A method for solving dynamic coupling transmission errors in a helical gear combined transmission system

Abstract

This invention discloses a method for solving the dynamic coupling transmission error of a helical gear combined transmission system. The method first obtains the basic parameters of the helical gear combined transmission system and establishes a three-dimensional model of the system. Second, it calculates the static transmission error and time-varying meshing stiffness during gear meshing based on finite element analysis. Next, it establishes an 18-DOF dynamic model of the helical gear combined transmission system, considering time-varying meshing stiffness, installation and machining errors, tooth flank clearance, and meshing damping. Then, it inputs gear parameters and operating conditions, including input torque, output torque, and input speed, and uses the fourth-order variable-step Runge-Kutta method to obtain the dynamic response of the helical gear combined transmission system. Finally, it obtains the dynamic coupling transmission error of the helical gear transmission system based on the dynamic solution results.

Description

Technical Field

[0001] This invention belongs to the field of dynamic response analysis technology of helical gear combined transmission systems, and particularly relates to a method for solving dynamic coupling transmission errors in helical gear combined transmission systems. Background Technology

[0002] Helical gear transmission systems are common mechanical power transmission devices, and are widely used in modern large-scale mechanical equipment such as shipbuilding, wind turbines, and construction machinery due to their high transmission efficiency, strong load-bearing capacity, and stable operation.

[0003] In recent years, in the field of national defense, the development goal of the Chinese Navy has shifted from "far-sea escort" to "far-sea defense," which places higher demands on ships. Helical gear transmission systems, through parallel operation, combine multiple power inputs and transmit them to the propeller, achieving parallel operation and overcoming the shortcomings of insufficient power from individual propellers. For ships, stealth is a crucial factor affecting safety; the lower the noise generated, the less easily the ship is detected by the enemy. Ship noise mainly originates from three parts: mechanics, hydrodynamics, and propellers, with mechanical noise being the primary source, mainly generated by the ship's gear transmission system. Therefore, the performance of the helical gear transmission system, as the ship's transmission system, significantly impacts the overall operational performance of the vessel. Considering the ship's stealth and the physical and mental health of the crew, the vibration and noise of the transmission system are also key factors that must be considered in the design. Therefore, conducting vibration and noise analysis research on helical gear transmission systems is a crucial challenge for improving ship operational efficiency.

[0004] As is well known, gear transmission is the transmission of power between the driving and driven gears through the meshing force generated along the meshing direction. Transmission error, defined as "the offset between the actual meshing position and the theoretical meshing position of the meshing gear pair," is a dynamic excitation generated along the meshing line and is a significant source of vibration and noise. Currently, most dynamic error analyses of helical gear transmission systems rely on simulation software, which is cumbersome and fails to adequately consider the coupling responses of multiple gear pairs under multi-input conditions. Therefore, designing an efficient dynamic transmission error analysis method that fully considers gear pair coupling under multi-input conditions is of great significance for the study of gear vibration and noise analysis. Summary of the Invention

[0005] The purpose of this invention is to solve the problems existing in the prior art and to provide a method for solving the dynamic coupling transmission error of a helical gear combined transmission system.

[0006] To achieve the above-mentioned objectives, the present invention specifically adopts the following technical solution:

[0007] A method for solving the dynamic coupling transmission error of a helical gear combined transmission system includes the following steps:

[0008] S1. Obtain the basic parameters of the helical gear combined transmission system;

[0009] S2. Based on the basic parameters obtained in S1, establish a three-dimensional model of the helical gear combined transmission system, and perform transient dynamic analysis on the three-dimensional model using the finite element analysis method. Based on the transient dynamic analysis results, obtain the static transmission error and time-varying meshing stiffness of the helical gear combined transmission system.

[0010] S3. Establish a dynamic model of the helical gear combined transmission system with 18 degrees of freedom, considering time-varying meshing stiffness, installation and machining errors, tooth backlash and meshing damping, including bending, torsion, shaft and pendulum motion.

[0011] S4. Substitute the static transmission error and time-varying meshing stiffness obtained in S2 into the dynamic model through Fourier transform, and solve the dynamic model using the fourth-order variable step size Runge-Kutta method.

[0012] S5. Obtain the dynamic coupling transmission error of the helical gear transmission system based on the dynamic solution results.

[0013] Based on the above scheme, each step can be implemented in the following preferred manner.

[0014] Preferably, in step S1, the basic parameters are the number of teeth of the first driving gear, the number of teeth of the second driving gear, the number of teeth of the driven gear, the normal module, the pressure angle of the pitch circle, the helix angle, the tooth width, the center distance, the tooth addendum coefficient, the clearance coefficient, and the rotational speed.

[0015] Preferably, in step S2, the specific process of performing transient dynamic analysis on the three-dimensional model using the finite element analysis method is as follows:

[0016] S21. Import the three-dimensional model of the helical gear combined transmission system into the finite element analysis software;

[0017] S22. Use finite element analysis software to group the contact surfaces of each gear to facilitate subsequent operations;

[0018] S23. After grouping, set the rotary connection pairs and tooth surface contact of each gear to the ground;

[0019] S24. Set the boundary conditions for the connection pair between the driving wheel and the driven wheel, wherein the boundary condition for the driving wheel is that the driving wheel rotates by a rotation angle, and the boundary condition for the connection pair between the driven wheel is the output torque of the driven wheel;

[0020] S25. Calculate the end time based on the input speed of the driving wheel and the output torque of the driven wheel, determine the analysis settings based on the end time, and determine the number of substeps for the determined analysis settings;

[0021] S26. Set up connection probes for the driving gear and driven gear respectively, and record the rotation angle output by the finite element analysis software to obtain the static transmission error and time-varying meshing stiffness of the gear.

[0022] Preferably, in step S2, the load transmission error of the gears during meshing is converted into the displacement difference generated on the meshing line of the gear pair and used as the static transmission error of the helical gear combined transmission system:

[0023]

[0024] Where LTE represents the load-bearing transmission error; R g θ represents the base circle radius of the driven wheel; g θ represents the angle of rotation of the driven wheel. p Indicates the rotation angle of the drive wheel; z p It is the number of teeth on the driving gear; z g This represents the number of teeth on the driven gear.

[0025] Preferably, in step S2, the time-varying meshing stiffness k of the gear... m The following formula is used for calculation:

[0026]

[0027] Among them, F n δ represents the normal meshing force of the gear pair along the line of meshing; n It represents the total elastic deformation during gear meshing.

[0028] Preferably, in step S3, the dynamic model is as follows:

[0029]

[0030]

[0031] Where, m p1 m p2 c represents the mass of the first and second driving wheels, respectively; p1x c p1y c p1z These represent the damping of the first drive wheel input shaft bearing in the x, y, and z directions, respectively; c p2x c p2y c p2z These represent the damping of the second drive wheel input shaft bearing in the x, y, and z directions, respectively; k p1x k p1yk p1z These represent the support stiffness of the first drive wheel input shaft bearing in the x, y, and z directions, respectively; k p2x k p2y k p2z These represent the support stiffness of the second drive wheel input shaft bearing in the x, y, and z directions, respectively; x p1 y p1 z p1 These represent the translational displacements of the first driving wheel in the x, y, and z directions, respectively; x p2 y p2 z p2 These represent the translational displacements of the second driving wheel in the x, y, and z directions, respectively; F x1 F y1 F z1 These represent the components of the force along the x, y, and z directions of the first gear pair, respectively; F x2 F y2 F z2 These represent the force components of the second gear pair along the x, y, and z directions, respectively; I p1 I p2 These represent the moments of inertia of the first and second driving wheels, respectively. The torsional angular displacement θ of the first driving wheel p1 The second derivative; The second driving wheel's torsional angular displacement θ p2 The second derivative of T; p1 T p2 F represents the input torque of the first and second driving wheels, respectively. n1 F n2 These represent the dynamic meshing forces of the first and second gear pairs, respectively; r p1 r p2 Φ represents the base circle radii of the first and second driving wheels, respectively; p1 Φ p2 c represents the oscillation displacement of the first and second driving wheels about the x-axis, respectively; p1θx c p1θy These represent the torsional oscillation damping of the first driving wheel in the x and y directions, respectively; c p2θx c p2θy These represent the torsional oscillation damping of the second driving wheel in the x and y directions, respectively; k p1θx k p1θy These represent the stiffness of the first driving wheel in the x and y directions, respectively; k p2θx k p2θy These represent the stiffness of the second driving wheel in the x and y directions, respectively; r p ′1、r p ′2 represents the pitch circle radius of the first and second driving gears, respectively; α1 represents the gear pressure angle; These represent the oscillation displacements of the first and second driving wheels around the y-axis, respectively. They represent The second derivative; They represent First derivative; m g c represents the mass of the driven wheel. gx c gy c gz These represent the damping of the driven wheel output shaft bearing in the x, y, and z directions, respectively; k gx k gy k gz These represent the support stiffness of the driven wheel output shaft bearing in the x, y, and z directions, respectively; x g y g z g These represent the translational displacements of the driven wheel in the x, y, and z directions, respectively; I g θ represents the moment of inertia of the driven wheel. g T represents the torsional angular displacement of the driven wheel. g This indicates the output torque of the driven wheel; r g The radius of the base circle of the driven gear is r. g ′ represents the pitch circle radius of the driven gear; Φ g c represents the oscillating displacement of the driven wheel about the x-axis; gθx c gθy These represent the torsional oscillation damping of the driven wheel in the x and y directions, respectively; k gθx k gθy These represent the stiffness of the driven wheel in the x and y directions, respectively. This represents the oscillating displacement of the driven wheel around the y-axis.

[0032] Preferably, in step S4, the Fourier transforms of the static transmission error and the time-varying meshing stiffness are as follows:

[0033] e(t) = e0 + e m sin(ωt+ψ)

[0034]

[0035] Where e(t) represents the dynamic transmission error; e0 represents the average value of the transmission error; e m The amplitude of the transmission error fluctuation is represented by ω; the gear meshing frequency is represented by t; the time variable is represented by ψ; the initial phase is represented by k. m (t) represents the time-varying meshing stiffness after Fourier transform; k0 represents the mean of the time-varying meshing stiffness; k j ψ represents the amplitude of the j-th order cosine component of the time-varying meshing stiffness; j represents the Fourier order; ψ j Indicates phase; ε αIndicates the degree of overlap of the end faces; m n Represents the normal modulus.

[0036] Compared with the prior art, the present invention has the following advantages:

[0037] The method of this invention can quickly obtain the dynamic transmission error of the helical gear combined transmission system without the need for a large number of finite element simulation calculations, and takes into account the coupling effect of parallel operation, which has certain supporting significance for the vibration and noise analysis of gears. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the execution flow of the method of the present invention;

[0039] Figure 2 This is a schematic diagram of a three-dimensional model of the helical gear combined transmission system provided in an embodiment of the present invention;

[0040] Figure 3 This is a schematic diagram of static transmission error obtained from finite element analysis provided in an embodiment of the present invention;

[0041] Figure 4 This is a schematic diagram of the dynamic coupling transmission error obtained by solving the dynamic model using the fourth-order variable step size Runge-Kutta method provided in this embodiment of the invention. Detailed Implementation

[0042] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. Technical features in the various embodiments of the present invention can be combined accordingly without mutual conflict.

[0043] In the description of this invention, it should be understood that the terms "first" and "second" are used only for descriptive purposes and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first" and "second" may explicitly or implicitly include at least one of those features.

[0044] like Figure 1 As shown, in a preferred embodiment of the present invention, the method for solving the dynamic coupling transmission error of the helical gear combined transmission system includes the following steps S1 to S5. The specific implementation process of each step will be described in detail below.

[0045] like Figure 1As shown, this embodiment takes a helical gear combined transmission system as the research object. To calculate the coupled dynamic transmission error of the helical gear combined transmission system, a method for solving the dynamic coupling transmission error of the helical gear combined transmission system considering two power inputs is designed. This method includes the following steps:

[0046] S1. Obtain the basic parameters of the helical gear combined transmission system.

[0047] It should be noted that, in this invention, the above-mentioned basic parameters are the number of teeth of the first driving gear, the number of teeth of the second driving gear, the number of teeth of the driven gear, the normal module, the pressure angle of the pitch circle, the helix angle, the tooth width, the center distance, the tooth addendum coefficient, the clearance coefficient, and the rotational speed.

[0048] It should be noted that, in this embodiment, the values ​​of the basic parameters of the helical gear combined transmission system are shown in Table 1. In Table 1, the values ​​of each basic parameter are merely an example set of values ​​given as an embodiment and are not intended to limit the invention. It is conceivable that, in actual use, the above basic parameters can be arbitrarily valued as needed.

[0049] Table 1. Basic parameters of helical gear combined transmission system

[0050]

[0051]

[0052] S2. Based on the basic parameters obtained in S1, establish a three-dimensional model of the helical gear combined transmission system, and perform transient dynamic analysis on the three-dimensional model using the finite element analysis method. Based on the transient dynamic analysis results, obtain the static transmission error and time-varying meshing stiffness of the helical gear combined transmission system.

[0053] It should be noted that, in step S2 of this invention, the specific process of performing transient dynamic analysis on the three-dimensional model using the finite element analysis method is as follows:

[0054] S21. Import the three-dimensional model of the helical gear combined transmission system into the finite element analysis software;

[0055] S22. Use finite element analysis software to group the contact surfaces of each gear to facilitate subsequent operations;

[0056] S23. After grouping, set the rotary connection pairs and tooth surface contact of each gear to the ground;

[0057] S24. Set the boundary conditions for the connection pair between the driving wheel and the driven wheel, wherein the boundary condition for the driving wheel is that the driving wheel rotates by a rotation angle, and the boundary condition for the connection pair between the driven wheel is the output torque of the driven wheel;

[0058] S25. Calculate the end time based on the input speed of the driving wheel and the output torque of the driven wheel, determine the analysis settings based on the end time, and determine the number of substeps for the determined analysis settings;

[0059] S26. Set up connection probes for the driving gear and driven gear respectively, and record the rotation angle output by the finite element analysis software to obtain the static transmission error and time-varying meshing stiffness of the gear.

[0060] It should be noted that the number of substeps mentioned above can be set as needed in actual use. In this embodiment S25, the number of substeps is set to 50.

[0061] It should be noted that in step S2, the static transmission error of the gear is defined as "the difference between the actual rotational displacement and the ideal rotational displacement of the driven gear", and the calculation formula is as follows:

[0062]

[0063] Where TE represents the transmission error, θ g θ represents the rotation angle of the driven wheel. p The z-axis represents the rotation angle of the drive wheel. p It is the number of teeth on the driving gear, z g This represents the number of teeth on the driven gear.

[0064] In this invention, for ease of understanding, the load transmission error (LTE) of the gears during meshing is converted into the displacement difference generated on the meshing line of the gear pair and used as the static transmission error of the helical gear combined transmission system:

[0065]

[0066] Where LTE represents the load-bearing transmission error; R g This indicates the base circle radius of the driven wheel.

[0067] It should be noted that in step S2, the gear does not generate elastic deformation when it is unloaded. However, considering the errors caused by gear modeling and mesh generation, this invention defines it as the no-load transmission error (NLTE). Finally, the comprehensive elastic deformation δ during gear meshing is obtained. n for:

[0068] δ n =LTE-NLTE

[0069] Therefore, in step S2, the time-varying meshing stiffness k of the gear m The following formula is used for calculation:

[0070]

[0071] Among them, F n This represents the normal meshing force of the gear pair along the line of meshing.

[0072] S3. Establish a dynamic model of the helical gear combined transmission system with 18 degrees of freedom (bending-torsion-shaft-swing) considering time-varying meshing stiffness, installation and machining errors, tooth backlash and meshing damping.

[0073] It should be noted that the dynamic model in step S3 is as follows:

[0074]

[0075]

[0076] Where, m p1 m p2 c represents the mass of the first and second driving wheels, respectively; p1x c p1y c p1z These represent the damping of the first drive wheel input shaft bearing in the x, y, and z directions, respectively; c p2x c p2y c p2z These represent the damping of the second drive wheel input shaft bearing in the x, y, and z directions, respectively; k p1x k p1y k p1z These represent the support stiffness of the first drive wheel input shaft bearing in the x, y, and z directions, respectively; k p2x k p2y k p2z These represent the support stiffness of the second drive wheel input shaft bearing in the x, y, and z directions, respectively; x p1 y p1 z p1 These represent the translational displacements of the first driving wheel in the x, y, and z directions, respectively. They represent x respectively p1 y p1 z p1 The second derivative; They represent x respectively p1 y p1 z p1 The first derivative; x p2 y p2 z p2 These represent the translational displacements of the second driving wheel in the x, y, and z directions, respectively. They represent x respectively p2 y p2 z p2 The second derivative; They represent x respectively p2 y p2 z p2 The first derivative; F x1 F y1 F z1 These represent the components of the force along the x, y, and z directions of the first gear pair, respectively; F x2 F y2 F z2 These represent the force components of the second gear pair along the x, y, and z directions, respectively; I p1 I p2 These represent the moments of inertia of the first and second driving wheels, respectively. The torsional angular displacement θ of the first driving wheel p1 The second derivative; The second driving wheel's torsional angular displacement θ p2 The second derivative of T; p1 T p2 F represents the input torque of the first and second driving wheels, respectively. n1 F n2 These represent the dynamic meshing forces of the first and second gear pairs, respectively; r p1 r p2 Φ represents the base circle radii of the first and second driving wheels, respectively; p1 Φ p2 These represent the oscillation displacements of the first and second driving wheels around the x-axis, respectively. Φ p1 φ p2 The second derivative; φ p1 φ p2 The first derivative; c p1θx c p1θy These represent the torsional oscillation damping of the first driving wheel in the x and y directions, respectively; c p2θx c p2θy These represent the torsional oscillation damping of the second driving wheel in the x and y directions, respectively; k p1θx k p1θy These represent the stiffness of the first driving wheel in the x and y directions, respectively; k p2θx k p2θy These represent the stiffness of the second driving wheel in the x and y directions, respectively; r p ′1、r p ′2 represents the pitch circle radius of the first and second driving gears, respectively; α1 represents the gear pressure angle; These represent the oscillation displacements of the first and second driving wheels around the y-axis, respectively. They represent The second derivative; They represent First derivative; m g c represents the mass of the driven wheel. gx c gy c gz These represent the damping of the driven wheel output shaft bearing in the x, y, and z directions, respectively; k gx k gy k gz These represent the support stiffness of the driven wheel output shaft bearing in the x, y, and z directions, respectively; x g y g z g These represent the translational displacements of the driven wheel in the x, y, and z directions, respectively. They represent x respectively g The second derivative and the first derivative; They represent y respectively g The second derivative and the first derivative; Indicate z g The first derivative; I g θ represents the moment of inertia of the driven wheel. g This represents the torsional angular displacement of the driven wheel; Represents θ g The second derivative of T; g This indicates the output torque of the driven wheel; r g The base circle radius of the driven gear is represented by r. g ′ represents the pitch circle radius of the driven gear; Φ g This represents the oscillation displacement of the driven wheel about the x-axis; Φ g The second derivative and the first derivative; c gθx c gθy These represent the torsional oscillation damping of the driven wheel in the x and y directions, respectively; k gθx k gθy These represent the stiffness of the driven wheel in the x and y directions, respectively. This represents the oscillation displacement of the driven wheel about the y-axis; They represent The second derivative and the first derivative.

[0077] S4. Substitute the static transmission error and time-varying meshing stiffness obtained in S2 into the dynamic model through Fourier transform, and solve the dynamic model using the fourth-order variable step size Runge-Kutta method.

[0078] It should be noted that, in step S4, the Fourier transforms of the static transmission error and the time-varying meshing stiffness are as follows:

[0079] e(t) = e0 + e m sin(ωt+ψ)

[0080]

[0081] Where e(t) represents the dynamic transmission error; e0 represents the average value of the transmission error; e m The amplitude of the transmission error fluctuation is represented by ω; the gear meshing frequency is represented by t; the time variable is represented by ψ; the initial phase is represented by k. m (t) represents the time-varying meshing stiffness after Fourier transform; k0 represents the mean of the time-varying meshing stiffness; k j ψ represents the amplitude of the j-th order cosine component of the time-varying meshing stiffness; j represents the Fourier order; ψ j Indicates phase; ε α Indicates the degree of overlap of the end faces; m n Represents the normal modulus.

[0082] S5. Obtain the dynamic coupling transmission error of the helical gear transmission system based on the dynamic solution results.

[0083] It should be noted that obtaining the dynamic coupling transmission error of the helical gear transmission system based on the dynamic solution results in step S5 is prior art for those skilled in the art, and will not be elaborated further. Furthermore, the method for solving the dynamic coupling transmission error in step S5 is the same as the method for calculating the static transmission error of the gear given in step S2, except that the method for obtaining the rotation angle variable is different. Step S2 is obtained through static transient dynamic analysis using the finite element analysis method, while step S5 is obtained by solving the dynamic model under load.

[0084] Furthermore, in step S5, the nonlinear modeling of the tooth flank clearance is as follows:

[0085]

[0086] Where, δ n denoted as , representing the relative displacement on the meshing surface of the gear pair, i.e., the comprehensive elastic deformation during gear meshing; b represents the tooth flank clearance.

[0087] Furthermore, in step S5, the formula for calculating the gear pair meshing damping is as follows:

[0088]

[0089] Where, ζ m Indicates the meshing damping ratio of the gear pair; r pi I represents the base circle radius of the i-th driving wheel; pi Let represent the moment of inertia of the i-th driving wheel.

[0090] To better demonstrate the specific implementation and technical effects of the present invention, the method for solving the dynamic coupling transmission error of a helical gear combined transmission system shown in steps S1 to S5 of the above preferred implementation is applied to a specific example.

[0091] Example

[0092] The specific implementation process of the dynamic coupling transmission error solution method for the helical gear combined transmission system used in this embodiment is as described above and will not be repeated here.

[0093] like Figure 2 As shown, Figure 2 As a research example of the present invention, a three-dimensional model of a marine GVW type gear is presented. The left and right sides represent the driving gears for motor input, and the middle represents the driven gear for output. At a given speed, the gear transmission process involves two pairs of gears. Gear pair I consists of the left driving gear and the driven gear, while gear pair II consists of the right driving gear and the driven gear.

[0094] like Figure 3 As shown, the static transmission error of gear pair I and gear pair II in the helical gear combined transmission system is shown. It can be seen that there is a certain phase difference between the two gear pairs, but the fluctuation amplitude and curve trend are basically similar.

[0095] like Figure 4 As shown, the input speed n1=n2=500r / min and the input torque T are given. p1 =T p2 The time-domain curve of the dynamic coupling transmission error of the helical gear combined transmission system is given when the torque is 2000 N*m. Analysis shows that gear pair I and gear pair II in the helical gear combined transmission system have a certain phase difference due to the interaction of meshing forces.

[0096] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A method for solving the dynamic coupling transmission error of a helical gear combined transmission system, characterized in that, Includes the following steps: S1. Obtain the basic parameters of the helical gear combined transmission system; S2. Based on the basic parameters obtained in S1, establish a three-dimensional model of the helical gear combined transmission system, and perform transient dynamic analysis on the three-dimensional model using the finite element analysis method. Based on the transient dynamic analysis results, obtain the static transmission error and time-varying meshing stiffness of the helical gear combined transmission system. S3. Establish a dynamic model of the helical gear combined transmission system with 18 degrees of freedom, considering time-varying meshing stiffness, installation and machining errors, tooth backlash and meshing damping, including bending, torsion, shaft and pendulum motion. S4. Substitute the static transmission error and time-varying meshing stiffness obtained in S2 into the dynamic model through Fourier transform, and solve the dynamic model using the fourth-order variable step size Runge-Kutta method. S5. Obtain the dynamic coupling transmission error of the helical gear transmission system based on the dynamic solution results; In step S2, the specific process of performing transient dynamic analysis on the three-dimensional model using the finite element analysis method is as follows: S21. Import the three-dimensional model of the helical gear combined transmission system into the finite element analysis software; S22. Use finite element analysis software to group the contact surfaces of each gear to facilitate subsequent operations; S23. After grouping, set the rotary connection pairs and tooth surface contact of each gear to the ground; S24. Set the boundary conditions for the connection pair between the driving wheel and the driven wheel, wherein the boundary condition for the driving wheel is that the driving wheel rotates by a rotation angle, and the boundary condition for the connection pair between the driven wheel is the output torque of the driven wheel; S25. Calculate the end time based on the input speed of the driving wheel and the output torque of the driven wheel, determine the analysis settings based on the end time, and determine the number of substeps for the determined analysis settings; S26. Set up connection probes for the driving gear and driven gear respectively, and record the rotation angle output by the finite element analysis software to obtain the static transmission error and time-varying meshing stiffness of the gear; In step S3, the dynamic model is as follows: ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； in, , These represent the masses of the first and second driving wheels, respectively. These respectively indicate the bearings of the first drive wheel input shaft at... Damping in direction; These respectively indicate the bearings of the second drive wheel input shaft at... Damping in direction; These respectively indicate the bearings of the first drive wheel input shaft at... Directional support stiffness; These respectively indicate the bearings of the second drive wheel input shaft at... Directional support stiffness; These respectively represent the first driving wheel in Translational displacement in the direction; These respectively indicate that the second driving wheel is in Translational displacement in the direction; These respectively represent the first gear pair along... Component of force in direction; These respectively indicate the second gear pair along Component of force in direction; These represent the moments of inertia of the first and second driving wheels, respectively. Indicates the torsional angular displacement of the first driving wheel The second derivative; Indicates the torsional angular displacement of the second driving wheel The second derivative; These represent the input torques of the first and second driving wheels, respectively. These represent the dynamic meshing forces of the first and second gear pairs, respectively. These represent the base circle radii of the first and second driving wheels, respectively. These represent the first and second driving wheels orbiting each other. The oscillation displacement of the shaft; These respectively represent the first driving wheel in Damping of torsional vibration in the direction; These respectively indicate that the second driving wheel is in Damping of torsional vibration in the direction; These respectively represent the first driving wheel in Stiffness in the directional direction; These respectively indicate that the second driving wheel is in Stiffness in the directional direction; These represent the pitch circle radii of the first and second driving wheels, respectively. Indicates the gear pressure angle; These represent the first and second driving wheels orbiting each other. The oscillation displacement of the shaft; They represent The second derivative; They represent The first derivative; Indicates the mass of the driven wheel; These respectively indicate the driven wheel output shaft bearing at... Damping in direction; These respectively indicate the driven wheel output shaft bearing at... Directional support stiffness; These respectively represent the driven wheel in Translational displacement in the direction; This represents the moment of inertia of the driven wheel; This represents the torsional angular displacement of the driven wheel; This indicates the output torque of the driven wheel; Indicates the base circle radius of the driven gear; Indicates the pitch circle radius of the driven gear; Indicates the rotation of the driven wheel The oscillation displacement of the shaft; These respectively represent the driven wheel in Damping of torsional vibration in the direction; These respectively represent the driven wheel in Stiffness in the directional direction; Indicates the driven wheel revolves around The oscillation displacement of the shaft.

2. The method for solving the dynamic coupling transmission error of a helical gear combined transmission system as described in claim 1, characterized in that, In step S1, the basic parameters are the number of teeth of the first driving gear, the number of teeth of the second driving gear, the number of teeth of the driven gear, the normal module, the pressure angle of the pitch circle, the helix angle, the tooth width, the center distance, the tooth addendum coefficient, the clearance coefficient, and the rotational speed.

3. The method for solving the dynamic coupling transmission error of a helical gear combined transmission system as described in claim 1, characterized in that, In step S2, the load transmission error of the gears during meshing is converted into the displacement difference generated on the meshing line of the gear pair and used as the static transmission error of the helical gear combined transmission system: ； in, Indicates the transmission error under load; Indicates the base circle radius of the driven wheel; Indicates the angle of rotation of the driven wheel; Indicates the rotation angle of the drive wheel; It is the number of teeth on the driving gear; This represents the number of teeth on the driven gear.

4. The method for solving the dynamic coupling transmission error of a helical gear combined transmission system as described in claim 1, characterized in that, In step S2, the time-varying meshing stiffness of the gear The following formula is used for calculation: ； in, This represents the normal meshing force of the gear pair along the line of meshing. It represents the total elastic deformation during gear meshing.

5. The method for solving the dynamic coupling transmission error of a helical gear combined transmission system as described in claim 1, characterized in that, In step S4, the Fourier transforms of static transmission error and time-varying meshing stiffness are as follows: ； ； ； ； in, Indicates dynamic transmission error; This represents the average value of the transmission error; Indicates the fluctuation amplitude of transmission error; This refers to the gear meshing frequency; Represents a time variable; This is the initial phase; This represents the time-varying meshing stiffness after Fourier transform; This represents the mean value of the time-varying meshing stiffness; Indicates the time-varying meshing stiffness. The amplitude of the cosine component; Indicates the Fourier order; Indicates phase; Indicates the degree of overlap of the end faces; Represents the normal modulus.

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