Spline pair wear life prediction analysis method based on Archard model

Abstract

The invention relates to the technical field of spline pair wear life prediction, in particular to a spline pair wear life prediction analysis method based on an Archard model.The spline pair wear life prediction analysis method comprises the steps that key parameters of a spline pair are obtained, then a standard parameter equation of an involute tooth profile is established, and an ideal geometric model of internal and external splines is constructed; manufacturing and assembling errors are introduced to form a three-dimensional geometric model, material parameters and boundary loading conditions are set, a nonlinear contact solving strategy is adopted, contact pressure distribution and relative slippage of a spline pair contact interface under the current calculation step length are obtained, then according to a wear model, a wear depth increment is calculated, and node coordinates are updated; and after each round of iteration, whether the accumulated wear depth reaches a preset limit or not is judged, if the accumulated wear depth does not reach the preset limit, circulation is continued, and if the accumulated wear depth reaches the preset limit, a service life prediction result is output, so that the precision and adaptability of spline pair service life evaluation can be improved.

Description

Technical Field

[0001] This invention relates to the field of spline wear life prediction technology, specifically a spline wear life prediction and analysis method based on the Archard model. Background Technology

[0002] Involute spline pairs, as typical key transmission components, are widely used in high-end equipment such as aero engines and automobiles. They operate under high speed, heavy load and complex load coupling for a long time. Driven by cyclic torque, the tooth surface is prone to relative slippage, which leads to wear, aggravates the expansion of meshing clearance, load distribution imbalance and tooth root stress concentration, and ultimately leads to fatigue crack propagation or even tooth root fracture, seriously threatening the safety and reliability of system operation.

[0003] Existing wear prediction methods are mostly based on the Archard model and often use the contact parameters of several key points on the tooth surface as representatives for simplified calculations. This makes it difficult to effectively reflect the spatial non-uniformity of tooth surface wear in the tooth profile and tooth length directions. In fact, within a complete meshing cycle, the contact pressure, relative sliding speed and radius of curvature at different positions on the spline tooth surface are dynamically changing, resulting in a significant non-uniform distribution of wear along the tooth surface. Local analysis limited to the "most dangerous point" not only fails to capture the overall evolution trend of the tooth profile, but also fails to describe the evolution mechanism of the coupling between tooth surface wear and contact state.

[0004] As the tooth profile geometry evolves with wear, the contact pressure distribution will also shift or reconstruct, thereby inducing new stress concentration areas. This process has obvious dynamic feedback characteristics. A single static "point" analysis is difficult to meet the requirements for accurately predicting the actual service life of spline pairs. Especially under the simplified assumption of ignoring the uneven actual load and multi-condition coupling factors, traditional prediction results often deviate significantly from the actual wear morphology and failure mode, which restricts the accuracy and engineering applicability of spline pair wear life assessment.

[0005] To address the aforementioned shortcomings, a technical solution is provided. Summary of the Invention

[0006] To address the aforementioned shortcomings of existing technologies, this invention provides a spline wear life prediction and analysis method based on the Archard model. This method effectively solves the problem in existing technologies that rely on simplified calculations based on single or representative points, making it difficult to accurately capture the tooth profile evolution and stress redistribution caused by spline wear.

[0007] To achieve the above objectives, the present invention can be implemented through the following technical solutions:

[0008] This invention provides a method for predicting and analyzing the wear life of spline pairs based on the Archard model, comprising the following steps:

[0009] S101: Obtain the key parameters of the spline pair, including geometric parameters, material parameters, operating condition parameters, and wear parameters;

[0010] S102: By establishing the standard parametric equation of the involute tooth profile, the internal and external splines are modeled to construct an ideal geometric model. Based on the ideal geometric model, manufacturing errors and assembly errors are introduced to construct a three-dimensional geometric model of the spline pair.

[0011] S103: Import the three-dimensional geometric model of the spline pair into the finite element simulation platform and perform the iterative stage of fretting wear analysis;

[0012] S104: Based on the finite element simulation platform, the contact mechanics analysis of the spline pair is carried out. Material parameters and boundary loading conditions are set, and a nonlinear contact solution strategy is adopted to obtain the contact pressure distribution and relative slip at the spline pair contact interface under the current calculation step.

[0013] S105: Calculate the wear depth increment of each node on the tooth surface within the current calculation step, according to the wear law;

[0014] S106: Based on the wear depth increment within the current time step, update the coordinates of the tooth surface nodes and generate the updated set of node coordinates;

[0015] S107: After completing the tooth surface geometry update, compare the current cumulative wear depth with the set wear tolerance limit to determine whether to terminate the analysis. If the cumulative wear depth has not reached the preset wear tolerance limit, return to step S103 to perform the next calculation step analysis. If the cumulative wear depth has reached the preset wear tolerance limit, terminate the iteration and output the life prediction result of the spline pair.

[0016] Furthermore, the specific process of constructing the ideal geometric model is as follows:

[0017] Define the coordinates of a point C on the base circle as (X... c Y c ):

[0018] X c =R b ·cos(β)

[0019] Y c =R b ·sin(β)

[0020] The length S of the tangent line extending from point C R The relationship with roll angle is:

[0021] S R =R b ·β

[0022] Among them, R b β represents the base circle radius, and β represents the roll angle.

[0023] The coordinates (X, Y) of point P on the involute corresponding to the roll angle β are obtained by translating point C by a distance S along the tangential direction. R Since the tangent direction is perpendicular to the radius direction, it can be expressed as:

[0024] X(β)=X c +S R sin(β)=R b ·cos(β)+(R b ·β)·sin(β)

[0025] Y(β)=Y c -S R ·cos(β)=R b ·sin(β)-(R b ·β)·cos(β)

[0026] After simplification, the standard parametric equations for the involute tooth profile are obtained:

[0027] X(β)=R b (cos(β)+βsin(β))

[0028] Y(β)=R b (sin(β)-βcos(β))

[0029] Among them, the involute tooth profile is the trajectory of any point on a straight line when a straight line rolls purely on the base circle;

[0030] In addition, to fully describe the tooth profile, it is necessary to combine the root transition curve and the tip circle with the involute tooth profile to form an ideal geometric model of the spline pair.

[0031] Furthermore, the specific process of constructing the three-dimensional geometric model of the spline pair is as follows:

[0032] Based on the ideal geometric model, manufacturing errors and assembly errors are further introduced, specifically:

[0033] Due to machining deviations during manufacturing, the actual width of each tooth groove will be inconsistent and the actual tooth thickness of each tooth will vary. Therefore, the actual range of values ​​for the tooth groove width E in a spline pair can be expressed as:

[0034] E∈[E min E max ]

[0035] The actual range of values ​​for spline tooth thickness can be expressed as follows:

[0036] S∈[Smin S max ]

[0037] Among them, E min E max S min S max These represent the set minimum actual tooth space width, maximum actual tooth space width, minimum actual tooth thickness, and maximum actual tooth thickness, respectively.

[0038] Manufacturing error is determined by the actual range of values ​​for tooth groove width and spline tooth thickness.

[0039] By translating the central axis of the internal or external spline as a whole radially by a predetermined distance L;

[0040] By rotating the axis of one spline relative to the other by a predetermined angle J;

[0041] Assembly error is determined by preset distance and preset included angle;

[0042] Manufacturing errors and assembly errors are superimposed on the standard tooth profile parameter model through mathematical perturbation, thereby constructing a three-dimensional geometric model of the spline pair.

[0043] Furthermore, the specific process of conducting contact mechanics analysis on the spline pair is as follows:

[0044] At the start of the i-th calculation step, a finite element model of a spline pair with multi-tooth contact characteristics is established based on the current three-dimensional geometric state of the spline pair. The model is constructed based on the actual structural dimensions and takes into account the actual tooth profile after the introduction of manufacturing and assembly errors.

[0045] Specify material properties for internal and external splines, including elastic modulus and Poisson's ratio;

[0046] Finite element meshing was performed on the entire three-dimensional geometric model of the spline pair. In the tooth surface contact area and the stress concentration area at the tooth root, a fine mesh was used, while in the area far from the contact interface, a relatively coarse mesh was used.

[0047] Set boundary and load conditions according to actual operating conditions, fix one end of the internal spline shaft and apply a preset torque T to the external spline. This torque is applied by applying coupling constraints and equivalent rotational torque at the shaft end node.

[0048] Furthermore, the specific process of employing the nonlinear contact solution strategy is as follows:

[0049] A contact pair relationship is defined between the inner and outer spline tooth surfaces. The contact area is set using a surface-to-surface contact unit, with one side being the contact surface and the other side being the target surface, in order to establish an effective contact pair.

[0050] The penalty function method is adopted as the contact algorithm. This method restricts the mutual penetration of the contact surfaces by introducing contact stiffness, and combines the Coulomb friction model to model the tangential sliding friction force on the tooth surface.

[0051] Among them, the contact equations adopt an incremental-iterative solution strategy, which divides the total target load into several sub-steps and applies the load step by step to improve numerical convergence and computational stability. In each sub-step, the normal contact pressure p(x, y, t) and tangential slip distance δ(x, y, t) of each node in the tooth surface contact area are solved.

[0052] By integrating the normal contact pressure p(x, y, t) and tangential slip distance δ(x, y, t) of each node in the tooth surface contact area under the current loading state, the contact pressure distribution and relative slip amount of the spline tooth surface contact interface under this calculation step size can be obtained.

[0053] Furthermore, the formula for calculating the wear depth increment of each node on the tooth surface within the current calculation step is: Δh(x,y,t)=K·p(x,y,t)·δ(x,y,t)·Δt, where K represents the set wear coefficient, Δt represents the current calculation step, and Δh(x,y,t) represents the wear depth increment.

[0054] Furthermore, the specific process of updating the coordinates of the tooth surface nodes is as follows:

[0055] The normal coordinate values ​​of each node on the tooth surface are reduced by the corresponding wear depth increment along its normal direction to generate an updated set of node coordinates.

[0056] Furthermore, the wear tolerance limit can be set based on any of the following criteria: preset total number of working cycles;

[0057] The cumulative wear depth at any node on the tooth surface reaches the allowable value of the material.

[0058] The reduction in spline tooth thickness exceeds structural safety standards;

[0059] The backlash caused by tooth surface wear exceeds the functional requirements.

[0060] The technical solution provided by this invention has the following advantages compared with the known prior art:

[0061] 1. Significantly improved prediction accuracy: This invention abandons the traditional single-point analysis method and accurately captures the non-uniform distribution characteristics of wear by discretizing the entire contact tooth surface. Its prediction results are highly consistent with the actual wear morphology, which significantly improves the accuracy of life prediction.

[0062] 2. Closer to actual working conditions: By introducing manufacturing and assembly errors in the model initialization stage, this invention can truly reflect the phenomenon of inter-tooth load concentration caused by errors, accurately predict early local wear driven by load concentration, and make the analysis results more meaningful in engineering practice.

[0063] 3. Achieved dynamic coupling analysis: This invention successfully simulated the dynamic coupling process of "non-uniform wear → tooth profile change → load redistribution" through the iterative cycle of "load calculation - wear calculation - geometric update", which profoundly revealed the intrinsic evolution mechanism of spline wear;

[0064] 4. Provides comprehensive design and maintenance basis: This invention can not only predict a single life value, but also output the wear depth cloud map, tooth profile evolution process and load distribution change history of the whole cycle. This detailed data can provide a strong digital basis for the optimized design of splines, the setting of wear thresholds and the formulation of condition-based maintenance strategies. Attached Figure Description

[0065] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0066] Figure 1 This is a flowchart of the overall calculation method for predicting spline wear according to the present invention.

[0067] Figure 2 This is a schematic diagram showing the geometric parameters of the involute spline pair.

[0068] Figure 3 This is a schematic diagram of a three-dimensional finite element model of the involute spline connection pair of the present invention.

[0069] Figure 4 It is a non-uniform contact pressure cloud map distributed along the spline tooth surface, obtained by finite element analysis.

[0070] Figure 5 It is a three-dimensional graph showing the tooth surface wear depth of the tooth with the maximum wear at the center of the involute spline pair shaft under the condition of wear reaching the limit, and the axial meshing wear depth of different numbers of teeth.

[0071] Figure 6 This is a three-dimensional graph showing the tooth surface wear depth and axial meshing wear depth of the involute spline pair with the greatest wear under the condition of axial misalignment (6µm) when the wear reaches the limit.

[0072] Figure 7This is a three-dimensional graph showing the wear depth of the tooth surface and the axial meshing wear depth of different numbers of teeth under the condition that the wear limit is reached and the involute spline secondary angle is misaligned (0.01°).

[0073] Figure 8 It is a three-dimensional graph showing the tooth surface wear depth of the tooth with the maximum wear under the condition of wear limit for involute spline pair compound misalignment (0.01°-4um) and the axial meshing wear depth of different numbers of teeth. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0075] like Figure 1 As shown, a method for predicting and analyzing the wear life of spline pairs based on the Archard model includes:

[0076] S101: Obtain the key parameters of the spline pair, including geometric parameters, material parameters, operating condition parameters, and wear parameters;

[0077] Among them, the geometric parameters include, but are not limited to, spline module, number of teeth, pressure angle, addendum circle, dedendum circle, tooth width, and tooth height;

[0078] Material parameters include, but are not limited to, the elastic modulus, Poisson's ratio, and hardness of the internal and external spline materials;

[0079] Operating parameters include, but are not limited to, applied torque, loading frequency, friction coefficient, and ambient temperature;

[0080] Wear parameters include, but are not limited to, maximum allowable wear depth and maximum number of iterations.

[0081] S102: By establishing the standard parametric equation of the involute tooth profile, the internal and external splines are modeled to construct an ideal geometric model. Based on the ideal geometric model, manufacturing errors and assembly errors are introduced to construct a three-dimensional geometric model of the spline pair.

[0082] Preferably, the standard parametric equations for the involute tooth profile are constructed as follows:

[0083] Define the coordinates of a point C on the base circle as (X... c Y c ):

[0084] X c =R b·cos(β)

[0085] Y c =R b ·sin(β)

[0086] The length S of the tangent line extending from point C R The relationship with roll angle is:

[0087] S R =R b ·β

[0088] Among them, R b It is represented by the base circle radius, and β is the roll angle (in radians);

[0089] The coordinates (X, Y) of point P on the involute corresponding to the roll angle β are obtained by translating point C by a distance S along the tangential direction. R Since the tangent direction is perpendicular to the radius direction, it can be expressed as:

[0090] X(β)=X c +S R sin(β)=R b ·cos(β)+(R b ·β)·sin(β)

[0091] Y(β)=Y c -S R ·cos(β)=R b ·sin(β)-(R b ·β)·cos(β)

[0092] After simplification, the standard parametric equations for the involute tooth profile are obtained:

[0093] X(β)=R b (cos(β)+βsin(β))

[0094] Y(β)=R b (sin(β)-βcos(β))

[0095] The involute tooth profile is the trajectory of any point on a straight line as it rolls purely on a base circle, as referenced from... Figure 2 ;

[0096] In addition, to fully describe the tooth profile, it is necessary to combine the geometric definitions of the tooth root transition curve and the tooth tip circle. This part is set according to the provisions in the specific mechanical design manual. Finally, the involute tooth profile, the tooth root transition curve and the tooth tip circle constitute the ideal geometric model of the spline pair, and serve as the basis for subsequent three-dimensional modeling by introducing manufacturing errors and assembly errors.

[0097] To accurately reflect the impact of manufacturing and assembly process errors on the spline pair meshing characteristics and wear behavior, this invention further introduces a geometric defect modeling mechanism based on the ideal geometric model as follows:

[0098] Manufacturing error modeling:

[0099] Due to machining deviations during manufacturing, the actual width of each tooth groove will be inconsistent and the actual tooth thickness of each tooth will vary. Therefore, the actual range of values ​​for the tooth groove width E in a spline pair can be expressed as:

[0100] E∈[E min， E max ]

[0101] The actual range of values ​​for spline tooth thickness can be expressed as follows:

[0102] S∈[S min S max ]

[0103] Among them, E min E max S min S max These represent the set minimum actual tooth space width, maximum actual tooth space width, minimum actual tooth thickness, and maximum actual tooth thickness, respectively.

[0104] Manufacturing error is determined by the actual range of values ​​for tooth groove width and spline tooth thickness.

[0105] Assembly error modeling:

[0106] Assembly errors mainly include the following two types:

[0107] The state of non-coincident axes is simulated by translating the central axis of the internal or external spline as a whole radially by a preset distance L.

[0108] The angular deviation that occurs during assembly is simulated by rotating the axis of one spline relative to the other by a preset included angle J.

[0109] Assembly error is determined by preset distance and preset included angle;

[0110] Manufacturing and assembly errors are superimposed on the standard tooth profile parameter model through mathematical perturbation, thereby constructing a three-dimensional geometric model of the spline pair, providing basic data support for subsequent contact analysis and wear simulation.

[0111] S103: Import the three-dimensional geometric model of the spline pair into the finite element simulation platform and begin the iterative phase of fretting wear analysis.

[0112] S104: Based on the finite element simulation platform Abaqus, contact mechanics analysis of spline pairs is performed. Material parameters and boundary loading conditions are set, and a nonlinear contact solution strategy is adopted to obtain the contact pressure distribution and relative slip at the spline pair contact interface under the current calculation step.

[0113] Preferably, the specific analysis process in this step includes the following steps:

[0114] At the beginning of the i-th calculation step (initial step size is i=0), a finite element model of a spline pair with multi-tooth contact characteristics is established based on the current three-dimensional geometric state of the spline pair (including the initial geometric model or the wear geometry after the previous calculation step). The model is built based on the actual structural dimensions and takes into account the actual tooth profile after the introduction of manufacturing and assembly errors.

[0115] The material properties, including elastic modulus and Poisson's ratio, are specified for the internal and external splines respectively, to accurately simulate the elastic response behavior of gear materials under load, and to provide a physical basis for subsequent contact pressure and slip calculations.

[0116] Finite element meshing was performed on the entire three-dimensional geometric model of the spline pair. In the tooth surface contact area and the stress concentration area at the tooth root, a fine mesh was used to improve the accuracy of local analysis, while a relatively coarse mesh was used in the area far from the contact interface to improve the overall computational efficiency.

[0117] According to the actual operating conditions, the boundary and load conditions are set. Preferably, one end of the inner spline shaft is fixed and a preset torque T is applied to the outer spline. This torque is applied by applying coupling constraints and equivalent rotational torque at the shaft end node to ensure that the load is transmitted uniformly along the axisymmetric manner.

[0118] Given that the contact state between the spline tooth surfaces undergoes contact-separation and geometric nonlinear response with changes in load, this invention employs a nonlinear contact analysis method to handle the complex contact response between tooth surfaces. The specific operation is as follows:

[0119] A contact pair relationship is defined between the inner and outer spline tooth surfaces. The contact area is set using a "face-to-face" contact unit, with one side being the contact surface and the other side being the target surface, in order to establish an effective contact pair.

[0120] To address potential contact penetration and slippage issues, the penalty function method is preferred as the contact algorithm. This method introduces contact stiffness to limit the mutual penetration of the contact surfaces and combines it with the Coulomb friction model to model the tangential slippage friction force on the tooth surface.

[0121] Among them, the contact equations adopt an incremental-iterative solution strategy, which divides the total target load into several sub-steps and applies the load step by step to improve numerical convergence and computational stability. In each sub-step, the normal contact pressure p(x, y, t) and tangential slip distance δ(x, y, t) of each node in the tooth surface contact area are solved.

[0122] By integrating the normal contact pressure p(x, y, t) and tangential slip distance δ(x, y, t) of each node in the tooth surface contact area under the current loading state, the contact pressure distribution and relative slip of the spline tooth surface contact interface under this calculation step size are obtained, providing basic input parameters for subsequent wear update and life prediction analysis.

[0123] S105: Evaluate the tooth surface wear within the current calculation step according to Archard's wear law. Specifically, calculate the wear depth increment Δh(x, y, t) at each node on the tooth surface using the following formula: Δh(x, y, t)=K·p(x, y, t)·δ(x, y, t)·Δt, where K represents the set wear coefficient and Δt represents the current calculation step.

[0124] S106: Based on the wear depth increment within the current time step, update the coordinates of the tooth surface nodes. Specifically, reduce the normal coordinate value of each node on the tooth surface by the corresponding wear depth increment along its normal direction to generate an updated set of node coordinates. Based on the above node coordinate update results, dynamically adjust the tooth surface geometry using ALE (Arbitrary Lagrangian–Eulerian) technology in Abaqus, thereby avoiding the tedious operations of traditional mesh reconstruction and re-dividing contact pairs and improving overall modeling efficiency.

[0125] S107: After completing the tooth surface geometry update, compare the current cumulative wear depth with the set wear tolerance limit to determine whether to continue to the next step of analysis. The wear tolerance limit can be set according to any of the following standards:

[0126] Preset total number of work cycles;

[0127] The cumulative wear depth at any node on the tooth surface reaches the allowable value of the material.

[0128] The reduction in spline tooth thickness exceeds structural safety standards;

[0129] The backlash caused by tooth surface wear exceeds the functional requirements.

[0130] If the cumulative wear depth does not reach the preset wear tolerance limit, let i = i + 1, and take the currently updated tooth surface geometry model as input, return to step S103 to continue the contact analysis of the next calculation step;

[0131] If the cumulative wear depth has reached the preset wear tolerance limit, the iteration process is terminated and the life output step S108 is entered.

[0132] S108: Output the life prediction results of the spline pair, including the predicted lifespan (total running time / number of runs from the beginning to the present, which is the predicted lifespan), the three-dimensional contour map of the final wear morphology of the spline pair, and the data on the evolution trend of contact load distribution at each time step throughout the wear process.

[0133] In one specific embodiment, after the Abaqus simulation software completes a single calculation of the spline wear depth using ALE (Adaptive Mesh), the spline tooth surface is updated, continuously accumulating the wear amount and comparing it with a set wear tolerance limit. A wear tolerance of 10 is set. 5 The number of wear tests is used to determine whether the spline has reached its limit, which serves as the predicted life of the spline pair. This wear process can output the tooth surface condition of the wear depth to intuitively show the wear state of the spline pair under the limit condition. Finally, under the condition of shaft alignment, the wear depth of the maximum tooth surface of the involute spline pair (a) and the axial meshing wear depth of different tooth numbers (b) are obtained. Figure 5 As shown, the tooth surface wear depth of the largest tooth under the condition of axial misalignment (6µm) in an involute spline pair is shown in (a), and the axial meshing wear depth of different tooth numbers is shown in (b). Figure 6 As shown, the tooth surface wear depth of the largest tooth (a) and the axial meshing wear depth of different numbers of teeth are shown under the condition of misalignment of the secondary angle of the involute spline (0.01°). Figure 7 As shown, the tooth surface wear depth of the maximum tooth under the condition of compound misalignment (0.01°-4µm) in an involute spline pair is shown in (a), and the axial meshing wear depth of different tooth numbers is shown in (b). Figure 8 As shown.

[0134] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement any of the methods described above;

[0135] A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements any of the methods described above.

[0136] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to any specific implementation. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for predicting and analyzing the wear life of spline pairs based on the Archard model, characterized in that, Includes the following steps: S101: Obtain the key parameters of the spline pair, including geometric parameters, material parameters, operating condition parameters, and wear parameters; S102: By establishing the standard parametric equation of the involute tooth profile, the internal and external splines are modeled to construct an ideal geometric model. Based on the ideal geometric model, manufacturing errors and assembly errors are introduced to construct a three-dimensional geometric model of the spline pair. S103: Import the three-dimensional geometric model of the spline pair into the finite element simulation platform and perform the iterative stage of fretting wear analysis; S104: Based on the finite element simulation platform, the contact mechanics analysis of the spline pair is carried out. Material parameters and boundary loading conditions are set, and a nonlinear contact solution strategy is adopted to obtain the contact pressure distribution and relative slip at the spline pair contact interface under the current calculation step. S105: Calculate the wear depth increment of each node on the tooth surface within the current calculation step, according to the wear law; S106: Based on the wear depth increment within the current time step, update the coordinates of the tooth surface nodes and generate the updated set of node coordinates; S107: After completing the tooth surface geometry update, compare the current cumulative wear depth with the set wear tolerance limit to determine whether to terminate the analysis. If the cumulative wear depth has not reached the preset wear tolerance limit, return to step S103 to perform the next calculation step analysis. If the cumulative wear depth has reached the preset wear tolerance limit, terminate the iteration and output the life prediction result of the spline pair.

2. The method for predicting and analyzing the wear life of spline pairs based on the Archard model according to claim 1, characterized in that, The specific process of constructing an ideal geometric model is as follows: Define the coordinates of a point C on the base circle as (X... c Y c ): X c =R b ·cos(β) Y c =R b ·sin(β) The length S of the tangent line extending from point C R The relationship with roll angle is: S R =R b ·b Among them, R b β represents the base circle radius, and β represents the roll angle. The coordinates (X, Y) of point P on the involute corresponding to the roll angle β are obtained by translating point C by a distance S along the tangential direction. R Since the tangent direction is perpendicular to the radius direction, it can be expressed as: X(β)=X c +S R ·sin(β)=R b ·cos(β)+(R b ·b)·sin(b) Y(β)=Y c -S R ·cos(β)=R b ·sin(β)-(R b ·β)·cos(β) After simplification, the standard parametric equations for the involute tooth profile are obtained: X(β)=R b (cos(β)+βsin(β)) Y(β)=R b (sin(β)-βcos(β)) Among them, the involute tooth profile is the trajectory of any point on a straight line when a straight line rolls purely on the base circle; In addition, to fully describe the tooth profile, it is necessary to combine the root transition curve and the tip circle with the involute tooth profile to form an ideal geometric model of the spline pair.

3. The method for predicting and analyzing the wear life of spline pairs based on the Archard model according to claim 2, characterized in that, The specific process of constructing the three-dimensional geometric model of the spline pair is as follows: Based on the ideal geometric model, manufacturing errors and assembly errors are further introduced, specifically: Due to machining deviations during manufacturing, the actual width of each tooth groove will be inconsistent and the actual tooth thickness of each tooth will vary. Therefore, the actual range of values ​​for the tooth groove width E in a spline pair can be expressed as: E∈[E min ,AND max ] The actual range of values ​​for spline tooth thickness can be expressed as follows: S∈[S min ,S max ] Among them, E min E max S min S max These represent the set minimum actual tooth space width, maximum actual tooth space width, minimum actual tooth thickness, and maximum actual tooth thickness, respectively. Manufacturing error is determined by the actual range of values ​​for tooth groove width and spline tooth thickness. By translating the central axis of the internal or external spline as a whole radially by a predetermined distance L; By rotating the axis of one spline relative to the other by a predetermined angle J; Assembly error is determined by preset distance and preset included angle; Manufacturing errors and assembly errors are superimposed on the standard tooth profile parameter model through mathematical perturbation, thereby constructing a three-dimensional geometric model of the spline pair.

4. The method for predicting and analyzing the wear life of spline pairs based on the Archard model according to claim 1, characterized in that, The specific process of performing contact mechanics analysis on spline pairs is as follows: At the start of the i-th calculation step, a finite element model of a spline pair with multi-tooth contact characteristics is established based on the current three-dimensional geometric state of the spline pair. The model is constructed based on the actual structural dimensions and takes into account the actual tooth profile after the introduction of manufacturing and assembly errors. Specify material properties for internal and external splines, including elastic modulus and Poisson's ratio; Finite element meshing was performed on the entire three-dimensional geometric model of the spline pair. In the tooth surface contact area and the stress concentration area at the tooth root, a fine mesh was used, while in the area far from the contact interface, a relatively coarse mesh was used. Set boundary and load conditions according to actual operating conditions, fix one end of the internal spline shaft and apply a preset torque T to the external spline. This torque is applied by applying coupling constraints and equivalent rotational torque at the shaft end node.

5. The method for predicting and analyzing the wear life of spline pairs based on the Archard model according to claim 4, characterized in that, The specific process of using the nonlinear contact solution strategy is as follows: A contact pair relationship is defined between the inner and outer spline tooth surfaces. The contact area is set using a surface-to-surface contact unit, with one side being the contact surface and the other side being the target surface, in order to establish an effective contact pair. The penalty function method is adopted as the contact algorithm. This method restricts the mutual penetration of the contact surfaces by introducing contact stiffness, and combines the Coulomb friction model to model the tangential sliding friction force on the tooth surface. Among them, the contact equations adopt an incremental-iterative solution strategy, which divides the total target load into several sub-steps and applies the load step by step to improve numerical convergence and computational stability. In each sub-step, the normal contact pressure p(x, y, t) and tangential slip distance δ(x, y, t) of each node in the tooth surface contact area are solved. By integrating the normal contact pressure p(x, y, t) and tangential slip distance δ(x, y, t) of each node in the tooth surface contact area under the current loading state, the contact pressure distribution and relative slip amount of the spline tooth surface contact interface under this calculation step size can be obtained.

6. The method for predicting and analyzing the wear life of spline pairs based on the Archard model according to claim 1, characterized in that, The formula for calculating the wear depth increment of each node on the tooth surface within the current calculation step is: Δh(x,y,t)=K·p(x,y,t)·δ(x,y,t)·Δt, where K represents the set wear coefficient, Δt represents the current calculation step, and Δh(x,y,t) represents the wear depth increment.

7. The method for predicting and analyzing the wear life of spline pairs based on the Archard model according to claim 1, characterized in that, The specific process of updating the coordinates of the tooth surface nodes is as follows: The normal coordinate values ​​of each node on the tooth surface are reduced by the corresponding wear depth increment along its normal direction to generate an updated set of node coordinates.

8. The method for predicting and analyzing the wear life of spline pairs based on the Archard model according to claim 1, characterized in that, The wear tolerance limit can be set according to any of the following criteria: preset total number of working cycles; The cumulative wear depth at any node on the tooth surface reaches the allowable value of the material. The reduction in spline tooth thickness exceeds structural safety standards; The backlash caused by tooth surface wear exceeds the functional requirements.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 8.

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