are constructed using the following formula: in, It represents the 3 degrees of freedom of the bending-torsion coupling excitation of the hth planetary gear of the second row of planetary gear sets; represents the mass matrix of the hth planetary gear in the second row; and They represent the dynamic meshing forces between the second row sun gear and the hth planetary gear and between the second row internal gear and the hth planetary gear respectively; represents the bearing support force between the second row planet carrier and the hth planet gear in the X and Y directions; Indicates the base circle radius of the second row of planetary gears; The bearing support forces of the second row planet carrier and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear of the second row planetary gear system, the displacement vector of the second row planet carrier, the time-varying nonlinear support stiffness of the second row planetary gear bearings and the support damping of the second row planetary gear bearings in the X and Y directions; The dynamic meshing force between the second-row sun gear and each planetary gear is calculated based on the meshing relative displacement between the second-row sun gear and each planetary gear, the tooth side clearance between the second-row sun gear and each planetary gear, the displacement vector of the second-row sun gear, the angular position of the meshing line of each planetary gear and the second-row sun gear from the X-axis, the distance from the center of each planetary gear to the center of the second-row sun gear, the base circle radius of the second-row sun gear, and the meshing stiffness and meshing damping between the second-row sun gear and each planetary gear.

7. The method according to claim 2, characterized in that: In the output end transmission shaft subsystem of the planetary speed change mechanism, a B10 support bearing is arranged on the output end transmission shaft, a B8 intermediate bearing supports the compound row input gear ring, a B9 intermediate bearing supports the compound row planet carrier, and the transmission shaft is the sun gear shaft, which meshes with the long planet gear of the compound row, and its meshing force generates meshing force components and torque in the X and Y directions on the transmission shaft.

8. The method according to claim 7, characterized in that: The dynamic equation of the output-end transmission shaft subsystem is a 5-degree-of-freedom dynamic equation of bending-torsion-pendulum coupling excitation. The following formula is used to construct the 5-degree-of-freedom dynamic equation of the output-end transmission shaft subsystem of bending-torsion-pendulum coupling excitation: Among them, q so =[x so ,y so ,θ xso ,θ yso ,θ zso ] represents the 5 degrees of freedom of the output transmission shaft; M so =diag([m so , m so , I xso , I yso , I zso ]) represents the mass matrix of the output transmission shaft; F o ={f xo , f yo , M θzo } T Represents the external load vector on the output transmission shaft; Respectively represent the support reaction forces of the B8 intermediate bearing, the B9 intermediate bearing and the B10 support bearing in the X and Y directions; It indicates the projection of the dynamic unbalanced force caused by the mass eccentricity of the C2 and C3 operating parts on the output end transmission shaft in the X and Y directions; It indicates the projection of the dynamic unbalanced moment caused by the mass eccentricity of the C2 and C3 operating parts on the output end transmission shaft in the X and Y directions; They respectively represent the coupling force of the C2 operating member / C3 operating member on the output end transmission shaft in the X and Y directions and the torsional direction when the operating member is combined; a b8 、a b9 and a b10 Respectively represent the distances from the B8 intermediate bearing, B9 intermediate bearing and B10 support bearing to the mass center of the output end transmission shaft; a p3 represents the distance from the compound row to the center of mass of the transmission shaft, a d3 Indicates the distance between the C2 control member and the C3 control member and the center of mass of the shaft; It represents the projection of the meshing force of the compound row on the sun gear of the output transmission shaft in the X and Y directions; Indicates the torque of the compound row on the sun gear of the output drive shaft; a o Indicates the distance between the input load and the center of mass of the output transmission shaft; The support reaction forces of the B8 intermediate bearing, the B9 intermediate bearing and the B10 support bearing in the output end transmission shaft subsystem in the X and Y directions are calculated based on the time-varying nonlinear support stiffness of the bearings, the displacements of the composite planetary carrier and the output end transmission shaft in the X and Y directions, and the distances from the center of mass of each bearing on the output end transmission shaft to the input shaft.

9. The method according to claim 2, characterized in that: In the compound row subsystem of the planetary speed change mechanism, the planet carrier includes a long planetary gear set and a short planetary gear set; wherein the long planetary gear set meshes with the sun gear and the input gear ring to form a row of planetary gear transmission; the short planetary gear set meshes with the long planetary gear set and the floating support ring to form another row of planetary gear transmission; the two rows of planetary gear transmissions form a compact compound planetary gear transmission through the meshing between the long planetary gear set and the short planetary gear set; power is input from the compound row input gear ring and output from the compound row planet carrier; For the planet carrier of the compound planetary gear system, which supports both the long planetary gear set and the short planetary gear set, the three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed; For the compound row input ring gear, it is coupled with the planet carrier of the second row planetary gear system of the planetary speed change mechanism and meshes with the compound row long planetary gear set, and a 3-DOF dynamic equation of its bending-torsion coupling excitation is constructed; For the composite long planetary gear set, which is meshed with the input ring gear, sun gear and short planetary gear set at the same time, the 3-DOF dynamic equation of its bending-torsion coupling excitation is constructed; For the composite short planetary gear set, which is meshed with the long planetary gear set and the floating ring gear at the same time, the three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed; For the compound row floating ring gear, which is meshed with the compound row planetary gear set, the three-degree-of-freedom dynamic equation of its bending-torsion coupling excitation is constructed.

10. The method according to claim 9, characterized in that: The dynamic equation of the planet carrier of the compound planetary gear system is constructed using the following formula: in, Represents the three degrees of freedom of the bending-torsion coupling excitation of the planet carrier of the compound planetary gear system; Represents the mass matrix of the planet carrier of the compound planetary gear system; Respectively represent the support reaction forces of the B7 intermediate bearing, the B8 intermediate bearing and the B9 intermediate bearing in the X and Y directions; It represents the bearing support force of the composite planet carrier and the u-th short planet gear in the X direction and the Y direction; It represents the bearing support force of the composite planet carrier and the u-th long planet gear in the X direction and the Y direction; It represents the coupling force between the planet carrier of the compound planetary gear system and the transmission mechanism case in the X and Y directions and the torsion direction when the C2 operating member / C3 operating member are combined; r c Indicates the distance from the center of the short planetary gear to the center of the planetary carrier; r lc Indicates the distance from the center of the long planet gear to the center of the planet carrier; represents the positioning angle of the uth short planetary gear; represents the positioning angle of the u-th long planet gear; The bearing support forces of the composite planet carrier and each short planet gear in the X direction and the Y direction are calculated based on the displacement vector of each short planet gear in the composite row, the support stiffness of the short planet gear bearing in the X direction and the Y direction, the support damping of the short planet gear bearing in the X direction and the Y direction, the distance from the center of the short planet gear to the center of the planet carrier, and the positioning angle of each short planet gear; The bearing support forces of the composite planet carrier and each long planet wheel in the X direction and the Y direction are calculated based on the displacement vector of each long planet wheel in the composite row, the support stiffness of the long planet wheel bearing in the X direction and the Y direction, the support damping of the long planet wheel bearing in the X direction and the Y direction, the distance from the center of the long planet wheel to the center of the planet carrier, and the positioning angle of each long planet wheel; The support reaction force of the B7 intermediate bearing in the planetary carrier of the compound row planetary gear system in the X and Y directions is calculated based on the time-varying nonlinear support stiffness of the bearing, the displacement of the compound row input gear ring in the X and Y directions, and the support damping of the bearing in the X and Y directions; The dynamic equation of the compound row input ring gear is constructed using the following formula: in, F represents the three degrees of freedom of the bending-torsion coupling excitation of the compound row input gear ring; ro ={f xro ,f yro ,M θzro } T represents the input load vector of the compound row input ring gear; F represents the mass matrix of the compound row input gear ring; rlpu represents the dynamic load of the u-th long planetary gear in the compound row and the input ring gear; ψ rpu Indicates the angular position of the meshing line between the u-th short planet gear in the compound row and the sun gear from the X axis; Indicates the base circle radius of the compound row input gear ring; The dynamic load of each long planetary gear of the compound row and the input gear ring is calculated based on the tooth side clearance between the inner gear ring and the corresponding long planetary gear, the displacement vector of the long planetary gear corresponding to the compound row, the angular position of the meshing line of the corresponding long planetary gear and the input gear ring from the X axis, the input gear ring base circle radius, the displacement of the input gear ring in the X direction, the Y direction and the torsional direction, and the displacement of the planet carrier in the torsional direction; The dynamic equation of the composite long-row planetary gear set is constructed using the following formula: in, represents the three degrees of freedom of the bending-torsion coupling excitation of the u-th long planetary gear in the composite row; represents the mass matrix of the u-th long planetary gear in the composite row; F slpu represents the dynamic load of the u-th long planetary gear in the composite row and the sun gear shaft; F rlpu F represents the dynamic load of the u-th long planetary gear in the compound row and the input ring gear; lppu represents the dynamic load of the u-th long planetary gear and the u-th short planetary gear in the compound row; ψ slpu represents the angle between the meshing line of the u-th long planetary gear in the composite row and the sun gear shaft and the X-axis; ψ rlpu represents the angle between the meshing line of the u-th long planetary gear in the compound row and the input ring gear and the X-axis; ψ lppu Indicates the angular position of the meshing line between the u-th long planetary gear and the u-th short planetary gear in the compound row from the X-axis; Indicates the base circle radius of the composite long planet gear; The dynamic load of the u-th long planetary gear and the u-th short planetary gear of the compound row is calculated based on the tooth side clearance of the u-th long planetary gear and the u-th short planetary gear, the displacement vector of the u-th long planetary gear, the displacement vector of the u-th short planetary gear, the angular position of the meshing line of the u-th long planetary gear and the u-th short planetary gear from the X-axis, and the base circle radius of the short planetary gear; The dynamic equation of the composite short-row planetary gear set is constructed using the following formula: in, represents the three degrees of freedom of the bending-torsion coupling excitation of the u-th short planetary gear in the composite row; F represents the mass matrix of the u-th short planetary gear in the composite row; frpu represents the dynamic load between the composite floating ring gear and the uth short planetary gear; ψ frpu Indicates the angular position of the meshing line between the composite row floating ring gear and the uth short planetary gear from the X axis; Indicates the base circle radius of the compound row short planetary gear; The dynamic load between the composite row floating ring gear and the u-th short planet gear is calculated based on the tooth side clearance between the composite row floating ring gear and each short planet gear, the displacement vector of the floating ring gear, the displacement in the torsion direction of the planet carrier, the meshing secondary pressure angle of the floating ring gear-short planet gear, the meshing stiffness and meshing damping between the floating ring gear and each short planet gear, and the base circle radius of the floating ring gear; The dynamic equation of the composite floating gear ring is constructed using the following formula: in, Represents the three degrees of freedom of bending-torsion coupling excitation of the composite row floating gear ring; Represents the mass matrix of the composite row floating gear ring; It represents the coupling force vector between the compound row floating ring gear and the transmission case when the C1 clutch is engaged; The coupling force vector between the compound row floating ring gear and the transmission mechanism case when the C1 clutch is engaged is calculated based on the coupling stiffness vector and the coupling damping vector between the compound row floating ring gear and the transmission mechanism case.

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