Rigid-flexible coupling simulation method for dynamic transmission error analysis of worm gear

Abstract

The application discloses a kind of rigid-flexible combined simulation worm gear dynamic transmission error analysis method, relative to prior art, by rigid-flexible combined simulation technical scheme, realize the high-precision analysis of worm gear transmission system dynamic transmission error;The method of the application can analyze the contribution of geometric error (including manufacturing error, assembly error and modification error) to transmission error alone, providing a theoretical basis for the geometric design optimization of the transmission system;By difference calculation method, dynamic comprehensive meshing error and dynamic transmission error are obtained respectively, and further elastic dynamic transmission error is obtained, the contribution of elastic deformation is separated from the total transmission error, although the nonlinear coupling effect of geometric error and elastic deformation error cannot be completely eliminated, but the contribution of elastic deformation to transmission accuracy can be approximately quantitatively evaluated.

Description

Technical Field

[0001] This invention belongs to the field of dynamic characteristic analysis technology of worm gear transmission systems, specifically a method for dynamic transmission error analysis of worm gears using rigid-flexible body co-simulation. Background Technology

[0002] Worm gear transmission systems, as important high-precision mechanical transmission devices, are widely used in modern industrial fields such as machinery manufacturing, automotive industry, and aerospace due to their large transmission ratio, compact structure, smooth operation, and high transmission accuracy. With the increasing demands for transmission accuracy and reliability in modern industry, especially in the manufacturing of high-end equipment such as precision machinery, CNC machine tools, and robots, dynamic transmission error analysis of worm gear transmission systems has become a key technical issue affecting the overall performance of these machines.

[0003] Transmission error refers to the deviation between the output shaft rotation angle and the theoretical rotation angle during actual transmission. It is an important indicator for evaluating transmission accuracy and vibration and noise characteristics. Traditional transmission error analysis methods typically consider the combined effects of manufacturing errors, assembly errors, profile errors, and material elastic deformation. Since the errors caused by gear tooth surface geometric deviations and material elastic deformation are both nonlinear and coupled, accurately analyzing the contribution of each error source in practical engineering applications still faces certain technical challenges.

[0004] In the development of error analysis techniques for worm gear drives, researchers have primarily focused on accurately assessing the combined impact of multiple error sources. However, in practical engineering, there is an urgent need to establish a dynamic solution method that combines rigid and flexible bodies to effectively separate and analyze geometric and elastic deformation errors. While traditional analysis methods can obtain the total transmission error, further exploration is needed in the separation of dynamic errors, particularly how to isolate the individual contributions of pure geometric and elastic deformation errors from the total transmission error.

[0005] Modern high-precision transmission equipment places higher demands on the dynamic characteristics of transmission systems under different operating conditions. Modeling the nonlinear characteristics of geometric error sources such as manufacturing errors, assembly errors, and shaping errors, as well as understanding the influence of these errors on dynamic transmission processes, requires more precise analytical methods. Simultaneously, with the widespread application of new materials in transmission systems, the influence mechanisms of different flexible materials on transmission errors and their quantitative comparative analysis methods urgently need development. Furthermore, the applicability analysis of transmission systems under various operating conditions, including constant torque, variable torque, impact loads, and alternating loads, is of great significance for guiding engineering design. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a method for analyzing the dynamic transmission error of worm gears using rigid-flexible body co-simulation, which can analyze the influence of geometric errors on the dynamic transmission error of worm gears independently, and quantitatively evaluate the contribution of elastic deformation to the dynamic transmission error of worm gears, so as to meet the technical requirements of modern high-precision transmission equipment for continuously improving transmission accuracy.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for dynamic transmission error analysis of worm gears using rigid-flexible body co-simulation includes the following steps: Step 1: Create a 3D model of the worm gear. Design the basic parameters of the worm gear based on the actual working conditions, and establish a three-dimensional model of the worm gear. Step 2: Establish a simulation model In the rigid body dynamics simulation environment of the finite element software, the worm and worm wheel are set as rigid body material properties to establish a rigid body dynamics simulation model; In the transient dynamics simulation environment of the finite element software, the worm and worm wheel are set as flexible material properties to establish a flexible dynamics simulation model; Step 3: Model Simulation Solution Under the same time step, load conditions, boundary conditions, and contact parameters, the rigid body dynamics simulation model and the flexible body dynamics simulation model are simulated and solved respectively, including: When performing simulation solutions on the rigid body dynamics simulation model, considering manufacturing, assembly, and shaping errors but not elastic deformation, the worm gear input angle is extracted. and worm gear output angle ; When simulating the flexible body dynamics model, the worm gear input angle is extracted while simultaneously considering elastic deformation, manufacturing, assembly, shaping errors, and dynamic vibration. and worm gear output angle ; Step 4: Error Calculation Calculate the dynamic comprehensive meshing error of the worm gear deviating from the ideal transmission angle. Dynamic transmission error due to the worm gear deviating from the ideal transmission angle :

[0008]

[0009] in: This refers to the worm gear transmission ratio; Step 5: Separation of Elastic Dynamic Transmission Errors Dynamic transmission error Subtract dynamic integrated meshing error The elastic dynamic transmission error considering the influence of elastic deformation is obtained by separation. :

[0010] Step Six: Error Conversion The elastic dynamic transmission error in the form of angular displacement is converted into a linear displacement error in the direction of the tooth surface normal to the meshing line. :

[0011] in: The radius of the worm gear base circle; The base circle helix angle.

[0012] Furthermore, the basic parameters include the number of worm threads, the number of worm wheel teeth, the module, the pressure angle, the helix angle, the tooth width, the center distance, the rotational speed, and the load torque.

[0013] Furthermore, the manufacturing errors include worm gear tooth profile error, worm lead error, and center distance deviation; the assembly errors include installation center distance offset, shaft tilt error, and clearance deviation; and the profile modification errors include nonlinear mismatch in tooth profile modification and discontinuity in tooth surface transition section.

[0014] Furthermore, in step three, the preprocessing parameters for model solving include time step, load magnitude, load direction, constraint boundary conditions, contact algorithm parameters, solver convergence criteria, and material density parameters.

[0015] Furthermore, in step two, the flexible material properties are set to at least two different sets, and the dynamic transmission error corresponding to each set of flexible material properties is calculated separately. A comparative analysis was conducted on the elastic dynamic transmission error under different combinations of flexible materials.

[0016] Furthermore, the flexible material properties are set into two groups: one group has the following properties: the worm gear is set to bronze material properties and the worm is set to structural steel material properties; the other group has the following properties: the worm gear is set to brass material properties and the worm is set to carbon steel material properties.

[0017] Furthermore, when simulating the flexible body dynamics model, a flexible body rotating probe is used to extract the input and output angles of the worm and worm wheel.

[0018] Furthermore, step four also includes calculating the rigid transmission error per step. And the transmission error of each step of the flexible body :

[0019]

[0020] in: For time step.

[0021] Furthermore, in step three, when simulating and solving the rigid body dynamics simulation model and the flexible body dynamics simulation model, the meshing condition of the worm and worm wheel is at least one of the following: constant torque condition, variable torque condition, impact load condition, and alternating load condition.

[0022] Furthermore, it also includes step seven: time-domain and frequency-domain analysis of dynamic transmission errors under different operating conditions: The calculated dynamic transmission error is subjected to a fast Fourier transform to obtain the frequency domain characteristics; The time-varying characteristics and frequency domain features of dynamic transmission error under different working conditions are analyzed to identify the main frequency components and amplitude variation patterns of dynamic transmission error.

[0023] The beneficial effects of this invention are as follows: This invention presents a rigid-flexible body co-simulation method for dynamic transmission error analysis of worm gears. Compared to existing technologies, this method achieves high-precision analysis of dynamic transmission errors in worm gear transmission systems through rigid-flexible body co-simulation. The method can separately analyze the contribution of geometric errors (including manufacturing errors, assembly errors, and shaping errors) to transmission errors, providing a theoretical basis for optimizing the geometric design of transmission systems. The dynamic comprehensive meshing error is obtained through a difference calculation method. and dynamic transmission error And further obtain the elastic dynamic transmission error. This allows us to separate the contribution of elastic deformation from the total transmission error. Although it cannot completely eliminate the nonlinear coupling effect between geometric error and elastic deformation error, it can approximately quantitatively assess the contribution of elastic deformation to transmission accuracy.

[0024] This invention, by comparing and analyzing at least two groups of flexible body material properties with different properties, can quantitatively analyze the influence of material characteristics on elastic transmission error, providing a scientific basis for material selection in engineering practice. The rigid-flexible body joint simulation analysis approach proposed in this invention provides a useful supplement to traditional transmission error analysis methods through comparative analysis.

[0025] The method of this invention is applicable to various load conditions, including constant torque conditions, variable torque conditions, impact load conditions, alternating load conditions, etc., and has good engineering applicability.

[0026] This invention supports time-domain and frequency-domain analysis, which can comprehensively reveal the characteristic laws of dynamic transmission errors. Based on a mature finite element software platform, it is easy to apply and promote in engineering. Attached Figure Description

[0027] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 This is a flowchart of the dynamic transmission error analysis method for worm gears using rigid-flexible body co-simulation according to the present invention. Figure 2 This is a schematic diagram of a three-dimensional model of a straight-profile toroidal worm gear transmission system; Figure 3 This is a diagram showing the error of each step of a rigid transmission. Figure 4 This is a diagram showing the transmission error of the flexible body at each step; Figure 5 This is a comparison chart of the stiffness and flexibility errors of the first group of flexible materials; Figure 6 This is the dynamic elastic transmission error diagram of the first group of flexible materials; Figure 7 This is a comparison chart of the stiffness and flexibility errors of the second group of flexible materials; Figure 8 This is the dynamic elastic transmission error diagram of the second group of flexible materials; Figure 9 This is a graph showing the difference in elastic dynamic transmission error between two sets of flexible materials. Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0029] This embodiment presents a method for analyzing the dynamic transmission error of worm gears using rigid-flexible body co-simulation. Taking a straight-profile toroidal worm gear of a certain type of high-precision transmission as the research object, an analysis method considering elastic deformation and the influence of multiple error sources is designed to calculate the dynamic transmission error of this transmission system. Straight-profile toroidal worm gears are characterized by large transmission ratio, high transmission accuracy, and strong load-bearing capacity, and are widely used in precision mechanical equipment. For example... Figure 2 The figure shown is a schematic diagram of a three-dimensional model of a straight-profile toroidal worm gear transmission system.

[0030] like Figure 1 As shown in this embodiment, the method for analyzing the dynamic transmission error of worm gears using rigid-flexible body co-simulation includes the following steps.

[0031] Step 1: Create a 3D model of the worm gear. The basic parameters of the worm gear are designed based on the actual working conditions, and a three-dimensional model of the worm gear is established.

[0032] Specifically, in this embodiment, the basic parameters include geometric parameters such as the number of worm threads, the number of worm wheel teeth, the module, the pressure angle, the helix angle, the tooth width, and the center distance, as well as operating parameters such as the rotational speed and the load.

[0033] In this embodiment, the basic parameters of the high-precision transmission straight-profile toroidal worm gear transmission system are shown in Table 1. The tooth surface of the straight-profile toroidal worm gear is a toroidal surface formed by rotating a straight generatrix around its axis, which has good meshing characteristics and high transmission accuracy. Specifically, the values ​​of each basic parameter in Table 1 are only a set of example values ​​given as an embodiment. In actual use, the values ​​of each basic parameter can be adjusted as needed.

[0034]

[0035] Step 2: Establish a simulation model (1) Establish a rigid body dynamics simulation model In the rigid body dynamics simulation environment of the finite element software, the worm and worm wheel are set as rigid body material properties to establish a rigid body dynamics simulation model.

[0036] Specifically, the 3D model of the straight-profile toroidal worm gear was imported into the finite element analysis software. The material properties of the worm and worm wheel were set as rigid bodies, and a rigid body dynamics simulation model was established for analyzing the influence of geometric errors separately. The tooth surface geometry of the straight-profile toroidal worm gear gives it excellent meshing performance in high-precision transmission. In the modeling process, the contact between each worm gear and the grounded rotary joint and the tooth surface was first set. Then, the boundary conditions of the driving and driven wheel joints were set. The boundary condition for the worm was rotation at 60 r / min, and the boundary condition for the worm wheel joint was the output torque of the driven wheel. The analysis settings and the number of substeps were determined based on the calculation end time. Finally, probes for the driving and driven wheel joints were set respectively, and the rotation angles output by the finite element analysis software were recorded.

[0037] (2) Establish a soft body dynamics simulation model In the transient dynamics simulation environment of the finite element software, the worm and worm wheel are set as flexible material properties to establish a flexible dynamics simulation model.

[0038] In the transient dynamics simulation environment of the finite element method (FEM) software, both the worm and worm wheel are set as flexible material properties to establish a simulation model that reflects the combined effects of geometric errors and elastic deformation errors during actual transmission. To compare and analyze the influence of different material properties, at least two different sets of flexible material properties are used, and the dynamic transmission error corresponding to each set of flexible material properties is solved separately. This study compares and analyzes the elastic dynamic transmission errors under different combinations of flexible materials. Specifically, in this embodiment, the flexible material properties are set into two groups: the first group has bronze material properties for the worm gear and structural steel material properties for the worm; the second group has brass material properties for the worm gear and carbon steel material properties for the worm. During the mesh generation process, the contact area between the worm and worm gear is selected by naming, and an automatic mesh generation method is used, with the mesh size controlled within 1 mm to ensure a balance between computational accuracy and efficiency.

[0039] Step 3: Model Simulation Solution Under the same time step, load conditions, boundary conditions, and contact parameters, the rigid body dynamics simulation model and the flexible body dynamics simulation model are respectively simulated and solved.

[0040] (1) Solving the rigid body dynamics simulation model When performing simulation solutions on the rigid body dynamics simulation model, considering manufacturing errors, assembly errors, and shaping errors but not elastic deformation, the worm gear input angle is extracted. and worm gear output angle .

[0041] Specifically, in this embodiment, the rigid body dynamics simulation model is simulated and solved. Under the working conditions of an input rotational speed of 60 r / min and a load torque of 50 Nm, and considering only geometric errors (including manufacturing errors, assembly errors, and shaping errors) while excluding the influence of elastic deformation, the worm gear input angle is extracted. and worm gear output angle This angle data is used for subsequent calculation of dynamic integrated meshing error, reflecting the transmission characteristics under the action of geometric error.

[0042] (2) Solving the soft body dynamics simulation model When simulating the flexible body dynamics model, the worm gear input angle is extracted under the condition of simultaneously considering elastic deformation, manufacturing error, assembly error, shaping error, and dynamic vibration. and worm gear output angle .

[0043] Specifically, in this embodiment, the flexible body dynamics simulation model is simulated and solved. Under the working conditions of an input rotational speed of 60 r / min and a load torque of 50 Nm, a flexible body rotating probe is used to extract the worm gear input angle. and worm gear output angle This angle data is used for subsequent calculation of dynamic transmission error, reflecting the transmission characteristics under the combined effect of geometric error and elastic deformation error.

[0044] Specifically, in this embodiment, manufacturing errors include worm gear tooth profile error, worm lead error, and center distance deviation; assembly errors include installation center distance offset, shaft tilt error, and clearance deviation; and profile modification errors include nonlinear mismatch in tooth profile modification and discontinuous features in the tooth surface transition section. These errors collectively cause nonlinear transmission errors during dynamic meshing.

[0045] In this embodiment, the preprocessing parameters for model solving include time step, load magnitude, load direction, constraint boundary conditions, contact algorithm parameters, solver convergence criteria, and material density parameters. Specifically, when simulating and solving rigid body dynamics and flexible body dynamics models, the preprocessing parameters remain the same, and the initial time step, minimum time step, and maximum time step are kept consistent to avoid inconsistent time steps.

[0046] In this embodiment, a flexible body rotation probe is used to extract the input and output angles of the worm and worm wheel when simulating the flexible body dynamics model. The flexible body rotation probe takes into account the overall rotation trend after local elastic deformation, resulting in higher accuracy.

[0047] In this embodiment, when simulating and solving the rigid body dynamics simulation model and the flexible body dynamics simulation model, the meshing condition of the worm and worm wheel is at least one of the following: constant torque condition, variable torque condition, impact load condition, and alternating load condition.

[0048] Step 4: Error Calculation Calculate the dynamic comprehensive meshing error of the worm gear deviating from the ideal transmission angle. Dynamic transmission error due to the worm gear deviating from the ideal transmission angle .

[0049] Specifically, the dynamic overall meshing error is caused by manufacturing errors, assembly errors, and shaping errors:

[0050] The dynamic transmission error is caused by the combined effect of geometric error and elastic deformation error.

[0051] in: The worm gear transmission ratio; in this embodiment, the transmission ratio is... = 60 / 2 = 30.

[0052] Specifically, in this embodiment, the error calculation also includes calculating the rigid transmission error per step. And the transmission error of each step of the flexible body :

[0053]

[0054] in: For time step.

[0055] like Figure 3 The diagram shown illustrates the transmission error at each step of the rigid body simulation, reflecting the changes in transmission error at each time step. Figure 4 The diagram shown is a transmission error graph for each step of the soft body simulation, illustrating the changes in transmission error at each time step during the soft body simulation process. Figure 3 and Figure 4 The comparison helps to understand the influence of elastic deformation on the transmission error of each step.

[0056] Step 5: Separation of Elastic Dynamic Transmission Errors Dynamic transmission error Subtract dynamic integrated meshing error The elastic dynamic transmission error considering the influence of elastic deformation is obtained by separation. The contribution of elastic deformation to transmission error can be approximated as follows:

[0057] Specifically, although the difference method cannot completely eliminate the nonlinear coupling effect between geometric error and elastic deformation error, it can effectively assess the relative contribution of elastic deformation.

[0058] In this embodiment, to compare and analyze the influence of different material properties, the flexible body material properties are set to at least two different groups, and the dynamic transmission error corresponding to each group of flexible body material properties is solved separately. The elastic dynamic transmission error under different combinations of flexible materials is compared and analyzed. Specifically, in this embodiment, the flexible material properties are set into two groups: the first group of flexible material properties is: the worm gear is set to bronze material properties, and the worm is set to structural steel material properties; the second group is: the worm gear is set to brass material properties, and the worm is set to carbon steel material properties.

[0059] In this embodiment, the influence of material properties on transmission error is evaluated by comparing and analyzing the elastic dynamic transmission errors obtained from two sets of flexible material properties. For example... Figure 5 and Figure 7 As shown, the figures are comparison diagrams of rigidity and flexibility errors for two sets of material combinations, clearly showing the differences between rigid body simulation and flexible body simulation. Figure 6 and Figure 8 The elastic dynamic transmission errors of the two material combinations are shown respectively, reflecting the influence of different material properties on elastic deformation errors. Figure 9 The graph shows the difference in elastic dynamic transmission error between two sets of flexible materials, which intuitively demonstrates the difference in the influence of material properties on elastic transmission error.

[0060] Step Six: Error Conversion The elastic dynamic transmission error in the form of angular displacement is converted into a linear displacement error in the direction of the tooth surface normal to the meshing line. :

[0061] in: The radius of the worm gear base circle; The base circle helix angle. In this embodiment, the worm gear base circle radius... =27.0169mm, base circle helix angle = 10°30'26''.

[0062] Step 7: Time-domain and frequency-domain analysis of dynamic transmission errors under different operating conditions. The calculated dynamic transmission error is subjected to a fast Fourier transform to obtain its frequency domain characteristics and identify the main frequency components.

[0063] The time-varying characteristics and frequency domain features of dynamic transmission error under different working conditions are analyzed to identify the main frequency components and amplitude variation patterns of dynamic transmission error.

[0064] Through the above steps and the analysis of the accompanying drawings, this embodiment can obtain high-precision dynamic transmission error analysis results for straight-profile toroidal worm gears, providing a theoretical basis for the precision design and optimization of transmission systems.

[0065] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for analyzing the dynamic transmission error of worm gears using rigid-flexible body co-simulation, characterized in that: Includes the following steps: Step 1: Create a 3D model of the worm gear. Design the basic parameters of the worm gear based on the actual working conditions, and establish a three-dimensional model of the worm gear. Step 2: Establish a simulation model In the rigid body dynamics simulation environment of the finite element software, the worm and worm wheel are set as rigid body material properties to establish a rigid body dynamics simulation model; In the transient dynamics simulation environment of the finite element software, the worm and worm wheel are set as flexible material properties to establish a flexible dynamics simulation model; Step 3: Model Simulation Solution Under the same time step, load conditions, boundary conditions, and contact parameters, the rigid body dynamics simulation model and the flexible body dynamics simulation model are simulated and solved respectively, including: When performing simulation solutions on the rigid body dynamics simulation model, considering manufacturing errors, assembly errors, and shaping errors but not elastic deformation, the worm gear input angle is extracted. and worm gear output angle ; When simulating the flexible body dynamics model, the worm gear input angle is extracted under the condition of simultaneously considering elastic deformation, manufacturing error, assembly error, shaping error, and dynamic vibration. and worm gear output angle ; Step 4: Error Calculation Calculate the dynamic comprehensive meshing error of the worm gear deviating from the ideal transmission angle. Dynamic transmission error due to the worm gear deviating from the ideal transmission angle : in: This refers to the worm gear transmission ratio; Step 5: Separation of Elastic Dynamic Transmission Errors Dynamic transmission error Subtract dynamic integrated meshing error The elastic dynamic transmission error considering the influence of elastic deformation is obtained by separation. : Step Six: Error Conversion The elastic dynamic transmission error in the form of angular displacement is converted into a linear displacement error in the direction of the tooth surface normal to the meshing line. : in: The radius of the worm gear base circle; The base circle helix angle.

2. The method for analyzing the dynamic transmission error of worm gears using rigid-flexible body co-simulation as described in claim 1, characterized in that: The basic parameters include the number of worm threads, the number of worm wheel teeth, the module, the pressure angle, the helix angle, the tooth width, the center distance, the rotational speed, and the load torque.

3. The method for analyzing the dynamic transmission error of worm gears using rigid-flexible body co-simulation as described in claim 1, characterized in that: The manufacturing errors include worm gear tooth profile error, worm lead error, and center distance deviation; the assembly errors include installation center distance offset, shaft tilt error, and clearance deviation; the profile modification errors include nonlinear mismatch in tooth profile modification and discontinuity in tooth surface transition section.

4. The method for analyzing the dynamic transmission error of worm gears using rigid-flexible body co-simulation as described in claim 1, characterized in that: In step three, the preprocessing parameters for model solving include time step, load magnitude, load direction, constraint boundary conditions, contact algorithm parameters, solver convergence criteria, and material density parameters.

5. The method for analyzing the dynamic transmission error of worm gears using rigid-flexible body co-simulation as described in claim 1, characterized in that: In step two, the flexible material properties are set to at least two different sets, and the dynamic transmission error corresponding to each set of flexible material properties is calculated. A comparative analysis was conducted on the elastic dynamic transmission error under different combinations of flexible materials.

6. The method for analyzing the dynamic transmission error of worm gears using rigid-flexible body co-simulation as described in claim 5, characterized in that: The flexible material properties are set into two groups: one group has the following properties: the worm gear is set to bronze material properties and the worm is set to structural steel material properties; the other group has the following properties: the worm gear is set to brass material properties and the worm is set to carbon steel material properties.

7. The method for analyzing the dynamic transmission error of worm gears using rigid-flexible body co-simulation as described in claim 1, characterized in that: When simulating the dynamics model of the flexible body, a flexible body rotating probe is used to extract the input and output angles of the worm and worm wheel.

8. The method for analyzing the dynamic transmission error of worm gears using rigid-flexible body co-simulation as described in claim 1, characterized in that: Step four also includes calculating the rigid transmission error per step. And the transmission error of each step of the flexible body : in: For time step.

9. The method for analyzing the dynamic transmission error of worm gears using rigid-flexible body co-simulation according to claim 1, characterized in that: In step three, when simulating and solving the rigid body dynamics simulation model and the flexible body dynamics simulation model, the meshing condition of the worm and worm wheel is at least one of the following: constant torque condition, variable torque condition, impact load condition, and alternating load condition.

10. The method for analyzing the dynamic transmission error of worm gears using rigid-flexible body co-simulation according to any one of claims 1-9, characterized in that: It also includes step seven: time-domain and frequency-domain analysis of dynamic transmission errors under different operating conditions: The calculated dynamic transmission error is subjected to a fast Fourier transform to obtain the frequency domain characteristics; The time-varying characteristics and frequency domain features of dynamic transmission errors under different working conditions are analyzed to identify the main frequency components and amplitude variation patterns of dynamic transmission errors.

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