Planetary gear transmission system nonlinear dynamics modeling method and system

Abstract

The invention discloses a nonlinear dynamic modeling method and system for a planetary gear transmission system, relates to the technical field of transmission systems, and is used for solving the technical problems that in a planetary gear dynamic modeling mode in the prior art, errors of a meshing area and meshing force are large, and the vibration phenomenon of the planetary transmission system cannot be accurately reflected. The invention discloses a nonlinear dynamic modeling method for a planetary gear transmission system. The nonlinear dynamic modeling method comprises the steps of determining a two-stage straight-tooth planetary gear transmission system; establishing a degree-of-freedom model of the external and internal meshing gear pair according to the transmission system; improving the time-varying meshing stiffness of an internal and external meshing pair of the transmission system by using a degree-of-freedom model; obtaining multi-source excitation of the transmission system containing the time-varying meshing angle and the position angle according to the degree-of-freedom model; establishing a nonlinear function of the relative displacement and the gear backlash of the internal and external meshing pairs along the meshing line direction, and acquiring the meshing force of each meshing pair; and according to the time-varying meshing stiffness, the multi-source excitation and the meshing force, establishing a multi-stage planetary transmission kinetic model.

Description

Technical Field

[0001] The present invention relates to the technical field of transmission systems, and more specifically, to a non-linear dynamics modeling method and system for a planetary gear transmission system. Background Art

[0002] Planetary transmission systems have the characteristics of compact structure, high precision, high load-bearing capacity, etc., and are widely used in high-end equipment in the fields of robots, precision machine tools, new energy vehicles, and aerospace.

[0003] In the prior art, during the operation of high-end equipment with a planetary transmission system as a power transmission unit, problems such as excessive vibration may occur, and even cause failures in the high-end equipment. Tracing the root cause, the main reason is that the existing non-linear planetary transmission dynamics modeling methods do not comprehensively consider the dynamic coupling influencing factors, thus unable to accurately reflect the vibration phenomenon of the planetary transmission system. Specifically, the prior art ignores the influence of the change in the center distance during actual operation on the time-varying mesh stiffness in the planetary gear dynamics modeling method, resulting in large errors in the meshing area and meshing force, and unable to accurately reflect the vibration phenomenon of the planetary transmission system. Summary of the Invention

[0004] The purpose of the present invention is to provide a non-linear dynamics modeling method and system for a planetary gear transmission system, which is used to solve the technical problem that the prior art ignores the influence of the change in the center distance during actual operation on the time-varying mesh stiffness and the time-varying characteristics of the meshing angle in the planetary gear dynamics modeling method, resulting in large errors in the meshing area and meshing force, and unable to accurately reflect the vibration phenomenon of the planetary transmission system. In view of this, the present invention is realized through the following solutions.

[0005] In a first aspect, the present invention provides a non-linear dynamics modeling method for a planetary gear transmission system, including: Determine a two-stage spur planetary gear transmission system; Establish a degree-of-freedom model of the external and internal meshing gear pairs according to the transmission system; Improve the time-varying mesh stiffness of the external and internal meshing pairs of the transmission system by using the degree-of-freedom model; Obtain the multi-source excitation of the transmission system including the time-varying meshing angle and position angle according to the degree-of-freedom model; the multi-source excitation includes eccentricity error and tooth profile error; Establish a non-linear function of the relative displacement and backlash along the meshing line direction of the external and internal meshing pairs, and obtain the meshing force of each meshing pair; Establish a multi-stage planetary transmission dynamics model according to the time-varying mesh stiffness, multi-source excitation, and the meshing force.

[0006] Compared with the prior art, in the non-linear dynamic modeling method of the planetary gear transmission system of the present invention, a two-stage spur planetary gear transmission system can be determined according to the physical object, and then a degree-of-freedom model of the external-internal meshing gear pair can be established based on the transmission system; further, the time-varying meshing stiffness of the internal and external meshing pairs of the transmission system can be improved by using the degree-of-freedom model; according to the degree-of-freedom model, multi-source excitations of the transmission system including the time-varying meshing angle and the position angle can be obtained; further, a non-linear function of the relative displacement and the backlash along the meshing line direction of the internal and external meshing pairs is established, and after obtaining the meshing force of each meshing pair, a multi-stage planetary transmission dynamic model can be established according to the time-varying meshing stiffness, multi-source excitations and meshing force, thereby completing the non-linear dynamic modeling of the planetary gear transmission system. In the above technical solution of the present invention, the influences of multi-source excitations such as the time-variability of the meshing angles of the internal and external meshing pairs, the relative position angle of the planetary gears, the time-varying meshing stiffness, the eccentricity error of the gears, the tooth profile deviation and the backlash on the vibration characteristics of the system can be taken into account at the same time, and the Lagrange method can be used to establish the translational-torsional dynamic model of the two-stage 2K-H planetary gear system, so that the established model has strong versatility and is applicable to the dynamic numerical simulation under any working conditions; further, the above technical solution considers the influence of the translational vibration of the gears in the actual situation on the meshing angles of the internal and external meshing pairs and the relative position angle of the planetary gears; further, the influence of the meshing angle and the position angle affected by the translational vibration on the time-varying meshing stiffness, the eccentricity error, the tooth profile deviation, and the influence of the change of the center distance during actual operation on the time-varying meshing stiffness are also considered, so that the accuracy of the model is higher and it has stronger non-linearity. Through the above technical solution of the present invention, the technical problem that the prior art ignores the influence of the change of the center distance during actual operation on the time-varying meshing stiffness and the time-varying characteristics of the meshing angle in the planetary gear dynamic modeling method, resulting in large errors in the meshing area and the meshing force and being unable to accurately reflect the vibration phenomenon of the planetary transmission system is solved.

[0007] Further, in the non-linear dynamic modeling method of the planetary gear transmission system of the present invention, the establishing a degree-of-freedom model of the external-internal meshing gear pair according to the transmission system includes: Defining the translational vibration displacement of the planetary gear according to the two-stage spur planetary gear transmission system; Determining the actual center distances of the external meshing pair and the internal meshing pair of the planetary gear according to the translational vibration displacement; Determining the meshing angles of the internal meshing pair and the external meshing pair, as well as the position angle of the planetary gear relative to the sun gear and the position angle of the planetary gear relative to the ring gear.

[0008] Further, in the non-linear dynamic modeling method of the planetary gear transmission system of the present invention, the translational vibration displacement of the planetary gear includes the lateral displacement and the longitudinal displacement of the planetary gear in the absolute coordinate system; the lateral displacement of the planetary gear in the absolute coordinate system is obtained by the following formula: ; Among them, represents the lateral displacement of the planet gear in the absolute coordinate system, represents the lateral translational vibration of the planet carrier in the absolute coordinate system, represents the translational vibration displacement of the planet gear relative to the planet carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the planet carrier, represents the initial center distance of the gear pair, represents the rated angular velocity of the planet carrier, represents time, represents the torsional vibration displacement of the planet carrier, represents the initial installation angle of the planet gear relative to the sun gear, represents the translational vibration displacement of the planet gear relative to the planet carrier along the tangent direction of the rotation of the planet carrier in the rotating coordinate system of the planet carrier, the subscript represents the number of planet gear stages, the subscript [[ID=2,2]] represents the number of planet gears, and the subscripts s, p, r, and c represent the sun gear, planet gear, ring gear, and planet carrier respectively; The longitudinal displacement of the planet gear in the absolute coordinate system is obtained by the following formula: ; Among them, represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the longitudinal translational vibration of the planet carrier in the absolute coordinate system, represents the translational vibration displacement of the planet gear relative to the planet carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the planet carrier, represents the initial center distance of the gear pair, represents the rated angular velocity of the planet carrier, represents time, represents the torsional vibration displacement of the planet carrier, represents the initial installation angle of the planet gear relative to the sun gear, represents the translational vibration displacement of the planet gear relative to the planet carrier along the tangent direction of the rotation of the planet carrier in the rotating coordinate system of the planet carrier, the subscript represents the number of planet gear stages, the subscript represents the number of planet gears, and the subscripts s, p, r, and c represent the sun gear, planet gear, ring gear, and planet carrier respectively.

[0009] Furthermore, in the non-linear dynamic modeling method of the planetary gear transmission system of the present invention, the actual center distance of the external meshing pair of the planetary gear is obtained by the following formula: ; Among them, represents the actual center distance of the external meshing pair of the planetary gear, Represents the lateral displacement of the planet gear in the absolute coordinate system, Represents the lateral translational vibration of the sun gear in the absolute coordinate system, Represents the longitudinal displacement of the planet gear in the absolute coordinate system, Represents the longitudinal translational vibration of the sun gear in the absolute coordinate system; And / or, the actual center distance of the internal meshing pair of the planetary gear is obtained by the following formula: ; where, Represents the actual center distance of the internal meshing pair of the planetary gear, Represents the lateral displacement of the planet gear in the absolute coordinate system, Represents the longitudinal displacement of the planet gear in the absolute coordinate system; And / or, the meshing angle of the external meshing pair is obtained by the following formula: ; Wherein, Represents the meshing angle of the external meshing pair, Represents the base circle radius of the sun gear, Represents the base circle radius of the planet gear, Represents the lateral displacement of the planet gear in the absolute coordinate system, Represents the lateral translational vibration of the sun gear in the absolute coordinate system, Represents the longitudinal displacement of the planet gear in the absolute coordinate system, Represents the longitudinal translational vibration of the sun gear in the absolute coordinate system; And / or, the meshing angle of the internal meshing pair is obtained by the following formula: ; where, Represents the meshing angle of the internal meshing pair, Represents the base circle radius of the ring gear, Represents the base circle radius of the planet gear, Represents the lateral displacement of the planet gear in the absolute coordinate system, Represents the longitudinal displacement of the planet gear in the absolute coordinate system; And / or, the position angle of the planet gear relative to the sun gear is obtained by the following formula: ; where, Represents the position angle of the planet gear relative to the sun gear, Represents the longitudinal displacement of the planet gear in the absolute coordinate system, Represents the longitudinal translational vibration of the sun gear in the absolute coordinate system, Represents the lateral displacement of the planet gear in the absolute coordinate system, Represents the lateral translational vibration of the sun gear in the absolute coordinate system; And / or, the angular position of the planet gear relative to the ring gear is obtained by the following formula: ; where represents the angular position of the planet gear relative to the ring gear, represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the lateral displacement of the planet gear in the absolute coordinate system.

[0010] Furthermore, in the method for non - linear dynamic modeling of the planetary gear transmission system of the present invention, during the process of using the degree - of - freedom model to improve the time - varying mesh stiffness of the internal and external meshing pairs of the transmission system, single - tooth and double - tooth meshing alternate; where: The time - varying mesh stiffness of the single - tooth meshing is: ; where represents the time - varying mesh stiffness of the single - tooth meshing, represents the Hertz contact stiffness of the single - tooth meshing, represents the bending stiffness of the driving gear tooth, represents the bending stiffness of the driven gear tooth, represents the shear stiffness of the driving gear tooth, represents the shear stiffness of the driven gear tooth, represents the axial compression stiffness of the driving gear tooth, represents the axial compression stiffness of the driven gear tooth, represents the flexible matrix stiffness of the driving gear tooth, represents the flexible matrix stiffness of the driven gear tooth; The time - varying mesh stiffness of the double - tooth meshing is: ; where represents the time - varying mesh stiffness of the double - tooth meshing, represents the Hertz contact stiffness of the nth pair of teeth, represents the bending stiffness of the driving gear of the nth pair of teeth, represents the bending stiffness of the driven gear of the nth pair of teeth, represents the shear stiffness of the driving gear of the nth pair of teeth, represents the shear stiffness of the driven gear of the nth pair of teeth, represents the axial compression stiffness of the driving gear of the nth pair of teeth, represents the axial compression stiffness of the driven gear of the nth pair of teeth, represents the flexible matrix stiffness of the driving gear of the nth pair of teeth, represents the flexible matrix stiffness of the driven gear of the nth pair of teeth; And / or, during the process of using the degree - of - freedom model to improve the time - varying mesh stiffness of the internal and external meshing pairs of the transmission system, within one meshing cycle Inside, the time of the single pair of teeth meshing area and the time of the double pair of teeth meshing area are respectively: , ; where, represents the time of the single pair of teeth meshing area, represents the time of the double pair of teeth meshing area, represents the meshing period, and P represents the gear contact ratio; And / or, due to the time-varying meshing angle, the contact ratio of the internal gear pair and the external gear pair changes in real time, which is expressed as: ; ; where, represents the contact ratio of the external gear pair, represents the contact ratio of the internal gear pair, represents the addendum circle radius of the sun gear, represents the base circle radius of the sun gear, represents the addendum circle radius of the planet gear, represents the base circle radius of the planet gear, represents the initial center distance of the gear pair, represents the meshing angle of the external meshing pair, represents the base pitch; represents the meshing angle of the internal meshing pair.

[0011] Furthermore, in the non-linear dynamic modeling method of the planetary gear transmission system of the present invention, the eccentricity error includes the meshing error of the sun gear eccentricity equivalent on the external meshing line meshing with the planet gear, the meshing error of the planet gear eccentricity equivalent on the external meshing line meshing with the sun gear, and the meshing error of the planet gear eccentricity equivalent on the internal meshing line meshing with the ring gear; And / or, the tooth profile error includes the equivalent tooth profile error of the tooth profile deviation of the external meshing gear converted on the meshing line, and the equivalent tooth profile error of the tooth profile deviation of the internal meshing gear converted on the meshing line.

[0012] Furthermore, in the non-linear dynamic modeling method of the planetary gear transmission system of the present invention, the meshing error of the sun gear eccentricity equivalent on the external meshing line meshing with the planet gear is expressed as: ; where, represents the meshing error of the sun gear eccentricity equivalent on the external meshing line meshing with the planet gear, represents the amplitude of the sun gear eccentricity error, represents the rated speed of the sun gear, represents the rated speed of the planet carrier, represents time, represents the meshing angle of the external meshing pair, represents the initial phase of the sun gear eccentricity, represents the initial installation angle of the planet gear relative to the sun gear; And / or, the meshing error of the equivalent planet gear eccentricity on the external meshing line meshing with the sun gear is expressed as: ; where represents the meshing error of the equivalent planet gear eccentricity on the external meshing line meshing with the sun gear, represents the amplitude of the planet gear eccentricity error, represents the rated speed of the planet gear, represents the rated speed of the planet carrier, represents time, represents the meshing angle of the external meshing pair, represents the initial phase of the planet gear eccentricity; And / or, the meshing error of the equivalent planet gear eccentricity on the internal meshing line meshing with the ring gear is expressed as: ; where represents the meshing error of the equivalent planet gear eccentricity on the internal meshing line meshing with the ring gear, represents the amplitude of the planet gear eccentricity error, represents the rated speed of the planet gear, represents the rated speed of the planet carrier, represents time, represents the meshing angle of the internal meshing pair, represents the initial phase of the planet gear eccentricity; And / or, the equivalent profile error of the profile deviation of the external meshing gear on the meshing line is expressed as: ; where represents the equivalent profile error of the profile deviation of the external meshing gear on the meshing line, represents the equivalent deviation amplitude of the external meshing pair, represents the th-level planet gear train meshing frequency, represents time, represents the position angle of the planet gear relative to the sun gear, represents the meshing angle of the external meshing pair, represents the th-level planet gear train meshing period; And / or, the equivalent profile error of the profile deviation of the internal meshing gear on the meshing line is expressed as: ; where represents the equivalent profile error of the profile deviation of the internal meshing gear on the meshing line, represents the equivalent deviation amplitude of the internal meshing pair, represents the Meshing frequency of the planetary gear train of level represents time, represents the position angle of the planetary gear relative to the sun gear, represents the meshing angle of the external meshing pair, represents the position angle of the planetary gear relative to the ring gear, represents the meshing angle of the internal meshing pair, represents the meshing period of the planetary gear train of level; And / or, the comprehensive meshing error of the external meshing pair considering the eccentricity error and profile error is expressed as: ; where, represents the comprehensive meshing error of the external meshing pair, represents the meshing error of the sun gear eccentricity equivalent on the external meshing line meshing with the planetary gear, represents the meshing error of the planetary gear eccentricity equivalent on the external meshing line meshing with the sun gear, represents the equivalent profile error of the external meshing gear profile deviation converted on the meshing line; And / or, the comprehensive meshing error of the internal meshing pair considering the eccentricity error and profile error is expressed as: ; where, represents the comprehensive meshing error of the internal meshing pair, represents the meshing error of the planetary gear eccentricity equivalent on the internal meshing line meshing with the ring gear, represents the equivalent profile error of the internal meshing gear profile deviation converted on the meshing line.

[0013] Furthermore, in the non-linear dynamics modeling method of the planetary gear transmission system of the present invention, the establishment of the non-linear function of the relative displacement and backlash along the meshing line of the internal and external meshing pairs, and the obtaining of the meshing force of each meshing pair include: Set the vibration direction of the compression gear meshing line as positive and the reverse as negative, then determine the relative displacement along the meshing line of the sun-planetary gear meshing pair and the relative displacement along the meshing line of the ring gear-planetary gear meshing pair; Determine the non-linear function of the displacement along the meshing line considering the backlash, and obtain the meshing forces of the external and internal meshing pairs.

[0014] Furthermore, in the non-linear dynamics modeling method of the planetary gear transmission system of the present invention, the relative displacement along the meshing line of the sun-planetary gear meshing pair is expressed as: ; where, represents the relative displacement along the meshing line of the sun-planetary gear meshing pair, represents the lateral translational vibration of the sun gear in the absolute coordinate system, Represents the lateral displacement of the planet gear in the absolute coordinate system, Represents the initial center distance of the gear pair, Represents the rated angular velocity of the planet carrier, Represents time, Represents the torsional vibration displacement of the planet carrier, Represents the initial installation angle of the planet gear relative to the sun gear, Represents the meshing angle of the external meshing pair, Represents the position angle of the planet gear relative to the sun gear, Represents the longitudinal translational vibration of the sun gear in the absolute coordinate system, Represents the longitudinal displacement of the planet gear in the absolute coordinate system, Represents the base circle radius of the sun gear, Represents the rated angular velocity of the sun gear, Represents the torsional vibration displacement of the sun gear, Represents the base circle radius of the planet gear, Represents the rated angular velocity of the planet gear, Represents the torsional vibration displacement of the planet gear, Represents the comprehensive meshing error of the external meshing pair; And / or, the relative displacement along the meshing line of the ring gear-planet gear meshing pair is expressed as: ; Wherein, Represents the relative displacement along the meshing line of the ring gear-planet gear meshing pair, Represents the lateral displacement of the planet gear in the absolute coordinate system, Represents the initial center distance of the gear pair, Represents the rated angular velocity of the planet carrier, Represents time, Represents the torsional vibration displacement of the planet carrier, Represents the initial installation angle of the planet gear relative to the sun gear, Represents the meshing angle of the internal meshing pair, Represents the position angle of the planet gear relative to the ring gear, Represents the longitudinal displacement of the planet gear in the absolute coordinate system, Represents the base circle radius of the ring gear, Represents the base circle radius of the planet gear, Represents the rated angular velocity of the planet gear, Represents the torsional vibration displacement of the planet gear, Represents the comprehensive meshing error of the internal meshing pair; And / or, the non-linear function of the displacement along the meshing line considering the backlash is expressed as: ; Wherein, Represents the non-linear function of the displacement along the meshing line, Represents the relative displacement along the meshing line of the internal meshing pair and the external meshing pair, Represents half of the backlash, Represents taking the absolute value; And / or, the meshing force of the external meshing pair is expressed as: ; where, Represents the meshing force of the external meshing pair, Represents the time-varying meshing stiffness of the external meshing pair, Represents the relative displacement function along the meshing line of the external meshing pair, Represents the relative displacement along the meshing line of the external meshing pair, Represents the meshing damping of the external meshing pair, and t represents time; And / or, the meshing force of the internal meshing pair is expressed as: ; where, Represents the meshing force of the internal meshing pair, Represents the time-varying meshing stiffness of the internal meshing pair, Represents the relative displacement function along the meshing line of the internal meshing pair, Represents the relative displacement along the meshing line of the internal meshing pair, Represents the meshing damping of the internal meshing pair, and t represents time; And / or, the multi-stage planetary transmission dynamics model includes the motion model of the sun gear; the motion model of the sun gear is expressed as: ; Where, Represents the mass of the sun gear, Represents the lateral vibration acceleration of the sun gear in the absolute coordinate system, Represents The support stiffness of the sun gear in the Represents the lateral translational vibration of the sun gear in the absolute coordinate system, Represents The support damping of the sun gear in the Represents the lateral vibration velocity of the sun gear in the absolute coordinate system, Represents the meshing force of the external meshing pair, Represents the relative displacement along the meshing line of the external meshing pair, Represents the Number of planet gears in the Represents the lateral vibration acceleration of the sun gear in the absolute coordinate system, Represents The support stiffness of the sun gear in the Represents the longitudinal translational vibration of the sun gear in the absolute coordinate system, Denote the sun gear support damping in the direction, and denote the longitudinal vibration velocity of the sun gear in the absolute coordinate system Denote the moment of inertia of the first-stage sun gear Denote the torsional vibration acceleration of the first-stage sun gear Denote the torsional stiffness of the first-stage sun gear Denote the torsional vibration displacement of the first-stage sun gear Denote the torsional damping of the first-stage sun gear Denote the torsional vibration velocity of the first-stage sun gear Denote the meshing force of the external meshing pair of the first-stage planetary gear train Denote the relative displacement along the meshing line of the external meshing pair of the first-stage planetary gear train Denote the system input torque acting on the first-stage sun gear Denote the moment of inertia of the second-stage sun gear Denote the torsional vibration acceleration of the second-stage sun gear Denote the inter-stage torsional stiffness connecting the first-stage planet carrier and the second-stage sun gear Denote the torsional vibration displacement of the second-stage sun gear Denote the torsional vibration displacement of the first-stage planetary gear Denote the inter-stage torsional damping connecting the first-stage planet carrier and the second-stage sun gear Denote the torsional vibration velocity of the second-stage sun gear Denote the torsional vibration velocity of the first-stage planet carrier Denote the meshing force of the second-stage external meshing pair Denote the relative displacement along the meshing line of the external meshing pair of the second-stage planetary gear train

[0015] In a second aspect, the present invention provides a non-linear dynamics modeling system for a planetary gear transmission system, comprising: A degree-of-freedom model determination module for determining a two-stage spur planetary gear transmission system; establishing a degree-of-freedom model of the external and internal meshing gear pairs according to the transmission system A meshing stiffness acquisition module for improving the time-varying meshing stiffness of the external and internal meshing pairs of the transmission system by using the degree-of-freedom model A multi-source excitation acquisition module for acquiring the multi-source excitation of the transmission system including the time-varying meshing angle and position angle according to the degree-of-freedom model; the multi-source excitation includes eccentricity error and tooth profile error A meshing force acquisition module for establishing a non-linear function of the relative displacement along the meshing line and the backlash of the external and internal meshing pairs, and acquiring the meshing force of each meshing pair A dynamic model establishment module, configured to establish a multi-stage planetary transmission dynamic model according to the time-varying meshing stiffness, multi-source excitation, and the meshing force.

[0016] Compared with the prior art, the beneficial effects of the planetary gear transmission system non-linear dynamics modeling system of the present invention are the same as those of the planetary gear transmission system non-linear dynamics modeling method described in the above technical solution, and will not be elaborated herein. Description of the Drawings

[0017] The drawings described herein are used to provide a further understanding of the present invention, and constitute a part of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention, and do not constitute an improper limitation to the present invention. In the drawings: Figure 1 It is a schematic diagram of a two-stage 2K-H planetary gear transmission system in the present invention; Figure 2 It is a schematic diagram of a translational and torsional dynamic model of a first-stage planetary gear in the planetary gear transmission system of the present invention; Figure 3 It is a schematic diagram of a six-degree-of-freedom model of an external meshing gear pair in the planetary gear transmission system of the present invention; Figure 4 It is a schematic diagram of a six-degree-of-freedom model of an internal meshing gear pair in the planetary gear transmission system of the present invention; Figure 5 It is a schematic diagram of the composition of the planetary gear transmission system non-linear dynamics modeling system of the present invention; Figure 6 It is a comparison diagram of the change of the contact ratio of the first-stage sun gear-planetary gear (sp11) in the planetary gear transmission system over time under different modeling methods; Figure 7 It is the meshing stiffness of the first-stage sun gear-planetary gear pair in the planetary gear transmission system of the present invention Time-domain comparison diagram under different contact ratios; Figure 8 It is the relative displacement of the first-stage sun gear-planetary gear along the meshing line in the planetary gear transmission system of the present invention Time-domain comparison diagram under different modeling methods; Figure 9 It is the relative displacement of the first-stage sun gear-planetary gear along the meshing line in the planetary gear transmission system of the present invention Frequency-domain comparison diagram under different modeling methods.

[0018] Reference Signs: Figures 1 to 4Among them, r represents the ring gear, s1 represents the sun gear in the first-stage planetary gear, s2 represents the sun gear in the second-stage planetary gear, p1 represents the planet gear in the first-stage planetary gear, p2 represents the planet gear in the second-stage planetary gear, c1 represents the carrier in the first-stage planetary gear, c2 represents the carrier in the second-stage planetary gear, T in is the input torque of the planetary gear transmission system, T out is the output torque of the planetary gear transmission system, O is the origin of coordinates, is the moment of inertia of the sun gear of the -th stage planetary gear, is the moment of inertia of the carrier of the -th stage planetary gear, is the moment of inertia of the ring gear of the -th stage planetary gear, is the moment of inertia of the -th stage planetary gear, the -th planet gear, is the mass of the sun gear of the -th stage planetary gear, is the mass of the carrier of the -th stage planetary gear, is the mass of the ring gear of the -th stage planetary gear, is the mass of the -th stage planetary gear, the -th planet gear, is the support stiffness of the sun gear of the -th stage planetary gear, is the support stiffness of the carrier of the -th stage planetary gear, is the support stiffness of the -th stage planetary gear, the -th planet gear, is the support damping of the sun gear of the -th stage planetary gear, is the support damping of the carrier of the -th stage planetary gear, is the support damping of the -th stage planetary gear, the -th planet gear, is the meshing stiffness of the meshing pair between the sun gear and the -th planet gear in the -th stage planetary gear, is the meshing stiffness of the meshing pair between the ring gear and the -th planet gear in the -th stage planetary gear, is the meshing stiffness of the meshing pair between the sun gear and the -th planet gear in the The meshing damping of a planetary gear pair is the meshing damping of the ring gear and the th planetary gear pair in the th stage planetary gear, is the comprehensive meshing error of the external meshing pair considering the eccentricity error and the profile deviation, is half of the initial backlash of the meshing pair, is the base circle radius of the sun gear in the th stage, is the revolution radius of the planetary gear in the th stage, is the base circle radius of the ring gear in the th stage, is the base circle radius of the th planetary gear in the th stage planetary gear, is the rotational angular velocity of the sun gear in the th stage, is the rotational angular velocity of the planet carrier in the th stage, is the self-rotational angular velocity of the th planetary gear in the th stage planetary gear, which is also the coordinate origin of the six-degree-of-freedom model of the external meshing pair of the planetary gear and the initial wheel center position of the th stage sun gear, is the initial wheel center position of the th planetary gear in the th stage planetary gear, is the vibration displacement of the sun gear in the horizontal direction in the th stage, is the vibration displacement of the sun gear in the vertical direction in the th stage, is the wheel center position of the sun gear after translational vibration in the th stage, is the abscissa of the wheel center of the th planetary gear in the th stage planetary gear after translational vibration, is the ordinate of the wheel center of the th planetary gear in the th stage planetary gear after translational vibration, is the wheel center position of the th planetary gear after translational vibration in the th stage planetary gear, which is the initial center distance of the internal and external meshing pairs, and is the The center distance variation between the sun gear and the th planet gear in the th stage planetary gear, is the initial installation angle of the th stage planetary gear relative to the sun gear, is the position angle of the th stage planetary gear relative to the sun gear. It is also the coordinate origin of the six-degree-of-freedom model of the internal meshing pair in the th stage planetary gear and the initial wheel center position of the th stage ring gear. After the gear undergoes translational vibration, it is the center distance variation between the ring gear and the th planet gear in the th stage planetary gear, is the position angle of the th

[0019] In order to make the technical problems, technical solutions, and beneficial effects to be solved by the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0020] It should be noted that when an element is referred to as being "fixed to" or "disposed on" another element, it can be directly on the other element or indirectly on the other element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or indirectly connected to the other element.

[0021] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, "a plurality" means two or more unless otherwise specifically defined. "Several" means one or more unless otherwise specifically defined.

[0022] In the prior art, during the operation of high-end equipment with a planetary transmission system as the power transmission unit, problems such as excessive vibration may occur, and even cause failures in the high-end equipment. Tracing the root cause, the main reason is that the existing non-linear planetary transmission dynamics modeling method does not comprehensively consider the dynamic coupling influencing factors, thus unable to accurately reflect the vibration phenomenon of the planetary transmission system. Specifically, the prior art ignores the influence of the change in the center distance during actual operation on the time-varying meshing stiffness in the planetary gear dynamics modeling method, resulting in large errors in the meshing area and meshing force, and unable to accurately reflect the vibration phenomenon of the planetary transmission system.

[0023] To solve the above technical problems, the present invention provides a non-linear dynamics modeling method for a planetary gear transmission system, including: Determine a two-stage spur planetary gear transmission system; Establish a degree-of-freedom model for the external and internal meshing gear pairs according to the transmission system; Improve the time-varying meshing stiffness of the external and internal meshing pairs of the transmission system by using the degree-of-freedom model; Obtain the multi-source excitation of the transmission system including the time-varying meshing angle and position angle according to the degree-of-freedom model; the multi-source excitation includes eccentricity error and profile error; Establish a non-linear function of the relative displacement and backlash along the meshing line direction of the external and internal meshing pairs, and obtain the meshing force of each meshing pair; Establish a multi-stage planetary transmission dynamics model according to the time-varying meshing stiffness, multi-source excitation and the meshing force.

[0024] In the case of adopting the above technical solution, in the non-linear dynamic modeling method of the planetary gear transmission system of the present invention, a two-stage spur planetary gear transmission system can be determined according to the physical object, and then a degree-of-freedom model of the external-internal meshing gear pair can be established according to the transmission system; further, the time-varying meshing stiffness of the internal and external meshing pairs of the transmission system can be improved by using the degree-of-freedom model; according to the degree-of-freedom model, multi-source excitations of the transmission system including time-varying meshing angles and position angles can be obtained; further, a non-linear function of the relative displacement and backlash along the meshing line direction of the internal and external meshing pairs is established, and after the meshing forces of each meshing pair are obtained, a multi-stage planetary transmission dynamic model can be established according to the time-varying meshing stiffness, multi-source excitations and meshing forces, so as to complete the non-linear dynamic modeling of the planetary gear transmission system. In the above technical solution of the present invention, the influences of multi-source excitations such as the time-variability of the meshing angles of the internal and external meshing pairs, the relative position angles of the planetary gears, time-varying meshing stiffness, eccentricity errors of the gears, tooth profile deviations and backlash on the vibration characteristics of the system can be taken into account at the same time, and the Lagrangian method can be used to establish a translational-torsional dynamic model of the two-stage 2K-H planetary gear system, so that the established model has strong versatility and is applicable to dynamic numerical simulations under any working conditions; further, the above technical solution considers the influence of the translational vibration of the gears in the actual situation on the meshing angles of the internal and external meshing pairs and the relative position angles of the planetary gears; further, the influence of the meshing angles and position angles affected by the translational vibration on the time-varying meshing stiffness, eccentricity errors, tooth profile deviations, and the influence of the change of the center distance during actual operation on the time-varying meshing stiffness are also considered, so that the accuracy of the model is higher and it has stronger non-linearity. Through the above technical solution of the present invention, the technical problem that in the prior art, the influence of the change of the center distance during actual operation on the time-varying meshing stiffness and the time-varying characteristics of the meshing angle are ignored in the planetary gear dynamic modeling method, resulting in large errors in the meshing area and meshing force and being unable to accurately reflect the vibration phenomenon of the planetary transmission system is solved.

[0025] To better understand the present invention, the content of the present invention will be further clarified below in conjunction with specific embodiments, but the content of the present invention is not limited to the following embodiments.

[0026] Embodiment 1 This embodiment provides a non-linear dynamic modeling method for a planetary gear transmission system, including: Step 1, determine a two-stage spur planetary gear transmission system; establish a degree-of-freedom model of the external-internal meshing gear pair according to the transmission system; Step 2, use the degree-of-freedom model to improve the time-varying meshing stiffness of the internal and external meshing pairs of the transmission system; Step 3, obtain multi-source excitations of the transmission system including time-varying meshing angles and position angles according to the degree-of-freedom model; the multi-source excitations include eccentricity errors and tooth profile errors; Step 4, establish a non - linear function of the relative displacement and backlash of the internal and external meshing pairs along the meshing line direction, and obtain the meshing force of each meshing pair; Step 5, establish a multi - stage planetary transmission dynamic model based on the time - varying meshing stiffness, multi - source excitation and the meshing force.

[0027] Embodiment 2 In a first aspect, this embodiment provides a non - linear dynamics modeling method for a planetary gear transmission system, including: S100, determine a two - stage spur planetary gear transmission system; establish a degree - of - freedom model of the external - internal meshing gear pairs according to the transmission system; Further, the content of step S100 includes: S101, define the translational vibration displacement of the planet gear according to the two - stage spur planetary gear transmission system; S102, determine the actual center distances of the external and internal meshing pairs of the planetary gear according to the translational vibration displacement; S103, determine the meshing angles of the internal and external meshing pairs, as well as the position angle of the planet gear relative to the sun gear and the position angle of the planet gear relative to the ring gear; Further, the translational vibration displacement of the planet gear includes the lateral displacement and longitudinal displacement of the planet gear in the absolute coordinate system; the lateral displacement of the planet gear in the absolute coordinate system is obtained by the following formula: ; where represents the lateral displacement of the planet gear in the absolute coordinate system, represents the lateral translational vibration of the carrier in the absolute coordinate system, represents the translational vibration displacement of the planet gear relative to the carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the carrier, represents the initial center distance of the gear pair, represents the rated angular velocity of the carrier, represents time, represents the torsional vibration displacement of the carrier, represents the initial installation angle of the planet gear relative to the sun gear, represents the translational vibration displacement of the planet gear relative to the carrier along the tangent direction of the carrier rotation in the rotating coordinate system of the carrier, the subscript represents the number of planetary gear stages, the subscript represents the number of planet gears, and the subscripts s, p, r and c represent the sun gear, planet gear, ring gear and carrier respectively; Further, the longitudinal displacement of the planet gear in the absolute coordinate system is obtained by the following formula: ; where represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the longitudinal translational vibration of the planet carrier in the absolute coordinate system, represents the translational vibration displacement of the planet gear relative to the planet carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the planet carrier, represents the initial center distance of the gear pair, represents the rated angular velocity of the planet carrier, represents time, represents the torsional vibration displacement of the planet carrier, represents the initial installation angle of the planet gear relative to the sun gear, represents the translational vibration displacement of the planet gear relative to the planet carrier along the tangent direction of the rotation of the planet carrier in the rotating coordinate system of the planet carrier, with the subscript represents the number of planet gear stages, with the subscript represents the number of planet gears. The subscripts s, p, r, and c represent the sun gear, planet gear, ring gear, and planet carrier respectively; Furthermore, the actual center distance of the external meshing pair of the planet gear is obtained by the following formula: ; wherein, represents the actual center distance of the external meshing pair of the planet gear, represents the lateral displacement of the planet gear in the absolute coordinate system, represents the lateral translational vibration of the sun gear in the absolute coordinate system, represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the longitudinal translational vibration of the sun gear in the absolute coordinate system; Furthermore, the actual center distance of the internal meshing pair of the planet gear is obtained by the following formula: ; wherein, represents the actual center distance of the internal meshing pair of the planet gear, represents the lateral displacement of the planet gear in the absolute coordinate system, represents the longitudinal displacement of the planet gear in the absolute coordinate system; Furthermore, the meshing angle of the external meshing pair is obtained by the following formula: ; wherein, represents the meshing angle of the external meshing pair, represents the base circle radius of the sun gear, represents the base circle radius of the planet gear, represents the lateral displacement of the planet gear in the absolute coordinate system, represents the lateral translational vibration of the sun gear in the absolute coordinate system, represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the longitudinal translational vibration of the sun gear in the absolute coordinate system; Furthermore, the meshing angle of the internal meshing pair is obtained by the following formula: ; where, represents the meshing angle of the internal meshing pair, represents the base circle radius of the ring gear, represents the base circle radius of the planet gear, represents the lateral displacement of the planet gear in the absolute coordinate system, represents the longitudinal displacement of the planet gear in the absolute coordinate system; Furthermore, the angular position of the planet gear relative to the sun gear is obtained by the following formula: ; where, represents the angular position of the planet gear relative to the sun gear, represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the longitudinal translational vibration of the sun gear in the absolute coordinate system, represents the lateral displacement of the planet gear in the absolute coordinate system, represents the lateral translational vibration of the sun gear in the absolute coordinate system; Furthermore, the angular position of the planet gear relative to the ring gear is obtained by the following formula: ; where, represents the angular position of the planet gear relative to the ring gear, represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the lateral displacement of the planet gear in the absolute coordinate system.

[0028] S200, improving the time-varying meshing stiffness of the internal and external meshing pairs of the transmission system by using the degree-of-freedom model; Furthermore, in step S200, single-tooth and double-tooth meshing alternate; where: The time-varying meshing stiffness of the single-tooth is: ; where, represents the time-varying meshing stiffness of the single-tooth, represents the Hertz contact stiffness of the single-tooth, represents the bending stiffness of the driving gear tooth, represents the bending stiffness of the driven gear tooth, represents the shear stiffness of the driving gear tooth, represents the shear stiffness of the driven gear tooth, represents the axial compression stiffness of the driving gear tooth, represents the axial compression stiffness of the driven gear tooth, represents the flexible matrix stiffness of the driving gear teeth, represents the flexible matrix stiffness of the driven gear teeth; Furthermore, the time-varying mesh stiffness of the double-pair teeth is: ; wherein, represents the time-varying mesh stiffness of the double-pair teeth, represents the Hertz contact stiffness of the nth pair of teeth, represents the bending stiffness of the driving gear of the nth pair of teeth, represents the bending stiffness of the driven gear of the nth pair of teeth, represents the shear stiffness of the driving gear of the nth pair of teeth, represents the shear stiffness of the driven gear of the nth pair of teeth, represents the axial compression stiffness of the driving gear of the nth pair of teeth, represents the axial compression stiffness of the driven gear of the nth pair of teeth, represents the flexible matrix stiffness of the driving gear of the nth pair of teeth, represents the flexible matrix stiffness of the driven gear of the nth pair of teeth; Furthermore, in the process of improving the time-varying mesh stiffness of the internal and external meshing pairs of the transmission system by using the degree-of-freedom model, within one meshing cycle the time of the single-pair teeth meshing zone and the time of the double-pair teeth meshing zone are respectively: , ; wherein, represents the time of the single-pair teeth meshing zone, represents the time of the double-pair teeth meshing zone, represents the meshing cycle, and P represents the gear contact ratio; Furthermore, due to the time-varying meshing angle, the contact ratios of the internal gear pair and the external gear pair change in real time, which is expressed as: ; ; wherein, represents the contact ratio of the external gear pair, represents the contact ratio of the internal gear pair, represents the addendum circle radius of the sun gear teeth, represents the base circle radius of the sun gear, represents the addendum circle radius of the planet gear teeth, represents the base circle radius of the planet gear, represents the initial center distance of the gear pair, represents the meshing angle of the external meshing pair, represents the base pitch; represents the meshing angle of the internal meshing pair.

[0029] S300, obtaining a multi-source excitation of a transmission system including a time-varying meshing angle and a position angle according to the degree of freedom model; the multi-source excitation includes an eccentricity error and a tooth profile error; Furthermore, in step S300, the eccentricity error includes the meshing error of the sun gear eccentricity equivalent to the external meshing line meshing with the planet gear, the meshing error of the planet gear eccentricity equivalent to the external meshing line meshing with the sun gear, and the meshing error of the planet gear eccentricity equivalent to the internal meshing line meshing with the ring gear; the tooth profile error includes the equivalent tooth profile error of the tooth profile deviation of the external meshing gear converted on the meshing line, and the equivalent tooth profile error of the tooth profile deviation of the internal meshing gear converted on the meshing line; Furthermore, the sun gear eccentricity is equivalent to the meshing error on the outer meshing line meshing with the planet gears, which is expressed as: ;in, It indicates the meshing error of the sun gear eccentricity equivalent to the external meshing line with the planet gear. Indicates the amplitude of the sun gear eccentricity error, Indicates the rated speed of the sun gear, Indicates the rated speed of the planet carrier, Indicates time, represents the engagement angle of the external toothing pair, represents the initial phase of the sun gear eccentricity, Indicates the initial installation angle of the planet gear relative to the sun gear; Furthermore, the meshing error of the planetary gear eccentricity, which is equivalent to the outer meshing line meshing with the sun gear, is expressed as: ;in, It indicates the meshing error of the planetary gear eccentricity equivalent to the external meshing line meshing with the sun gear. Indicates the planetary gear eccentricity error amplitude, Indicates the rated speed of the planetary gear. Indicates the rated speed of the planet carrier, Indicates time, represents the engagement angle of the external toothing pair, Indicates the initial phase of the planetary gear eccentricity; Furthermore, the meshing error of the planetary gear eccentricity, which is equivalent to the meshing error on the inner meshing line meshing with the ring gear, is expressed as: ;in, It indicates the meshing error of the planetary gear eccentricity on the internal meshing line of the gear ring. Indicates the planetary gear eccentricity error amplitude, Indicates the rated speed of the planetary gear. Indicates the rated speed of the planet carrier, Indicates time, represents the engagement angle of the internal meshing pair, Represents the initial phase of the planetary gear eccentricity; Further, the profile deviation of the external meshing gear is converted into the equivalent profile error on the meshing line, expressed as: ; where Represents the equivalent profile error on the meshing line converted from the profile deviation of the external meshing gear, Represents the equivalent deviation amplitude of the external meshing pair, Represents the -th order planetary gear train meshing frequency, Represents time, Represents the position angle of the planetary gear relative to the sun gear, Represents the meshing angle of the external meshing pair, Represents the -th order planetary gear train meshing period; Further, the profile deviation of the internal meshing gear is converted into the equivalent profile error on the meshing line, expressed as: ; where Represents the equivalent profile error on the meshing line converted from the profile deviation of the internal meshing gear, Represents the equivalent deviation amplitude of the internal meshing pair, Represents the -th order planetary gear train meshing frequency, Represents time, Represents the position angle of the planetary gear relative to the sun gear, Represents the meshing angle of the external meshing pair, Represents the position angle of the planetary gear relative to the ring gear, Represents the meshing angle of the internal meshing pair, Represents the -th order planetary gear train meshing period; Further, the comprehensive meshing error of the external meshing pair considering the eccentricity error and profile error is expressed as: ; where Represents the comprehensive meshing error of the external meshing pair, Represents the meshing error of the sun gear eccentricity equivalent on the external meshing line meshing with the planetary gear, Represents the meshing error of the planetary gear eccentricity equivalent on the external meshing line meshing with the sun gear, Represents the equivalent profile error on the meshing line converted from the profile deviation of the external meshing gear; Further, the comprehensive meshing error of the internal meshing pair considering the eccentricity error and profile error is expressed as: ; where Represents the comprehensive meshing error of the internal meshing pair, It represents the meshing error when the eccentricity of the planet gear is equivalent on the internal meshing line meshing with the ring gear. It represents the equivalent tooth profile error when the tooth profile deviation of the internal meshing gear is transformed on the meshing line.

[0030] S400: Establish a non-linear function of the relative displacement and backlash along the meshing line of the internal and external meshing pairs, and obtain the meshing force of each meshing pair. Furthermore, the content of step S400 includes: S401: Set the vibration direction of the compression gear meshing line as positive and the reverse as negative, then determine the relative displacement along the meshing line of the sun-planet gear meshing pair and the relative displacement along the meshing line of the ring gear-planet gear meshing pair. S402: Determine the non-linear function of the displacement along the meshing line considering the backlash, and obtain the meshing forces of the external meshing pair and the internal meshing pair. Furthermore, the relative displacement along the meshing line of the sun-planet gear meshing pair is expressed as: ; Wherein, represents the relative displacement along the meshing line of the sun-planet gear meshing pair, represents the lateral translational vibration of the sun gear in the absolute coordinate system, represents the lateral displacement of the planet gear in the absolute coordinate system, represents the initial center distance of the gear pair, represents the rated angular velocity of the planet carrier, represents the time, represents the torsional vibration displacement of the planet carrier, represents the initial installation angle of the planet gear relative to the sun gear, represents the meshing angle of the external meshing pair, represents the position angle of the planet gear relative to the sun gear, represents the longitudinal translational vibration of the sun gear in the absolute coordinate system, represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the base circle radius of the sun gear, represents the rated angular velocity of the sun gear, represents the torsional vibration displacement of the sun gear, represents the base circle radius of the planet gear, represents the rated angular velocity of the planet gear, represents the torsional vibration displacement of the planet gear, represents the comprehensive meshing error of the external meshing pair; Furthermore, the relative displacement along the meshing line of the ring gear-planet gear meshing pair is expressed as: ; Wherein, Represents the relative displacement along the meshing line of the ring gear - planet gear meshing pair, Represents the lateral displacement of the planet gear in the absolute coordinate system, Represents the initial center distance of the gear pair, Represents the rated angular velocity of the planet carrier, Represents time, Represents the torsional vibration displacement of the planet carrier, Represents the initial installation angle of the planet gear relative to the sun gear, Represents the meshing angle of the internal meshing pair, Represents the position angle of the planet gear relative to the ring gear, Represents the longitudinal displacement of the planet gear in the absolute coordinate system, Represents the base circle radius of the ring gear, Represents the base circle radius of the planet gear, Represents the rated angular velocity of the planet gear, Represents the torsional vibration displacement of the planet gear, Represents the comprehensive meshing error of the internal meshing pair; Furthermore, considering the non - linear function of the displacement along the meshing line due to backlash, it is expressed as: ; where, Represents the non - linear function of the displacement along the meshing line, Represents the relative displacement along the meshing line of the internal and external meshing pairs, Represents half of the backlash, Represents taking the absolute value; Furthermore, the meshing force of the external meshing pair is expressed as: ; where, Represents the meshing force of the external meshing pair, Represents the time - varying meshing stiffness of the external meshing pair, Represents the relative displacement function along the meshing line of the external meshing pair, Represents the relative displacement along the meshing line of the external meshing pair, Represents the meshing damping of the external meshing pair, t represents time; Furthermore, the meshing force of the internal meshing pair is expressed as: ; where, Represents the meshing force of the internal meshing pair, Represents the time - varying meshing stiffness of the internal meshing pair, Represents the relative displacement function along the meshing line of the internal meshing pair, Represents the relative displacement along the meshing line of the internal meshing pair, Represents the meshing damping of the internal meshing pair, t represents time.

[0031] S500, establishing a multi-stage planetary transmission dynamics model according to the time-varying meshing stiffness, multi-source excitation, and the meshing force; Furthermore, in step S500, the multi-stage planetary transmission dynamics model includes a motion model of the sun gear, a motion model of the planet carrier, and a motion model of the planet gear; The motion model of the sun gear can be: ; in, represents the mass of the sun gear, represents the lateral vibration acceleration of the sun gear in the absolute coordinate system, express Sun gear support stiffness in direction, represents the lateral translation vibration of the sun gear in the absolute coordinate system, express Sun gear support damping in direction, represents the lateral vibration speed of the sun gear in the absolute coordinate system, represents the meshing force of the external meshing pair, It represents the relative displacement of the external meshing pair along the meshing line, Indicates the The number of planetary gears in the first-stage planetary gear train, represents the lateral vibration acceleration of the sun gear in the absolute coordinate system, express Sun gear support stiffness in direction, represents the longitudinal translation vibration of the sun gear in the absolute coordinate system, express Sun gear support damping in direction, represents the longitudinal vibration speed of the sun gear in the absolute coordinate system, represents the moment of inertia of the first-stage sun gear, Indicates the torsional vibration acceleration of the first-stage sun gear, represents the torsional stiffness of the first-stage sun gear, represents the torsional vibration displacement of the first-stage sun gear, Indicates the torsional damping of the first-stage sun gear, Indicates the torsional vibration speed of the first-stage sun gear, It represents the meshing force of the outer meshing pair of the first stage planetary gear system, It represents the relative displacement of the outer meshing pair of the first stage planetary gear system along the meshing line. represents the system input torque acting on the first-stage sun gear, represents the moment of inertia of the second-stage sun gear, Indicates the torsional vibration acceleration of the second-stage sun gear, Denotes the torsional stiffness between the first-stage planet carrier and the second-stage sun gear. Denotes the torsional vibration displacement of the second-stage sun gear. Denotes the torsional vibration displacement of the first-stage planet gear. Denotes the torsional damping between the first-stage planet carrier and the second-stage sun gear. Denotes the torsional vibration velocity of the second-stage sun gear. Denotes the torsional vibration velocity of the first-stage planet carrier. Denotes the meshing force of the second-stage external meshing pair. Denotes the relative displacement along the meshing line of the external meshing pair of the second-stage planetary gear train.

[0032] Furthermore, the motion model of the planet carrier can be: ; Wherein, Denotes the number of planet gears in the th-stage planetary gear train, Denotes the th planet gear in the th-stage planetary gear train, Denotes the translational vibration displacement of the th planet gear relative to the planet carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the Denotes the initial center distance of the gear pair, Denotes the th-stage torsional vibration acceleration of the planet carrier, Denotes the translational vibration displacement of the th planet gear relative to the planet carrier along the tangent direction of the rotation of the planet carrier in the rotating coordinate system of the th-stage planetary gear train, Denotes the th-stage rated angular velocity of the planet carrier, Denotes the th-stage torsional vibration velocity of the planet carrier, Denotes the translational vibration velocity of the th planet gear relative to the planet carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the th-stage planetary gear train, Denotes the translational vibration acceleration of the th planet gear relative to the planet carrier along the tangent direction of the rotation of the planet carrier in the rotating coordinate system of the th-stage planetary gear train, Denotes time, Denotes the th-stage torsional vibration displacement of the planet carrier, Denotes the th-stage The initial installation angle of a planetary gear relative to the sun gear Indicates the th translational vibration velocity of the planetary gear relative to the planet carrier along the tangential direction of the planet carrier rotation in the rotating coordinate system of the planet carrier Indicates the th translational vibration acceleration of the planetary gear relative to the planet carrier along the line connecting the centers of the sun gear and the planetary gear in the rotating coordinate system of the planet carrier Indicates the mass of the planet carrier at the Indicates the lateral vibration acceleration of the planet carrier at the th level in the absolute coordinate system Indicates the support stiffness of the planet carrier in the x - direction at the Indicates the lateral vibration displacement of the planet carrier at the th level in the absolute coordinate system Indicates the support damping of the planet carrier in the x - direction at the Indicates the lateral vibration velocity of the planet carrier at the th level in the absolute coordinate system Indicates the contact force between the sun gear and the th planetary gear in the th planetary gear set Indicates the relative displacement along the line of action between the sun gear and the th planetary gear in the th planetary gear set Indicates the contact force between the ring gear and the th planetary gear in the th planetary gear set Indicates the support stiffness of the planet carrier in the y - direction at the Indicates the longitudinal vibration displacement of the planet carrier at the th level in the absolute coordinate system Indicates the support damping of the planet carrier in the y - direction at the Indicates the th level in the absolute coordinate system mass of the th planetary gear in the first - level planetary gear train Denotes the translational vibration acceleration of the n-th planet gear in the first stage relative to the carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the carrier, Denotes the translational vibration displacement of the n-th planet gear in the first stage relative to the carrier along the tangent direction of the carrier rotation in the rotating coordinate system of the carrier, Denotes the translational vibration displacement of the n-th planet gear in the first stage relative to the carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the carrier, Denotes the translational vibration acceleration of the n-th planet gear in the first stage relative to the carrier along the tangent direction of the carrier rotation in the rotating coordinate system of the carrier, Denotes the translational vibration velocity of the n-th planet gear in the first stage relative to the carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the carrier, Denotes the translational vibration velocity of the n-th planet gear in the first stage relative to the carrier along the tangent direction of the carrier rotation in the rotating coordinate system of the carrier, Denotes the rotational angular velocity of the first-stage carrier, Denotes the torsional vibration velocity of the first-stage carrier, Denotes the lateral vibration acceleration of the first-stage carrier in the absolute coordinate system, Denotes the longitudinal vibration acceleration of the first-stage carrier in the absolute coordinate system, Denotes the torsional vibration displacement of the first-stage carrier, Denotes the initial installation angle of the n-th planet gear in the first stage relative to the sun gear, Denotes the moment of inertia of the first-stage carrier, Denotes the moment of inertia of the n-th planet gear in the first stage, [[ID=......]]...... Denotes the torsional vibration acceleration of the n-th planet gear in the first stage, ...... Denotes the inter-stage torsional stiffness connecting the first-stage carrier and the second-stage sun gear, Denotes the torsional vibration displacement of the second-stage sun gear, Denotes the inter-stage torsional damping connecting the first-stage carrier and the second-stage sun gear, Denotes the torsional vibration velocity of the second-stage sun gear, Denotes the meshing force of the meshing pair between the sun gear and the n-th planet gear in the first-stage planetary gear, Denotes the relative displacement along the meshing line of the meshing pair between the sun gear and the n-th planet gear in the first-stage planetary gear, Denotes the meshing force of the ring gear and the th planet gear pair in the first-stage planetary gear, Denotes the relative displacement along the meshing line of the ring gear and the th planet gear pair in the first-stage planetary gear; Denotes the mass of the th planet gear in the second-stage planetary gear train, Denotes the translational vibration acceleration of the th planet gear relative to the planet carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the planet carrier, Denotes the translational vibration displacement of the th planet gear relative to the planet carrier along the tangent direction of the planet carrier rotation in the rotating coordinate system of the planet carrier, Denotes the translational vibration displacement of the th planet gear relative to the planet carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the planet carrier, Denotes the translational vibration acceleration of the th planet gear relative to the planet carrier along the tangent direction of the planet carrier rotation in the rotating coordinate system of the planet carrier, Denotes the translational vibration velocity of the th planet gear relative to the planet carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the planet carrier, Denotes the translational vibration velocity of the th planet gear relative to the planet carrier along the tangent direction of the planet carrier rotation in the rotating coordinate system of the planet carrier, Denotes the angular velocity of the second-stage planet carrier rotation, Denotes the torsional vibration velocity of the second-stage planet carrier, Denotes the lateral vibration acceleration of the second-stage planet carrier in the absolute coordinate system, Denotes the longitudinal vibration acceleration of the second-stage planet carrier in the absolute coordinate system, Denotes the torsional vibration displacement of the second-stage planet gear, Denotes the initial installation angle of the th planet gear relative to the sun gear in the second stage, Denotes the moment of inertia of the second-stage planet carrier, Denotes the moment of inertia of the th planet gear in the second stage, Denotes the torsional vibration acceleration of the th planet gear in the second stage, Denotes the meshing force of the sun gear and the th planet gear pair in the second-stage planetary gear, Denotes the relative displacement along the meshing line of the ring gear and the th planet gear pair in the second-stage planetary gear, represents the meshing force of the ring gear and the th planet gear meshing pair in the second-stage planetary gear, represents the relative displacement along the meshing line of the ring gear and the th planet gear meshing pair in the second-stage planetary gear, represents the output torque of the planetary gear transmission system.

[0033] Furthermore, the motion model of the planet gear can be: ; where represents the mass of the th planet gear in the -stage planetary gear train, represents the lateral vibration acceleration of the -stage planet carrier in the absolute coordinate system, represents the rotational angular velocity of the -stage planet carrier, represents time, represents the torsional vibration displacement of the -stage planet carrier, represents the initial installation angle of the th planet gear in the -stage relative to the sun gear, represents the longitudinal vibration acceleration of the -stage planet carrier in the absolute coordinate system, represents the translational vibration acceleration of the th planet gear in the -stage relative to the planet carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the planet carrier, represents the translational vibration velocity of the th planet gear in the -stage relative to the planet carrier along the tangent direction of the rotation of the planet carrier in the rotating coordinate system of the planet carrier, represents the torsional vibration acceleration of the -stage planet carrier, represents the translational vibration displacement of the th planet gear in the -stage relative to the planet carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the planet carrier, represents the initial center distance of the gear pair, represents the -stage torsional vibration velocity of the planet carrier, represents the translational vibration velocity of the th planet gear in the -stage relative to the planet carrier along the tangent direction of the rotation of the planet carrier in the rotating coordinate system of the planet carrier, represents the The support stiffness of the nth planetary gear relative to the planet carrier in the x direction, the support damping of the nth planetary gear relative to the planet carrier in the y direction, the translational vibration velocity of the nth planetary gear relative to the planet carrier along the line connecting the centers of the sun gear and the planetary gear in the rotating coordinate system of the planet carrier, the meshing force of the nth stage of the planetary gear system between the sun gear and the nth planetary gear pair, the relative displacement along the meshing line of the nth stage of the planetary gear system between the sun gear and the nth planetary gear pair, the meshing force of the nth stage of the planetary gear system between the ring gear and the nth planetary gear pair, the relative displacement along the meshing line of the nth stage of the planetary gear system between the ring gear and the nth planetary gear pair, the support stiffness of the nth planetary gear relative to the planet carrier in the y direction, the support damping of the nth planetary gear relative to the planet carrier in the y direction, the moment of inertia of the nth planetary gear in the planetary gear train, the torsional vibration acceleration of the nth planetary gear, the torsional vibration displacement of the nth planetary gear.

[0034] Based on the above technical solution of this embodiment, a certain type of two-stage 2K-H planetary gear transmission system is modeled and numerically simulated. The gear parameters of each stage of the planetary gear transmission system are the same, as shown in Table 1 below. The Runge-Kutta method is used to solve the numerical simulation of the translational-torsional vibration, and the time-domain diagram, frequency-domain diagram, and phase trajectory diagram of the planetary gear transmission system are obtained.

[0034]

[0035] Table 1 Planetary Gear Transmission System Parameter Table Sun gear Planet gear Ring gear Number of teeth 18 23 66 Module (mm) 5.5 5.5 5.5 Pressure angle (°) 20 20 20 Addendum modification coefficient 0.5504 0.55 0.5049 Center distance (mm) 118 118 118 Furthermore, the multi-stage planetary transmission dynamic model established by the above technical solution is numerically solved to obtain the steady-state response of the 2K-H planetary gear transmission system. Taking the first-stage external meshing pair as an example, the results are compared with the two-stage planetary gear traditional translational torsional dynamic model and the two-stage planetary gear traditional translational torsional dynamic model that only considers the time-varying pressure angle. The variation of the contact ratio with time is as Figure 6 shown. It can be seen that the contact ratio under the traditional modeling method is a fixed value, indicating that the technical solution proposed by the present invention takes into account the change of the contact characteristics caused by the radial displacement of the gear, and has stronger nonlinearity compared with the model that only considers the time-varying pressure angle. The influence of different contact ratios on the external meshing stiffness of the system within one meshing cycle is as Figure 7 shown. The time-domain diagram of the relative displacement along the meshing line of the first-stage planetary gear external meshing pair under different modeling methods is as Figure 8 shown. It can be seen that the vibration response of the displacement along the meshing line obtained by the existing technology is periodic. The modeling method proposed by the present invention has stronger nonlinearity compared with the previous two. The frequency-domain diagram of the relative displacement along the meshing line of the first-stage planetary gear external meshing pair under different modeling methods is as Figure 9 shown. It can be seen from the figure that the main frequency distributions of different methods are the same, but the amplitudes are different. The modeling method proposed by the present invention has more frequency components and stronger nonlinearity. It can be seen from the figure that the contact ratio after considering the time-varying meshing angle has time-varying characteristics, reflecting the change of the contact ratio caused by the radial displacement of the gear during actual operation; the time-varying meshing stiffness based on the potential energy method is different at different contact ratios, especially when changing from the double-tooth meshing area to the single-tooth meshing area, the stiffness changes greatly; in the time-frequency domain diagram, the transmission system has strong nonlinearity.

[0036] In the second aspect, this embodiment provides a non-linear dynamics modeling system for a planetary gear transmission system, including: A degree-of-freedom model determination module, configured to determine a two-stage spur planetary gear transmission system; establish a degree-of-freedom model of the external and internal meshing gear pairs according to the transmission system; A meshing stiffness acquisition module, which uses the degree-of-freedom model to improve the time-varying meshing stiffness of the internal and external meshing pairs of the transmission system; A multi-source excitation acquisition module, configured to obtain the multi-source excitation of the transmission system including the time-varying meshing angle and the position angle according to the degree-of-freedom model; the multi-source excitation includes eccentricity error and tooth profile error; A meshing force acquisition module, configured to establish a non-linear function of the relative displacement along the meshing line and the backlash of the internal and external meshing pairs, and obtain the meshing forces of each meshing pair; A dynamics model establishment module, configured to establish a multi-stage planetary transmission dynamics model according to the time-varying meshing stiffness, multi-source excitation, and the meshing force.

[0037] In the description of the above embodiments, specific features, structures, materials, or characteristics may be combined in any one or more embodiments or examples in a suitable manner.

[0038] As described above, the specific embodiments of the present invention are only described, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claimed rights.

Claims

1. A non-linear dynamics modeling method for a planetary gear transmission system, characterized in that include: Identify the two-stage spur planetary gear transmission system; Establishing a degree of freedom model of an external and internal meshing gear pair according to the transmission system; Using the degree of freedom model to improve the time-varying meshing stiffness of the internal and external meshing pairs of the transmission system; Acquiring a multi-source excitation of a transmission system including a time-varying meshing angle and a position angle according to the degree of freedom model; the multi-source excitation including an eccentricity error and a tooth profile error; Establish the nonlinear function of the relative displacement and tooth side clearance of the internal and external meshing pairs along the meshing line direction, and obtain the meshing force of each meshing pair; A multi-stage planetary transmission dynamics model is established according to the time-varying meshing stiffness, multi-source excitation and the meshing force.

2. The non-linear dynamics modeling method of the planetary gear transmission system according to claim 1, characterized in that, The method of establishing a degree of freedom model of the external and internal meshing gear pair according to the transmission system includes: defining the translational vibration displacement of the planetary gears according to the two-stage spur planetary gear transmission system; Determine the actual center distance between the outer meshing pair and the inner meshing pair of the planetary gear according to the translational vibration displacement; Determine the meshing angles of the internal and external meshing pairs, as well as the position angles of the planetary gears relative to the sun gear and the position angles of the planetary gears relative to the ring gear.

3. The non-linear dynamic modeling method of the planetary gear transmission system according to claim 2, characterized in that The translational vibration displacement of the planetary gear includes the lateral displacement and longitudinal displacement of the planetary gear in the absolute coordinate system; the lateral displacement of the planetary gear in the absolute coordinate system is obtained by the following formula: ； Among them, represents the lateral displacement of the planet gear in the absolute coordinate system, represents the lateral translational vibration of the planet carrier in the absolute coordinate system, represents the translational vibration displacement of the planet gear relative to the planet carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the planet carrier, represents the initial center distance of the gear pair, represents the rated angular velocity of the planet carrier, represents time, represents the torsional vibration displacement of the planet carrier, represents the initial installation angle of the planet gear relative to the sun gear, represents the translational vibration displacement of the planet gear relative to the planet carrier along the tangent direction of the rotation of the planet carrier in the rotating coordinate system of the planet carrier, the subscript represents the number of planet gear stages, the subscript represents the number of planet gears, the subscripts s, p, r, and c represent the sun gear, planet gear, ring gear, and planet carrier respectively; The longitudinal displacement of the planetary gear in the absolute coordinate system is obtained by the following formula: ； Among them, represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the longitudinal translational vibration of the planet carrier in the absolute coordinate system, represents the translational vibration displacement of the planet gear relative to the planet carrier along the line connecting the centers of the sun gear and the planet gear in the rotating coordinate system of the planet carrier, represents the initial center distance of the gear pair, represents the rated angular velocity of the planet carrier, represents time, represents the torsional vibration displacement of the planet carrier, represents the initial installation angle of the planet gear relative to the sun gear, represents the translational vibration displacement of the planet gear relative to the planet carrier along the tangent direction of the rotation of the planet carrier in the rotating coordinate system of the planet carrier, with the subscript represents the number of planet gear stages, with the subscript represents the number of planet gears. The subscripts s, p, r, and c represent the sun gear, planet gear, ring gear, and planet carrier respectively.

4. The non - linear dynamics modeling method of the planetary gear transmission system according to claim 3, characterized in that, The actual center distance of the outer meshing pair of the planetary gear is obtained by the following formula: ； Among them, represents the actual center distance of the external meshing pair of the planetary gear, represents the lateral displacement of the planetary gear in the absolute coordinate system, represents the lateral translational vibration of the sun gear in the absolute coordinate system, represents the longitudinal displacement of the planetary gear in the absolute coordinate system, represents the longitudinal translational vibration of the sun gear in the absolute coordinate system; And / or, the actual center distance of the internal meshing pair of the planetary gears is obtained by the following formula: ; wherein, represents the actual center distance of the internal meshing pair of the planetary gear, represents the lateral displacement of the planetary gear in the absolute coordinate system, represents the longitudinal displacement of the planetary gear in the absolute coordinate system; And / or, the meshing angle of the external meshing pair is obtained by the following formula: ； Among them, represents the meshing angle of the external meshing pair, represents the base circle radius of the sun gear, represents the base circle radius of the planet gear, represents the lateral displacement of the planet gear in the absolute coordinate system, represents the lateral translational vibration of the sun gear in the absolute coordinate system, represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the longitudinal translational vibration of the sun gear in the absolute coordinate system; And / or, the meshing angle of the internal meshing pair is obtained by the following formula: ; wherein, represents the engagement angle of the internal engagement pair, represents the base circle radius of the ring gear, represents the base circle radius of the planet gear, represents the lateral displacement of the planet gear in the absolute coordinate system, represents the longitudinal displacement of the planet gear in the absolute coordinate system; And / or, the position angle of the planet gear relative to the sun gear is obtained by the following formula: ; wherein, represents the angular position of the planet gear relative to the sun gear, represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the longitudinal translational vibration of the sun gear in the absolute coordinate system, represents the lateral displacement of the planet gear in the absolute coordinate system, represents the lateral translational vibration of the sun gear in the absolute coordinate system; And / or, the position angle of the planetary gear relative to the ring gear is obtained by the following formula: ; wherein, represents the angular position of the planet gear relative to the ring gear, represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the lateral displacement of the planet gear in the absolute coordinate system.

5. The non-linear dynamics modeling method of the planetary gear transmission system according to claim 4, characterized in that In the process of using the degree of freedom model to improve the time-varying meshing stiffness of the internal and external meshing pairs of the transmission system, a single pair of teeth and a double pair of teeth are alternately engaged; wherein: The time-varying meshing stiffness of the single pair of teeth is: ; among which, represents the time-varying meshing stiffness of a single pair of teeth, represents the Hertz contact stiffness of a single pair of teeth, represents the bending stiffness of the driving gear teeth, represents the bending stiffness of the driven gear teeth, represents the shear stiffness of the driving gear teeth, represents the shear stiffness of the driven gear teeth, represents the axial compression stiffness of the driving gear teeth, represents the axial compression stiffness of the driven gear teeth, represents the flexible matrix stiffness of the driving gear teeth, represents the flexible matrix stiffness of the driven gear teeth; The time-varying meshing stiffness of the two pairs of teeth is: ； Among them, represents the time-varying meshing stiffness of the double pair of teeth, represents the Hertz contact stiffness of the nth pair of teeth, represents the bending stiffness of the driving wheel of the nth pair of teeth, represents the bending stiffness of the driven wheel of the nth pair of teeth, represents the shear stiffness of the driving wheel of the nth pair of teeth, represents the shear stiffness of the driven wheel of the nth pair of teeth, represents the axial compression stiffness of the driving wheel of the nth pair of teeth, represents the axial compression stiffness of the driven wheel of the nth pair of teeth, represents the flexible matrix stiffness of the driving wheel of the nth pair of teeth, represents the flexible matrix stiffness of the driven wheel of the nth pair of teeth; And / or, in the process of improving the time-varying meshing stiffness of the internal and external meshing pairs of the transmission system by using the degree-of-freedom model, within one meshing cycle the time of the single-tooth meshing zone and the time of the double-tooth meshing zone are respectively: , wherein, represents the time of the single-tooth meshing zone, represents the time of the double-tooth meshing zone, represents the meshing cycle, and P represents the gear contact ratio; And / or, due to the time-varying nature of the meshing angle, the degree of contact between the internal gear pair and the external gear pair changes in real time, which can be expressed as: ； ； Among them, represents the contact ratio of the external gear pair, represents the contact ratio of the internal gear pair, represents the addendum circle radius of the sun gear, represents the base circle radius of the sun gear, represents the addendum circle radius of the planet gear, represents the base circle radius of the planet gear, represents the initial center distance of the gear pair, represents the pressure angle of the external meshing pair, represents the base pitch; represents the pressure angle of the internal meshing pair.

6. The non-linear dynamic modeling method of the planetary gear transmission system according to claim 5, characterized in that, The eccentricity error includes the meshing error of the sun gear eccentricity equivalent to the outer meshing line meshing with the planet gear, the meshing error of the planet gear eccentricity equivalent to the outer meshing line meshing with the sun gear, and the meshing error of the planet gear eccentricity equivalent to the inner meshing line meshing with the ring gear; And / or, the tooth profile error includes an equivalent tooth profile error on the meshing line converted from the tooth profile deviation of the external meshing gear, and an equivalent tooth profile error on the meshing line converted from the tooth profile deviation of the internal meshing gear.

7. The non - linear dynamics modeling method of the planetary gear transmission system according to claim 6, characterized in that, The meshing error of the equivalent sun gear eccentricity on the external meshing line meshing with the planet gear is expressed as: ; where represents the meshing error of the equivalent sun gear eccentricity on the external meshing line meshing with the planet gear, represents the amplitude of the sun gear eccentricity error, represents the rated speed of the sun gear, represents the rated speed of the planet carrier, represents time, represents the meshing angle of the external meshing pair, represents the initial phase of the sun gear eccentricity, represents the initial installation angle of the planet gear relative to the sun gear; And / or, the meshing error of the equivalent planetary gear eccentricity on the external meshing line meshing with the sun gear is expressed as: ; where represents the meshing error of the equivalent planetary gear eccentricity on the external meshing line meshing with the sun gear, represents the amplitude of the planetary gear eccentricity error, represents the rated speed of the planetary gear, represents the rated speed of the planet carrier, represents time, represents the meshing angle of the external meshing pair, represents the initial phase of the planetary gear eccentricity; And / or, the meshing error of the equivalent planetary gear eccentricity on the internal meshing line meshing with the ring gear is expressed as: ; where represents the meshing error of the equivalent planetary gear eccentricity on the internal meshing line meshing with the ring gear, represents the amplitude of the planetary gear eccentricity error, represents the rated speed of the planetary gear, represents the rated speed of the planet carrier, represents time, represents the meshing angle of the internal meshing pair, represents the initial phase of the planetary gear eccentricity; And / or, the tooth profile deviation of the external meshing gear is converted into an equivalent tooth profile error on the meshing line, which is expressed as: ; among which, represents the equivalent profile error of the tooth profile deviation of the external meshing gear transformed on the meshing line, represents the equivalent deviation amplitude of the external meshing pair, represents the th-order planetary gear train meshing frequency, represents time, represents the position angle of the planetary gear relative to the sun gear, represents the meshing angle of the external meshing pair, represents the th-order planetary gear train meshing period; And / or, the tooth profile deviation of the internal meshing gear is converted into an equivalent tooth profile error on the meshing line, which is expressed as: ; among which, represents the equivalent profile error of the internal gear pair's profile deviation transformed on the meshing line, represents the equivalent deviation amplitude of the internal gear pair, represents the th order planetary gear train meshing frequency, represents time, represents the position angle of the planetary gear relative to the sun gear, represents the meshing angle of the external gear pair, represents the position angle of the planetary gear relative to the ring gear, represents the meshing angle of the internal gear pair, represents the th order planetary gear train meshing period; And / or, the comprehensive meshing error of the external meshing pair considering the eccentricity error and the tooth profile error is expressed as: ; among them, represents the comprehensive meshing error of the external meshing pair, represents the meshing error of the sun gear eccentricity equivalent on the external meshing line meshing with the planet gear, represents the meshing error of the planet gear eccentricity equivalent on the external meshing line meshing with the sun gear, represents the equivalent profile error of the tooth profile deviation of the external meshing gear converted on the meshing line; And / or, the comprehensive meshing error of the internal meshing pair considering the eccentricity error and tooth profile error is expressed as: ; among them, represents the comprehensive meshing error of the internal meshing pair, represents the meshing error of the planetary gear eccentricity equivalent on the internal meshing line meshing with the ring gear, represents the equivalent profile error of the profile deviation of the internal meshing gear converted on the meshing line.

8. The non-linear dynamic modeling method of the planetary gear transmission system according to claim 7, characterized in that Establishing a non-linear function of the relative displacement and backlash of the internal and external meshing pairs along the meshing line, and obtaining the meshing forces of each meshing pair, includes: Setting the vibration direction of the compression gear meshing line as positive and the opposite as negative, then determining the relative displacement along the meshing line of the sun-planet gear meshing pair and the relative displacement along the meshing line of the ring-planet gear meshing pair; Determining the non-linear function of the displacement along the meshing line considering the backlash, and obtaining the meshing forces of the external meshing pair and the internal meshing pair.

9. The non-linear dynamics modeling method of the planetary gear transmission system according to claim 8, characterized in that The relative displacement along the meshing line of the sun-planet gear meshing pair is expressed as: ； Among them, represents the relative displacement along the meshing line of the sun-planet gear pair, represents the lateral translational vibration of the sun gear in the absolute coordinate system, represents the lateral displacement of the planet gear in the absolute coordinate system, represents the initial center distance of the gear pair, represents the rated angular velocity of the planet carrier, represents time, represents the torsional vibration displacement of the planet carrier, represents the initial installation angle of the planet gear relative to the sun gear, represents the meshing angle of the external meshing pair, represents the position angle of the planet gear relative to the sun gear, represents the longitudinal translational vibration of the sun gear in the absolute coordinate system, represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the base circle radius of the sun gear, represents the rated angular velocity of the sun gear, represents the torsional vibration displacement of the sun gear, represents the base circle radius of the planet gear, represents the rated angular velocity of the planet gear, represents the torsional vibration displacement of the planet gear, represents the comprehensive meshing error of the external meshing pair; And / or, the relative displacement along the meshing line of the ring-planet gear meshing pair is expressed as: ； Among them, represents the relative displacement along the meshing line of the ring gear - planet gear meshing pair, represents the lateral displacement of the planet gear in the absolute coordinate system, represents the initial center distance of the gear pair, represents the rated angular velocity of the planet carrier, represents time, represents the torsional vibration displacement of the planet carrier, represents the initial installation angle of the planet gear relative to the sun gear, represents the meshing angle of the internal meshing pair, represents the position angle of the planet gear relative to the ring gear, represents the longitudinal displacement of the planet gear in the absolute coordinate system, represents the base circle radius of the ring gear, represents the base circle radius of the planet gear, represents the rated angular velocity of the planet gear, represents the torsional vibration displacement of the planet gear, represents the comprehensive meshing error of the internal meshing pair; And / or, the non-linear function of the displacement along the meshing line considering the backlash is expressed as: ; wherein, represents the displacement non-linear function along the engagement line, represents the relative displacement along the engagement line of the internal engagement pair and the external engagement pair, represents half of the backlash, represents taking the absolute value; And / or, the meshing force of the external meshing pair is expressed as: ; wherein, represents the meshing force of the external meshing pair, represents the time-varying meshing stiffness of the external meshing pair, represents the relative displacement function of the external meshing pair along the meshing line, represents the relative displacement of the external meshing pair along the meshing line, represents the meshing damping of the external meshing pair, and t represents time; And / or, the meshing force of the internal meshing pair is expressed as: ; among which, represents the meshing force of the internal meshing pair, represents the time-varying meshing stiffness of the internal meshing pair, represents the relative displacement function of the internal meshing pair along the meshing line, represents the relative displacement of the internal meshing pair along the meshing line, represents the meshing damping of the internal meshing pair, and t represents time; And / or, the multi-stage planetary transmission dynamics model includes the motion model of the sun gear; the motion model of the sun gear is expressed as: ； Among them, represents the sun gear mass, represents the transverse vibration acceleration of the sun gear in the absolute coordinate system, represents the sun gear support stiffness in the represents the transverse translational vibration of the sun gear in the absolute coordinate system, represents the sun gear support damping in the represents the transverse vibration velocity of the sun gear in the absolute coordinate system, represents the meshing force of the external meshing pair, represents the relative displacement of the external meshing pair along the meshing line, represents the number of planet gears in the represents the transverse vibration acceleration of the sun gear in the absolute coordinate system, represents the sun gear support stiffness in the represents the longitudinal translational vibration of the sun gear in the absolute coordinate system, represents the sun gear support damping in the represents the longitudinal vibration velocity of the sun gear in the absolute coordinate system, represents the moment of inertia of the first-stage sun gear, represents the torsional vibration acceleration of the first-stage sun gear, represents the torsional stiffness of the first-stage sun gear, represents the torsional vibration displacement of the first-stage sun gear, represents the torsional damping of the first-stage sun gear, represents the torsional vibration velocity of the first-stage sun gear, represents the meshing force of the external meshing pair of the first-stage planetary gear train, represents the relative displacement of the external meshing pair of the first-stage planetary gear train along the meshing line, represents the system input torque acting on the first-stage sun gear, represents the moment of inertia of the second-stage sun gear, represents the torsional vibration acceleration of the second-stage sun gear, represents the inter-stage torsional stiffness connecting the first-stage planet carrier and the second-stage sun gear, represents the torsional vibration displacement of the second-stage sun gear, represents the torsional vibration displacement of the first-stage planet gear, represents the inter-stage torsional damping connecting the first-stage planet carrier and the second-stage sun gear, represents the torsional vibration velocity of the second-stage sun gear, represents the torsional vibration velocity of the first-stage planet carrier, Denotes the meshing force of the second-stage external meshing pair. Denotes the relative displacement along the meshing line of the external meshing pair of the second-stage planetary gear train.

10. A non-linear dynamics modeling system for a planetary gear transmission system, characterized in that, Including: A degree-of-freedom model determination module, configured to determine a two-stage spur planetary gear transmission system; and establish a degree-of-freedom model of the external and internal meshing gear pairs according to the transmission system; A meshing stiffness acquisition module, which uses the degree-of-freedom model to improve the time-varying meshing stiffness of the external and internal meshing pairs of the transmission system; A multi-source excitation acquisition module, configured to obtain the multi-source excitation of the transmission system including the time-varying meshing angle and position angle according to the degree-of-freedom model; the multi-source excitation includes eccentricity error and profile error; A meshing force acquisition module, configured to establish a non-linear function of the relative displacement and backlash of the internal and external meshing pairs along the meshing line, and obtain the meshing forces of each meshing pair; A dynamics model establishment module, configured to establish a multi-stage planetary transmission dynamics model according to the time-varying meshing stiffness, multi-source excitation and the meshing force.

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