Harmonic reducer flexible gear multi-axial fatigue life prediction method

Abstract

The invention relates to the technical field of data processing, in particular to a harmonic reducer flexible gear multi-axial fatigue life prediction method. The method comprises the steps that firstly, discrete processing is conducted on a flexible gear structure of the harmonic reducer, and a splitting unit grid containing state parameters is obtained; based on the state parameters contained in the splitting unit grid, calculating a unit splitting trend function, and constructing an overall energy field evolution function; then, based on the overall energy field evolution function and a structural failure threshold, determining a preliminary predicted life, and correcting the geometric disturbance coefficient to obtain a corrected geometric disturbance coefficient and a corrected overall energy field evolution function; and finally, based on the corrected overall energy field evolution function and the preliminary predicted life, obtaining the final predicted life of the harmonic reducer flexible gear. The technical problems that fatigue life evaluation is not accurate, a crack propagation path is not clear, wear-induced geometric disturbance cannot be fed back dynamically, and coupling expression of local cracking evolution and overall structure failure lacks are solved.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method for predicting the fatigue life of a multi-axis flexure in a harmonic reducer. Background Technology

[0002] Harmonic reducers, as core components of precision transmission systems, are widely used in fields such as industrial robots, aerospace, and medical equipment where positioning accuracy and transmission rigidity are extremely critical. Among these, the flexspline, as a key flexible transmission component, experiences extremely complex stress states. It typically operates under long-term conditions of high-frequency repetitive meshing, cyclic loading, and multi-axis linkage, making it highly susceptible to structural fatigue failure caused by factors such as microcrack initiation, fatigue propagation, and wear instability. Currently, fatigue life assessment of flexsplines mainly relies on static calculations using SN curves, stress-life empirical regression models, or the Miner linear damage accumulation method. These methods are essentially based on idealized operating conditions and uniaxial stress loading, making it difficult to effectively reflect real service mechanisms such as multiaxial alternating stress, nonlinear meshing, and material micro-damage evolution. Especially in the presence of localized meshing stress concentration and surface wear-induced geometric disturbances, traditional models often fail to capture key precursors to life abrupt changes. With the development of intelligent manufacturing, digital twins, and high-reliability prediction technologies, higher requirements are placed on flexspline life prediction. These methods not only need to possess highly interpretable, adaptable, and accurate modeling mechanisms, but also support the dynamic capture of the evolution of local damage mechanisms and real-time assessment of system-level life. However, existing methods generally neglect the nonlinear coupling relationship between local crack propagation behavior and overall fatigue failure in flexspline structures, failing to provide clear spatial distribution paths or temporal evolution trends. This results in problems such as large fluctuations in accuracy, slow response, and weak adjustment capabilities in life prediction. Summary of the Invention

[0003] This invention provides a method for predicting the multi-axis fatigue life of a harmonic reducer flexure, in order to solve the technical problems of inaccurate fatigue life assessment, unclear crack propagation path, inability to dynamically feed back wear-induced geometric disturbances, and lack of coupled expression between local fracture evolution and overall structural failure under actual multi-axis stress conditions.

[0004] The present invention provides a method for predicting the fatigue life of a multi-shaft flexspline in a harmonic reducer, comprising the following steps: S1. Discretize the flexible wheel structure of the harmonic reducer to obtain a fragmented element mesh containing state parameters; calculate the element fragmentation trend function based on the state parameters contained in the fragmented element mesh; construct the overall energy field evolution function based on the element fragmentation trend function. S2. Compare the overall energy field evolution function with the structural failure threshold to determine the preliminary predicted lifetime; based on the geometric perturbation coefficient in the state parameters contained in the fractured element mesh, obtain the corrected geometric perturbation coefficient and the corrected overall energy field evolution function; based on the corrected overall energy field evolution function and the preliminary predicted lifetime, obtain the final predicted lifetime of the harmonic reducer flexure.

[0005] Preferably, S1 specifically includes: Based on the state parameters contained in the fractured cell mesh, a nonlinear superposition mechanism of multivariable coupled fields is introduced to obtain the cell fracture trend function.

[0006] Preferably, S1 specifically includes: Based on the unit fragmentation trend function, a spatial scale correction function is introduced to construct the overall energy field evolution function.

[0007] Preferably, S2 specifically includes: When the overall energy field evolution function reaches or exceeds the structural failure threshold, fatigue failure is determined to have occurred; based on the overall energy field evolution function, the preliminary predicted lifetime is calculated.

[0008] Preferably, S2 specifically includes: Based on the geometric disturbance coefficient in the state parameters contained in the fractured element mesh, a wear disturbance feedback mechanism is introduced to correct the geometric disturbance coefficient.

[0009] Preferably, S2 specifically includes: In the wear disturbance feedback mechanism, the corrected geometric disturbance coefficient is obtained by combining the local curvature change rate of wear depth and the stress angle change rate.

[0010] Preferably, S2 specifically includes: Substituting the corrected geometric perturbation coefficients into the overall energy field evolution function yields the corrected overall energy field evolution function.

[0011] Preferably, S2 specifically includes: By introducing an overall crack propagation suppression coefficient, the time integral of the modified overall energy field evolution function is multiplied by the average value of the overall crack propagation suppression coefficient to calculate the final predicted life of the flexure of the harmonic reducer.

[0012] The beneficial effects of the technical solution of the present invention are: 1. By employing a Voronoi cell partitioning algorithm guided by energy density mutation rate and geometric curvature change rate, combined with a gradient-based watershed algorithm, fracturing hotspot regions are delineated and fracturing cell meshes are constructed. This allows for the dynamic capture of the aggregation and evolution of fracturing hotspots in flexible structures, establishing a bridge between local spatial response and global failure. The fracturing cell mesh is no longer a traditional uniform partition or equidistant structure, but rather its partitioning boundary is determined by the failure mechanism itself, offering advantages such as clear physical meaning, high prediction efficiency, and strong response sensitivity.

[0013] 2. By constructing an element fragmentation trend function, which integrates multi-source state variables such as local energy density, the angle between the principal stress direction and the mesh geometric reference axis, wear disturbance, and periodic excitation response, a highly nonlinear and high-dimensional coupled quantitative expression method for energy density instability is established. The element fragmentation trend function can not only simulate the failure trend of static stress concentration, but also maintain continuous modeling capability for the structural fragmentation process under dynamic loads and wear-induced deformation environments, greatly enhancing the early warning capability for the early stages of fatigue evolution.

[0014] 3. By weighting the fragmentation trend functions of all units and introducing a spatial scale correction function, a global energy field evolution function is constructed, achieving nonlinear integrated modeling from the local behavior of microstructures to the global system response. In particular, the global energy field evolution function not only reflects when the flexible wheel structure is most dangerous, but also dynamically reveals "which areas are concentrated in danger," possessing strong structural health assessment and maintenance guidance capabilities, and having practical value for engineering diagnosis.

[0015] 4. By designing a complete decision path from local fracturing trend to system energy state, and then to structural failure time, a "evolution-judgment-termination" time logic is formed, and the cumulative energy effect is further obtained through integration. Combined with a weighted averaging mechanism of microcrack proliferation gain factors, the final predicted lifetime is output. This method derives the lifetime criterion solely through the evolution of the flexible wheel structure's state, possessing high interpretability, high transparency, and reversible verifiability, making it more reliable in engineering compared to traditional black-box prediction models. Attached Figure Description

[0016] Figure 1 This is a flowchart of a multi-axis fatigue life prediction method for a harmonic reducer flexspline according to the present invention. Detailed Implementation

[0017] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0019] The following description, in conjunction with the accompanying drawings, details a specific scheme for predicting the fatigue life of a multi-axis flexure in a harmonic reducer, as provided by this invention.

[0020] See attached document Figure 1 The diagram illustrates a flowchart of a multi-axis fatigue life prediction method for a harmonic reducer flexspline provided by an embodiment of the present invention. The method includes the following steps: S1. Discretize the flexible wheel structure of the harmonic reducer to obtain a fragmented element mesh containing state parameters; calculate the element fragmentation trend function based on the state parameters contained in the fragmented element mesh; construct the overall energy field evolution function based on the element fragmentation trend function.

[0021] The flexible gear structure of the harmonic reducer, such as the fixed end flange (connecting to the input end), the middle thin-walled cylinder (the area where elastic deformation occurs), and the external gear ring area (meshing with the rigid wheel), is discretized. Specifically, firstly, based on 3D laser scanning or high-precision industrial CT imaging technology, the actual geometric model of the flexible gear tooth surface and overall structure is obtained. Then, based on the obtained actual geometric model, a 3D finite element model is established using ANSYS or Abaqus platforms, and multi-field coupled boundary conditions, including torsional torque, radial interference force, and meshing contact force, are introduced into the 3D finite element model. The stress-energy distribution spectrum of the flexible gear structure is obtained through thermo-mechanical-contact multiphysics simulation calculations. Further, using the maximum principal stress field, contact pressure field, and local strain concentration areas extracted from the stress-energy distribution spectrum through thermo-mechanical-contact coupled simulations performed in ANSYS or Abaqus platforms, combined with the material stress gradient direction obtained based on the stress field, the flexible gear structure is divided into multiple fracture hotspot regions by calling the gradient segmentation-based watershed algorithm in scikit-image using Python. Finally, in the fracture hotspot regions, according to the joint criteria of energy density mutation rate and geometric curvature change rate, the Voronoi cell partitioning algorithm is executed in the MATLAB environment to generate irregular element meshes, i.e., fracture element meshes, for each fracture hotspot region. The energy density mutation rate represents the rate of change of energy density, expressed using the Laplacian operator. The geometric curvature change rate measures the rapid change in the local geometric curvature of a flexible surface or structural boundary in space with respect to its position. It is a key quantity representing surface morphology perturbations and is used to identify geometrically unstable regions on a material surface caused by wear, processing errors, or fatigue deformation. The energy density mutation rate and geometric curvature change rate, as a joint standard, represent the mechanical instability and geometric perturbation in the structure, respectively. The fractured element mesh carries multiple state parameters, including local energy density, geometric perturbation coefficient, the angle between the principal stress direction and the mesh geometric reference axis, fracture frequency modulation parameters, and microcrack multiplication gain factor, which continuously change during subsequent processing and are fed back into the evolution path.

[0022] It is the local energy density, representing the total strain energy density carried by the i-th fractured element mesh at time t, specifically: ; in, It is the first The volume of each fractured element mesh is obtained directly from the three-dimensional finite element model; Indicates the time of the i-th fractured cell mesh. The next Line number The stress tensor components of the column; Indicates the first A fragmented cell grid at time [time] The strain tensor components in the i-th row and j-th column below; the strain tensor components and stress tensor components are obtained based on the stress tensor and strain tensor extracted from the finite element simulation platform (such as ANSYS or Abaqus); It is the strain energy density term, used to represent the energy accumulation due to elastic deformation; It is the thermal excitation energy conversion coefficient, obtained by consulting existing material calibration data based on literature. It is the first The temperature of each fractured cell grid at time t was determined by infrared thermography experiments.

[0023] Geometric perturbation coefficient , indicating the first A fragmented cell grid at time [time] The geometric perturbation coefficient is used to measure the geometric perturbation coefficient of the first... A fragmented cell grid at time [time] The degree of geometric profile instability caused by localized wear, i.e., the tendency for stress concentration resulting from abrupt curvature changes caused by localized wear on the tooth surface. The formula for calculating the geometric disturbance coefficient is as follows: ; in, It is the spatial discrete spacing in the sliding direction, used to characterize the discrete precision of contour sampling, and determines the granularity of the numerical derivative calculation. It is determined by the spatial resolution of the wear point cloud, such as the sampling density of the Keyence scanner, such as 0.1. It is the first The profile height function of each fractured unit grid along the sliding direction is obtained by constructing the wear point cloud in MATLAB using spline fitting based on the three-dimensional scanning of wheel teeth (such as Keyence microscopic white light profilometer). It is the contour curvature, used to reflect the degree of local "depression or convexity".

[0024] The angle between the principal stress direction and the mesh geometric reference axis It is the first A fragmented cell grid at time [time] The angle between the principal stress direction and the mesh geometric reference axis, i.e. the angle between the maximum principal stress direction and the flexural axis, is used to capture the directional evolution trend of stress. The principal stress direction is exported by User Field Output (UVARM) or Python extraction tools, and then calculated by the three-dimensional vector angle formula.

[0025] Plier frequency modulation parameters It is the first The fragmentation frequency modulation parameters of the fragmentation cell grid at time t are used to control the fragmentation frequency modulation parameters of the first fragmentation cell grid. The unsteady-state frequency of crack periodic growth in a fractured cell grid is obtained by recording the stress repetition number of the fractured cell grid through physical experiments, extracting the effective cycles using the existing rainflow counting method, and then dividing by the total time.

[0026] Microfibrillation gain factor It is the first The microcrack proliferation gain factor of the i-th fractured cell grid at time t is used to reflect the spatial diffusion capability of cracks in the i-th fractured cell grid. The number of cracks is extracted by scanning electron microscopy (SEM) or X-ray computed tomography (XCT), and then fitted using weighted spline regression. The derivative term, i.e., the crack growth rate, is obtained by numerical difference of the fitted curve, and then divided by the area of ​​the i-th fractured cell grid to obtain the microcrack proliferation gain factor of the i-th fractured cell grid. The area of ​​the i-th fractured cell grid is the projected cross-sectional area of ​​the i-th fractured cell grid.

[0027] Based on the state parameters contained in the fractured cell grid, a cell fracture trend function is defined for each fractured cell grid, which serves as the function for each fractured cell grid at time step [time value missing]. The failure trend index is obtained by constructing a cell fragmentation trend function to quantitatively express the energy density instability of each fragmented cell grid caused by stress evolution, wear disturbance, and periodic loading. Based on the nonlinear superposition mechanism of multivariable coupled fields, the cell fragmentation trend function is as follows: ; in, It is the unit fragmentation trend function, representing the first... A fragmented cell grid at time [time] The local cleavage activity, i.e., the first A fragmented cell grid at time [time] The failure trend indicator is used to determine the failure trend of the first The energy density instability of each fractured cell grid caused by stress evolution, wear disturbance, and periodic loading is quantitatively expressed. This is the energy gradient sensitivity coefficient, used to adjust the exponential response strength of energy field changes to the fracturing trend. It is determined based on the J-integral method widely used in fracture mechanics, with a reference value range of [value missing]. ; This is the stress direction amplification factor, used to control the amplification or suppression effect of the deviation of the principal stress direction on the fracture trend. It is determined based on a Bayesian optimization method using data-driven fitting regression, with a reference value range of [value missing]. ; It is the first A fragmented cell grid at time [time] The angle between the principal stress direction and the grid geometric reference axis, i.e. the angle between the maximum principal stress direction and the flexural axis, is used to capture the directional evolution trend of stress. Indicates the first A fragmented cell grid at time [time] The energy density Laplace operator is a local energy density. The spatial second derivative is used to represent how energy is transferred to the surroundings in the fractured cell grid; It is the first A fragmented cell grid at time [time] Local energy density; It is the first A fragmented cell grid at time [time] The geometric perturbation coefficient; It is the first A fragmented cell grid at time [time] The microfission proliferation gain factor is used to reflect the first Spatial propagation capability of cracks in a fractured cell grid; It is the first A fragmented cell grid at time [time] The cracking frequency modulation parameter is used to control the unsteady frequency of crack periodic growth in the i-th cracking unit grid. It is a periodic response amplification factor used to enhance local lysis activity. The nonlinear fluctuations in the response to external periodic excitation were determined using existing dynamic fatigue testing methods, with a reference range of values. ; It is a principal stress direction correction term, used to represent the effect on the fracture trend when the principal stress direction is inconsistent with the principal axis of the material; It is an exponential amplification term of local energy density change, used to simulate the effect of energy concentration on the accelerated initiation of cracks, and to simulate the effect of energy transfer and focusing behavior in the microscale space inside the flexible wheel structure on the fatigue evolution path. This indicates the damping effect caused by the skewness of the principal stress direction, and is used to adjust the actual effect of exponential growth under different loading directions. It is a coupled modulation term of morphological perturbation-microcrack propagation, used to simulate the dynamic competition between surface wear perturbation and microcrack propagation; It is a periodic excitation response modulation factor used to simulate the fatigue response fluctuation of a flexible wheel under periodic loading (such as harmonic generator excitation).

[0028] The cell fragmentation trend function models the dynamic and complex behavior of spatial fragmentation through the interdependence and nonlinear coupling of variables, establishing the basic dynamic unit for fragmentation propagation, namely the failure trend index of the fragmentation cell mesh. This makes it possible to subsequently construct the overall energy field evolution.

[0029] Based on the A fragmented cell grid at time [time] Failure trend index A global energy field evolution function is constructed. This function aggregates local fragmentation behaviors and maps them to the whole, describing the trend of fatigue evolution on a macroscopic scale. The global energy field evolution function is: ; in, It is the overall energy field evolution function, used to describe the evolution of the energy field at time t. Below, the total energy splitting activity in the multi-scale splitting coupling unit inside the flexure of the entire harmonic reducer, that is, the total energy splitting activity in the basic dynamic unit of splitting propagation; It is the total number of fragmented cell grids. ; It is the first The importance weighting factor of each fractured element mesh is used to reflect its influence on the overall failure of the flexible wheel structure, including its normalized importance in stress hotspot areas, wear integration areas, and crack initiation prone areas. It is determined through three-dimensional surface profile testing using equipment such as Zeiss, Bruker, and Keyence, with a reference value range of [missing value]. ,and ; It is the first The distance from the center point of each fractured element mesh to the rotation center of the flexible wheel is calculated based on the three-dimensional coordinates in the three-dimensional finite element model. The radius of the flex wheel's mean diameter circle is the radial distance between the neutral circle of the flex wheel's outer teeth and the flex wheel's rotation center when it is not subjected to load deformation. It is obtained by performing point cloud scanning on the flex wheel's gear ring using a three-dimensional contour scanning device, such as Zeiss, Keyence, or Bruker. This is a spatial scale correction function used to limit the contribution of boundary fractured cell grids and enhance the dominant role of the central fractured cell grid in the overall failure trend.

[0030] S2. Compare the overall energy field evolution function with the structural failure threshold to determine the preliminary predicted lifetime; based on the geometric perturbation coefficient in the state parameters contained in the fractured element mesh, obtain the corrected geometric perturbation coefficient and the corrected overall energy field evolution function; based on the corrected overall energy field evolution function and the preliminary predicted lifetime, obtain the final predicted lifetime of the harmonic reducer flexure.

[0031] The evolution function of the overall energy field This serves as a macroscopic state representation describing the total energy dissipation activity of the flexure in a harmonic reducer at a certain point in time, and is correlated with the introduced structural failure threshold. By comparing the results, once the structural failure threshold is reached or exceeded, fatigue failure is determined, and a preliminary predicted lifespan is obtained. : ; in, This is a preliminary prediction of the fatigue limit life of the flexible gear; It is the structural failure threshold, which can be calibrated based on the wear fracture point in the experimental fatigue test curve determined by controlled fatigue loading experiments on the flexure of the harmonic reducer or its equivalent specimen.

[0032] Specifically, to maintain time-varying accuracy, the continuous disturbance changes of the flexspline structure geometry caused by actual wear throughout the fatigue process are reversed and applied to the energy evolution path; a wear disturbance feedback mechanism is introduced to dynamically correct the geometric disturbance coefficient. To match the real-time state, the formula for correcting the geometric perturbation coefficient is as follows: ; in, It is the first Geometric perturbation coefficients after correction of each fractured cell grid; This is the first disturbance adjustment coefficient, used to control the contribution of the "local curvature change rate of wear depth" to the correction of the geometric disturbance coefficient, that is, the weight of the flexspline structure morphology change in the geometric disturbance coefficient. It is determined by back-calculation using fatigue testing and wear point cloud comparison method, and the reference value range is [value missing]. ; This is the second disturbance adjustment coefficient, used to control the influence of the "stress angle change rate" on the geometric disturbance coefficient. It is the modulation factor of the load path disturbance of the flexible wheel structure on the local instability evolution. It is determined by back-calculation using fatigue test and wear point cloud comparison method, and the reference value range is [missing value]. ; It is the first Each fragmented cell grid at the current time step The change in wear depth within the tooth surface, i.e. the normal thickness lost by the tooth surface material due to friction and wear, is derived from the friction pair contact model under mixed lubrication conditions, such as the improved Archard model. It is the second derivative term in space, representing the... The location of each fractured cell grid is along the main sliding direction. The local curvature change rate of the wear depth of the shaft is used to characterize the degree of curvature change caused by uneven wear of the tooth surface material. It is a marker of wear-induced geometric instability and is obtained by numerical difference calculation in the spatial domain using the existing wear distribution function. It is the rate of change of stress angle, representing the angle between the principal stress direction and the geometric reference axis of the mesh. The rate of change over time is used to reflect the dynamic rotational behavior of a local material under load.

[0033] The formula for correcting the geometric perturbation coefficient reflects the direct regulation of the fracture energy field by wear and stress path evolution, realizing a causal closed-loop feedback between wear and fatigue.

[0034] The corrected geometric perturbation coefficients are then substituted into the overall energy field evolution function. In this process, the corrected overall energy field evolution function is obtained. Finally, by integrating the corrected global energy field evolution function at the current time step, the overall energy evolution curve is obtained. Combined with the overall crack average adjustment term, the final prediction expression for fatigue life is formed: ; in, It is the final predicted life of the flexure of the harmonic reducer, that is, the comprehensive life estimate of the flexure of the harmonic reducer under the current operating environment. It is the modified global energy field evolution function The integral over time is used to describe the cumulative time of fragmentation activity; Indicates the overall crack propagation suppression coefficient; It is the overall crack averaging adjustment term, used to integrate the modified overall energy field evolution function over time. Perform corrections.

[0035] In the final predicted life calculation formula, the integral of the modified overall energy field evolution function over time is multiplied by the average value of the overall crack propagation suppression coefficient to form the comprehensive life estimate of the flexible wheel under the current operating environment.

[0036] In summary, a method for predicting the fatigue life of the multi-shaft flexure in a harmonic reducer has been developed.

[0037] The order of the embodiments is for illustrative purposes only and does not represent the superiority or inferiority of the embodiments. The processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0038] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0039] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for predicting the fatigue life of a multi-shaft flexspline in a harmonic reducer, characterized in that, Includes the following steps: S1. Discretize the flexural structure of the harmonic reducer to obtain a fragmented element mesh containing state parameters; Calculate the cell fragmentation trend function based on the state parameters contained in the fragmented cell mesh; Based on the unit fragmentation trend function, an overall energy field evolution function is constructed; S2. Compare the overall energy field evolution function with the structural failure threshold to determine the preliminary predicted lifetime; based on the geometric perturbation coefficient in the state parameters contained in the fractured element mesh, obtain the corrected geometric perturbation coefficient and the corrected overall energy field evolution function; based on the corrected overall energy field evolution function and the preliminary predicted lifetime, obtain the final predicted lifetime of the harmonic reducer flexure.

2. The method for predicting the fatigue life of a multi-shaft flexspline in a harmonic reducer according to claim 1, characterized in that, S1 specifically includes: Based on the state parameters contained in the fractured cell mesh, a nonlinear superposition mechanism of multivariable coupled fields is introduced to obtain the cell fracture trend function.

3. The method for predicting the fatigue life of a multi-shaft flexspline in a harmonic reducer according to claim 2, characterized in that, S1 specifically includes: Based on the unit fragmentation trend function, a spatial scale correction function is introduced to construct the overall energy field evolution function.

4. The method for predicting the fatigue life of a multi-shaft flexspline in a harmonic reducer according to claim 1, characterized in that, S2 specifically includes: When the overall energy field evolution function reaches or exceeds the structural failure threshold, fatigue failure is determined to have occurred; based on the overall energy field evolution function, the preliminary predicted lifetime is calculated.

5. The method for predicting the fatigue life of a multi-shaft flexspline in a harmonic reducer according to claim 1, characterized in that, S2 specifically includes: Based on the geometric disturbance coefficient in the state parameters contained in the fractured element mesh, a wear disturbance feedback mechanism is introduced to correct the geometric disturbance coefficient.

6. The method for predicting the fatigue life of a multi-shaft flexspline in a harmonic reducer according to claim 5, characterized in that, S2 specifically includes: In the wear disturbance feedback mechanism, the corrected geometric disturbance coefficient is obtained by combining the local curvature change rate of wear depth and the stress angle change rate.

7. The method for predicting the fatigue life of a multi-shaft flexspline in a harmonic reducer according to claim 6, characterized in that, S2 specifically includes: Substituting the corrected geometric perturbation coefficients into the overall energy field evolution function yields the corrected overall energy field evolution function.

8. The method for predicting the fatigue life of a multi-shaft flexspline in a harmonic reducer according to claim 7, characterized in that, S2 specifically includes: By introducing an overall crack propagation suppression coefficient, the time integral of the modified overall energy field evolution function is multiplied by the average value of the overall crack propagation suppression coefficient to calculate the final predicted life of the flexure of the harmonic reducer.

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