Harmonic reducer dynamics simulation method and system based on rigid-flexible coupling

Abstract

The invention provides a harmonic reducer dynamic simulation method and system based on rigid-flexible coupling. The harmonic reducer dynamic simulation method comprises the steps that a harmonic reducer assembly model set is constructed; performing geometric repair on the harmonic reducer assembly model set, and adding material attribute parameters to the harmonic reducer assembly model set after geometric repair to obtain an attribute assembly model set; performing rigid body kinematic pair setting and contact setting on the attribute component model set, and performing flexibility processing on a flexible gear model in the attribute component model set based on an adaptive grid division method to obtain a rigid-flexible component model set; performing component coupling assembly and interference inspection on the rigid-flexible component model set to obtain a rigid-flexible coupling harmonic reducer model, and performing dynamic simulation to obtain simulation data; performing multi-dimensional performance analysis on the rigid-flexible coupling harmonic reducer model to obtain a performance index set; and optimizing and updating the rigid-flexible coupling harmonic reducer model according to a difference value between the performance index set and a performance index threshold value.

Description

Technical Field

[0001] This invention relates to the field of harmonic reducer simulation technology, and in particular to a dynamic simulation method and system for harmonic reducers based on rigid-flexible coupling. Background Technology

[0002] Harmonic reducers, as core transmission components of high-end equipment, have become essential components for critical parts such as robot joints, satellite attitude adjustment mechanisms, and precision machine tool spindles due to their advantages of high transmission accuracy, large transmission ratio, and small volume-to-mass ratio. Their transmission performance and reliability directly determine the operating accuracy, stability, and service life of the equipment. Therefore, dynamic simulation analysis that closely reflects actual working conditions is a core aspect of high-end equipment development.

[0003] However, the current mainstream harmonic reducer dynamics simulation methods in the industry have significant technical limitations: existing methods mostly adopt a pure rigid body modeling approach, defining all components such as cams, flexures, and rigid wheels as rigid bodies. They can only calculate basic mechanical parameters such as inter-tooth contact area and contact force, completely ignoring the elastic deformation of the flexure under load. The elastic deformation of the flexure directly affects the overall material stiffness, transmission efficiency, transmission error, and fatigue life. Pure rigid body models cannot calculate the above key indicators, resulting in a large deviation between simulation results and actual working conditions. Summary of the Invention

[0004] (a) Technical problems to be solved To address the shortcomings of existing technologies, this invention provides a dynamic simulation system for harmonic reducers based on rigid-flexible coupling. This system has the advantages of rigid-flexible coupling modeling and collaborative calculation of performance indicators, and solves the problem of low simulation accuracy caused by pure rigid modeling and chaotic simulation process in the dynamic simulation of harmonic reducers.

[0005] (II) Technical Solution To achieve the above objectives, the present invention provides the following technical solution: This invention provides a dynamic simulation method for harmonic reducers based on rigid-flexible coupling, comprising the following steps: Based on preset design parameters, a set of harmonic reducer component models is constructed, which includes a cam model, a bearing inner sleeve model, a bearing outer sleeve model, a ball model, a cage model, a flex wheel model, and a rigid wheel model. Import the harmonic reducer component model set into the RecurDyn platform, perform geometric repair on the harmonic reducer component model set, and add material property parameters to the geometrically repaired harmonic reducer component model set to obtain the property component model set. Rigid body kinematic pairs and contact settings are applied to the attribute component model set to obtain a primary component model set. Then, the primary component model set is subjected to flexible body processing to obtain a rigid-flexible component model set. Based on the design parameters, the rigid-flexible component model set is coupled and assembled and interference checked to obtain a rigid-flexible coupled harmonic reducer model. The dynamic simulation of the rigid-flexible coupled harmonic reducer model is then performed on the RecurDyn platform to obtain simulation data. Based on simulation data, a multi-dimensional performance analysis of the rigid-flexible coupled harmonic reducer model was conducted to obtain a set of performance indicators, which include overall material stiffness, transmission efficiency, transmission error, and fatigue life of the flex wheel. The rigid-flexible coupled harmonic reducer model is optimized and updated based on the difference between the performance index set and the performance index threshold, and then the simulation is terminated.

[0006] According to a preferred embodiment of the present invention, rigid body kinematic pairs and contact settings are performed on the attribute component model set to obtain a primary component model set, including: Set the cam model, ball model, cage model, and rigid wheel model in the attribute component model set as rigid body components, and set the flexible wheel model, bearing inner sleeve model, and bearing outer sleeve model in the primary component model set as flexible body components. A contact kinematic pair is set up between the cam model and the flexure wheel model, and the contact stiffness and contact damping coefficient between the cam model and the flexure wheel model are calculated based on the equivalent contact algorithm. Rolling contact pairs are set up for the bearing inner sleeve model, ball model, and bearing outer sleeve model, and the rolling contact force and rolling friction coefficient between the bearing inner sleeve model, ball model, and bearing outer sleeve model are calculated based on the contact penalty function. A sliding guide kinematic pair is set up for the cage model and the ball model, and the sliding friction coefficient between the cage model and the ball model is extracted; A tooth surface meshing kinematic pair is set up for the flexible wheel model and the rigid wheel model, and the meshing stiffness and meshing damping coefficient between the flexible wheel model and the rigid wheel model are calculated based on the tooth surface contact strength algorithm. The contact settings of the attribute component model set are performed based on contact stiffness, contact damping coefficient, rolling contact force, rolling friction coefficient, sliding friction coefficient, meshing stiffness, and meshing damping coefficient to obtain the primary component model set.

[0007] According to another preferred embodiment of the present invention, the contact stiffness and contact damping coefficient between the cam model and the flexure model are calculated based on the equivalent contact algorithm, including: Obtain the cam elastic modulus and cam Poisson's ratio of the cam model, and the flexure elastic modulus and flexure Poisson's ratio of the flexure model, and calculate the equivalent elastic modulus based on the cam elastic modulus, cam Poisson's ratio, flexure elastic modulus and flexure Poisson's ratio; Obtain the cam curvature radius and flexure curvature radius at the contact point between the cam model and the flexure model, respectively, and calculate the equivalent curvature radius based on the cam curvature radius and flexure curvature radius; Obtain the flexible wheel wall thickness and the radius of the flexible wheel neutral layer of the flexible wheel model, and calculate the wall thickness correction coefficient based on the flexible wheel wall thickness and the radius of the flexible wheel neutral layer; The equivalent contact stiffness is calculated based on the equivalent elastic modulus and the equivalent radius of curvature, and the contact stiffness is calculated by multiplying the equivalent contact stiffness by the wall thickness correction factor. Obtain the equivalent contact mass of the flexible wheel model and the equivalent contact mass of the rigid wheel model, and calculate the contact damping coefficient based on the equivalent contact mass of the flexible wheel, the equivalent contact mass of the rigid wheel, and the contact stiffness.

[0008] According to another preferred embodiment of the present invention, the rolling contact force and rolling friction coefficient between the bearing inner sleeve model, the ball model, and the bearing outer sleeve model are calculated based on the contact penalty function, including: Obtain the normal penetration depth and penetration velocity between the bearing inner sleeve model, the ball model, and the bearing outer sleeve model; Calculate the rolling contact stiffness and rolling damping coefficient between the bearing inner sleeve model, the ball model, and the bearing outer sleeve model; Based on the step penalty function, the rolling contact force between the bearing inner sleeve model, the ball model, and the bearing outer sleeve model is calculated according to the normal penetration depth, penetration speed, rolling contact stiffness, and rolling damping coefficient. Obtain the material lubrication state of the bearing inner sleeve model, ball model, and bearing outer sleeve model, and extract the rolling friction coefficient based on the material lubrication state.

[0009] According to another preferred embodiment of the present invention, the primary component model set is subjected to flexible body processing to obtain a rigid-flexible component model set, including: Finite element mesh transformation is performed on each flexible body component in the primary component model set to obtain a flexible body finite element mesh group, and the component geometric data group of the flexible body finite element mesh group is extracted. Based on the graph attention mechanism, the geometric data group of the component is weighted and aggregated with neighboring nodes to obtain the geometric topology feature group; Based on the geometric topological feature set, multi-scale feature encoding and upsampling density decoding are performed on the flexible finite element mesh set to obtain the mesh density distribution map set. An initial mesh model group is established for the flexible finite element mesh group based on the mesh density distribution map group, and the initial mesh model group is locally adaptively refined to obtain a smooth mesh model group; The smooth mesh model group is verified for mesh independence and mesh quality. The smooth mesh model group that has passed the verification is used to update and replace each flexible body component in the primary component model set to obtain the rigid-flexible component model set.

[0010] According to another preferred embodiment of the present invention, a multi-dimensional performance analysis is performed on a rigid-flexible coupled harmonic reducer model based on simulation data to obtain a set of performance indicators, including: Based on Hooke's law, the stiffness of the flexure and the bearing were calculated using simulation data, and the overall material stiffness was calculated based on the stiffness of the flexure and the bearing. The input power and output power are calculated based on simulation data, and the ratio of output power to input power is used as the transmission efficiency. The actual transmission ratio and the theoretical transmission ratio are calculated based on simulation data, and the transmission error is calculated based on the actual transmission ratio and the theoretical transmission ratio. Based on the rainflow counting method, the set of flexural stress amplitudes and the set of stress cycle counts corresponding to the set of flexural stress amplitudes are statistically derived from simulation data. The total number of fatigue failure cycles is calculated based on the pre-acquired material stress-life curve, linear cumulative damage formula, flexural stress amplitude set, and stress cycle number set. The stress cycle frequency is calculated based on the simulation time and number of cycles in the simulation data, and the fatigue life of the flexure is calculated based on the total number of fatigue failure cycles and the stress cycle frequency. The overall material stiffness, transmission efficiency, transmission error, and flexspline fatigue life are compiled into a set of performance indicators.

[0011] According to another preferred embodiment of the present invention, a rigid-flexible component model set is coupled and interference checked based on design parameters to obtain a rigid-flexible coupled harmonic reducer model, including: Based on the design parameters, coordinate transformation and assembly positioning are performed on each component model in the rigid-flexible component model set to obtain the assembled harmonic reducer model. Based on the kinematic pairs of the rigid-flexible component model set, the positioning constraints and clearance adjustments are applied to the assembled harmonic reducer model to obtain the primary harmonic reducer model. Static and dynamic interference checks were performed on the primary harmonic reducer model, and interference check reports were obtained. Based on the interference inspection report, the primary harmonic reducer model was constrained and optimized to obtain a rigid-flexible coupled harmonic reducer model.

[0012] According to another preferred embodiment of the present invention, geometric repair of the harmonic reducer component model set includes: Redundancy features are obtained by performing size filtering and high curvature feature identification on the harmonic reducer component model. The redundant features in the model region corresponding to the redundant features in the harmonic reducer component model are optimized and the surface is filled. The surface continuity analysis and gap detection were performed on the harmonic reducer assembly after surface filling, and the gap detection results were obtained. Based on the gap detection results, gap repair and surface smoothing are performed on the harmonic reducer components.

[0013] According to another preferred embodiment of the present invention, a harmonic reducer component model set is constructed based on preset design parameters, including: A flexible wheel model is constructed based on the involute tooth profile function and preset design parameters. A rigid wheel model is constructed based on the tooth profile envelope method, according to the flexible wheel model and design parameters. A bearing assembly model is constructed based on the design parameters. The bearing assembly model includes the bearing inner sleeve model, the bearing outer sleeve model, the ball model, and the cage model. Based on the bearing assembly model and design parameters, a cam model is constructed, and the cam model, bearing inner sleeve model, bearing outer sleeve model, ball model, cage model, flex wheel model, and rigid wheel model are combined into a harmonic reducer assembly model set.

[0014] To achieve at least one of the above-mentioned objectives, the present invention further provides a dynamic simulation system for a harmonic reducer based on rigid-flexible coupling. The system includes a component construction module, an attribute addition module, a rigid-flexible processing module, a model simulation module, a performance analysis module, and an update and optimization module, wherein: The component construction module is used to build a set of harmonic reducer component models based on preset design parameters. The set of harmonic reducer component models includes a cam model, a bearing inner sleeve model, a bearing outer sleeve model, a ball model, a cage model, a flex wheel model, and a rigid wheel model. The attribute addition module is used to import the harmonic reducer component model set into the RecurDyn platform, perform geometric repair on the harmonic reducer component model set, and add material property parameters to the geometrically repaired harmonic reducer component model set to obtain the attribute component model set. The rigid-flexible processing module is used to set rigid body kinematic pairs and contact settings on the attribute component model set to obtain a primary component model set, and to perform flexible body processing on the primary component model set to obtain a rigid-flexible component model set. The model simulation module is used to perform component coupling assembly and interference checks on the rigid-flexible component model set based on design parameters to obtain a rigid-flexible coupled harmonic reducer model. The module also performs dynamic simulation on the rigid-flexible coupled harmonic reducer model based on the RecurDyn platform to obtain simulation data. The performance analysis module is used to perform multi-dimensional performance analysis on the rigid-flexible coupling harmonic reducer model based on simulation data, and obtain a set of performance indicators, including overall material stiffness, transmission efficiency, transmission error and flex wheel fatigue life. The update and optimization module is used to optimize and update the rigid-flexible coupling harmonic reducer model based on the difference between the performance index set and the performance index threshold, and then end the simulation.

[0015] The present invention further provides a computer-readable storage medium storing a computer program, which is executed by a processor to implement the above-described method for dynamic simulation of a harmonic reducer based on rigid-flexible coupling.

[0016] (III) Beneficial Effects Compared with existing technologies, this invention provides a dynamic simulation method and system for harmonic reducers based on rigid-flexible coupling, which has the following advantages: This dynamic simulation method for harmonic reducers based on rigid-flexible coupling calculates contact stiffness and damping coefficient using an equivalent contact algorithm, which can realistically reflect the elastic deformation of the flexure and the load distribution on the tooth surface. By constructing a rolling contact force model through a step penalty function, the penetration instability problem can be avoided and the stability of the numerical solution can be improved. The extraction of friction coefficient and the calculation of tooth meshing parameters further supplement the energy loss and dynamic response characteristics between the contact pairs, significantly improving the physical reality, stability and calculation accuracy of the dynamic simulation of the harmonic reducer, and providing a high-fidelity physical constraint basis for subsequent rigid-flexible coupling dynamic simulation.

[0017] This dynamic simulation method for harmonic reducers based on rigid-flexible coupling achieves joint adaptive optimization of geometric and mechanical features in the mesh generation of flexible components such as flex wheels by combining graph attention mechanism and adaptive mesh generation method. By utilizing meshing and geometric feature extraction, it can accurately capture complex contours and thickness variation regions, avoiding oversimplification caused by traditional uniform meshing. Through a dual verification mechanism, it can ensure the stability and accuracy of finite element calculation results, thereby significantly improving the realism of stress and deformation simulation of flex wheels, reducing simulation errors, and providing a high-fidelity physical constraint basis for subsequent rigid-flexible coupling dynamic simulation.

[0018] This dynamic simulation method for harmonic reducers based on rigid-flexible coupling achieves quantitative performance evaluation of the rigid-flexible coupling model of the harmonic reducer through a multi-dimensional performance collaborative analysis mechanism. By combining simulation data with Hooke's law, the mechanical stiffness of the flexure and bearings can be accurately obtained, reflecting the structural support characteristics. Through power and transmission ratio analysis, transmission efficiency and motion accuracy can be quantified, providing a basis for evaluating energy transfer quality. By introducing the rainflow counting method and material stress-life curves, the fatigue life of the flexure can be predicted in the simulation domain, thus completing the life assessment without actual destructive testing. By unifying structural performance, transmission performance, and fatigue reliability in the same data chain, the three-dimensional performance of the harmonic reducer (strength, efficiency, and life) can be evaluated simultaneously, improving the accuracy of the dynamic simulation. Attached Figure Description

[0019] Figure 1 The diagram shows a flowchart of a dynamic simulation method for a harmonic reducer based on rigid-flexible coupling according to the present invention. Detailed Implementation

[0020] The following description is intended to disclose the present invention and enable those skilled in the art to implement it. The preferred embodiments described below are merely examples, and other obvious modifications will occur to those skilled in the art. The basic principles of the invention defined in the following description can be applied to other embodiments, modifications, improvements, equivalents, and other technical solutions that do not depart from the spirit and scope of the invention.

[0021] It is understood that the term "a" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of an element can be one, while in another embodiment, the number of the element can be multiple, and the term "a" should not be understood as a limitation on the number.

[0022] Example 1: Please combine Figure 1 This invention discloses a dynamic simulation method for harmonic reducers based on rigid-flexible coupling, the method comprising the following steps: Based on preset design parameters, a set of harmonic reducer component models is constructed. The set of harmonic reducer component models includes a cam model, a bearing inner sleeve model, a bearing outer sleeve model, a ball model, a cage model, a flex wheel model, and a rigid wheel model.

[0023] The design parameters refer to the model design parameters of each component of the harmonic reducer, including the shape, size, and assembly position of each component. These design parameters conform to the nominal dimensions and tolerance ranges in the design drawings of the harmonic reducer (according to GB / T30819-2014 "Basic Parameters of Harmonic Gear Transmission"). A harmonic reducer is a mechanical device that achieves high-precision transmission based on the elastic deformation of a flexure. It mainly consists of a cam, a flexure, and a rigid wheel. The working principle of the harmonic reducer is that the flexure undergoes controllable elastic deformation through the cam and bearing assembly, meshing with the rigid wheel to transmit motion and power, thereby achieving a high reduction ratio. The bearing assembly consists of an inner bearing sleeve, an outer bearing sleeve, balls, and a cage. Specifically, a set of harmonic reducer component models is constructed based on preset design parameters, including: A flexible wheel model is constructed based on the involute tooth profile function and preset design parameters. A rigid wheel model is constructed based on the tooth profile envelope method, according to the flexible wheel model and design parameters. A bearing assembly model is constructed based on the design parameters. The bearing assembly model includes the bearing inner sleeve model, the bearing outer sleeve model, the ball model, and the cage model. Based on the bearing assembly model and design parameters, a cam model is constructed, and the cam model, bearing inner sleeve model, bearing outer sleeve model, ball model, cage model, flex wheel model, and rigid wheel model are combined into a harmonic reducer assembly model set.

[0024] Specifically, a harmonic reducer component model set can be constructed based on parametric 3D modeling software such as SolidWorks 2023 and UGNX 2206. The involute tooth profile function is a mathematical expression describing the geometry of the involute tooth profile. The design parameters when constructing the rigid wheel model are as follows: tooth profile (module m = 0.6mm, pressure angle...). =20°), wall thickness 3mm (tolerance ±0.05mm), tooth surface roughness Ra=0.8μm; the tooth profile envelope method is used to describe the boundary characteristics between the tooth profile surfaces of the flexible wheel model and the rigid wheel model. The design parameters when constructing the rigid wheel model are as follows: cumulative tooth pitch error ≤0.02mm; the design parameters when constructing the bearing assembly model are as follows: ball diameter of ball model 10mm (tolerance ±0.002mm), cage model window clearance 0.02mm; the design parameters when constructing the cam model are as follows: eccentricity 5mm (tolerance ±0.01mm), profile roundness 0.005mm.

[0025] Import the harmonic reducer component model set into the RecurDyn platform, perform geometric repair on the harmonic reducer component model set, and add material property parameters to the geometrically repaired harmonic reducer component model set to obtain the property component model set.

[0026] In detail, to achieve more accurate dynamic simulations, it is necessary to further verify and check the accuracy of the models of each component of the harmonic reducer, and add material property parameters to them. Importing the harmonic reducer component model set into the RecurDyn platform involves converting the model format of the harmonic reducer component model set and then importing the converted model set into the RecurDyn platform. The individual models in the harmonic reducer component model set can be CAD-type models from 3D modeling software. Model format conversion refers to converting the 3D model into a neutral format such as STEP or IGES, and finally into the B-Rep format that the RecurDyn platform can recognize.

[0027] In this embodiment of the invention, geometric repair of the harmonic reducer component model set includes: Redundancy features are obtained by performing size filtering and high curvature feature identification on the harmonic reducer component model. The redundant features in the model region corresponding to the redundant features in the harmonic reducer component model are optimized and the surface is filled. The surface continuity analysis and gap detection were performed on the harmonic reducer assembly after surface filling, and the gap detection results were obtained. Based on the gap detection results, gap repair and surface smoothing are performed on the harmonic reducer components.

[0028] Among them, size filtering refers to detecting redundant features that do not conform to the design size requirements of each component. For example, process holes with a diameter of less than 2mm on the flexible wheel component are regarded as redundant features. High curvature feature recognition refers to identifying redundant features that exceed the threshold curvature of the model based on the high curvature features of the harmonic reducer component model and a machine learning model. Redundant feature optimization refers to deleting redundant hole features or restoring the original edges of chamfer features. Redundant feature optimization can be performed using the Geometry Doctor function of the RecurDyn platform. Surface filling refers to repairing and filling the deleted hole features. Surface filling can be performed using the Non-Uniform Rational B-Splines (NURBS) method.

[0029] Specifically, surface continuity analysis can be performed using curvature comb analysis or zebra stripe analysis. Gap detection can be performed using the bounding box recognition algorithm of the Model Check function on the RecurDyn platform. The gap detection results include the gap size and the location information of the problem area. Gap repair can be performed by automatically closing gaps using the stitching tool on the RecurDyn platform or by using a method based on local surface reconstruction. Surface smoothing can be performed using the Laplacian smoothing algorithm, thereby optimizing the model accuracy.

[0030] In detail, adding material property parameters to the geometrically repaired harmonic reducer component model set results in a property component model set. This means adding corresponding material property parameters to each model in the harmonic reducer component model set based on the actual material properties of each component. For example, the material of the flexible wheel model in the harmonic reducer component model set is set to 40CrNiMoA alloy structural steel, the material of the cam model and rigid wheel model is set to 45 steel, and the material of the bearing component model is set to GCr15 high carbon chromium bearing steel. Corresponding material properties such as elastic modulus, Poisson's ratio, density, and fatigue strength are configured for each model.

[0031] Among these methods, optimizing redundant features can eliminate local stress concentration interference in the model, making the deformation analysis during simulation more realistic. By performing assembly repair, the continuity of the contact pair can be ensured, reducing penetration errors in dynamic simulation. By adding material property parameters, a realistic physical basis can be provided for subsequent dynamic simulation, thereby improving the accuracy of the simulation.

[0032] The primary component model set is obtained by setting rigid body kinematic pairs and contact settings on the attribute component model set, and then the primary component model set is processed to make it flexible to obtain a rigid-flexible component model set.

[0033] Since the components of the harmonic reducer include both flexible and rigid bodies, in order to achieve more accurate dynamic simulation, it is necessary to perform corresponding rigidification and flexibility treatment on each component.

[0034] In this embodiment of the invention, rigid body kinematic pairs and contact settings are applied to the attribute component model set to obtain a primary component model set, including: Set the cam model, ball model, cage model, and rigid wheel model in the attribute component model set as rigid body components, and set the flexible wheel model, bearing inner sleeve model, and bearing outer sleeve model in the primary component model set as flexible body components. A contact kinematic pair is set up between the cam model and the flexure wheel model, and the contact stiffness and contact damping coefficient between the cam model and the flexure wheel model are calculated based on the equivalent contact algorithm. Rolling contact pairs are set up for the bearing inner sleeve model, ball model, and bearing outer sleeve model, and the rolling contact force and rolling friction coefficient between the bearing inner sleeve model, ball model, and bearing outer sleeve model are calculated based on the contact penalty function. A sliding guide kinematic pair is set up for the cage model and the ball model, and the sliding friction coefficient between the cage model and the ball model is extracted; A tooth surface meshing kinematic pair is set up for the flexible wheel model and the rigid wheel model, and the meshing stiffness and meshing damping coefficient between the flexible wheel model and the rigid wheel model are calculated based on the tooth surface contact strength algorithm. The contact settings of the attribute component model set are performed based on contact stiffness, contact damping coefficient, rolling contact force, rolling friction coefficient, sliding friction coefficient, meshing stiffness, and meshing damping coefficient to obtain the primary component model set.

[0035] Among them, rigid body components refer to idealized model components that do not deform, while flexible body components refer to real models that take into account elastic deformation. Existing methods mostly adopt the pure rigid body modeling approach, defining all components such as cams, flexible wheels, and rigid wheels as rigid bodies. They can only calculate basic mechanical parameters such as inter-tooth contact area and contact force, completely ignoring the elastic deformation of the flexible wheel under load.

[0036] Specifically, the contact stiffness and contact damping coefficient between the cam model and the flexure model are calculated based on the equivalent contact algorithm, including: Obtain the cam elastic modulus and cam Poisson's ratio of the cam model, and the flexure elastic modulus and flexure Poisson's ratio of the flexure model, and calculate the equivalent elastic modulus based on the cam elastic modulus, cam Poisson's ratio, flexure elastic modulus and flexure Poisson's ratio; Obtain the cam curvature radius and flexure curvature radius at the contact point between the cam model and the flexure model, respectively, and calculate the equivalent curvature radius based on the cam curvature radius and flexure curvature radius; Obtain the flexible wheel wall thickness and the radius of the flexible wheel neutral layer of the flexible wheel model, and calculate the wall thickness correction coefficient based on the flexible wheel wall thickness and the radius of the flexible wheel neutral layer; The equivalent contact stiffness is calculated based on the equivalent elastic modulus and the equivalent radius of curvature, and the contact stiffness is calculated by multiplying the equivalent contact stiffness by the wall thickness correction factor. Obtain the equivalent contact mass of the flexible wheel model and the equivalent contact mass of the rigid wheel model, and calculate the contact damping coefficient based on the equivalent contact mass of the flexible wheel, the equivalent contact mass of the rigid wheel, and the contact stiffness.

[0037] The cam's elastic modulus, cam Poisson's ratio, flexure's elastic modulus, flexure's Poisson's ratio, cam's radius of curvature, flexure's radius of curvature, flexure's wall thickness, flexure's neutral layer radius, flexure's equivalent contact mass, and rigid wheel's equivalent contact mass can be obtained through the RecurDyn platform. The equivalent elastic modulus is calculated by dividing the difference between 1 and the square of the cam's Poisson's ratio by the cam's elastic modulus, and by dividing the difference between 1 and the square of the flexure's Poisson's ratio by the flexure's elastic modulus. The reciprocal of this ratio is taken as the equivalent elastic modulus. The equivalent radius of curvature is calculated by summing the reciprocals of the flexure's radius of curvature and the cam's radius of curvature, and taking the reciprocal of this sum as the equivalent elastic modulus. The calculation method for the equivalent radius of curvature and wall thickness correction coefficient is as follows: calculate the ratio of the flexible wheel wall thickness to the radius of the flexible wheel neutral layer, multiply the ratio by a preset empirical coefficient, and add 1 to the product to obtain the wall thickness correction coefficient; the calculation method for the equivalent contact stiffness is as follows: multiply the square root of the equivalent radius of curvature by the equivalent elastic modulus by 4 / 3 to obtain the equivalent contact stiffness; the calculation method for the contact damping coefficient is as follows: extract the contact damping ratio based on the preset metal contact damping experimental data, multiply the weighted sum of the equivalent contact mass of the flexible wheel and the equivalent contact mass of the rigid wheel by the contact stiffness, calculate the square root of the product, multiply the square root by the contact damping ratio by 2 to obtain the contact damping coefficient.

[0038] Specifically, the rolling contact force and rolling friction coefficient between the bearing inner sleeve model, the ball model, and the bearing outer sleeve model are calculated based on the contact penalty function, including: Obtain the normal penetration depth and penetration velocity between the bearing inner sleeve model, the ball model, and the bearing outer sleeve model; Calculate the rolling contact stiffness and rolling damping coefficient between the bearing inner sleeve model, the ball model, and the bearing outer sleeve model; Based on the step penalty function, the rolling contact force between the bearing inner sleeve model, the ball model, and the bearing outer sleeve model is calculated according to the normal penetration depth, penetration speed, rolling contact stiffness, and rolling damping coefficient. Obtain the material lubrication state of the bearing inner sleeve model, ball model, and bearing outer sleeve model, and extract the rolling friction coefficient based on the material lubrication state.

[0039] The normal penetration depth, penetration velocity, and material lubrication state can be obtained through the RecurDyn platform. The calculation method for rolling contact stiffness is the same as that for contact stiffness in the above steps, and the calculation method for rolling damping coefficient is the same as that for contact damping coefficient in the above steps, so it will not be repeated here. The calculation of rolling contact force based on the step penalty function includes: using the STEP step function to calculate the step coefficient between the normal penetration depth and the rolling damping coefficient, multiplying the step coefficient by the penetration velocity to obtain the damping term, multiplying the rolling contact stiffness by the 1.5th power of the penetration velocity to obtain the rolling term, and adding the rolling term to the damping term to obtain the rolling contact force. The material lubrication state refers to the type of lubrication material used, which can be oil lubrication or grease lubrication. The rolling friction coefficient is 0.001 for oil lubrication and 0.003 for grease lubrication. The extraction method for the sliding friction coefficient is the same as that for the rolling friction coefficient. The meshing stiffness can be calculated using the tooth surface contact strength formula (such as ISO 6336 standard), and the meshing damping coefficient can be calculated by mapping with reference to the gear meshing damping experimental data.

[0040] Specifically, by calculating the contact stiffness and damping coefficient using the equivalent contact algorithm, the elastic deformation of the flexure and the load distribution on the tooth surface can be accurately reflected. By constructing a rolling contact force model using the step penalty function, the penetration instability problem can be avoided and the stability of the numerical solution can be improved. The extraction of the friction coefficient and the calculation of the tooth meshing parameters further supplement the energy loss and dynamic response characteristics between the contact pairs, significantly improving the physical reality, stability and calculation accuracy of the harmonic reducer dynamic simulation, and providing a high-fidelity physical constraint basis for subsequent rigid-flexible coupling dynamic simulation.

[0041] In detail, the primary component model set is processed into a flexible body to obtain a rigid-flexible component model set, including: Finite element mesh transformation is performed on each flexible body component in the primary component model set to obtain a flexible body finite element mesh group, and the component geometric data group of the flexible body finite element mesh group is extracted. Based on the graph attention mechanism, the geometric data group of the component is weighted and aggregated with neighboring nodes to obtain the geometric topology feature group; Based on the geometric topological feature set, multi-scale feature encoding and upsampling density decoding are performed on the flexible finite element mesh set to obtain the mesh density distribution map set. An initial mesh model group is established for the flexible finite element mesh group based on the mesh density distribution map group, and the initial mesh model group is locally adaptively refined to obtain a smooth mesh model group; The smooth mesh model group is verified for mesh independence and mesh quality. The smooth mesh model group that has passed the verification is used to update and replace each flexible body component in the primary component model set to obtain the rigid-flexible component model set.

[0042] The RecurDyn platform's geometric kernel can be used for finite element mesh transformation. The component geometric data set includes curvature maps, wall thickness gradient maps, stress distribution maps, and finite element mesh vertex and edge data. Weighted aggregation of neighbor nodes based on a graph attention mechanism involves inputting the component geometric data set into a pre-defined attention graph neural network. The graph attention mechanism of the attention graph neural network learns the features between mesh vertices and edges, identifies high stress concentration areas and deformation-sensitive areas, and weights and aggregates neighbor nodes to output the corresponding topological features. A pre-defined U-Net encoder can be used for multi-... Scale feature encoding is performed, and upsampling density decoding is carried out using the U-Net decoder. Each grid density distribution map in the grid density distribution map group corresponds to the target grid cell size of each flexible body component. Establishing an initial grid model group for the flexible body finite element mesh group based on the grid density distribution map group refers to mapping the grid density distribution map group to the grid size based on linear scaling transformation, and establishing the initial grid model group for the flexible body finite element mesh group based on the mapped grid size. Local adaptive grid density refinement refers to recursively subdividing and refining the grid model corresponding to the high-density area in the grid density distribution map, thereby ensuring a smooth transition of grid cell size.

[0043] Specifically, the rules for mesh independence verification can be that when the mesh size is reduced by 10%, the fluctuation of the maximum stress calculation value of the flexible wheel is ≤3%. Mesh quality verification refers to ensuring that the element distortion rate is ≤5% and the aspect ratio is ≤10 using the MeshQualityCheck tool on the RecurDyn platform. When the mesh independence verification fails, the density prediction parameters of U-Net are adjusted. When the mesh quality verification fails, the unqualified mesh elements are re-divided. Update and replacement refers to converting the smooth mesh model group into a flexible body model while retaining material properties, geometric features and constraint interfaces, and replacing the model of the corresponding flexible body component.

[0044] In detail, by combining graph attention mechanism and adaptive mesh generation method, joint adaptive optimization of geometric and mechanical features is achieved in the mesh generation of flexible components such as flex wheels. By utilizing meshing and geometric feature extraction, complex contours and thickness variation regions can be accurately captured, avoiding oversimplification caused by traditional uniform meshing. Through a dual verification mechanism, the stability and accuracy of finite element calculation results can be ensured, thereby significantly improving the realism of stress and deformation simulation of flex wheels, reducing simulation errors, and providing a high-fidelity physical constraint basis for subsequent rigid-flexible coupling dynamic simulation.

[0045] Based on the design parameters, the rigid-flexible component model set is coupled and assembled, and interference is checked to obtain a rigid-flexible coupled harmonic reducer model. The dynamic simulation of the rigid-flexible coupled harmonic reducer model is then performed on the RecurDyn platform to obtain simulation data.

[0046] Specifically, based on design parameters, the rigid-flexible component model set is subjected to component coupling assembly and interference checks to obtain a rigid-flexible coupled harmonic reducer model, including: Based on the design parameters, coordinate transformation and assembly positioning are performed on each component model in the rigid-flexible component model set to obtain the assembled harmonic reducer model. Based on the kinematic pairs of the rigid-flexible component model set, the positioning constraints and clearance adjustments are applied to the assembled harmonic reducer model to obtain the primary harmonic reducer model. Static and dynamic interference checks were performed on the primary harmonic reducer model, and interference check reports were obtained. Based on the interference inspection report, the primary harmonic reducer model was constrained and optimized to obtain a rigid-flexible coupled harmonic reducer model.

[0047] The RecurDyn platform's Positioning tool can be used for coordinate transformation and assembly positioning. Coordinate transformation refers to adjusting the coordinates of each component model according to the position information of each component in the design parameters. Assembly positioning refers to assembling each component model according to parameters such as eccentricity or center distance in the design parameters. The RecurDyn platform's Constraint Equation tool can be used for positioning constraints and clearance adjustment. Positioning constraints refer to ensuring that each component does not interfere with each other in the initial position based on the multi-body constraints of the kinematic pairs. Clearance adjustment refers to adjusting the window clearance between each component. For example, the interference between the bearing inner sleeve model and the cam model is 0.008mm, thereby achieving perfect alignment. The RecurDyn platform's Interference Check tool can be used for static interference checks and dynamic interference checks. Static interference checks refer to detecting the overlapping area of ​​the assembly in the initial position, with an interference tolerance of 0.001mm. Dynamic interference checks refer to simulating the motion trajectory over a period of time and checking whether interference occurs in each component model during the motion. The interference check report includes the interference location, interference amount, and severity. The RecurDyn platform's Move tool can be used for this purpose. The Component tool performs constraint optimization, which involves fine-tuning the position and constraint tolerances of each component and then returning to perform static and dynamic interference checks.

[0048] Specifically, dynamic simulation of a rigid-flexible coupled harmonic reducer model is performed on the RecurDyn platform. The simulation data is obtained by setting simulation parameters and monitoring parameters based on actual conditions, and then inputting these parameters into the RecurDyn platform for dynamic simulation. The simulation parameters include simulation time, simulation step size, load conditions (such as input torque and output load), and boundary conditions (such as fixed constraints and motion drive). The load conditions and boundary conditions need to be set according to the actual operating conditions of the harmonic reducer (such as rated speed and rated load) to best reproduce the actual operating state. The monitoring parameters include motion trajectory, stress conditions, elastic deformation of the flexure assembly, and flexure stress time. The simulation process includes the motion history, loads on each component, and load displacements. For example, the simulation time is 60 seconds (covering 10 transmission cycles), with a step size of 0.001 seconds. The loads are: 50 N·m torque at the input end and 1000 r / min speed, and a fixed load of 5000 N·m at the output end. The boundary conditions are: fixed bearing outer sleeve, rotational drive at the input end, and torque constraint at the output end. The monitoring parameters include: flexure load, flexure elastic deformation, flexure tooth surface contact force, radial deformation, input and output angular velocities, relative bearing displacement, and flexure stress time history (sampling frequency 1000 Hz). The RecurDyn software will simulate the transmission process of the harmonic reducer based on the rigid-flexible coupling model, and calculate the motion trajectory, force conditions, and elastic deformation of each component in real time.

[0049] Specifically, by optimizing component coordinate positioning, kinematic pair constraints, and clearance based on design parameters, high-precision assembly and coupling of rigid and flexible components of the harmonic reducer were achieved, ensuring accurate matching of the model at the geometric and mechanical levels. By utilizing both static and dynamic interference checks, abnormal interference or clearance between components can be effectively identified, avoiding non-physical interference or numerical divergence during the simulation phase, thus providing a reliable foundation for subsequent performance analysis.

[0050] Based on simulation data, a multi-dimensional performance analysis was conducted on the rigid-flexible coupled harmonic reducer model to obtain a set of performance indicators, which includes overall material stiffness, transmission efficiency, transmission error, and fatigue life of the flex wheel.

[0051] Specifically, a multi-dimensional performance analysis of the rigid-flexible coupled harmonic reducer model is conducted based on simulation data, resulting in a set of performance indicators, including: Based on Hooke's law, the stiffness of the flexure and the bearing were calculated using simulation data, and the overall material stiffness was calculated based on the stiffness of the flexure and the bearing. The input power and output power are calculated based on simulation data, and the ratio of output power to input power is used as the transmission efficiency. The actual transmission ratio and the theoretical transmission ratio are calculated based on simulation data, and the transmission error is calculated based on the actual transmission ratio and the theoretical transmission ratio. Based on the rainflow counting method, the set of flexural stress amplitudes and the set of stress cycle counts corresponding to the set of flexural stress amplitudes are statistically derived from simulation data. The total number of fatigue failure cycles is calculated based on the pre-acquired material stress-life curve, linear cumulative damage formula, flexural stress amplitude set, and stress cycle number set. The stress cycle frequency is calculated based on the simulation time and number of cycles in the simulation data, and the fatigue life of the flexure is calculated based on the total number of fatigue failure cycles and the stress cycle frequency. The overall material stiffness, transmission efficiency, transmission error, and flexspline fatigue life are compiled into a set of performance indicators.

[0052] Specifically, calculating the stiffness of the flexible wheel and the bearing stiffness based on Hooke's Law and simulation data involves extracting the flexible wheel load, maximum elastic deformation of the flexible wheel, bearing load, and maximum load displacement of the bearing from the simulation data. The ratio of the flexible wheel load to the maximum elastic deformation of the flexible wheel is taken as the stiffness of the flexible wheel, and the ratio of the bearing load to the maximum load displacement of the bearing is taken as the stiffness of the bearing. Calculating the overall material stiffness based on the stiffness of the flexible wheel and the bearing stiffness involves taking the sum of the reciprocal of the stiffness of the flexible wheel and the reciprocal of the stiffness of the bearing as the reciprocal of the overall material stiffness.

[0053] Specifically, calculating the input power and output power based on simulation data involves extracting the input torque, input angular velocity, output torque, and output angular velocity from the simulation data, using the product of the input torque and input angular velocity as the input power, and the product of the output torque and output angular velocity as the output power. Calculating the actual transmission ratio and theoretical transmission ratio based on simulation data includes extracting the number of teeth on the rigid wheel and the flexible wheel from the simulation data, using the ratio of the input angular velocity to the output angular velocity as the actual transmission ratio, and the ratio of the number of teeth on the rigid wheel to the number of teeth on the flexible wheel as the theoretical transmission ratio. Calculating the transmission error based on the actual and theoretical transmission ratios involves calculating the absolute difference between the actual and theoretical ratios, and using the ratio of this absolute difference to the theoretical transmission ratio as the transmission error. Statistically calculating the set of flexible wheel stress amplitudes and the corresponding set of stress cycle counts based on the simulation data using the rainflow counting method involves statistically extracting the time history of the flexible wheel stress in the simulation data using the rainflow counting method to obtain different flexible wheel stress amplitudes and their corresponding stress cycle counts.

[0054] Based on pre-acquired material stress-life curves, linear cumulative damage formulas, flexible wheel stress amplitude sets, and stress cycle count sets, the total number of fatigue failure cycles is calculated from the simulation data, including: Based on the obtained material fatigue index and fatigue constant, and the stress-life curve, the following fatigue life formula is derived: in, The amplitude of the kth type of stress; Let f be the fatigue life corresponding to the kth type of stress amplitude; The fatigue index of the material; The fatigue constant of the material; Based on the matching relationship between the set of stress amplitudes of the flexible wheel and the set of stress cycle numbers, k types of stress amplitudes are obtained. Corresponding number of stress cycles ; The fatigue life corresponding to various stress amplitudes is calculated based on the following linear cumulative damage formula: in: The stress cycle number represents the stress amplitude of the k-th type. Let be the fatigue life of the kth type of stress amplitude; The fatigue index of the material; The sum of all fatigue lives is taken as the total number of fatigue failure cycles.

[0055] Specifically, calculating the stress cycle frequency based on the simulation time and number of cycles in the simulation data means calculating the stress cycle frequency using the following formula: in: The stress cycle number represents the stress amplitude of the k-th type. The simulation time is the time value in the simulation data. The fatigue index of the material. is the stress cycle frequency.

[0056] The fatigue life of a flexible wheel is calculated based on the total number of fatigue failure cycles and the stress cycle frequency. This means dividing the total number of fatigue failure cycles by the product of the stress cycle frequency and 3600 to obtain the fatigue life of the flexible wheel.

[0057] Specifically, through a multi-dimensional performance collaborative analysis mechanism, quantitative performance evaluation of the rigid-flexible coupling model of the harmonic reducer was achieved. By combining simulation data with Hooke's law, the mechanical stiffness of the flexure and bearings can be accurately obtained, reflecting the structural support characteristics. Through power and transmission ratio analysis, transmission efficiency and motion accuracy can be quantified, providing a basis for evaluating energy transfer quality. By introducing the rainflow counting method and material stress-life curve, the fatigue life of the flexure can be predicted in the simulation domain, thus completing the life assessment without actual destructive testing. By unifying structural performance, transmission performance, and fatigue reliability in the same data chain, the three-dimensional performance of the harmonic reducer—strength, efficiency, and life—can be evaluated simultaneously, improving the accuracy of dynamic simulation.

[0058] Determine whether the set of performance metrics meets the performance metric threshold.

[0059] Among them, the performance index thresholds refer to the preset transmission efficiency threshold and the flexible wheel fatigue life threshold. When the transmission efficiency in the performance index set is greater than the transmission efficiency threshold and the flexible wheel fatigue life is greater than the flexible wheel fatigue life threshold, it is considered to be satisfied; otherwise, it is considered not satisfied.

[0060] When the performance index set does not meet the performance index threshold, tooth profile optimization is performed on the rigid-flexible component model set, and the steps of component coupling assembly and interference checking based on design parameters are returned.

[0061] Among them, tooth profile optimization refers to optimizing the tooth profile of the flexible wheel model and the rigid wheel model in the rigid-flexible component model set based on the difference between the performance index set and the performance index threshold. In this case, tooth profile optimization can be performed by adjusting the pressure angle compensation parameter or the tooth profile offset coefficient in the design parameters.

[0062] The simulation ends when the set of performance metrics meets the performance metric threshold.

[0063] Specifically, by using a tooth profile optimization strategy based on a performance index set, result-oriented simulation optimization of harmonic reducers can be achieved, improving the performance of harmonic reducer products and thus increasing simulation efficiency.

[0064] Example 2: This invention discloses a dynamic simulation system for a harmonic reducer based on rigid-flexible coupling. The system includes a component construction module, an attribute addition module, a rigid-flexible processing module, a model simulation module, a performance analysis module, and an update and optimization module, wherein: The component construction module is used to build a set of harmonic reducer component models based on preset design parameters. The set of harmonic reducer component models includes a cam model, a bearing inner sleeve model, a bearing outer sleeve model, a ball model, a cage model, a flex wheel model, and a rigid wheel model. The attribute addition module is used to import the harmonic reducer component model set into the RecurDyn platform, perform geometric repair on the harmonic reducer component model set, and add material property parameters to the geometrically repaired harmonic reducer component model set to obtain the attribute component model set. The rigid-flexible processing module is used to set rigid body kinematic pairs and contact settings on the attribute component model set to obtain a primary component model set, and to perform flexible body processing on the primary component model set to obtain a rigid-flexible component model set. The model simulation module is used to perform component coupling assembly and interference checks on the rigid-flexible component model set based on design parameters to obtain a rigid-flexible coupled harmonic reducer model. The module also performs dynamic simulation on the rigid-flexible coupled harmonic reducer model based on the RecurDyn platform to obtain simulation data. The performance analysis module is used to perform multi-dimensional performance analysis on the rigid-flexible coupling harmonic reducer model based on simulation data, and obtain a set of performance indicators, including overall material stiffness, transmission efficiency, transmission error and flex wheel fatigue life. The update and optimization module is used to optimize and update the rigid-flexible coupling harmonic reducer model based on the difference between the performance index set and the performance index threshold, and then end the simulation.

[0065] The processes described above with reference to the flowcharts in the embodiments disclosed in this invention can be implemented as computer software programs. The embodiments disclosed in this invention include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication component, and / or installed from a removable medium. When the computer program is executed by a central processing unit (CPU), it performs the functions defined in the methods of this application. It should be noted that the computer-readable medium described above in this application can be a computer-readable signal medium or a computer-readable storage medium, or any combination of the two. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wire segments, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on a computer-readable medium may be transmitted using any suitable medium, including but not limited to: wireless segments, wire segments, optical fibers, RF, etc., or any suitable combination thereof.

[0066] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0067] Those skilled in the art should understand that the embodiments of the present invention described above and shown in the accompanying drawings are merely examples and do not limit the present invention. The purpose of the present invention has been fully and effectively achieved. The functions and structural principles of the present invention have been shown and explained in the embodiments. Without departing from the stated principles, the implementation of the present invention may have any variations or modifications.

Claims

1. A dynamic simulation method for harmonic reducers based on rigid-flexible coupling, characterized in that, The method includes: A set of harmonic reducer component models is constructed based on preset design parameters. The set of harmonic reducer component models includes a cam model, a bearing inner sleeve model, a bearing outer sleeve model, a ball model, a cage model, a flex wheel model, and a rigid wheel model. The harmonic reducer component model set is imported into the RecurDyn platform, the harmonic reducer component model set is geometrically repaired, and material property parameters are added to the geometrically repaired harmonic reducer component model set to obtain the property component model set. The attribute component model set is subjected to rigid body kinematic pair setting and contact setting to obtain a primary component model set, and the primary component model set is subjected to soft body flexibility processing to obtain a rigid-flexible component model set. Based on the design parameters, the rigid-flexible component model set is coupled and assembled with components and interference is checked to obtain a rigid-flexible coupled harmonic reducer model. The rigid-flexible coupled harmonic reducer model is then subjected to dynamic simulation based on the RecurDyn platform to obtain simulation data. Based on the simulation data, a multi-dimensional performance analysis was performed on the rigid-flexible coupling harmonic reducer model to obtain a set of performance indicators, which includes overall material stiffness, transmission efficiency, transmission error, and flex wheel fatigue life. The rigid-flexible coupled harmonic reducer model is optimized and updated based on the difference between the performance index set and the performance index threshold, and the simulation ends.

2. The dynamic simulation method for a harmonic reducer based on rigid-flexible coupling according to claim 1, characterized in that, The process of setting rigid body kinematic pairs and contact settings on the attribute component model set to obtain a primary component model set includes: The cam model, ball model, cage model, and rigid wheel model in the attribute component model set are set as rigid body components, and the flexible wheel model, bearing inner sleeve model, and bearing outer sleeve model in the primary component model set are set as flexible body components. A contact kinematic pair is set between the cam model and the flexure wheel model, and the contact stiffness and contact damping coefficient between the cam model and the flexure wheel model are calculated based on the equivalent contact algorithm. Rolling contact pairs are set up for the bearing inner sleeve model, the ball model, and the bearing outer sleeve model, and the rolling contact force and rolling friction coefficient between the bearing inner sleeve model, the ball model, and the bearing outer sleeve model are calculated based on the contact penalty function. A sliding guide kinematic pair is set up for the cage model and the ball model, and the sliding friction coefficient between the cage model and the ball model is extracted; A tooth surface meshing kinematic pair is set up for the flexible wheel model and the rigid wheel model, and the meshing stiffness and meshing damping coefficient between the flexible wheel model and the rigid wheel model are calculated based on the tooth surface contact strength algorithm. Based on the contact stiffness, contact damping coefficient, rolling contact force, rolling friction coefficient, sliding friction coefficient, meshing stiffness, and meshing damping coefficient, the contact settings of the attribute component model set are performed to obtain the primary component model set.

3. The dynamic simulation method for a harmonic reducer based on rigid-flexible coupling according to claim 2, characterized in that, The calculation of the contact stiffness and contact damping coefficient between the cam model and the flexure model based on the equivalent contact algorithm includes: Obtain the cam elastic modulus and cam Poisson's ratio of the cam model, and the flexure elastic modulus and flexure Poisson's ratio of the flexure model, and calculate the equivalent elastic modulus based on the cam elastic modulus, the cam Poisson's ratio, the flexure elastic modulus, and the flexure Poisson's ratio; The cam curvature radius and the flex wheel curvature radius at the contact point between the cam model and the flex wheel model are obtained respectively, and the equivalent curvature radius is calculated based on the cam curvature radius and the flex wheel curvature radius. Obtain the flexible wheel wall thickness and the flexible wheel neutral layer radius of the flexible wheel model, and calculate the wall thickness correction coefficient based on the flexible wheel wall thickness and the flexible wheel neutral layer radius; The equivalent contact stiffness is calculated based on the equivalent elastic modulus and the equivalent radius of curvature, and the contact stiffness is calculated by multiplying the equivalent contact stiffness by the wall thickness correction factor. Obtain the equivalent contact mass of the flexible wheel model and the equivalent contact mass of the rigid wheel model, and calculate the contact damping coefficient based on the equivalent contact mass of the flexible wheel, the equivalent contact mass of the rigid wheel, and the contact stiffness.

4. The dynamic simulation method for a harmonic reducer based on rigid-flexible coupling according to claim 2, characterized in that, The calculation of the rolling contact force and rolling friction coefficient between the bearing inner sleeve model, the ball model, and the bearing outer sleeve model based on the contact penalty function includes: Obtain the normal penetration depth and penetration speed between the bearing inner sleeve model, the ball model, and the bearing outer sleeve model; Calculate the rolling contact stiffness and rolling damping coefficient between the bearing inner sleeve model, the ball model, and the bearing outer sleeve model; Based on the step penalty function, the rolling contact force between the inner bearing model, the ball model, and the outer bearing model is calculated according to the normal penetration depth, the penetration speed, the rolling contact stiffness, and the rolling damping coefficient. Obtain the material lubrication state of the bearing inner sleeve model, the ball model, and the bearing outer sleeve model, and extract the rolling friction coefficient based on the material lubrication state.

5. The dynamic simulation method for a harmonic reducer based on rigid-flexible coupling according to claim 2, characterized in that, The process of performing flexible body processing on the primary component model set to obtain a rigid-flexible component model set includes: The finite element mesh transformation is performed on each flexible body component in the primary component model set to obtain a flexible body finite element mesh group, and the component geometric data group of the flexible body finite element mesh group is extracted. Based on the graph attention mechanism, the geometric data group of the component is weighted and aggregated with neighboring nodes to obtain a geometric topology feature group; Based on the geometric topological feature set, the flexible finite element mesh set is subjected to multi-scale feature encoding and upsampling density decoding to obtain a mesh density distribution map set. Based on the mesh density distribution map group, an initial mesh model group is established for the flexible finite element mesh group, and the initial mesh model group is locally adaptively refined to obtain a smooth mesh model group; The smooth mesh model group is subjected to mesh independence verification and mesh quality verification. The smooth mesh model group that has passed the verification is used to update and replace each soft body component in the primary component model set to obtain a rigid-flexible component model set.

6. The dynamic simulation method for a harmonic reducer based on rigid-flexible coupling according to claim 1, characterized in that, The multi-dimensional performance analysis of the rigid-flexible coupled harmonic reducer model based on the simulation data yields a set of performance indicators, including: Based on Hooke's law, the stiffness of the flexure and the stiffness of the bearing are calculated from the simulation data, and the overall material stiffness is calculated based on the stiffness of the flexure and the stiffness of the bearing. The input power and output power are calculated based on the simulation data, and the ratio of the output power to the input power is used as the transmission efficiency. The actual transmission ratio and the theoretical transmission ratio are calculated based on the simulation data, and the transmission error is calculated based on the actual transmission ratio and the theoretical transmission ratio. Based on the rainflow counting method, the set of flexural stress amplitudes and the set of stress cycle counts corresponding to the set of flexural stress amplitudes are statistically derived from the simulation data. The total number of fatigue failure cycles is calculated based on the pre-acquired material stress-life curve, linear cumulative damage formula, the set of stress amplitude of the flexible wheel, and the set of stress cycle counts. The stress cycle frequency is calculated based on the simulation time and number of cycles in the simulation data, and the fatigue life of the flexure is calculated based on the total number of fatigue failure cycles and the stress cycle frequency. The overall material stiffness, transmission efficiency, transmission error, and flexspline fatigue life are compiled into a set of performance indicators.

7. The dynamic simulation method for a harmonic reducer based on rigid-flexible coupling according to claim 1, characterized in that, The process of performing component coupling assembly and interference checks on the rigid-flexible component model set based on the design parameters to obtain a rigid-flexible coupled harmonic reducer model includes: Based on the design parameters, coordinate transformation and assembly positioning are performed on each component model in the rigid-flexible component model set to obtain the assembled harmonic reducer model. Based on the kinematic pairs of the rigid-flexible component model set, the assembly harmonic reducer model is subjected to positioning constraints and clearance adjustment to obtain the primary harmonic reducer model. Static interference checks and dynamic interference checks were performed on the primary harmonic reducer model, and interference check reports were obtained. Based on the interference inspection report, the primary harmonic reducer model is constrained and optimized to obtain a rigid-flexible coupled harmonic reducer model.

8. The dynamic simulation method for a harmonic reducer based on rigid-flexible coupling according to claim 1, characterized in that, The geometric repair of the harmonic reducer component model set includes: The harmonic reducer component model is subjected to size filtering and high curvature feature identification to obtain redundant features; The model region corresponding to the redundant features in the harmonic reducer component model is optimized for redundant features and filled with curved surfaces. The surface continuity analysis and gap detection were performed on the harmonic reducer assembly after surface filling, and the gap detection results were obtained. Based on the gap detection results, the gap of the harmonic reducer assembly is repaired and the surface is smoothed.

9. The dynamic simulation method for a harmonic reducer based on rigid-flexible coupling according to claim 1, characterized in that, The harmonic reducer component model set constructed based on preset design parameters includes: A flexible wheel model is constructed based on the involute tooth profile function and preset design parameters. Based on the tooth profile envelope method, a rigid wheel model is constructed according to the flexible wheel model and the design parameters. A bearing assembly model is constructed based on the design parameters, wherein the bearing assembly model includes a bearing inner sleeve model, a bearing outer sleeve model, a ball model, and a cage model; Based on the bearing assembly model and the design parameters, a cam model is constructed, and the cam model, the inner bearing sleeve model, the outer bearing sleeve model, the ball model, the cage model, the flex wheel model, and the rigid wheel model are assembled into a harmonic reducer assembly model set.

10. A dynamic simulation system for a harmonic reducer based on rigid-flexible coupling, characterized in that, The system includes a component construction module, an attribute addition module, a rigidity / flexibility handling module, a model simulation module, a performance analysis module, and an update and optimization module, wherein: The component construction module is used to construct a harmonic reducer component model set based on preset design parameters. The harmonic reducer component model set includes a cam model, a bearing inner sleeve model, a bearing outer sleeve model, a ball model, a cage model, a flexible wheel model, and a rigid wheel model. The attribute addition module is used to import the harmonic reducer component model set into the RecurDyn platform, perform geometric repair on the harmonic reducer component model set, and add material property parameters to the geometrically repaired harmonic reducer component model set to obtain the attribute component model set. The rigid-flexible processing module is used to set rigid body kinematic pairs and contact settings on the attribute component model set to obtain a primary component model set, and to perform flexible body processing on the primary component model set to obtain a rigid-flexible component model set. The model simulation module is used to perform component coupling assembly and interference checks on the rigid-flexible component model set based on the design parameters to obtain a rigid-flexible coupled harmonic reducer model, and to perform dynamic simulation on the rigid-flexible coupled harmonic reducer model based on the RecurDyn platform to obtain simulation data. The performance analysis module is used to perform multi-dimensional performance analysis on the rigid-flexible coupling harmonic reducer model based on the simulation data to obtain a set of performance indicators, wherein the set of performance indicators includes overall material stiffness, transmission efficiency, transmission error and flex wheel fatigue life. The update and optimization module is used to optimize and update the rigid-flexible coupling harmonic reducer model based on the difference between the performance index set and the performance index threshold, and then end the simulation.

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