Dynamic coupling transmission error solving method for helical gear combined transmission system

Abstract

The invention discloses a dynamic coupling transmission error solving method for a helical gear combined transmission system. The method comprises the following steps: firstly, acquiring basic parameters of the helical gear combined transmission system and establishing a three-dimensional model of the helical gear combined transmission system; secondly, static transmission errors and time-varying meshing stiffness in the gear meshing process are calculated based on finite element analysis; secondly, establishing a bending-twisting-shaft-swinging 18-degree-of-freedom kinetic model of the helical gear combined transmission system considering time-varying meshing rigidity, installation errors, machining errors, gear backlash and meshing damping; inputting gear parameters and working conditions, including parameters such as input torque, output torque and input rotating speed, and acquiring dynamic response of the helical gear combined transmission system by adopting a four-order variable-step Runge-Kutta method; and finally, obtaining a dynamic coupling transmission error of the helical gear transmission system according to a dynamic solving result.

Description

Technical Field

[0001] The invention belongs to the technical field of dynamic response analysis of a helical gear combined transmission system, and in particular relates to a method for solving a dynamic coupling transmission error of a helical gear combined transmission system. Background Art

[0002] As a common mechanical power transmission device, the helical gear combined transmission system is widely used in modern large-scale mechanical equipment such as the shipbuilding industry, wind turbines, and engineering machinery due to its 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 been adjusted from "far sea escort" to "far sea defense", which means that higher requirements are placed on ships. The helical gear combined transmission system merges multiple input powers through parallel confluence, and then transmits them to the propeller to achieve parallel operation, which solves the problem of insufficient power of a single power in the past. For ships, their concealment is a crucial factor affecting the safety of ships. The smaller the noise generated by the ship, the less likely the ship is to be discovered by the enemy. Ship noise mainly comes from three parts: machinery, hydrodynamics and propellers. Among them, mechanical noise is the main source of noise for ships, and mechanical noise is mainly generated by the gear transmission system of the ship. Therefore, as the transmission system of the ship, the performance of the helical gear combined transmission system greatly affects the operating performance of the entire ship. Considering the concealment of the ship and the physical and mental health of the personnel on board, the vibration and noise of the transmission system are also key factors that should be considered in the design. Therefore, conducting vibration and noise analysis research on the helical gear combined transmission system is a key problem to improve the operating efficiency of ships.

[0004] As we all know, gear transmission is the transmission of power between the driving wheel and the driven wheel by the meshing force generated by the gear pair along the meshing direction. According to its concept, the transmission error is "the offset displacement between the actual meshing position of the meshing gear pair and the theoretical meshing position". It can be seen that the transmission error is the dynamic excitation generated in the direction of the meshing line, and it is also one of the important sources of vibration and noise. At present, the dynamic error analysis of the helical gear combined transmission system is mostly analyzed with the help of simulation software, and the calculation process is cumbersome. And it fails to fully consider the coupling response of multiple pairs of gear pairs under multiple input conditions. Therefore, designing an efficient dynamic transmission error analysis method that fully considers the coupling of gear pairs under multiple input conditions is of great significance for the vibration and noise analysis of gears. Summary of the invention

[0005] The purpose of the present 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] In order to achieve the above-mentioned invention object, the present invention specifically adopts the following technical solutions:

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

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

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

[0010] S3. Establish a dynamic model of the bending-torsion-axis-swing 18-degree-of-freedom of the helical gear combined transmission system considering time-varying meshing stiffness, installation error and processing error, tooth side clearance and meshing damping;

[0011] S4. The static transmission error and time-varying meshing stiffness obtained in S2 are introduced into the dynamic model through Fourier transformation, and the dynamic model is solved by 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 specific manner.

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

[0015] Preferably, in step S2, the specific process of performing transient dynamic analysis on the three-dimensional model by 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 pair and tooth surface contact of each gear connected to the earth;

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

[0020] S25. Calculate the end time according to the input speed of the driving wheel and the output torque of the driven wheel, determine the analysis settings according to the end time, and determine the number of sub-steps for the determined analysis settings;

[0021] S26. Set the connecting sub-probes of the driving wheel and the driven wheel 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 transmission error of the gear during the meshing process is converted into a 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 transmission error; R g Indicates the base circle radius of the driven wheel; θ g Indicates the rotation angle of the driven wheel; θ p Indicates the rotation angle of the driving wheel; z p is the number of teeth on the driving gear; z g is the number of driven gear teeth.

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

[0026]

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

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

[0029]

[0030]

[0031] Among them, m p1 、m p2 Represent the masses of the first driving wheel and the second driving wheel respectively; c p1x 、c p1y 、c p1z They represent the damping of the first driving wheel input shaft bearing in the x, y, and z directions respectively; c p2x 、c p2y 、c p2z They represent the damping of the second driving wheel input shaft bearing in the x, y, and z directions respectively; k p1x , k p1y, k p1z They represent the support stiffness of the first driving wheel input shaft bearing in the x, y, and z directions respectively; k p2x , k p2y , k p2z They represent the support stiffness of the second driving wheel input shaft bearing in the x, y, and z directions respectively; p1 ,y p1 、z p1 Respectively represent the translational displacement of the first driving wheel in the x, y, and z directions; p2 ,y p2 、z p2 Respectively represent the translational displacement of the second driving wheel in the x, y, and z directions; F x1 、F y1 、F z1 Respectively represent the component forces of the first gear pair along the x, y, and z directions; F x2 、F y2 、F z2 Respectively represent the component forces of the second gear pair along the x, y, and z directions; I p1 ,I p2 denote the moment of inertia of the first driving wheel and the second driving wheel respectively; Represents the torsional angular displacement of the first driving wheel θ p1 The second derivative of The second driving wheel torsional displacement θ p2 The second derivative of T p1 , T p2 Represent the input torque of the first driving wheel and the second driving wheel respectively; F n1 、F n2 Respectively represent the dynamic meshing force of the first gear pair and the second gear pair; r p1 、r p2 Respectively represent the base circle radius of the first driving wheel and the second driving wheel; Φ p1 , Φ p2 They represent the swing displacement of the first driving wheel and the second driving wheel around the x-axis respectively; c p1θx 、c p1θy They represent the torsional vibration damping of the first driving wheel in the x and y directions respectively; c p2θx 、c p2θy Respectively represent the torsional vibration damping of the second driving wheel in the x and y directions; k p1θx , k p1θy Respectively represent the stiffness of the first driving wheel in the x and y directions; k p2θx , k p2θy Respectively represent the stiffness of the second driving wheel in the x and y directions; r p ′1, r p ′2 represents the pitch radius of the first driving wheel and the second driving wheel respectively; α1 represents the gear pressure angle; They represent the swing displacement of the first driving wheel and the second driving wheel around the y-axis respectively; Respectively The second derivative of Respectively The first derivative of g Indicates the mass of the driven wheel; c gx 、c gy 、c gz They represent the damping of the output shaft bearing of the driven wheel in the x, y, and z directions respectively; k gx , k gy , k gz Respectively represent the support stiffness of the output shaft bearing of the driven wheel in the x, y, and z directions; g ,y g 、z g Respectively represent the translational displacement of the driven wheel in the x, y, and z directions; I g Represents the moment of inertia of the driven wheel; θ g Represents the torsional angular displacement of the driven wheel; T g Represents the output torque of the driven wheel; r g Indicates the base circle radius of the driven wheel; r g ' represents the pitch radius of the driven wheel; Φ g represents the swing displacement of the driven wheel around the x-axis; c gθx 、c gθy They represent the torsional vibration damping of the driven wheel in the x and y directions respectively; k gθx , k gθy Respectively represent the stiffness of the driven wheel in the x and y directions; Represents the swing displacement of the driven wheel around the y-axis.

[0032] Preferably, in step S4, the Fourier transform of the static transmission error and the time-varying meshing stiffness is 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 represents the fluctuation amplitude of the transmission error; ω is the gear meshing frequency; t represents the time variable; ψ is the initial phase; k m (t) represents the time-varying meshing stiffness after Fourier transformation; k0 represents the mean value of the time-varying meshing stiffness; k j represents the amplitude of the jth order cosine component of the time-varying meshing stiffness; j represents the Fourier order; ψ j Indicates phase; ε αIndicates the end face overlap; m n Represents the normal modulus.

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

[0037] The method of the present invention can quickly obtain the dynamic transmission error of the helical gear combined transmission system without a large amount of finite element simulation calculations, and takes into account the coupling effect of the parallel working condition, which has a certain supporting significance for the vibration and noise analysis of the gear. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Schematic diagram of the execution flow of the method of the present invention;

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

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

[0041] Figure 4 It 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 an embodiment of the present invention. DETAILED DESCRIPTION

[0042] In order to make the above-mentioned purpose, features and advantages of the present invention more obvious and easy to understand, the specific implementation mode of the present invention is described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. The technical features in each embodiment of the present invention can be combined accordingly without conflicting with each other.

[0043] In the description of the present invention, it should be understood that the terms "first" and "second" are only used for the purpose of distinguishing descriptions, and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features.

[0044] like Figure 1 As shown, in a preferred implementation of the present invention, the above-mentioned 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 is described in detail below.

[0045] like Figure 1As shown, this embodiment takes the helical gear combined transmission system as the research object, and designs a method for solving the dynamic coupled transmission error of the helical gear combined transmission system under the condition of two power inputs in order to calculate the coupled dynamic transmission error of the helical gear combined transmission system. The method comprises the following steps:

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

[0047] It should be noted that, in the present invention, the above basic parameters are the number of teeth of the first driving wheel, the number of teeth of the second driving wheel, the number of teeth of the driven wheel, the normal module, the pitch circle pressure angle, the helix angle, the tooth width, the center distance, the tooth top height coefficient, the top 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 the basic parameters are only a set of example values ​​given as an embodiment, and are not limitations of the present invention. It is conceivable that the above basic parameters can be arbitrarily set as needed in actual use.

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

[0050]

[0051]

[0052] S2. A three-dimensional model of the helical gear combined transmission system is established according to the basic parameters obtained in S1, and a transient dynamic analysis is performed on the three-dimensional model by the finite element analysis method. Based on the transient dynamic analysis results, the static transmission error and time-varying meshing stiffness of the helical gear combined transmission system are obtained.

[0053] It should be noted that, in step S2 of the present invention, the specific process of performing transient dynamic analysis on the three-dimensional model by 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 pair and tooth surface contact of each gear connected to the earth;

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

[0058] S25. Calculate the end time according to the input speed of the driving wheel and the output torque of the driven wheel, determine the analysis settings according to the end time, and determine the number of sub-steps for the determined analysis settings;

[0059] S26. Set the connecting sub-probes of the driving wheel and the driven wheel 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 sub-steps can be set as needed in actual use. In this embodiment S25, the value of the number of sub-steps 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 rotation displacement of the driven wheel and the ideal rotation displacement", and the calculation formula is as follows:

[0062]

[0063] Where TE represents the transmission error, θ g Indicates the rotation angle of the driven wheel, θ p Indicates the rotation angle of the driving wheel, z p is the number of teeth on the driving gear, z g is the number of driven gear teeth.

[0064] In the present invention, for ease of understanding, the load transmission error (LTE) of the gear during the meshing process 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 transmission error; R g Indicates the base circle radius of the driven wheel.

[0067] It should be noted that in step S2, when the gear is not loaded, no elastic deformation will occur. However, considering the errors caused by gear modeling and meshing, the present invention defines it as the transmission error (No-load transmission error, NLTE) of the gear under no load. Finally, the comprehensive elastic deformation δ during the gear meshing process is obtained. n for:

[0068] δ n =LTE-NLTE

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

[0070]

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

[0072] S3. Establish a dynamic model of the bending-torsion-axis-swing 18-degree-of-freedom of the helical gear combined transmission system considering time-varying meshing stiffness, installation error and processing error, tooth side clearance and meshing damping.

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

[0074]

[0075]

[0076] Among them, m p1 、m p2 Represent the masses of the first driving wheel and the second driving wheel respectively; c p1x 、c p1y 、c p1z They represent the damping of the first driving wheel input shaft bearing in the x, y, and z directions respectively; c p2x 、c p2y 、c p2z They represent the damping of the second driving wheel input shaft bearing in the x, y, and z directions respectively; k p1x , k p1y , k p1z They represent the support stiffness of the first driving wheel input shaft bearing in the x, y, and z directions respectively; k p2x , k p2y , k p2z They represent the support stiffness of the second driving wheel input shaft bearing in the x, y, and z directions respectively; p1 ,y p1 、z p1 Respectively represent the translational displacement of the first driving wheel in the x, y, and z directions; Respectively represent x p1 ,y p1 、z p1 The second derivative of Respectively represent x p1 ,y p1 、z p1 The first derivative of x p2 ,y p2 、z p2 Respectively represent the translational displacement of the second driving wheel in the x, y, and z directions; Respectively represent x p2 ,y p2 、z p2 The second derivative of Respectively represent x p2 ,y p2 、z p2 The first derivative of x1 、F y1 、F z1 Respectively represent the component forces of the first gear pair along the x, y, and z directions; F x2 、F y2 、F z2 Respectively represent the component forces of the second gear pair along the x, y, and z directions; I p1 ,I p2 denote the moment of inertia of the first driving wheel and the second driving wheel respectively; Represents the torsional angular displacement of the first driving wheel θ p1 The second derivative of The second driving wheel torsional displacement θ p2 The second derivative of T p1 、T p2 Represent the input torque of the first driving wheel and the second driving wheel respectively; F n1 、F n2 Respectively represent the dynamic meshing force of the first gear pair and the second gear pair; r p1 、r p2 Respectively represent the base circle radius of the first driving wheel and the second driving wheel; Φ p1 , Φ p2 They represent the swing displacement of the first driving wheel and the second driving wheel around the x-axis respectively; Respectively represent Φ p1 ,φ p2 The second derivative of Respectively represent φ p1 ,φ p2 The first derivative of p1θx 、c p1θy They represent the torsional vibration damping of the first driving wheel in the x and y directions respectively; c p2θx 、c p2θy Respectively represent the torsional vibration damping of the second driving wheel in the x and y directions; k p1θx , k p1θy Respectively represent the stiffness of the first driving wheel in the x and y directions; k p2θx , k p2θy Respectively represent the stiffness of the second driving wheel in the x and y directions; r p ′1, r p ′2 represents the pitch radius of the first driving wheel and the second driving wheel respectively; α1 represents the gear pressure angle; They represent the swing displacement of the first driving wheel and the second driving wheel around the y-axis respectively; Respectively The second derivative of Respectively The first derivative of g Indicates the mass of the driven wheel; c gx 、c gy 、c gz They represent the damping of the output shaft bearing of the driven wheel in the x, y, and z directions respectively; k gx , k gy , k gz Respectively represent the support stiffness of the output shaft bearing of the driven wheel in the x, y, and z directions; g ,y g 、z g Respectively represent the translational displacement of the driven wheel in the x, y, and z directions; Respectively represent x g The second and first derivatives of ; Respectively represent y g The second and first derivatives of ; Indicates z g The first derivative of g Represents the moment of inertia of the driven wheel; θ g Indicates the torsional angular displacement of the driven wheel; Represents θ g The second derivative of T g Represents the output torque of the driven wheel; r g Indicates the base circle radius of the driven wheel; r g ' represents the pitch radius of the driven wheel; Φ g represents the swing displacement of the driven wheel around the x-axis; Respectively represent Φ g The second and first derivatives of gθx 、c gθy They represent the torsional vibration damping of the driven wheel in the x and y directions respectively; k gθx , k gθy Respectively represent the stiffness of the driven wheel in the x and y directions; represents the swing displacement of the driven wheel around the y-axis; Respectively The second and first derivatives of .

[0077] S4. The static transmission error and time-varying meshing stiffness obtained in S2 are introduced into the dynamic model through Fourier transformation, and the dynamic model is solved by the fourth-order variable step-size Runge-Kutta method.

[0078] It should be noted that in step S4, the Fourier transform of the static transmission error and the time-varying meshing stiffness is specifically 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 represents the fluctuation amplitude of the transmission error; ω is the gear meshing frequency; t represents the time variable; ψ is the initial phase; k m (t) represents the time-varying meshing stiffness after Fourier transformation; k0 represents the mean value of the time-varying meshing stiffness; k j represents the amplitude of the jth order cosine component of the time-varying meshing stiffness; j represents the Fourier order; ψ j Indicates phase; ε α Indicates the end face overlap; 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, in step S5, obtaining the dynamic coupling transmission error of the helical gear transmission system according to the dynamic solution result is a prior art for those skilled in the art, and no further description is given. In addition, the method of solving the dynamic coupling transmission error in step S5 is the same as the method of solving the static transmission error of the gear given in step S2, except that the method of obtaining the rotation angle variable is different. Step S2 is obtained by applying the finite element analysis method to perform static transient dynamic analysis, and step S5 is obtained by solving the dynamic model under load.

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

[0085]

[0086] Among them, δ n is the relative displacement on the meshing surface of the gear pair, that is, the comprehensive elastic deformation during the gear meshing process; b represents the tooth side half clearance.

[0087] Furthermore, in step S5, the gear pair meshing damping calculation formula is:

[0088]

[0089] Among them, m Represents the meshing damping ratio of the gear pair; r pi I represents the base circle radius of the i-th driving wheel; pi represents the moment of inertia of the i-th driving wheel.

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

[0091] Example

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

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

[0094] like Figure 3 As shown, it is the static transmission error of gear pair I and gear pair II in the helical gear combined transmission system. It can be seen that there is a certain phase difference between the two pairs of 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 p1 =T p2 =2000N*m, the time domain curve of the dynamic coupling transmission error of the helical gear combined transmission system. According to the analysis, there is a certain phase difference between the gear pair I and the gear pair II of the helical gear combined transmission system due to the interaction of the meshing force.

[0096] The above-described embodiment is only a preferred solution of the present invention, but it is not intended to limit the present invention. A person skilled in the relevant technical field may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent replacement or equivalent transformation falls 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: The following steps are involved: S1. Obtain the basic parameters of the helical gear combined transmission system; S2. Establish a three-dimensional model of the helical gear combined transmission system according to the basic parameters obtained in S1, and perform transient dynamic analysis on the three-dimensional model by finite element analysis method, and obtain the static transmission error and time-varying meshing stiffness of the helical gear combined transmission system based on the transient dynamic analysis results; S3. Establish a dynamic model of the bending-torsion-axis-swing 18-degree-of-freedom of the helical gear combined transmission system considering time-varying meshing stiffness, installation error and processing error, tooth side clearance and meshing damping; S4. The static transmission error and time-varying meshing stiffness obtained in S2 are introduced into the dynamic model through Fourier transformation, and the dynamic model is solved by 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.

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

3. A method for solving the dynamic coupling transmission error of a helical gear combined transmission system as claimed in claim 1, characterized in that: In step S2, the specific process of performing transient dynamic analysis on the three-dimensional model by 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 pair and tooth surface contact of each gear connected to the earth; S24. Setting boundary conditions of the driving wheel and the driven wheel connection pair, wherein the boundary condition of the driving wheel is that the driving wheel rotates at a rotation angle, and the boundary condition of the driven wheel connection pair is the output torque of the driven wheel; S25. Calculate the end time according to the input speed of the driving wheel and the output torque of the driven wheel, determine the analysis settings according to the end time, and determine the number of sub-steps for the determined analysis settings; S26. Set the connecting sub-probes of the driving wheel and the driven wheel 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.

4. A method for solving the dynamic coupling transmission error of a helical gear combined transmission system as claimed in claim 1, characterized in that: In step S2, the transmission error of the gear during the meshing process 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: Where, LTE represents the load transmission error; R g Indicates the base circle radius of the driven wheel; θ g Indicates the rotation angle of the driven wheel; θ p Indicates the rotation angle of the driving wheel; z p is the number of teeth on the driving gear; z g is the number of driven gear teeth.

5. The method for solving the dynamic coupling transmission error of a helical gear combined transmission system according to claim 1, characterized in that: In step S2, the time-varying mesh stiffness k of the gear is m The calculation is done using the following formula: Among them, F n Indicates the normal meshing force of the gear pair along the meshing line; δ n It represents the comprehensive elastic deformation during gear meshing.

6. A method for solving the dynamic coupling transmission error of a helical gear combined transmission system as claimed in claim 1, characterized in that: In step S3, the kinetic model is as follows: Among them, m p1 、m p2 Represent the masses of the first driving wheel and the second driving wheel respectively; c p1x 、c p1y 、c p1z They represent the damping of the first driving wheel input shaft bearing in the x, y, and z directions respectively; c p2x 、c p2y 、c p2z They represent the damping of the second driving wheel input shaft bearing in the x, y, and z directions respectively; k p1x , k p1y , k p1z They represent the support stiffness of the first driving wheel input shaft bearing in the x, y, and z directions respectively; k p2x , k p2y , k p2z They represent the support stiffness of the second driving wheel input shaft bearing in the x, y, and z directions respectively; p1 ,y p1 、z p1 Respectively represent the translational displacement of the first driving wheel in the x, y, and z directions; p2 ,y p2 、z p2 Respectively represent the translational displacement of the second driving wheel in the x, y, and z directions; F x1 、F y1 、F z1 Respectively represent the component forces of the first gear pair along the x, y, and z directions; F x2 、F y2 、F z2 Respectively represent the component forces of the second gear pair along the x, y, and z directions; I p1 ,I p2 denote the moment of inertia of the first driving wheel and the second driving wheel respectively; Represents the torsional angular displacement of the first driving wheel θ p1 The second derivative of The second driving wheel torsional displacement θ p2 The second derivative of T p1 , T p2 Represent the input torque of the first driving wheel and the second driving wheel respectively; F n1 、F n2 Respectively represent the dynamic meshing force of the first gear pair and the second gear pair; r p1 、r p2 Respectively represent the base circle radius of the first driving wheel and the second driving wheel; Φ p1 , Φ p2 They represent the swing displacement of the first driving wheel and the second driving wheel around the x-axis respectively; c p1θx 、c p1θy They represent the torsional vibration damping of the first driving wheel in the x and y directions respectively; c p2θx 、c p2θy Respectively represent the torsional vibration damping of the second driving wheel in the x and y directions; k p1θx , k p1θy Respectively represent the stiffness of the first driving wheel in the x and y directions; k p2θx , k p2θy Respectively represent the stiffness of the second driving wheel in the x and y directions; r′ p1 , r′ p2 They represent the pitch circle radius of the first driving wheel and the second driving wheel respectively; α1 represents the gear pressure angle; They represent the swing displacement of the first driving wheel and the second driving wheel around the y-axis respectively; Respectively The second derivative of Respectively The first derivative of g Indicates the mass of the driven wheel; c gx 、c gy 、c gz They represent the damping of the output shaft bearing of the driven wheel in the x, y, and z directions respectively; k gx , k gy , k gz Respectively represent the support stiffness of the output shaft bearing of the driven wheel in the x, y, and z directions; g ,y g 、z g Respectively represent the translational displacement of the driven wheel in the x, y, and z directions; I g Represents the moment of inertia of the driven wheel; θ g Represents the torsional angular displacement of the driven wheel; T g Represents the output torque of the driven wheel; r g Indicates the base circle radius of the driven wheel; r' g Indicates the pitch radius of the driven wheel; Φ g represents the swing displacement of the driven wheel around the x-axis; c gθx 、c gθy They represent the torsional vibration damping of the driven wheel in the x and y directions respectively; k gθx , k gθy Respectively represent the stiffness of the driven wheel in the x and y directions; Represents the swing displacement of the driven wheel around the y-axis.

7. A method for solving dynamic coupling transmission error of a helical gear combined transmission system as claimed in claim 1, characterized in that: In step S4, the Fourier transform of the static transmission error and the time-varying meshing stiffness is as follows: e(t)=e0+e m sin(ωt+ψ) Where, e(t) represents the dynamic transmission error; e0 represents the average value of the transmission error; e m represents the fluctuation amplitude of the transmission error; ω is the gear meshing frequency; t represents the time variable; ψ is the initial phase; k m (t) represents the time-varying meshing stiffness after Fourier transformation; k0 represents the mean value of the time-varying meshing stiffness; k j represents the amplitude of the jth order cosine component of the time-varying meshing stiffness; j represents the Fourier order; ψ j Indicates phase; ε α Indicates the end face overlap; m n Represents the normal modulus.

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