Method for predicting dynamic characteristics of planetary gear mechanism under multi-point support and bending-torsional coupling excitation

Abstract

The present application relates to a kind of planetary gear mechanism multi-point support bending-torsional coupling excitation dynamic characteristics estimation method, belong to planetary gear technical field, it is difficult to predict and inhibit the problem that multi-point support bearing under actual working condition dynamic load due to the bending-torsional vibration of transmission shaft and the dynamic coupling effect between the dynamic load of planetary gear set exists.Method includes: obtaining the parameters of each planetary gear component of planetary gear mechanism and each bearing parameter;Based on each bearing parameter, the time-varying nonlinear support stiffness of bearing is calculated;Based on the time-varying nonlinear support stiffness of bearing and the parameters of each planetary gear component, the subsystem dynamics model of planetary gear mechanism is established;When the inner and outer rings of intermediate bearing rotate simultaneously in the given time step, the dynamic load f o And deformation δ o Of bearing outer ring by planetary carrier / bearing seat, and the dynamic load f i And deformation δ i Of inner ring by transmission shaft, and the support stiffness and dynamic response of system at current time are calculated, the subsystem dynamics model of planetary gear mechanism is solved using four-order Runge-Kutta numerical iterative algorithm, and the dynamic response of planetary gear mechanism in next time step is obtained, and the dynamic characteristics estimation is completed by iterative cycle until.

Description

Technical Field

[0001] This invention relates to the field of planetary gear technology, and in particular to a method for predicting the dynamic characteristics of multi-point support bending and torsional coupling excitation in a planetary transmission mechanism. Background Technology

[0002] An automatic transmission is a type of automotive transmission system that automatically adjusts the gear ratio according to different driving conditions and vehicle speed, thereby improving fuel economy and driving comfort. Automatic transmissions generally use planetary gear drives, which offer advantages such as good transmission stability, high load-bearing capacity, long service life, smooth gear shifting, and the ability to achieve a wide range of gear ratios. They meet the high reliability requirements of vehicles, thus improving vehicle reliability and safety.

[0003] However, in planetary transmission mechanisms, the bending moment of the drive shaft supported by the multiple rolling bearing elements and the torque of the planetary gear set's dynamic meshing force directly affect the bending and torsional vibrations of the drive shaft. On the other hand, the bending and torsional vibrations of the drive shaft change the inner ring displacement of each support bearing and the meshing displacement of each sun gear-planet gear, thereby affecting the dynamic load of the multi-point support bearings and the dynamic meshing force of the planetary gear set. That is, the bending and torsional vibrations of the drive shaft are dynamically coupled with the dynamic loads of the multi-point support bearings and the planetary gear set. Predicting the dynamic characteristics of planetary transmission mechanisms is difficult, and there is currently no analytical method for the dynamic characteristics of high power density planetary transmission mechanisms. Summary of the Invention

[0004] Based on the above analysis, the present invention aims to provide a method for predicting the dynamic characteristics of multi-point support bending-torsional coupling excitation in planetary transmission mechanisms. This method addresses the problems of difficulty in accurately modeling the dynamic coupling effect between the bending-torsional vibration of the transmission shaft and the dynamic load of the multi-point support bearings and planetary gear sets, as well as the lack of effective methods to predict and suppress the dynamic load of the multi-point support bearings under actual working conditions.

[0005] The objective of this invention is mainly achieved through the following technical solutions:

[0006] This invention provides a method for predicting the dynamic characteristics of a planetary transmission mechanism with multi-point support and bending-torsional coupling excitation, wherein the planetary transmission mechanism adopts a dual-rotor structure; the method includes:

[0007] Obtain the parameters of each planetary gear component and each bearing of the planetary transmission 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 parameters of the bearing 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 planetary gear component, a subsystem dynamic model of the planetary gear mechanism is established; wherein, the planetary gear mechanism subsystem includes an input shaft subsystem, a double planetary gear subsystem, an output transmission shaft subsystem, and a compound gear subsystem;

[0010] Within a given time step, calculate the dynamic load f of the planetary carrier / bearing housing on the outer ring of the bearing when the inner and outer rings of the intermediate bearing rotate simultaneously. o and deformation δ o and the dynamic load f of the drive shaft on the inner ring i and deformation δ i The system's support stiffness and dynamic response at the current moment are calculated. The dynamic models of each subsystem of the planetary transmission mechanism are combined and solved using the fourth-order Runge-Kutta numerical iteration algorithm to obtain the dynamic response of the planetary transmission mechanism in the next time step. The process is iterated until the dynamic characteristics prediction 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 Indicates the combined normal contact stiffness between the inner rollers and the inner and outer rings of the bearing; n represents the contact factor; N represents the total number of inner rollers in the bearing; A0 represents the relative distance between the centers of curvature of the grooves before deflection of the inner and outer raceways of the bearing; A j This represents the relative distance between the centers of curvature of the grooves at the j-th roller inside the bearing after the inner and outer raceways have deflected. δ represents the azimuth angle of the j-th roller in the bearing at time t; jr This represents the radial distance between the centers of curvature of the inner and outer ring grooves at the j-th roller inside the bearing after deflection.

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

[0015] Furthermore, the dynamic equations of the input axle system are 5-DOF dynamic equations for bending-torsional-pendulum coupled excitation. The following equations are used to construct the 5-DOF dynamic equations of the input axle system for bending-torsional-pendulum coupled excitation:

[0016]

[0017] Where, qsi =[x si ,y si ,θ xsi ,θ ysi ,θ zsi ] indicates 5 degrees of freedom for the input axis; (f xi ,f yi ) represents the input load of the front-end hydraulic torque converter of the planetary transmission mechanism on 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 axis; These represent the supporting reaction forces in the X and Y directions of the B1 support bearing, B2 intermediate bearing, B3 intermediate bearing, B4 intermediate bearing, and B5 intermediate bearing in the input shaft subsystem, respectively. These represent the projections of the meshing forces of the first and second planetary gear trains on the input shaft in the X and Y directions, respectively. This represents the projection of the dynamic unbalance force caused by the mass eccentricity of the CH control component on the input shaft in the X and Y directions. This represents the projection of the dynamic unbalance torque caused by mass eccentricity of the CH control element on the input shaft in the X and Y directions; These represent the coupling forces exerted on the input shaft by the CH actuator in the X and Y directions and the torsional direction, respectively; a b1 a b2 a b3 a b4 and a b5 These represent the distances from the five bearings to the center of mass of the input shaft; a p1 and a p2 These represent the distances from the first and second planetary arrays to the centroid of the input axis, respectively; a i This indicates the distance of the input load from the shaft's center of mass; a d1 This indicates the distance of the CH control element from the center of mass of the shaft; and These represent the torques of the first and second planetary gear trains relative to the input shaft, respectively.

[0018] The support reactions 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 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 centroid distance of each bearing on the input shaft to the input shaft.

[0019] Furthermore, in the dual planetary gear train system of the planetary transmission mechanism, the planet carrier of the first planetary gear train is connected to the internal gear ring of the second planetary gear train, and the power is input from the sun gear shaft and output from the planet carrier of the second planetary gear train.

[0020] For the planet carrier of the first row of planetary gear system, which supports each planet gear of the first row of planetary gear system, construct its three-degree-of-freedom dynamic equations for bending-torsional coupled excitation;

[0021] For the component consisting of the first row of internal gear rings and the second row of planetary carriers, which meshes with the first row of planetary gear sets and supports the second row of planetary gear sets, construct its three-degree-of-freedom dynamic equations for bending-torsional coupling excitation;

[0022] For the first row of planetary gear sets, which simultaneously meshes with the sun gear and the first row of internal gear rings, a 3-degree-of-freedom dynamic equation is constructed for the bending-torsional coupling excitation of each planetary gear.

[0023] For the second row of internal gear rings, which mesh with the second row of planetary gear sets, construct a 3-degree-of-freedom dynamic equation for its bending-torsional coupled excitation;

[0024] For the second row of planetary gears, which meshes with both the sun gear and the second row of internal gear rings, a three-degree-of-freedom dynamic equation is constructed for the bending-torsional coupling excitation of each planetary gear.

[0025] Furthermore, the dynamic equations of the planet carrier of the first row of planetary gear systems are constructed using the following formula:

[0026]

[0027] in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the planet carrier of the first-row planetary gear system; This represents the mass matrix of the first row of planetary carriers; These represent the supporting reaction forces of intermediate bearings B2 and B3 in the X and Y directions, respectively. R represents the bearing support force of the first planet carrier and the h-th planet gear in the X and Y directions; c1 This indicates the distance from the center of the planetary gear to the center of the first row of planet carriers; This indicates the positioning angle of the h-th planetary gear in the first row of the planet carrier; These represent the coupling forces exerted on the input shaft by the CH actuator in the X and Y directions and the torsional direction, respectively, when engaged. This represents the coupling force vector between the first row of planetary carriers and the planetary transmission mechanism when the CR clutch is engaged;

[0028] The bearing support forces of the first row of planetary carriers and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear in 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.

[0029] The coupling force vector between the first row of planetary carriers and the planetary transmission mechanism is calculated based on the displacement vector of the first row of planetary carriers, the coupling stiffness vector of the CR clutch, and the coupling damping vector when the CR clutch is engaged; it is set to 0 when the CR clutch is disengaged.

[0030] The following equations can be used to construct the dynamic equations of the component consisting of the first row of internal gear rings and the second row of planetary carriers:

[0031]

[0032] in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the component consisting of the first row of internal gear rings and the second row of planetary carriers; F rco ={f xrco ,f yrco M θzrco} T This represents the output load vector of the component consisting of the first row of internal gear rings and the second row of planetary carriers. This represents the mass matrix of the component consisting of the first row of internal gear rings and the second row of planetary carriers. R represents the bearing support force of the second-row planetary carrier and the h-th planetary gear in the X and Y directions; c2 This 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 gears; This indicates the position angle of the h-th planetary gear in the second row; This represents the dynamic load between the first row of internal gear rings and the h-th planetary gear; These represent the supporting reaction forces in the X and Y directions for intermediate bearings B4, B5, and B6, respectively. This indicates the angular position of the meshing line between the h-th planetary gear in the first row and the internal gear ring in the first row from the X-axis;

[0033] The bearing support forces of the second-row planetary carrier and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear in the second-row planetary gear train, the displacement vector of the second-row planetary 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 internal gear rings and each planetary gear is calculated based on the meshing relative displacement between the first row of internal gear rings and each planetary gear, the tooth flank clearance between the first row of internal gear rings and each planetary gear, the displacement vector of the first row of internal gear rings, the angular position of the meshing line between each planetary gear and the first row of internal gear rings from the X-axis, the distance from the center of each planetary gear to the center of the first row of internal gear rings, the base circle radius of the first row of internal gear rings, and the meshing stiffness and meshing damping between the first row of internal gear rings and each planetary gear.

[0035] The dynamic equations for each planetary gear in the first row of planetary gear sets are constructed using the following formula:

[0036]

[0037] in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the h-th planetary gear in the first row of planetary gear sets; This represents the mass matrix of the h-th planetary gear in the first row; and These represent the dynamic meshing forces of the first row of sun gears down to the h-th planet gear and the first row of internal gear rings down to the h-th planet gear, respectively. This represents the bearing support force of the first planet carrier and the h-th planet gear in the X and Y directions; This indicates the base circle radius of the first row of planetary gears;

[0038] The bearing support forces of the first row of planetary carriers and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear in 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.

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

[0040] The dynamic equations for the second row of internal gears are constructed using the following formula:

[0041]

[0042] in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the second row of internal gear rings; This represents the mass matrix of the second row of internal gear rings; This represents the coupling force vector between the second-row planetary carrier and the planetary transmission mechanism when the CL clutch is engaged. This represents the dynamic meshing force between the second row of internal gear rings and the h-th planetary gear; This indicates the angular position of the meshing line between the h-th planetary gear and the internal gear ring from the X-axis; Indicates the base circle radius of the second row of internal gears;

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

[0044]

[0045] in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the h-th planetary gear in the second row of planetary gear sets; This represents the mass matrix of the h-th planetary gear in the second row; and These represent the dynamic meshing forces of the second row sun gear to the h-th planet gear and the second row internal gear ring to the h-th planet gear, respectively. This indicates the bearing support force of the second-row planetary carrier and the h-th planetary gear in the X and Y directions; This indicates the base circle radius of the second row of planetary gears;

[0046] The bearing support forces of the second-row planetary carrier and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear in the second-row planetary gear train, the displacement vector of the second-row planetary 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 planet gear is calculated based on the relative meshing displacement between the second-row sun gear and each planet gear, the tooth flank clearance between the second-row sun gear and each planet gear, the displacement vector of the second-row sun gear, the angular position of the meshing line between each planet gear and the second-row sun gear from the X-axis, the distance from the center of each planet 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 planet gear.

[0048] Furthermore, in the output drive shaft subsystem of the planetary gear transmission mechanism, a B10 support bearing is provided on the output drive shaft, a B8 intermediate bearing supports the composite gear input ring gear, a B9 intermediate bearing supports the composite gear planet carrier, and the drive shaft is a sun gear shaft that meshes with the composite gear long planet gear. The meshing force generates meshing force components in the X and Y directions and torque on the drive shaft.

[0049] Furthermore, the dynamic equations of the output drive shaft subsystem are 5-DOF dynamic equations of bending-torsional-pendulum coupled excitation. The following equations are used to construct the 5-DOF dynamic equations of the output drive shaft subsystem under bending-torsional-pendulum coupled excitation:

[0050]

[0051] Where, q so =[x so ,y so ,θ xso ,θ yso ,θ zso [] indicates 5 degrees of freedom for the output drive shaft; M so =diag([m so ,m so ,I xso ,I yso ,I zso ]) represents the mass matrix of the output drive shaft; F o ={f xo ,f yo M θzo} T This represents the external load vector on the output drive shaft; These represent the supporting reaction forces in the X and Y directions for intermediate bearings B8, B9, and B10, respectively. This represents the projection of the dynamic imbalance force caused by the mass eccentricity of the C2 and C3 operating components on the output drive shaft in the X and Y directions. This represents the projection of the dynamic unbalance torque caused by mass eccentricity of the C2 and C3 operating components on the output drive shaft in the X and Y directions. These represent the coupling forces exerted on the output drive shaft by the C2 and C3 actuators in the X and Y directions and the torsional direction, respectively, when they are engaged; a b8 a b9 and a b10 These represent the distances from the B8 intermediate bearing, B9 intermediate bearing, and B10 support bearing to the center of mass of the output drive shaft, respectively; a p3 a represents the distance from the compound pile to the center of mass of the drive shaft. d3 This indicates the distance of the C2 and C3 control components from the center of mass of the shaft; This represents the projection of the meshing force of the composite gearbox on the sun gear of the output drive shaft in the X and Y directions; This indicates the torque of the compound drive on the sun gear of the output drive shaft; a o This indicates the distance between the input load and the center of mass of the output drive shaft;

[0052] The supporting reaction forces of the intermediate bearings B8, B9, and B10 in the X and Y directions of the output drive shaft subsystem are calculated based on the time-varying nonlinear support stiffness of the bearings, the displacement of the composite planetary carrier and the output drive shaft in the X and Y directions, and the centroid distance from each bearing on the output drive shaft to the input shaft.

[0053] Furthermore, in the compound planetary gear system of the planetary transmission 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 ring gear to form a row of planetary gear transmissions; the short planetary gear set meshes with the long planetary gear set and the floating support ring to form another row of planetary gear transmissions; 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 gear input ring gear and output from the compound gear planet carrier;

[0054] For a planet carrier of a composite planetary gear system, which simultaneously supports both long and short planetary gear sets, a 3-degree-of-freedom dynamic equation for its bending-torsional coupled excitation is constructed.

[0055] For the composite input gear ring, it is coupled with the planet carrier of the second row of planetary gear train of the planetary transmission mechanism, and meshes with the composite long planetary gear set, thus constructing its three-degree-of-freedom dynamic equations for bending-torsional coupling excitation;

[0056] For the composite long planetary gear set, it meshes with the input gear ring, the sun gear and the short planetary gear set at the same time, and constructs its three-degree-of-freedom dynamic equations for bending-torsional coupling excitation;

[0057] For a composite short planetary gear set, which simultaneously meshes with a long planetary gear set and a floating ring gear, a 3-DOF dynamic equation for its bending-torsional coupled excitation is constructed.

[0058] For a composite floating gear ring, which meshes with a composite planetary gear set, a 3-DOF dynamic equation for its bending-torsional coupled excitation is constructed.

[0059] Furthermore, the dynamic equations of the planet carrier of the composite planetary gear system are constructed using the following formula:

[0060]

[0061] in, This represents the 3 degrees of freedom of the bending-torsional coupled excitation of the planet carrier in the composite planetary gear system; This represents the mass matrix of the planet carrier in a composite planetary gear system. These represent the supporting reaction forces in the X and Y directions for intermediate bearings B7, B8, and B9, respectively. This represents the bearing support force of the composite planetary carrier and the u-th short planetary gear in the X and Y directions; This represents the bearing support force of the composite planetary carrier and the u-th long planetary gear in the X and Y directions; This indicates the coupling force between the planetary carrier of the compound planetary gear system and the transmission housing in the X and Y directions, as well as the torsional direction, when the C2 / C3 control components are engaged; r c This represents the distance from the center of the short planetary gear to the center of the planet carrier; r lc This indicates the distance from the center of the long planetary gear to the center of the planet carrier; This represents the positioning angle of the u-th short planetary gear; This represents the positioning angle of the u-th long planetary gear;

[0062] 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 planetary carrier, 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 angle of each short planetary gear.

[0063] The bearing support forces of the composite planetary carrier and each long planetary gear in the X and Y directions are calculated based on the displacement vectors of each long planetary gear in the composite planetary carrier, the support stiffness of the long planetary gear bearings in the X and Y directions, the support damping of the long planetary gear bearings in the X and Y directions, the distance from the center of the long planetary gear to the center of the planetary carrier, and the positioning angle of each long planetary gear.

[0064] The support reaction force of the intermediate bearing B7 in the planetary carrier of the composite 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 composite 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 equations of the composite input gear ring are constructed using the following formula:

[0066]

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

[0068] The dynamic loads of each long planetary gear in the compound gear set and the input gear ring are calculated based on the tooth backlash of the internal gear ring and the corresponding long planetary gear, the displacement vector of the corresponding long planetary gear in the compound gear set, the angular position of the meshing line between the corresponding long planetary gear and the input gear ring from the X-axis, the base circle radius of the input gear ring, the displacement of the input gear ring along the X-direction, Y-direction and torsional direction and the displacement of the planet carrier in the torsional direction.

[0069] The dynamic equations of the composite planetary gear set are constructed using the following formula:

[0070]

[0071] in, This represents the 3 degrees of freedom of the bending-torsional coupled excitation of the u-th long planetary gear in the composite array; F represents the mass matrix of the u-th long planetary gear in the composite arrangement; slpu F represents the dynamic load on the axis of the u-th long planetary gear in the composite array and the sun gear; rlpu F represents the dynamic load between the u-th long planetary gear in the compound gear arrangement and the input gear ring; lppu ψ represents the dynamic load between the u-th long planetary gear and the u-th short planetary gear in the composite arrangement; slpu ψ represents the angle between the line of meshing of the u-th long planetary gear and the sun gear axis and the X-axis; rlpu ψ represents the angle between the line of meshing of the u-th long planetary gear in the compound gear set and the input gear ring and the X-axis; lppu This 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 arrangement from the X-axis; Indicates the base circle radius of the composite planetary gear;

[0072] The dynamic load of the u-th long planetary gear and the u-th short planetary gear in the compound gear set is calculated based on the tooth backlash 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 equations of the composite short planetary gear set are constructed using the following formula:

[0074]

[0075] in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the u-th short planetary gear in the composite array; F represents the mass matrix of the u-th short planetary gear in the composite arrangement; frpu ψ represents the dynamic load between the compound floating gear ring and the u-th short planetary gear;frpu This indicates the angular position of the compound floating gear ring relative to the X-axis from the meshing line of the u-th short planetary gear; Indicates the base circle radius of the composite short planetary gear set;

[0076] The dynamic load between the composite floating gear ring and the u-th short planetary gear is calculated based on the tooth backlash between the composite floating gear ring and each short planetary gear, the displacement vector of the floating gear ring, the displacement in the torsional direction of the planetary carrier, the pressure angle of the floating gear ring-short planetary gear meshing pair, the meshing stiffness and meshing damping between the floating gear ring and each short planetary gear, and the base circle radius of the floating gear ring.

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

[0078]

[0079] in, This represents the 3 degrees of freedom of the bending-torsional coupled excitation of the composite floating gear ring; This represents the mass matrix of the composite floating gear ring; This represents the coupling force vector between the compound floating gear ring and the transmission mechanism housing when the C1 clutch is engaged;

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

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

[0082] 1. This invention establishes a method for predicting the dynamic characteristics of planetary transmission mechanisms through multi-point support bending and torsional coupling excitation. This method enables simulation analysis and optimization design of the motion characteristics and transmission performance of the mechanism, thereby improving its working efficiency and transmission stability, and 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 transmission mechanism by coupling the motion equations of multiple degrees of freedom of each component, while ensuring high computational efficiency. It also considers 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. By estimating the dynamic characteristics of the planetary transmission mechanism, this invention can predict the motion state and transmission characteristics of the mechanism under different working conditions, thereby providing a reliable reference for the design and optimization of mechanical systems and improving the reliability and service life of mechanical systems.

[0085] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0086] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0087] Figure 1 This is a schematic diagram of the planetary transmission mechanism in an embodiment of the present invention;

[0088] Figure 2 This is a flowchart illustrating a method for predicting the dynamic characteristics of a planetary transmission mechanism with multi-point support and bending-torsional coupling excitation in an embodiment of the present invention.

[0089] Figure 3 This is a schematic diagram of the geometric dimensions of the ball bearing and the center of curvature of the raceway before and after deflection in an embodiment of the present invention.

[0090] Figure 4 This is a schematic diagram illustrating the solution of the bearing pseudo-dynamic model using the Newton-Raphson iteration method in an embodiment of the present invention.

[0091] Figure 5 This is a schematic diagram of the dynamic model of the input shaft bending-torsional-pinch coupling excitation of the planetary transmission mechanism in an embodiment of the present invention;

[0092] Figure 6 This is a schematic diagram of the bending-torsional coupling dynamics model of the first row of planetary gear systems in an embodiment of the present invention;

[0093] Figure 7 This is a schematic diagram of the bending-torsional coupling dynamics model of the second row of planetary gear system in an embodiment of the present invention;

[0094] Figure 8 This is a schematic diagram of the bending and torsional dynamics model of the double planetary gearbox at the input end of the planetary transmission mechanism in an embodiment of the present invention;

[0095] Figure 9 This is a schematic diagram of the bending and torsional dynamics model of the output shaft of the planetary transmission mechanism in an embodiment of the present invention;

[0096] Figure 10 This is a schematic diagram of the planar dynamics model of the composite planetary gear system in an embodiment of the present invention.

[0097] Figure label:

[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 gear set; 12-Second planetary gear set; 13-Compound gear set; 14-CH operating element; 15-CR clutch; 16-CL clutch; 17-C1 clutch; 18-C2 operating element; 19-C3 operating element; Detailed Implementation

[0099] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form 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 intended to limit the scope of the present invention.

[0100] A specific embodiment of the present invention discloses a method for predicting the dynamic characteristics of a planetary transmission mechanism under multi-point support bending-torsional coupling excitation, such as... Figure 1 As shown, the planetary gear transmission mechanism adopts a dual-rotor structure, which can effectively shorten the rotor support span and reduce the weight of the planetary gear transmission mechanism. The planetary gear transmission mechanism includes a three-row planetary gear train (first planetary gear set 11, second planetary gear set 12, and compound planetary gear set 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 to the chassis, and the inner ring rotates with the rotor; the outer ring of the intermediate bearing rotates with the planet carrier or outer rotor, and the inner ring rotates with the rotor; the planetary gear transmission mechanism also includes components for controlling the operation of the clutch or brake in the transmission mechanism (CH operating element 14, CR clutch 15, CL clutch 16, C1 clutch 17, C2 operating element 18, and C3 operating element 19).

[0101] Specifically, the right end of the gearbox housing is the input end of the gearbox, including a two-row planetary gear transmission system, two support bearings, and four intermediate bearings. Power is introduced through the input shaft, passed through the planet carrier of the second row of planetary gears, and output to the compound planetary gear system at the left end. The left end of the gearbox housing is the output end of the gearbox, including a three-row compound planetary gear transmission system, one support bearing, and three intermediate bearings. The power of the planetary gearbox is transmitted through the compound planetary carrier. Different gear ratios and torque outputs are achieved by controlling the clutches / brakes of different operating components of the gearbox, and by the splitting or engaging of the friction plates and steel plates, through an electro-hydraulic system.

[0102] Furthermore, such as Figure 2 As shown, a method for predicting the dynamic characteristics of a planetary transmission mechanism under multi-point support bending-torsional coupling excitation includes the following steps S1-S4:

[0103] Step S1: Obtain the parameters of each planetary gear component and each bearing of the planetary transmission 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 parameters of the bearing 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; planet gears, which are gears that rotate and mesh around the sun gear and are usually mounted on a planet carrier; an internal gear ring, which is a gear that surrounds the planet gears and is usually fixed to the housing of the transmission; and a planet carrier, which is a component for supporting the planet gears and allowing them to rotate around the sun gear.

[0105] Its parameters include, but are not limited to: number of teeth, which is the number of teeth on the planetary gear, determining the tooth profile shape and gear ratio, and having a significant impact on the transmission ratio and meshing characteristics; module, a measure of gear size, which is related to the size of the teeth; among them, the larger the module, the taller the gear tooth profile, the stronger the load-bearing capacity, and the larger the volume; pressure angle, the angle between the tooth profiles when the gears mesh, which affects the contact stress and transmission efficiency of the gears; gear mass, the weight of the gear, which affects the moment of inertia of the gear, and thus affects the dynamic response and balance of the gear; Young's modulus of the gear, the elastic modulus of the material, which affects the deformation and stress distribution of gear materials under load; Poisson's ratio, the ratio of lateral shrinkage of a material under axial tension, which affects the dimensional stability of gear materials under load.

[0106] The bearing parameters include: inner diameter (the diameter of the inner ring of the bearing, which determines the size of the shaft the bearing can fit); outer diameter (the diameter of the outer ring of the bearing, which determines the required installation space); width (the width of the bearing, which affects its load-bearing capacity and installation space); roller diameter (the diameter of the rolling elements, which determines the bearing's load-bearing capacity and stiffness); stiffness (the degree of deformation of the bearing under load, which determines its ability to resist deformation); damping (the friction and energy dissipation characteristics inside the bearing); clearance (the gap between the rolling elements and the inner and outer rings, which affects the bearing's running smoothness, noise level, and lifespan); and Young's modulus (the elastic modulus of the bearing, which affects the bearing's deformation and stress distribution under load).

[0107] Step S2: Calculate the time-varying nonlinear support stiffness of the bearing based on the bearing parameters.

[0108] Specifically, bearing support stiffness is a necessary parameter for the dynamic characteristics of the simulation system. Existing simulation systems assume the bearing stiffness to be a constant value, such as 1*10. 8The N / m model ignores the nonlinear relationship between bearing stiffness and the increase in support load, leading to inaccurate modeling and prediction of the dynamic characteristics of the multi-point support system in planetary transmission mechanisms. The inner ring of the intermediate bearing supports the shaft, and the outer ring supports the planetary carrier. Both rings rotate simultaneously and bear loads or deformations simultaneously, resulting in nonlinear (the greater the load or deformation, the greater the stiffness) and time-varying (roller revolution causes stiffness to change over time) support stiffness parameters for both inner and outer ring deformation. By integrating the calculated time-varying support stiffness parameters into the bending-torsional coupled excitation dynamic model of the planetary transmission mechanism, the dynamic characteristics of the system can be predicted more accurately.

[0109] like Figure 3 As shown, when the bearing is under load, the generalized deflection displacement of its inner and outer rings in the X, Y, and Z directions causes a change in the distance between the inner and outer rings and the center of curvature of the grooves. From this, the relative distance A0 between the centers of curvature of the grooves before the inner and outer raceways deflection can be obtained:

[0110] A0=(R iw +r iw )-(R ow +r ow (1)

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

[0112] The relative distance A between the centers of curvature of the grooves after the inner and outer raceways deflect at the j-th roller. j The calculation formula is as follows:

[0113]

[0114] Where, δ jr and δ jz These represent the relative distances along the radial and axial directions between the centers of curvature of the inner and outer grooves at the j-th roller after deflection, respectively. The calculation formula is as follows:

[0115]

[0116] Where, δ ix and δ ox These represent the deflection displacements of the inner and outer rings along the X-axis, respectively; δ iy and δ oy These represent the deflection displacements of the inner and outer rings along the Y-axis, respectively; δ iz and δ ozThese represent the deflection displacements of the inner and outer rings along the Z-axis (i.e., axial direction), respectively; φ j This represents the azimuth angle of the j-th roller relative to the X-axis; r L This refers to the radial clearance of the bearing.

[0117] Furthermore, such as Figure 4 As shown, considering the time-varying position distribution of the rolling elements in the rolling bearing, and also taking into account the overall radial deflection displacement of the bearing under load, the time-varying nonlinear support stiffness of the bearing in the X and Y directions is calculated using the following formula based on Hertzian contact theory:

[0118]

[0119] Among them, K s This indicates the combined normal contact stiffness between the bearing's inner rollers and the inner and outer rings; n represents the contact factor, set to 10 / 9 for line contact and 3 / 2 for point contact; N represents the total number of inner rollers in the bearing; A0 represents the relative distance between the centers of curvature of the grooves before deflection of the bearing's inner and outer raceways; A j This represents the relative distance between the centers of curvature of the grooves at the j-th roller inside the bearing after the inner and outer raceways have deflected. δ represents the azimuth angle of the j-th roller in the bearing at time t; jr This represents the radial distance between the centers of curvature of the inner and outer ring grooves at the j-th roller inside the bearing after deflection.

[0120] Step S3: Based on the time-varying nonlinear support stiffness of the bearing and the parameters of each planetary gear component, establish a subsystem dynamic model of the planetary transmission mechanism; wherein, the planetary transmission mechanism subsystem includes an input shaft subsystem, a double planetary gear subsystem, an output transmission shaft subsystem, and a composite gear subsystem.

[0121] Specifically, based on the structure and dynamics of the planetary gear mechanism, a bending-torsional-swing model of the drive shaft and a bending-torsional model of the planetary gear train are established. The planetary gear set and the drive shaft are coupled through the nonlinear time-varying support stiffness of multi-point support bearings to predict the dynamic response of each component of the planetary gear mechanism system.

[0122] The planetary transmission mechanism comprises four subsystems: an input shaft, a double planetary gear set, an output drive shaft, and a composite gear set. Five multi-point support bearings exist between the input shaft and the double planetary gear set, and three multi-point support bearings exist between the output drive shaft and the composite gear set. Dynamic models of the four subsystems are established, and the coupling of the dynamic models of the different systems is achieved through 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] Furthermore, such as Figure 5As shown, in the input shaft subsystem of the planetary gear transmission mechanism, B1 support bearing 1 is located at the input end; the outer rings of B2 intermediate bearing 2 and B3 intermediate bearing 3 support the planet carrier of the first row of planetary gear trains; the outer rings of B4 intermediate bearing 4 and B5 intermediate bearing 5 support the planet carrier of the second row of planetary gear trains; the input shaft is the sun gear shaft, which meshes with the planet gears of the two rows of planetary gear trains, and its meshing force generates meshing force components in the X and Y directions and torque on the input shaft.

[0124] Specifically, the support bearing supports the rotating shaft, bears radial loads, maintains stable shaft operation, and reduces vibration and wear caused by loads. The planet carrier is the component that supports the planet gears and allows them to rotate around the sun gear. The intermediate bearing is used to transmit power and support the planet carrier, ensuring smooth operation of the planetary gear train. The input shaft, also known as the sun gear shaft, meshes with the planet gears of the two sets of planetary gears. In a planetary gear system, the sun gear is the central gear, meshing with the planet gears to transmit power. When the input shaft (sun gear shaft) meshes with the planet gears, a meshing force is generated. This force has components not only in the axial direction (along the direction of the input shaft) but also in the X and Y directions (i.e., transverse). These components affect the input shaft, causing displacement or vibration in these directions. Simultaneously, the meshing force also generates torque, affecting the rotational motion of the input shaft. Each bearing on the input shaft also generates support forces and bending moments in the X and Y directions. Furthermore, the dynamic imbalance force and torque generated by the CH operating cylinder due to mass eccentricity and misalignment also act on the input shaft.

[0125] Furthermore, the dynamic equations of the input axle system are 5-DOF dynamic equations for bending-torsional-pendulum coupled excitation. According to Newton's second law, the following equations are used to construct the 5-DOF dynamic equations of the input axle system for bending-torsional-pendulum coupled excitation:

[0126]

[0127] Where, q si =[x si ,y si ,θ xsi ,θ ysi ,θ zsi ] indicates 5 degrees of freedom for the input axis; (f xi ,f yi ) represents the input load of the front-end hydraulic torque converter of the planetary transmission mechanism on 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 axis; These represent the supporting reaction forces in the X and Y directions of the B1 support bearing, B2 intermediate bearing, B3 intermediate bearing, B4 intermediate bearing, and B5 intermediate bearing in the input shaft subsystem, respectively. These represent the projections of the meshing forces of the first and second planetary gear trains on the input shaft in the X and Y directions, respectively. This represents the projection of the dynamic unbalance force caused by the mass eccentricity of the CH control component on the input shaft in the X and Y directions. This represents the projection of the dynamic unbalance torque caused by mass eccentricity of the CH control element on the input shaft in the X and Y directions; These represent the coupling forces exerted on the input shaft by the CH actuator in the X and Y directions and the torsional direction, respectively; a b1 a b2 a b3 a b4 and a b5 These represent the distances from the five bearings to the center of mass of the input shaft; a p1 and a p2 These represent the distances from the first and second planetary arrays to the centroid of the input axis, respectively; a i This indicates the distance of the input load from the shaft's center of mass; a d1 This indicates the distance of the CH control element from the center of mass of the shaft; and These represent the torques of the first and second planetary gear trains on the input shaft, respectively.

[0128] The support reaction forces of the 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 planetary carrier, the second planetary carrier, and the sun gear shaft in the X and Y directions, and the centroid distances of each bearing on the input shaft to the input shaft.

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

[0130]

[0131] in, x si These represent the displacements of the first planet carrier, the second planet carrier, and the sun gear axis in the X direction, respectively. The support stiffness of bearings 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 respectively calculated using formula (4). The numbers represent the support damping of bearings 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. In this embodiment, the damping ratio is set to a constant value, with an exemplary value of 0.01 to 0.05.

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

[0133]

[0134] in, y si These represent the displacements in the Y direction of the first planetary carrier, the second planetary carrier, and the sun gear axis, respectively. The support stiffness of bearings 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 respectively calculated using formula (4). The following represent the support damping of bearings 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. In this embodiment, the damping ratio is set to a constant value, with an exemplary value of 0.01 to 0.05.

[0135] When CH actuator 14 is engaged, the coupling force between the first planet carrier and the sun gear shaft is calculated using the following formula.

[0136]

[0137] in, This represents the coupling stiffness vector of CH control element 14; This represents the coupling damping vector of CH control element 14; This represents the displacement vector of the first row of planetary carriers.

[0138] When CH actuator 14 disengages, K CH =0, C CH =0.

[0139] Specifically, such as Figure 6 As shown, the projections of the meshing force of the first-row planetary gear train on the input shaft in the X and Y directions, as well as the torque, are calculated using the following formula:

[0140]

[0141] Among them, R s Indicates the radius of the base circle of the sun gear; This indicates the angular position of the line of mesh between the k-th planet gear and the sun gear in the first row of planetary gear trains, from the X-axis. This is the dynamic load between the sun gear and the kth planet gear in the first row of planetary gear train.

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

[0143]

[0144] in, This indicates the angular position of the line of mesh between the k-th planet gear and the sun gear in the second-row planetary gear train, from the X-axis. This is the dynamic load between the sun gear and the kth planet gear in the first row of planetary gear train.

[0145] It should be noted that the angular position of the line of mesh between the kth planet gear and the sun gear in the first / second row of planetary gear trains, from the X-axis, is calculated using the following formula: Where, φ k α represents the position angle of the k-th planetary gear. sp The pressure angle of the sun gear-planet gear meshing;

[0146] The dynamic load between the sun gear and the k-th planet gear of the first / second row planetary 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] Where, δ spk This represents the relative displacement between the sun gear and the k-th planet gear during meshing; b spk The backlash between the sun gear and the k-th planet gear is represented by x. pk y pk θ zpk θ represents the displacement of the k-th planetary gear along the X-axis, Y-axis, and torsional direction, respectively; zc The displacement in the direction of planetary carrier torsion; r cpke represents the distance from the center of the k-th planetary gear to the center of the sun gear; spk This represents the transmission error between the sun gear and the k-th planet gear along the meshing line; its value is related to parameters such as gear tooth profile error and modification. spk and c spk These represent the meshing stiffness and meshing damping between the sun gear and the k-th planet gear, respectively.

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

[0151] The meshing damping between the sun gear and each planet gear is calculated using the following formula:

[0152]

[0153] Where ζ represents the meshing damping ratio, which is a constant value, and is set to 0.07 in this embodiment; m si and m pk These represent the mass of the sun gear axis and the mass of the kth planet gear, respectively.

[0154] Furthermore, such as Figure 8 As shown, a dynamic model of the first and second row coupled system at the input end of the planetary gear train is established. In the double planetary gear train subsystem of the planetary gear train, the planet carrier of the first row of planetary gear train is connected to the internal gear ring of the second row of planetary gear train. Power is input from the sun gear shaft and output from the planet carrier of the second row of planetary gear train.

[0155] For the planet carrier of the first row of planetary gear system, which supports each planet gear of the first row of planetary gear system, construct its three-degree-of-freedom dynamic equations for bending-torsional coupled excitation.

[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 via their outer edges and connect to the planet carrier via their inner edges. This design enables the planetary gears to transmit power between the sun gear and the planet carrier.

[0157] It should be noted that when the CR clutch 15 is engaged (i.e., locking the planetary carrier so that it cannot rotate), and the CH control element 14 and CL clutch 16 are disengaged (i.e., the power of the input shaft is not transmitted to the planetary carrier and the brake does not apply additional locking), the planetary carrier is connected to the planetary transmission mechanism housing. At this time, because 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 transmission mechanism is negative (i.e., reverse gear). When the CH control element 14 is engaged (i.e., allowing the power of the input shaft to be transmitted to the planetary carrier), and the CR clutch 15 and 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 any increase or decrease in speed. At this time, the transmission ratio of the two rows of planetary gear trains on the right end of the planetary transmission mechanism is 1:1 (i.e., forward high gear).

[0158] Furthermore, based on Newton's second law, the following equation is used to construct the three-degree-of-freedom dynamic equations for the bending-torsional coupled excitation of the planet carrier of the first-row planetary gear system:

[0159]

[0160] in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the planet carrier of the first-row planetary gear system; This represents the mass matrix of the first row of planetary carriers; These represent the supporting reaction forces of intermediate bearings B2 and B3 in the X and Y directions, respectively. R represents the bearing support force of the first planet carrier and the h-th planet gear in the X and Y directions; c1 This indicates the distance from the center of the planetary gear to the center of the first row of planet carriers; This indicates the positioning angle of the h-th planetary gear in the first row of the planet carrier; These represent the coupling forces exerted on the input shaft by the CH actuator in the X and Y directions and the torsional direction, respectively, when engaged. This represents the coupling force vector between the first row of planetary carriers and the planetary transmission mechanism when the CR clutch is engaged.

[0161] Furthermore, the bearing support forces of the first row of planetary carriers and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear in 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 planetary carriers and each planetary gear in the X and Y directions are calculated using the following formula:

[0163]

[0164] in, This represents the displacement vector of the h-th planetary gear in the first row; These 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); These represent the support damping of the first row of planetary gear bearings in the X and Y directions, respectively.

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

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

[0167]

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

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

[0170] Furthermore, for the component consisting of the first row of internal gear rings and the second row of planetary carriers, which meshes with the first row of planetary gear sets and supports the second row of planetary gear sets, a three-degree-of-freedom dynamic equation for its bending-torsional coupled excitation is constructed.

[0171] Specifically, the component meshes with the first row of planetary gear sets to transmit power, while simultaneously supporting the second row of planetary gear sets and providing them with rotational support.

[0172] Furthermore, according to Newton's second law, the dynamic equations of the component consisting of the first row of internal gear rings and the second row of planetary carriers are constructed using the following formula:

[0173]

[0174] in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the component consisting of the first row of internal gear rings and the second row of planetary carriers; F rco ={f xrco ,f yrco M θzrco} TThis represents the output load vector of the component consisting of the first row of internal gear rings and the second row of planetary carriers. This represents the mass matrix of the component consisting of the first row of internal gear rings and the second row of planetary carriers. R represents the bearing support force of the second-row planetary carrier and the h-th planetary gear in the X and Y directions; c2 This 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 gears; This indicates the position angle of the h-th planetary gear in the second row; This represents the dynamic load between the first row of internal gear rings and the h-th planetary gear; These represent the supporting reaction forces in the X and Y directions for intermediate bearings B4, B5, and B6, respectively. This indicates the angular position of the meshing line between the h-th planetary gear in the first row and the internal gear ring in the first row from the X-axis.

[0175] Furthermore, the bearing support forces of the second-row planetary carrier and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear in the second-row planetary gear train, the displacement vector of the second-row planetary 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 planetary carrier and each planetary gear in the X and Y directions are calculated using the following formula:

[0177]

[0178] in, This represents the displacement vector of the h-th planetary gear in the second row; These represent the support stiffness of the second row of planetary gear bearings in the X and Y directions, respectively, and are calculated using formula (4); These represent the support damping of the second row of planetary gear bearings in the x and y directions, respectively.

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

[0180] Specifically, the dynamic load F between the internal gear ring and the h-th planetary gear is calculated using the following formula. rph :

[0181]

[0182] Where, δ rph This represents the relative displacement of meshing between the internal gear ring and the h-th planetary gear; b rph Indicates the tooth flank clearance between the internal gear ring and the h-th planetary gear; x r y r θ zr θ represents the displacement of the internal gear ring along the X, Y, and torsional directions, respectively; zc Displacement in the direction of planetary carrier torsion; α rp ψ represents the pressure angle of the internal gear ring-planet gear meshing pair; rph This is represented by the angular position of the meshing line between the h-th planetary gear and the internal gear ring from the X-axis; r cph R represents the distance from the center of the h-th planetary gear to the center of the internal gear ring; r Indicates the base circle radius of the internal gear ring; e rph This represents the transmission error between the internal gear ring and the h-th planetary gear along the meshing line; k rph and c rph These represent the meshing stiffness and meshing damping of the h-th planetary gear and the internal gear ring, respectively.

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

[0184] The meshing damping between the internal gear ring and each planetary gear is calculated using the following formula:

[0185]

[0186] Where ζ represents the meshing damping ratio, which is a constant value, and is set to 0.07 in this embodiment; m r and m ph These represent the masses of the internal gear ring and the h-th planetary gear, respectively.

[0187] Furthermore, for the first row of planetary gear sets, which simultaneously meshes with the sun gear and the first row of internal gear rings, a 3-degree-of-freedom dynamic equation is constructed for the bending-torsional coupling excitation of each planetary gear.

[0188] Specifically, the first row of planetary gear sets consists of multiple planetary gears that mesh not only with the sun gear but also with the first row of internal gear rings. This dual meshing relationship means that the planetary gear set is affected by both the sun gear and constrained by the internal gear rings during transmission, thus exhibiting complex bending-torsional coupling behavior in dynamics.

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

[0190]

[0191] in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the h-th planetary gear in the first row of planetary gear sets; This represents the mass matrix of the h-th planetary gear in the first row; and These represent the dynamic meshing forces of the first row of sun gears down to the h-th planet gear and the first row of internal gear rings down to the h-th planet gear, respectively. This represents the bearing support force of the first planet carrier and the h-th planet gear in the X and Y directions; This indicates the base circle radius of the first row of planetary gears.

[0192] The bearing support force of the first row of planetary carriers and each planetary gear in the X and Y directions The values ​​are calculated based on the displacement vectors of each planetary gear in 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.

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

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

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

[0196] Furthermore, for the second row of internal gear rings, which mesh with the second row of planetary gear sets, a 3-degree-of-freedom dynamic equation for its bending-torsional coupled excitation is constructed.

[0197] Specifically, the internal gear ring is a ring with teeth inside that mesh with the outer teeth of the planet gears. The function of the second row of internal gear rings is to transmit torque and change the transmission ratio, while its motion is affected by meshing with the planet gears.

[0198] It should be noted that when the CL clutch 16 engages (locking the second row of internal gear rings, preventing them from rotating), and the CH operating element 14 and CR clutch 15 disengage (meaning the input shaft's power is not transmitted to the planet carrier or sun gear, and the CR clutch 15 disengages, meaning the first row of internal gear rings is not locked and can rotate freely), the second row of internal gear rings is connected to the planetary transmission housing. At this time, the transmission ratio of the two rows of planetary gears on the right end of the planetary transmission mechanism is 1:3.111 (i.e., low forward gear). In this case, the rotation of the input shaft is transmitted to the second row of internal gear rings through the first row of planetary gears. Because the second row of internal gear rings is locked, it rotates together with the housing, and the housing's rotational speed is 1 / 3.111 times the input shaft speed, i.e., low gear, to provide greater torque output, suitable for situations requiring greater traction, such as climbing hills or starting acceleration.

[0199] Furthermore, based on Newton's second law, the dynamic equations for the second row of internal gears are constructed using the following formula:

[0200]

[0201] in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the second row of internal gear rings; This represents the mass matrix of the second row of internal gear rings; This represents the coupling force vector between the second-row planetary carrier and the planetary transmission mechanism when the CL clutch is engaged. This represents the dynamic meshing force between the second row of internal gear rings and the h-th planetary gear; This indicates the angular position of the meshing line between the h-th planetary gear and the internal gear ring from the X-axis; This 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 rings and the h-th planetary gear. It is calculated using formula (18).

[0203] The coupling force vector between the second planetary carrier and the planetary transmission mechanism when the CL clutch 16 is engaged is calculated using the following formula.

[0204]

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

[0206] When CL clutch 16 disengages, K CL =0, C CL =0.

[0207] Furthermore, for the second row of planetary gear sets, which simultaneously meshes with the sun gear and the second row of internal gear rings, a three-degree-of-freedom dynamic equation is constructed for the bending-torsional coupling excitation of each planetary gear.

[0208] Specifically, the second-row planetary gear set consists of multiple planetary gears that mesh not only with the sun gear but also with the second-row internal gear ring. This dual meshing relationship means that the planetary gear set is influenced by both the sun gear and constrained by the internal gear ring during transmission, thus exhibiting complex bending-torsional coupling behavior in dynamics.

[0209] Furthermore, based on Newton's second law, the dynamic equations for each planetary gear in the second row of planetary gear sets are constructed using the following formula:

[0210]

[0211] in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the h-th planetary gear in the second row of planetary gear sets; This represents the mass matrix of the h-th planetary gear in the second row; and These represent the dynamic meshing forces of the second row sun gear to the h-th planet gear and the second row internal gear ring to the h-th planet gear, respectively. This indicates the bearing support force of the second-row planetary carrier and the h-th planetary gear in the X and Y directions; This indicates the base circle radius of the second row of planetary gears.

[0212] The bearing support force of the second-row planetary carrier and each planetary gear in the X and Y directions The values ​​are calculated based on the displacement vectors of each planetary gear in the second-row planetary gear train, the displacement vector of the second-row planetary 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.

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

[0214] Dynamic meshing force between the second sun gear and each planet gear The values ​​are calculated based on the relative displacement of the meshing between the second row sun gear and each planet gear, the tooth flank clearance between the second row sun gear and each planet gear, the displacement vector of the second row sun gear, the angular position of the meshing line between each planet gear and the second row sun gear from the X-axis, the distance from the center of each planet 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 planet gear.

[0215] Specifically, the dynamic meshing force between the second row of sun gears and each planet gear is calculated using formula (11).

[0216] Furthermore, such as Figure 9 As shown, in the output drive shaft subsystem of the planetary gear transmission mechanism, a B10 support bearing is provided on the output drive shaft, a B8 intermediate bearing supports the composite gear input ring gear, a B9 intermediate bearing supports the composite gear planet carrier, the drive shaft is the sun gear shaft, and it meshes with the composite gear long planet gear. The meshing force generates meshing force components in the X and Y directions and torque on the drive shaft.

[0217] Specifically, in the output drive shaft subsystem of the planetary gearbox, the B10 support bearing supports the drive shaft, bears radial and axial loads from the drive shaft, and maintains the stability and accuracy of the drive shaft; the B8 and B9 intermediate bearings transmit loads and support the planetary gear train, ensuring its smooth operation; the compound gear input ring gear is a component in the planetary gear system, meshing with the planetary gears and participating in power transmission; the compound gear planet carrier is a component that supports the planetary gears and allows them to rotate around the sun gear; the sun gear shaft meshes with the planetary gears, transmitting power through this meshing. When the sun gear shaft meshes with the long planetary gears of the compound gear, a meshing force is generated. This force has components not only in the axial direction (along the drive shaft) but also in the X and Y directions (i.e., transverse). These components affect the drive shaft, causing displacement or vibration in these directions. Simultaneously, the meshing force also generates torque, affecting the rotational motion of the drive shaft. This torque is crucial for the drive shaft's power transmission, determining its output speed and torque.

[0218] It should be noted that the dynamic unbalance force and torque generated by the mass eccentricity and skewness of C2 control component 18 and C3 control component 19 also act on the drive shaft.

[0219] Furthermore, the dynamic equations of the output-end transmission shaft subsystem are 5-DOF dynamic equations of bending-torsional-pendulum coupled excitation. Based on Newton's second law, the following equations are used to construct the 5-DOF dynamic equations of the output-end transmission shaft subsystem under bending-torsional-pendulum coupled excitation:

[0220]

[0221] Where, q so =[x so ,y so ,θ xso ,θ yso ,θ zso [] indicates 5 degrees of freedom for the output drive shaft; M so =diag([m so ,m so,I xso ,I yso ,I zso ]) represents the mass matrix of the output drive shaft; F o ={f xo ,f yo M θzo} T This represents the external load vector on the output drive shaft; These represent the supporting reaction forces in the X and Y directions for intermediate bearings B8, B9, and B10, respectively. This represents the projection of the dynamic imbalance force caused by the mass eccentricity of the C2 and C3 operating components on the output drive shaft in the X and Y directions. This represents the projection of the dynamic unbalance torque caused by mass eccentricity of the C2 and C3 operating components on the output drive shaft in the X and Y directions. These represent the coupling forces exerted on the output drive shaft by the C2 and C3 actuators in the X and Y directions and the torsional direction, respectively, when they are engaged; a b8 a b9 and a b10 These represent the distances from the B8 intermediate bearing, B9 intermediate bearing, and B10 support bearing to the center of mass of the output drive shaft, respectively; a p3 a represents the distance from the compound pile to the center of mass of the drive shaft. d3 This indicates the distance of the C2 and C3 control components from the center of mass of the shaft; This represents the projection of the meshing force of the composite gearbox on the sun gear of the output drive shaft in the X and Y directions; This indicates the torque of the compound drive on the sun gear of the output drive shaft; a o This indicates the distance between the input load and the center of mass of the output drive shaft.

[0222] The supporting reaction forces of the intermediate bearings B8, B9, and B10 in the X and Y directions of the output drive shaft subsystem are calculated based on the time-varying nonlinear support stiffness of the bearings, the displacement of the composite planetary carrier and the output drive shaft in the X and Y directions, and the centroid distance from each bearing on the output drive shaft to the input shaft.

[0223] Specifically, the support reactions of intermediate bearings B8, B9, and B10 in the X and Y directions are calculated using the following formula:

[0224]

[0225] in, x so y so These represent the displacements of the composite planetary carrier and the drive shaft in the X and Y directions, respectively. The support stiffness of intermediate bearing 8 (B8), intermediate bearing 9 (B9), and support bearing 10 (B10) in the X and Y directions are respectively calculated using formula (4). The terms B8 (intermediate bearing 8), B9 (intermediate bearing 9), and B10 (support bearing 10) represent the support damping in the X and Y directions, respectively. In this embodiment, the damping ratio is set to a constant value, with an exemplary value of 0.01 to 0.05.

[0226] It should be noted that in the output drive shaft subsystem, when the C2 control element 18 is engaged (i.e., locking the relative movement between the sun gear shaft and the planetary gearbox housing, allowing them to rotate synchronously), and the C3 control element 19 and C1 clutch 17 are disengaged, the sun gear shaft is connected to the planetary gearbox housing. At this time, the transmission ratio of the left-end compound gearbox of the planetary gearbox is 1:1.442, indicating that the rotational speed of the sun gear shaft is 1.442 times the rotational speed of the housing, which is used for specific driving conditions. When the C3 control element 19 is engaged (i.e., locking the relative movement between the sun gear shaft and the compound gearbox planetary carrier, allowing them to rotate synchronously), and the C2 control element 18 and C1 clutch 17 are disengaged, the sun gear shaft is connected to the compound gearbox planetary carrier. At this time, the transmission ratio of the left-end compound gearbox of the planetary gearbox is 1:1, indicating that the rotational speed of the sun gear shaft is the same as the rotational speed of the compound gearbox planetary carrier, which is used for high-speed driving.

[0227] When C2 actuator 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, This represents the coupling stiffness vector of the C2 control element 18; This represents the coupling damping vector of C2 control element 18.

[0230] When C3 actuator 19 is engaged, the coupling force vectors of the output drive shaft in the X and Y directions and the torsional direction are calculated using the following formula.

[0231]

[0232] in, This represents the coupling stiffness vector of C3 control element 19; This represents the coupling damping vector of C3 control element 19; This represents the displacement vector of the composite planetary carrier.

[0233] Specifically, the projections of the meshing force between the compound gear and the sun gear on the drive shaft in the X and Y directions, as well as the torque, are calculated using the following formula:

[0234]

[0235] in, Indicates the base circle radius of the composite sun gear; ψ slpu Indicates as Figure 10 The angular position of the line of mesh between the u-th long planetary gear and the sun gear in the compound arrangement shown is calculated using the following formula: in, α represents the position angle of the u-th long planetary gear in the composite arrangement; slp F represents the pressure angle of the sun gear-long planet gear meshing; slpu The dynamic load between the sun gear and the u-th long planet gear is represented by the following formula:

[0236]

[0237] Where, δ slpu This indicates the relative displacement of meshing between the compound sun gear and the u-th long planet gear; b slpu The backlash between the sun gear and the u-th planet gear is represented by x. lpu y lpu θ zlpu This represents the displacement of the u-th long planetary gear along the X, Y, and torsional directions; r clpu R represents the distance from the center of the u-th long planetary gear to the center of the sun gear; s R represents the base circle radius of the composite sun gear; lp Indicates the base circle radius of the long planetary gear; e slpu This represents the transmission error between the sun gear and the u-th long planet gear along the meshing line. This value is related to parameters such as gear tooth profile error and modification; k slpu and c slpu These represent the meshing stiffness and meshing damping between the composite sun gear and the u-th long planet gear, respectively.

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

[0239] The meshing damping between the sun gear and each of the long planetary gears is calculated using the following formula:

[0240]

[0241] Where ζ is the meshing damping ratio, a constant value, set to 0.07 in this embodiment; m so and m lpu These represent the mass of the sun gear axis and the mass of the u-th long planet gear, respectively.

[0242] Furthermore, such as Figure 10As shown, in the compound planetary gear system of the planetary transmission 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 ring gear 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 input ring gear and output from the compound planetary carrier.

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

[0244] Furthermore, for the planet carrier of the composite planetary gear system, which simultaneously supports both long and short planetary gear sets, a three-degree-of-freedom dynamic equation for its bending-torsional coupled excitation is constructed.

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

[0246] Furthermore, based on Newton's second law, the dynamic equations of the planet carrier of the composite planetary gear system are constructed using the following formula:

[0247]

[0248] Where, q This represents the 3 degrees of freedom of the bending-torsional coupled excitation of the planet carrier in the composite planetary gear system; This represents the mass matrix of the planet carrier in a composite planetary gear system. These represent the supporting reaction forces in the X and Y directions for intermediate bearings B7, B8, and B9, respectively. This represents the bearing support force of the composite planetary carrier and the u-th short planetary gear in the X and Y directions; This represents the bearing support force of the composite planetary carrier and the u-th long planetary gear in the X and Y directions; This indicates the coupling force between the planetary carrier of the compound planetary gear system and the transmission housing in the X and Y directions, as well as the torsional direction, when the C2 / C3 control components are engaged; r c This represents the distance from the center of the short planetary gear to the center of the planet carrier; r lc This indicates the distance from the center of the long planetary gear to the center of the planet carrier; This represents the positioning angle of the u-th short planetary gear; This represents the positioning angle of the u-th long planetary gear.

[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 planetary carrier, 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 angle of each short planetary gear.

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

[0251]

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

[0253] Furthermore, the bearing support forces of the composite planetary carrier and each long planetary gear in the X and Y directions are calculated based on the displacement vectors of each long planetary gear in the composite planetary carrier, the support stiffness of the long planetary gear bearings in the X and Y directions, the support damping of the long planetary gear bearings in the X and Y directions, the distance from the center of the long planetary gear to the center of the planetary carrier, and the positioning angle of each long planetary gear.

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

[0255]

[0256] in, Let represent the displacement vector of the u-th long planetary gear in the composite arrangement; These represent the support stiffness of the long planetary gear bearing in the X and Y directions, respectively, and are calculated using formula (4); These represent the support damping of the long planetary gear bearing in the x and y directions, respectively; r lc This indicates the distance from the center of the long planetary gear to the center of the planet carrier; This represents the positioning angle of the u-th long planetary gear.

[0257] Furthermore, the support reaction force of the intermediate bearing B7 in the planetary carrier of the composite 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 composite 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 supporting reaction forces of intermediate bearing 7 (B7) in the planet carrier of the composite planetary gear system in the X and Y directions are calculated using the following formula:

[0259]

[0260] in, These represent the displacements of the compound gear input ring in the X and Y directions, respectively; The support stiffness of intermediate bearing 7 in the X and Y directions respectively are represented by formula (4); These represent the support damping of intermediate bearing 7 in the X and Y directions, respectively.

[0261] When C2 control element 18 is engaged, the coupling force vector between the composite planetary carrier and the transmission mechanism housing is calculated using the following formula:

[0262]

[0263] in, This represents the coupling stiffness vector of the C2 control element 18; This represents the coupling damping vector of C2 control element 18.

[0264] When C3 control element 19 is engaged, the coupling force vector between the composite planetary carrier and the drive shaft is calculated using the following formula.

[0265]

[0266] in, This represents the coupling stiffness vector of C3 control element 19; This represents the coupling damping vector of C3 control element 19; This represents the displacement vector of the composite drive shaft of the speed change mechanism.

[0267] When C2 control element 18 disengages, K C2 =0, C C2 =0 when C3 control element 19 disengages K C3 =0, C C3 =0.

[0268] Furthermore, for the composite input gear ring, it is coupled with the planet carrier of the second row of planetary gear train of the planetary transmission mechanism, and simultaneously meshes with the composite long planetary gear set, thus constructing its three-degree-of-freedom dynamic equations for bending-torsional coupling excitation.

[0269] Specifically, the motion of the composite gear input ring is affected by the connection with the planet carrier and the meshing with the long planet gear. Its dynamic equation needs to take into account the supporting forces from the connection with the planet carrier and the meshing with the long planet gear, as well as the torque generated due to the meshing.

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

[0271]

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

[0273] The dynamic loads of each long planetary gear in the compound gear set and the input gear ring are calculated based on the tooth flank clearance of the internal gear ring and the corresponding long planetary gear, the displacement vector of the corresponding long planetary gear in the compound gear set, the angular position of the meshing line of the corresponding long planetary gear and the input gear ring from the X-axis, the base circle radius of the input gear ring, the displacement of the input gear ring along the X-direction, Y-direction and torsional direction, and the displacement of the planet carrier in the torsional direction.

[0274] Specifically, the dynamic loads on each planetary gear in the composite gear set and the input gear ring are calculated using the following formula:

[0275]

[0276] in, This represents the coupling stiffness vector between the component consisting of the first row of internal gear rings and the second row of planetary carriers at the input end of the planetary transmission mechanism and the composite row of input gear rings at the output end. This represents the coupling damping vector between the component consisting of the first row of internal gear rings and the second row of planetary carriers at the input end of the planetary transmission mechanism and the composite row of input gear rings at the output end.

[0277] The dynamic load F between the u-th long planetary gear and the input gear ring is calculated using the following formula. rlpu :

[0278]

[0279] Where, δ rlpu This represents the relative displacement of meshing between the compound gear input ring and the u-th long planetary gear; b rlpu Indicates the tooth flank clearance between the internal gear ring and the u-th long planetary gear; x r y r θzr θ represents the displacement of the input gear ring along the X, Y, and torsional directions; zc Displacement in the direction of planetary carrier torsion; α rlp ψ represents the pressure angle of the meshing pair between the input gear ring and the long planetary gear; rlpu This indicates the angular position of the line of mesh between the u-th long planetary gear and the input gear ring from the X-axis; r clpu R represents the distance from the center of the u-th long planetary gear to the center of the input gear ring; r Indicates the base circle radius of the gear ring; e rlpu This represents the transmission error between the input gear ring and the u-th long planetary gear along the meshing line; k rlpu c rlpu These represent the meshing stiffness and meshing damping between the input gear ring and the u-th long planetary gear, respectively.

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

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

[0282]

[0283] Where ζ represents the meshing damping ratio, which is a constant value, and is set to 0.07 in this embodiment; m r and m lpu These represent the input gear ring and the mass of the u-th long planetary gear, respectively.

[0284] Furthermore, for the composite long planetary gear set, which simultaneously meshes with the input ring gear, the sun gear, and the short planetary gear set, a 3-DOF dynamic equation for its bending-torsional coupled excitation is constructed.

[0285] Specifically, the compound planetary gear set meshes with the input ring gear, enabling the input ring gear to transmit power to the long planetary gears; the compound planetary gear set meshes with the sun gear, allowing the sun gear to influence the rotational speed and direction of the long planetary gears; the long planetary gear set meshes with the short planetary gear set, forming the second stage of transmission in the compound planetary gear system.

[0286] Furthermore, based on Newton's second law, the dynamic equations of the composite planetary gear set are constructed using the following formula:

[0287]

[0288] in, This represents the 3 degrees of freedom of the bending-torsional coupled excitation of the u-th long planetary gear in the composite array; F represents the mass matrix of the u-th long planetary gear in the composite arrangement;slpu F represents the dynamic load on the axis of the u-th long planetary gear in the composite array and the sun gear; rlpu F represents the dynamic load between the u-th long planetary gear in the compound gear arrangement and the input gear ring; lppu ψ represents the dynamic load between the u-th long planetary gear and the u-th short planetary gear in the composite arrangement; slpu ψ represents the angle between the line of meshing of the u-th long planetary gear and the sun gear axis and the X-axis; rlpu ψ represents the angle between the line of meshing of the u-th long planetary gear in the compound gear set and the input gear ring and the X-axis; llpu This 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 arrangement from the X-axis; This indicates the radius of the base circle of the composite planetary gear.

[0289] The dynamic load of the u-th long planetary gear and the u-th short planetary gear in the composite gear set is calculated based on the tooth backlash 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.

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

[0291]

[0292] Where, δ lppu b represents the meshing relative displacement between the u-th long planetary gear and the u-th short planetary gear; lppu The backlash between the u-th long planetary gear and the u-th short planetary gear is represented by x. pu y pu θ zpu θ represents the displacement of the u-th short planetary gear along the X, Y, and torsional directions, respectively; zc Displacement in the direction of planetary carrier torsion; α lppu This represents the pressure angle of the u-th long planetary gear-short planetary gear meshing pair; This represents the angular position of the meshing line between the u-th long planetary gear and the k-th short planetary gear from the X-axis; r cpu R represents the distance from the center of the u-th short planetary gear to the center of the internal gear ring; p e is the radius of the base circle of the short planetary gear; lppu This 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 These represent the meshing stiffness and meshing damping between each pair of long and short planetary gears, respectively; γ p This indicates the positioning angle of the short planetary gear.

[0293] It should be noted that the magnitude and amplitude of the meshing stiffness 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 using the energy method.

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

[0295]

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

[0297] Furthermore, for the composite short planetary gear set, which simultaneously meshes with the long planetary gear set and the floating ring gear, a 3-DOF dynamic equation for its bending-torsional coupled excitation is constructed.

[0298] Specifically, each short planet gear in the compound planetary gear set meshes with a corresponding long planet gear to transmit power between the planet carrier and the floating ring gear; the short planet gears mesh with the floating ring gear to transmit power between the floating ring gear and the short planet gears. After power is transmitted to the short planet gear set through the long planet gear set, it is then transmitted to other parts of the system through the meshing of the short planet gears with the floating ring gear, enabling the compound planetary gear system to achieve various transmission ratios and power distributions.

[0299] Furthermore, according to Newton's second law, the dynamic equations of the compound short planetary gear set are constructed using the following formula:

[0300]

[0301] in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the u-th short planetary gear in the composite array; F represents the mass matrix of the u-th short planetary gear in the composite arrangement; frpu ψ represents the dynamic load between the compound floating gear ring and the u-th short planetary gear; frpu This indicates the angular position of the compound floating gear ring relative to the X-axis from the meshing line of the u-th short planetary gear; This indicates the base circle radius of the composite short planetary gear set.

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

[0303] Specifically, the dynamic load F between the compound floating gear ring and the u-th short planetary gear is calculated using the following formula. frpu :

[0304]

[0305] Where, δ frpu This indicates the relative displacement of the compound floating gear ring and the u-th short planetary gear during meshing; b frpu This represents the tooth flank clearance between the compound floating gear ring and the u-th short planetary gear; x fr y fr θ zfr θ represents the displacement of the floating gear ring along the X, Y, and torsional directions, respectively; zc Displacement in the direction of planetary carrier torsion; α frp ψ represents the pressure angle of the floating gear ring-short planetary gear meshing pair; frpu This indicates the angular position of the floating gear ring relative to the X-axis from the line of meshing with the u-th short planetary gear; r cpu R represents the distance from the center of the u-th short planetary gear to the center of the floating gear ring; fr Indicates the base circle radius of the floating gear ring; e frpu This represents the transmission error between the floating gear ring and the u-th short planetary gear along the meshing line; k frpu and c frpu These represent the meshing stiffness and meshing damping between the composite floating gear ring and the u-th short planetary gear, respectively.

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

[0307] Calculate the meshing damping between the input gear ring and each short planetary gear using the following formula:

[0308]

[0309] Where ζ is the meshing damping ratio, a constant value, set to 0.07 in this embodiment; m fr and m pu Let the masses of the floating gear ring and the u-th short planetary gear be represented respectively.

[0310] Furthermore, for the composite floating gear ring, which meshes with the composite planetary gear set, a 3-degree-of-freedom dynamic equation for its bending-torsional coupled excitation is constructed.

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

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

[0313]

[0314] in, This represents the 3 degrees of freedom of the bending-torsional coupled excitation of the composite floating gear ring; This represents the mass matrix of the composite floating gear ring; This represents the coupling force vector between the compound floating gear ring and the transmission mechanism housing when the C1 clutch is engaged.

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

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

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

[0318]

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

[0320] When clutch C1 17 disengages, 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 planetary carrier / bearing housing on the outer ring of the bearing. o and deformation δ o and the dynamic load f of the drive shaft on the inner ring i and deformation δ i The system's support stiffness and dynamic response at the current moment are calculated. The dynamic models of each subsystem of the planetary transmission mechanism are combined and solved using the fourth-order Runge-Kutta numerical iteration algorithm to obtain the dynamic response of the planetary transmission mechanism in the next time step. The process is iterated until the dynamic characteristics prediction is completed.

[0322] Specifically, the initial vibration displacement q0 and the initial vibration velocity of the system are set at the initial time t0 of the differential equation. The initial support stiffness K of each bearing is calculated as 0 based on the weight of each component and the static load borne by each support bearing is estimated. The initial support stiffness K of each bearing is obtained using formula (4) in step S2. b0 Set the numerical integration step size Δt, and based on the time-varying support stiffness of the bearing at the previous iteration time, substitute it into the dynamic model of each subsystem of the planetary transmission mechanism described in step S3 to calculate the dynamic response of the system at the current time until the simulation cutoff time is reached, so as to realize the simulation and prediction of the dynamic characteristics of the bending and torsional coupling excitation of the multi-point support components of the planetary transmission mechanism.

[0323] In summary, the method for predicting the dynamic characteristics of a planetary transmission mechanism with multi-point support and bending-torsional coupling excitation according to an embodiment of the present invention has the following beneficial effects:

[0324] 1. This invention establishes a method for predicting the dynamic characteristics of planetary transmission mechanisms through multi-point support bending and torsional coupling excitation. This method enables simulation analysis and optimization design of the motion characteristics and transmission performance of the mechanism, thereby improving its working efficiency and transmission stability, and 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 transmission mechanism by coupling the motion equations of multiple degrees of freedom of each component, while ensuring high computational efficiency. It also considers 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. By estimating the dynamic characteristics of the planetary transmission mechanism, this invention can predict the motion state and transmission characteristics of the mechanism under different working conditions, thereby providing a reliable reference for the design and optimization of mechanical systems and improving the reliability and service life of mechanical systems.

[0327] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the dynamic characteristics of a planetary transmission mechanism under multi-point support bending-torsional coupling excitation, characterized in that, The planetary transmission mechanism employs a dual-rotor structure; the method includes: Obtain the parameters of each planetary gear component and each bearing of the planetary transmission 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 parameters of the bearing 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 planetary gear component, a subsystem dynamic model of the planetary gear mechanism is established; wherein, the planetary gear mechanism subsystem includes an input shaft subsystem, a double planetary gear subsystem, an output transmission shaft subsystem, and a compound gear subsystem; Within a given time step, calculate the dynamic load f of the planetary carrier / bearing housing on the outer ring of the bearing when the inner and outer rings of the intermediate bearing rotate simultaneously. o and deformation δ o and the dynamic load f of the drive shaft on the inner ring i and deformation δ i The system's support stiffness and dynamic response at the current moment are calculated. The dynamic models of each subsystem of the planetary transmission mechanism are combined and solved using the fourth-order Runge-Kutta numerical iteration algorithm to obtain the dynamic response of the planetary transmission mechanism in the next time step. The process is iterated until the dynamic characteristics prediction 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 formula: Among them, K n Indicates the combined normal contact stiffness between the inner rollers and the inner and outer rings of the bearing; n represents the contact factor; N represents the total number of inner rollers in the bearing; A0 represents the relative distance between the centers of curvature of the grooves before deflection of the inner and outer raceways of the bearing; A j This represents the relative distance between the centers of curvature of the grooves at the j-th roller inside the bearing after the inner and outer raceways have deflected. δ represents the azimuth angle of the j-th roller in the bearing at time t; jr This represents the radial distance between the centers of curvature of the inner and outer ring grooves at the j-th roller inside the bearing after deflection.

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

4. The method according to claim 3, characterized in that, The dynamic equations of the input axle system are 5-DOF dynamic equations for bending-torsional-pendulum coupled excitation. The following equations are used to construct the 5-DOF dynamic equations of the input axle system for bending-torsional-pendulum coupled excitation: Where, q si =[x si ,y si ,θ xsi ,θ ysi ,θ zsi ] indicates 5 degrees of freedom for the input axis; (f xi ,f yi ) represents the input load of the front-end hydraulic torque converter of the planetary transmission mechanism on the input shaft in the X and Y directions; M θzi Indicates input torque; M si =diag([m si ,m si ,Ix si ,Iy si ,Iz si ]) represents the mass matrix of the sun gear axis; These represent the supporting reaction forces in the X and Y directions of the B1 support bearing, B2 intermediate bearing, B3 intermediate bearing, B4 intermediate bearing, and B5 intermediate bearing in the input shaft subsystem, respectively. These represent the projections of the meshing forces of the first and second planetary gear trains on the input shaft in the X and Y directions, respectively. This represents the projection of the dynamic unbalance force caused by the mass eccentricity of the CH control component on the input shaft in the X and Y directions. This represents the projection of the dynamic unbalance torque caused by mass eccentricity of the CH control element on the input shaft in the X and Y directions; These represent the coupling forces exerted on the input shaft by the CH actuator in the X and Y directions and the torsional direction, respectively; a b1 a b2 a b3 a b4 and a b5 These represent the distances from the five bearings to the center of mass of the input shaft; a p1 and a p2 These represent the distances from the first and second planetary arrays to the centroid of the input axis, respectively; a i This indicates the distance of the input load from the shaft's center of mass; a d1 This indicates the distance of the CH control element from the center of mass of the shaft; and These represent the torques of the first and second planetary gear trains relative to the input shaft, respectively. The support reactions 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 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 centroid distance of each bearing on the input shaft to the input shaft.

5. The method according to claim 2, characterized in that, In the dual planetary gear train system of the planetary transmission mechanism, the planet carrier of the first planetary gear train is connected to the internal gear ring of the second planetary gear train. Power is input from the sun gear shaft and output from the planet carrier of the second planetary gear train. For the planet carrier of the first row of planetary gear system, which supports each planet gear of the first row of planetary gear system, construct its three-degree-of-freedom dynamic equations for bending-torsional coupled excitation; For the component consisting of the first row of internal gear rings and the second row of planetary carriers, which meshes with the first row of planetary gear sets and supports the second row of planetary gear sets, construct its three-degree-of-freedom dynamic equations for bending-torsional coupling excitation; For the first row of planetary gear sets, which simultaneously meshes with the sun gear and the first row of internal gear rings, a 3-degree-of-freedom dynamic equation is constructed for the bending-torsional coupling excitation of each planetary gear. For the second row of internal gear rings, which mesh with the second row of planetary gear sets, construct a 3-degree-of-freedom dynamic equation for its bending-torsional coupled excitation; For the second row of planetary gears, which meshes with both the sun gear and the second row of internal gear rings, a three-degree-of-freedom dynamic equation is constructed for the bending-torsional coupling excitation of each planetary gear.

6. The method according to claim 5, characterized in that, The dynamic equations of the planet carrier for the first row of planetary gear systems are constructed using the following formula: in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the planet carrier of the first-row planetary gear system; This represents the mass matrix of the first row of planetary carriers; These represent the supporting reaction forces of intermediate bearings B2 and B3 in the X and Y directions, respectively. R represents the bearing support force of the first planet carrier and the h-th planet gear in the X and Y directions; c1 This indicates the distance from the center of the planetary gear to the center of the first row of planet carriers; This indicates the positioning angle of the h-th planetary gear in the first row of the planet carrier; These represent the coupling forces exerted on the input shaft by the CH actuator in the X and Y directions and the torsional direction, respectively, when engaged. This represents the coupling force vector between the first row of planetary carriers and the planetary transmission mechanism when the CR clutch is engaged; The bearing support forces of the first row of planetary carriers and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear in 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. The coupling force vector between the first row of planetary carriers and the planetary transmission mechanism is calculated based on the displacement vector of the first row of planetary carriers, the coupling stiffness vector of the CR clutch, and the coupling damping vector when the CR clutch is engaged; it is set to 0 when the CR clutch is disengaged. The following equations can be used to construct the dynamic equations of the component consisting of the first row of internal gear rings and the second row of planetary carriers: in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the component consisting of the first row of internal gear rings and the second row of planetary carriers; F rco ={f xrco ,f yrco M θzrco } T This represents the output load vector of the component consisting of the first row of internal gear rings and the second row of planetary carriers. This represents the mass matrix of the component consisting of the first row of internal gear rings and the second row of planetary carriers. R represents the bearing support force of the second-row planetary carrier and the h-th planetary gear in the X and Y directions; c2 This 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 gears; This indicates the position angle of the h-th planetary gear in the second row; This represents the dynamic load between the first row of internal gear rings and the h-th planetary gear; These represent the supporting reaction forces in the X and Y directions for intermediate bearings B4, B5, and B6, respectively. This indicates the angular position of the meshing line between the h-th planetary gear in the first row and the internal gear ring in the first row from the X-axis; The bearing support forces of the second-row planetary carrier and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear in the second-row planetary gear train, the displacement vector of the second-row planetary 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 internal gear rings and each planetary gear is calculated based on the meshing relative displacement between the first row of internal gear rings and each planetary gear, the tooth flank clearance between the first row of internal gear rings and each planetary gear, the displacement vector of the first row of internal gear rings, the angular position of the meshing line between each planetary gear and the first row of internal gear rings from the X-axis, the distance from the center of each planetary gear to the center of the first row of internal gear rings, the base circle radius of the first row of internal gear rings, and the meshing stiffness and meshing damping between the first row of internal gear rings and each planetary gear. The dynamic equations for each planetary gear in the first row of planetary gear sets are constructed using the following formula: in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the h-th planetary gear in the first row of planetary gear sets; This represents the mass matrix of the h-th planetary gear in the first row; and These represent the dynamic meshing forces of the first row of sun gears down to the h-th planet gear and the first row of internal gear rings down to the h-th planet gear, respectively. This represents the bearing support force of the first planet carrier and the h-th planet gear in the X and Y directions; This indicates the base circle radius of the first row of planetary gears; The bearing support forces of the first row of planetary carriers and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear in 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. The dynamic meshing force between the first row of sun gears and each planet gear is calculated based on the relative meshing displacement between the first row of sun gears and each planet gear, the tooth flank clearance between the first row of sun gears and each planet gear, the displacement vector of the first row of sun gears, the angular position of the meshing line between each planet gear and the first row of sun gears from the X-axis, the distance from the center of each planet gear to the center of the first row of sun gears, the base circle radius of the first row of sun gears, and the meshing stiffness and meshing damping between the first row of sun gears and each planet gear. The dynamic equations for the second row of internal gears are constructed using the following formula: in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the second row of internal gear rings; This represents the mass matrix of the second row of internal gear rings; This represents the coupling force vector between the second-row planetary carrier and the planetary transmission mechanism when the CL clutch is engaged. This represents the dynamic meshing force between the second row of internal gear rings and the h-th planetary gear; This indicates the angular position of the meshing line between the h-th planetary gear and the internal gear ring from the X-axis; Indicates the base circle radius of the second row of internal gears; The dynamic equations for each planetary gear in the second row of planetary gear sets are constructed using the following formula: in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the h-th planetary gear in the second row of planetary gear sets; This represents the mass matrix of the h-th planetary gear in the second row; and These represent the dynamic meshing forces of the second row sun gear to the h-th planet gear and the second row internal gear ring to the h-th planet gear, respectively. This indicates the bearing support force of the second-row planetary carrier and the h-th planetary gear in the X and Y directions; This indicates the base circle radius of the second row of planetary gears; The bearing support forces of the second-row planetary carrier and each planetary gear in the X and Y directions are calculated based on the displacement vectors of each planetary gear in the second-row planetary gear train, the displacement vector of the second-row planetary 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 planet gear is calculated based on the relative meshing displacement between the second-row sun gear and each planet gear, the tooth flank clearance between the second-row sun gear and each planet gear, the displacement vector of the second-row sun gear, the angular position of the meshing line between each planet gear and the second-row sun gear from the X-axis, the distance from the center of each planet 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 planet gear.

7. The method according to claim 2, characterized in that, In the output drive shaft subsystem of the planetary gear transmission mechanism, a B10 support bearing is provided on the output drive shaft, a B8 intermediate bearing supports the composite gear input ring gear, a B9 intermediate bearing supports the composite gear planet carrier, the drive shaft is the sun gear shaft, and it meshes with the composite gear long planet gear. The meshing force generates meshing force components in the X and Y directions and torque on the drive shaft.

8. The method according to claim 7, characterized in that, The dynamic equations of the output drive shaft subsystem are 5-DOF dynamic equations for bending-torsional-pendulum coupled excitation. The following equations are used to construct the 5-DOF dynamic equations of the output drive shaft subsystem for bending-torsional-pendulum coupled excitation: Where, q so =[x so ,y so ,θ xso ,θ yso ,θ zso [] indicates 5 degrees of freedom for the output drive shaft; M so =diag([m so ,m so ,I xso ,I yso ,I zso ]) represents the mass matrix of the output drive shaft; F o ={f xo ,f yo M θzo } T This represents the external load vector on the output drive shaft; These represent the supporting reaction forces in the X and Y directions for intermediate bearings B8, B9, and B10, respectively. This represents the projection of the dynamic imbalance force caused by the mass eccentricity of the C2 and C3 operating components on the output drive shaft in the X and Y directions. This represents the projection of the dynamic unbalance torque caused by mass eccentricity of the C2 and C3 operating components on the output drive shaft in the X and Y directions. These represent the coupling forces exerted on the output drive shaft by the C2 and C3 actuators in the X and Y directions and the torsional direction, respectively, when they are engaged; a b8 a b9 and a b10 These represent the distances from the B8 intermediate bearing, B9 intermediate bearing, and B10 support bearing to the center of mass of the output drive shaft, respectively; a p3 a represents the distance from the compound pile to the center of mass of the drive shaft. d3 This indicates the distance of the C2 and C3 control components from the center of mass of the shaft; This represents the projection of the meshing force of the composite gearbox on the sun gear of the output drive shaft in the X and Y directions; This indicates the torque of the compound drive on the sun gear of the output drive shaft; a o This indicates the distance between the input load and the center of mass of the output drive shaft; The supporting reaction forces of the intermediate bearings B8, B9, and B10 in the X and Y directions of the output drive shaft subsystem are calculated based on the time-varying nonlinear support stiffness of the bearings, the displacement of the composite planetary carrier and the output drive shaft in the X and Y directions, and the centroid distance from each bearing on the output drive shaft to the input shaft.

9. The method according to claim 2, characterized in that, In the compound planetary gear system of the planetary transmission 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 ring gear 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 input ring gear and output from the compound planetary carrier; For a planet carrier of a composite planetary gear system, which simultaneously supports both long and short planetary gear sets, a 3-degree-of-freedom dynamic equation for its bending-torsional coupled excitation is constructed. For the composite input gear ring, it is coupled with the planet carrier of the second row of planetary gear train of the planetary transmission mechanism, and meshes with the composite long planetary gear set, thus constructing its three-degree-of-freedom dynamic equations for bending-torsional coupling excitation; For the composite long planetary gear set, it meshes with the input gear ring, the sun gear and the short planetary gear set at the same time, and constructs its three-degree-of-freedom dynamic equations for bending-torsional coupling excitation; For a composite short planetary gear set, which simultaneously meshes with a long planetary gear set and a floating ring gear, a 3-DOF dynamic equation for its bending-torsional coupled excitation is constructed. For a composite floating gear ring, which meshes with a composite planetary gear set, a 3-DOF dynamic equation for its bending-torsional coupled excitation is constructed.

10. The method according to claim 9, characterized in that, The dynamic equations of the planet carrier of the composite planetary gear system are constructed using the following formula: in, This represents the 3 degrees of freedom of the bending-torsional coupled excitation of the planet carrier in the composite planetary gear system; This represents the mass matrix of the planet carrier in a composite planetary gear system. These represent the supporting reaction forces in the X and Y directions for intermediate bearings B7, B8, and B9, respectively. This represents the bearing support force of the composite planetary carrier and the u-th short planetary gear in the X and Y directions; This represents the bearing support force of the composite planetary carrier and the u-th long planetary gear in the X and Y directions; This indicates the coupling force between the planetary carrier of the compound planetary gear system and the transmission housing in the X and Y directions, as well as the torsional direction, when the C2 / C3 control components are engaged; r c This represents the distance from the center of the short planetary gear to the center of the planet carrier; r lc This indicates the distance from the center of the long planetary gear to the center of the planet carrier; This represents the positioning angle of the u-th short planetary gear; This represents the positioning angle of the u-th long planetary gear; 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 planetary carrier, 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 angle of each short planetary gear. The bearing support forces of the composite planetary carrier and each long planetary gear in the X and Y directions are calculated based on the displacement vectors of each long planetary gear in the composite planetary carrier, the support stiffness of the long planetary gear bearings in the X and Y directions, the support damping of the long planetary gear bearings in the X and Y directions, the distance from the center of the long planetary gear to the center of the planetary carrier, and the positioning angle of each long planetary gear. The support reaction force of the intermediate bearing B7 in the planetary carrier of the composite 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 composite input gear ring in the X and Y directions, and the support damping of the bearing in the X and Y directions. The dynamic equations of the composite input gear ring are constructed using the following formula: in, F represents the three degrees of freedom of the bending-torsional coupled excitation of the composite gear ring input; ro ={f xro ,f yro M θzro } T This represents the input load vector of the composite gear ring; F represents the mass matrix of the compound gear input ring; rlpu ψ represents the dynamic load between the u-th long planetary gear in the compound arrangement and the input gear ring; rpu This indicates the angular position of the line of mesh between the u-th short planetary gear in the compound arrangement and the sun gear, from the X-axis. Indicates the base circle radius of the compound gear input gear ring; The dynamic loads of each long planetary gear in the compound gear set and the input gear ring are calculated based on the tooth backlash of the internal gear ring and the corresponding long planetary gear, the displacement vector of the corresponding long planetary gear in the compound gear set, the angular position of the meshing line between the corresponding long planetary gear and the input gear ring from the X-axis, the base circle radius of the input gear ring, the displacement of the input gear ring along the X-direction, Y-direction and torsional direction and the displacement of the planet carrier in the torsional direction. The dynamic equations of the composite planetary gear set are constructed using the following formula: in, This represents the 3 degrees of freedom of the bending-torsional coupled excitation of the u-th long planetary gear in the composite array; F represents the mass matrix of the u-th long planetary gear in the composite arrangement; slpu F represents the dynamic load on the axis of the u-th long planetary gear in the composite array and the sun gear; rlpu F represents the dynamic load between the u-th long planetary gear in the compound gear arrangement and the input gear ring; lppu ψ represents the dynamic load between the u-th long planetary gear and the u-th short planetary gear in the composite arrangement; slpu ψ represents the angle between the line of meshing of the u-th long planetary gear and the sun gear axis and the X-axis; rlpu ψ represents the angle between the line of meshing of the u-th long planetary gear in the compound gear set and the input gear ring and the X-axis; lppu This 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 arrangement from the X-axis; Indicates the base circle radius of the composite planetary gear; The dynamic load of the u-th long planetary gear and the u-th short planetary gear in the compound gear set is calculated based on the tooth backlash 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 equations of the composite short planetary gear set are constructed using the following formula: in, This represents the 3 degrees of freedom of the bending-torsional coupling excitation of the u-th short planetary gear in the composite array; F represents the mass matrix of the u-th short planetary gear in the composite arrangement; frpu ψ represents the dynamic load between the compound floating gear ring and the u-th short planetary gear; frpu This indicates the angular position of the compound floating gear ring relative to the X-axis from the meshing line of the u-th short planetary gear; Indicates the base circle radius of the composite short planetary gear set; The dynamic load between the composite floating gear ring and the u-th short planetary gear is calculated based on the tooth backlash between the composite floating gear ring and each short planetary gear, the displacement vector of the floating gear ring, the displacement in the torsional direction of the planetary carrier, the pressure angle of the floating gear ring-short planetary gear meshing pair, the meshing stiffness and meshing damping between the floating gear ring and each short planetary gear, and the base circle radius of the floating gear ring. The dynamic equations of the composite floating gear ring are constructed using the following formula: in, This represents the 3 degrees of freedom of the bending-torsional coupled excitation of the composite floating gear ring; This represents the mass matrix of the composite floating gear ring; This represents the coupling force vector between the compound floating gear ring and the transmission mechanism housing when the C1 clutch is engaged; The coupling force vector between the compound floating gear ring and the transmission mechanism housing when the C1 clutch is engaged is calculated based on the coupling stiffness vector and coupling damping vector between the compound floating gear ring and the transmission mechanism housing.

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