A double-sided micro-motion wear evaluation method for angular misalignment involute spline pair

Abstract

This invention provides a method for assessing double-sided fretting wear of angularly misaligned involute splines. The method includes steps such as establishing a single-tooth geometric model of the spline pair, calculating the maximum misalignment angle of the spline pair under angular misalignment conditions, establishing a global model and a single-tooth pair model of the spline pair, obtaining the overall load characteristics of the spline pair, determining the wear increment scaling factor, mapping the wear results to the global model, and updating the wear amount and mesh state of each node in the global model. This invention can improve the prediction accuracy of double-sided fretting wear of angularly misaligned splines while controlling the mesh size and computational cost, providing support for fretting wear analysis and parametric calculation of splines with multiple teeth, large tooth width, and heavy loads.

Description

Technical Field

[0001] This invention relates to the field of contact mechanics simulation technology, and in particular to a method for evaluating double-sided fretting wear of angularly misaligned involute spline pairs. Background Technology

[0002] Spline pairs, due to their high load-bearing capacity, high transmission accuracy, and compact structure, have been widely used in aero-engines, gas turbines, vehicle transmission systems, and heavy-duty machinery, serving as core transmission components for torque transmission and motion synchronization in these systems. In actual service, spline pairs typically withstand complex conditions such as torque, bending moment, axial force, and alternating loads. Due to unavoidable factors such as machining errors, assembly deviations, shaft deformation, and uneven support stiffness, angular misalignment commonly exists between internal and external splines. This causes the tooth surface contact state to deviate from ideal uniform meshing, inducing fretting wear under minute relative displacements. Fretting wear continuously alters the contact geometry of the spline tooth surfaces, further affecting load distribution, contact pressure, and slippage state, forming an evolutionary process where wear and contact state are coupled, which is one of the important mechanisms leading to spline pair failure.

[0003] Currently, finite element analysis methods for fretting wear of spline pairs are mainly divided into two categories. The first category uses a refined model of the complete spline pair, which can realistically reflect the multi-tooth meshing and overall stress state. However, the number of meshes in the contact area is enormous, resulting in extremely high computational costs for a single wear cycle, particularly under conditions of multiple teeth, large tooth width, and heavy loads. This leads to excessively long simulation cycles, making it difficult to meet the practical needs of engineering design and life assessment. The second category uses a locally simplified model, which can significantly reduce the computational scale. However, due to the simplified boundary conditions, it cannot accurately characterize the overall structural deformation and multi-tooth load distribution relationship, leading to systematic deviations in the calculation results of local tooth surface contact stress and slippage, and insufficient reliability of wear prediction results. Furthermore, existing methods generally only consider contact and wear on one side of the tooth surface, ignoring the actual situation where contact and wear may occur on both sides of the internal and external splines under angular misalignment conditions. The inherent defects of unilateral wear analysis systematically underestimate the actual wear range and cumulative wear effect, resulting in a long-term inaccurate assessment of the true damage state of the spline pair. The continued existence of this state causes serious distortion in life assessment results based on wear prediction, lacks reliable quantitative basis for structural design optimization, and ultimately leads to actual hazards such as unexpected decrease in transmission accuracy, premature failure of tooth surfaces, and even unplanned shutdown of transmission systems during equipment service, posing a potential threat to the safe operation of high-reliability equipment such as aero engines and gas turbines.

[0004] Therefore, developing a method for evaluating the double-sided fretting wear of angularly misaligned involute spline pairs is of great significance. Summary of the Invention

[0005] The purpose of this invention is to provide a method for evaluating double-sided fretting wear of angularly misaligned involute spline pairs, in order to solve the problems existing in the prior art.

[0006] The technical solution adopted to achieve the purpose of this invention is as follows: a method for evaluating double-sided fretting wear of an angularly misaligned involute spline pair, comprising the following steps:

[0007] S1) Using finite element analysis software, geometric models of internal and external spline single teeth are established using internal and external spline single teeth as modeling units, and the material properties of each single tooth model are defined.

[0008] S2) Assemble and position the internal and external spline single-tooth models to construct the simulation sub-model. Simultaneously, array the internal and external spline single-tooth models circumferentially to form a complete spline pair geometric model. After completing the assembly and positioning, construct the global simulation model.

[0009] S3) Perform structured mesh generation on the global simulation model and the simulation sub-model respectively.

[0010] S4) Calculate the maximum allowable misalignment angle of the spline pair relative motion under angular misalignment conditions.

[0011] S5) Establish simulation analysis steps for the global simulation model and the simulation sub-model, including a wear analysis step and a rotation analysis step. The wear analysis step is used to define the two-sided fretting wear behavior, and the rotation analysis step is used to characterize the relative motion within a single rotation cycle.

[0012] S6) Based on the contact and motion characteristics of the spline pair under angular misalignment conditions, set the interaction properties, boundary conditions, and load conditions for the global simulation model and the sub-simulation model respectively.

[0013] S7) Create solution jobs for the global simulation model and the simulation sub-model respectively, and configure the corresponding user subroutine files.

[0014] S8) Submit a global analysis job, define the displacement changes of each node on each tooth surface of the complete spline pair through user subroutines, and solve to obtain the displacement field distribution of the global simulation model.

[0015] S9) Using the local displacement field of the global analysis job as the boundary condition, submit the local analysis job, define the displacement change of a single tooth on each node of the two tooth surfaces through the user subroutine, and calculate and output the contact stress and contact displacement field variables.

[0016] S10) Based on the contact stress and contact displacement results output in step S9), calculate the wear amount of each node on the two tooth surfaces of the local single tooth pair and each node on each tooth surface of the complete spline pair under the current wear cycle, update the cumulative wear amount of each node, and then return to step S8) to enter the next wear cycle until the preset number of cycles is reached.

[0017] Furthermore, in step S3), a sparse structured mesh is used for the global simulation model, and a fine structured mesh is used for the sub-simulation models, so as to achieve high-precision solution of the contact field variables of the sub-models while reducing the overall computational overhead.

[0018] Further, in step S4), by performing tooth position expansion around the rotation axis and skew transformation around the non-rotation axis on the tooth profile point set of paired teeth in space, the tooth profile interference is determined using the two-dimensional projection line segment intersection criterion, and the skew angle corresponding to the first occurrence of interference is taken as the maximum allowable skew angle for the relative motion of the spline pair. The coordinate calculation formula for the skew transformation is:

[0019] (1)

[0020] (2)

[0021] in, Let be the three-dimensional coordinates of the set of tooth profile points on one side of a pair of teeth in space. The tooth position angle about the axis of rotation. It is the deflection angle about the non-rotational axis.

[0022] Furthermore, in step S5), the step size of the rotation analysis step is set so that the spline pair has several discrete spatial positions within a single rotation cycle, so as to fully characterize the relative motion process within a rotation cycle.

[0023] Furthermore, in step S6), the inner and outer spline contact surfaces are designated as master and slave surfaces to simulate double-sided fretting wear. The friction behavior in the contact tangential direction is defined using a penalty function algorithm, while the contact normal direction uses a hard contact constraint model and allows separation after contact.

[0024] Furthermore, in step S6), adaptive mesh regions, adaptive mesh constraints, and adaptive mesh controls are defined for the tooth surface contact areas of the global simulation model and the simulation sub-model, respectively. In the adaptive mesh constraints, user-defined rules are used to define the mesh motion form to achieve dynamic updating of the tooth surface geometry during the wear process.

[0025] Furthermore, in step S7), the user subroutine file is the UMESHMOTION subroutine, and the global analysis job and the local analysis job are configured with independent UMESHMOTION subroutine files respectively.

[0026] Furthermore, in step S9), output variables are set, and contact-related field variables such as contact stress and contact displacement are output at the end of each unit time step.

[0027] Further, in step S10), the current cyclic wear of each node on both tooth surfaces of the local single tooth pair is calculated based on the contact stress, relative slip in each direction, and wear coefficient output from the local analysis operation. The wear of the coarse-grid nodes on each tooth surface of the complete spline pair is obtained by interpolation from the wear of the corresponding fine-grid nodes of the sub-model. Fine mesh nodes in a wear cycle The formula for calculating the current cyclic wear is as follows:

[0028] (3)

[0029] in, The wear coefficient is denoted as . For the first Contact stress of the frame. , For the first The relative slippage of the frame in two directions. This represents the total number of frames of the output field results within a single rotation cycle.

[0030] Furthermore, in step S10), a wear jump method is used to accelerate the wear evolution process. First, the wear distribution within a representative cycle is calculated. Then, the wear increment scaling factor is determined based on the maximum wear increment allowed by a single geometric update. One numerical update represents multiple actual wear cycles, improving computational efficiency while ensuring the stability of wear iteration updates. If the global coarse mesh nodes... Corresponding to four fine mesh nodes The interpolation weights are respectively Then the coarse mesh nodes in the current loop The amount of wear is:

[0031] (4)

[0032] For both the complete spline pair geometry model and the local single-tooth pair geometry model, the wear distribution within a representative cycle is first calculated. Then, the wear amount of that cycle is amplified based on the maximum allowable wear increment. One numerical update represents multiple actual cycles. That is, the wear jump method is used to accelerate the wear evolution process and improve the efficiency of fretting wear iteration calculation. The main calculation formulas are as follows:

[0033] (5)

[0034] (6)

[0035] (7)

[0036] in, The maximum wear increment allowed for a single geometric update. Indicates the first The wear increment scaling factor in the next wear update, also known as the wear jump factor. and The first Fine mesh nodes after secondary wear update and coarse grid nodes The cumulative wear and tear.

[0037] The technical effects of this invention are beyond doubt:

[0038] A. It is applicable to the fretting wear analysis of spline pairs under angular misalignment conditions, especially suitable for wear prediction of spline pairs with multiple teeth, large tooth width, and heavy load. It can better reflect the overall load, local contact and wear evolution characteristics of spline pairs during actual service.

[0039] B. The simulation method combining global model and sub-model takes into account both the overall load realism and the accuracy of local wear calculation. While ensuring the accuracy of local tooth surface wear calculation, it significantly reduces the model size and calculation cost, and improves the efficiency of wear iteration calculation.

[0040] C. By comprehensively considering the fretting wear behavior of the tooth surfaces on both sides of the internal and external splines, compared with the analysis method that only considers the wear of one side of the tooth surface, it can more comprehensively describe the wear evolution law of the tooth surfaces on both sides of the spline pair under the state of angular misalignment, and improve the rationality of the wear prediction results;

[0041] D. By introducing a wear increment scaling factor to constrain the maximum wear increment of a single geometric update, the stability of wear iteration updates is ensured while reducing redundant loop calculations, effectively improving the efficiency of wear evolution simulation analysis.

[0042] The E. Spline pair double-sided micro-motion wear simulation calculation framework can automatically complete the entire process of node extraction, coordinate transformation, boundary mapping, wear calculation and morphology update. It demonstrates convenience in realizing the unified encapsulation of spline pair geometric information and calculation parameters, and has good parameterization and process-oriented features. It lays the technical foundation for the development of automated wear simulation calculation plug-ins and significantly improves the engineering application applicability of the simulation process. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating the wear simulation method.

[0044] Figure 2 Mesh generation diagram for the complete spline pair geometric model;

[0045] Figure 3 This is a mesh diagram of the local single-tooth geometric model;

[0046] Figure 4 This is a cloud map showing the contact stress distribution on the internal spline tooth surface.

[0047] Figure 5 This is a cloud map showing the wear depth distribution on the spline gear tooth surface. Detailed Implementation

[0048] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0049] Example 1:

[0050] See Figures 1-5 This embodiment provides a method for evaluating double-sided fretting wear of an angularly misaligned involute spline pair, including the following steps:

[0051] S1) Using finite element analysis software, geometric models of internal and external spline single teeth are established using internal and external spline single teeth as modeling units, and the material properties of each single tooth model are defined.

[0052] S2) Assemble and position the internal and external spline single-tooth models to construct the simulation sub-model. Simultaneously, array the internal and external spline single-tooth models circumferentially to form a complete spline pair geometric model. After completing the assembly and positioning, construct the global simulation model.

[0053] S3) Perform structured mesh generation on the global simulation model and the simulation sub-model respectively.

[0054] S4) Calculate the maximum allowable misalignment angle of the spline pair relative motion under angular misalignment conditions.

[0055] S5) Establish simulation analysis steps for the global simulation model and the simulation sub-model, including a wear analysis step and a rotation analysis step. The wear analysis step is used to define the two-sided fretting wear behavior, and the rotation analysis step is used to characterize the relative motion within a single rotation cycle.

[0056] S6) Based on the contact and motion characteristics of the spline pair under angular misalignment conditions, set the interaction properties, boundary conditions, and load conditions for the global simulation model and the sub-simulation model respectively.

[0057] S7) Create solution jobs for the global simulation model and the simulation sub-model respectively, and configure the corresponding user subroutine files.

[0058] S8) Submit a global analysis job, define the displacement changes of each node on each tooth surface of the complete spline pair through user subroutines, and solve to obtain the displacement field distribution of the global simulation model.

[0059] S9) Using the local displacement field of the global analysis job as the boundary condition, submit the local analysis job, define the displacement change of a single tooth on each node of the two tooth surfaces through the user subroutine, and calculate and output the contact stress and contact displacement field variables.

[0060] S10) Based on the contact stress and contact displacement results output in step S9), calculate the wear amount of each node on the two tooth surfaces of the local single tooth pair and each node on each tooth surface of the complete spline pair under the current wear cycle, update the cumulative wear amount of each node, and then return to step S8) to enter the next wear cycle until the preset number of cycles is reached.

[0061] Example 2:

[0062] The main content of this embodiment is the same as that of embodiment 1. In step S3), a sparse structured mesh is used for the global simulation model and a fine structured mesh is used for the sub-models to achieve high-precision solution of the contact field variables of the sub-models while reducing the overall computational overhead.

[0063] Example 3:

[0064] The main content of this embodiment is the same as that of Embodiment 1 or 2. In step S4), the tooth profile point set of paired teeth in space is expanded around the rotation axis and deflected around the non-rotation axis. The two-dimensional projection line segment intersection criterion is used to determine tooth profile interference. The deflection angle corresponding to the first interference is taken as the maximum allowable deflection angle for the relative motion of the spline pair. The coordinate calculation formula for the deflection transformation is:

[0065] (1)

[0066] (2)

[0067] in, Let be the three-dimensional coordinates of the set of tooth profile points on one side of a pair of teeth in space. The tooth position angle about the axis of rotation. It is the deflection angle about the non-rotational axis.

[0068] Example 4:

[0069] The main content of this embodiment is the same as any one of embodiments 1 to 3. In step S5), the step size of the rotation analysis step is set so that the spline pair has several discrete spatial positions within a single rotation cycle, so as to fully characterize the relative motion process within a rotation cycle.

[0070] Example 5:

[0071] The main content of this embodiment is the same as any one of embodiments 1 to 4. In step S6), the inner and outer spline contact surfaces are set as master and slave surfaces to simulate double-sided fretting wear. The friction behavior in the contact tangential direction is defined using a penalty function algorithm, and the contact normal direction adopts a hard contact constraint model and allows separation after contact.

[0072] Example 6:

[0073] The main content of this embodiment is the same as any one of embodiments 1 to 5. In step S6), adaptive mesh regions, adaptive mesh constraints and adaptive mesh control are defined for the tooth surface contact areas of the global simulation model and the simulation sub-model, respectively. In the adaptive mesh constraints, user-defined rules are used to define the mesh motion form to achieve dynamic updating of the tooth surface geometry during the wear process.

[0074] Example 7:

[0075] The main content of this embodiment is the same as any one of embodiments 1 to 6. In step S7), the user subroutine file is the UMESHMOTION subroutine, and the global analysis job and the local analysis job are configured with independent UMESHMOTION subroutine files respectively.

[0076] Example 8:

[0077] The main content of this embodiment is the same as any one of embodiments 1 to 6. In step S9), output variables are set, and contact-related field variables such as contact stress and contact displacement are output at the end of each unit time step.

[0078] Example 9:

[0079] The main content of this embodiment is the same as any one of embodiments 1 to 7. In step S10), the current cyclic wear amount of each node on the two tooth surfaces of the local single tooth pair is calculated based on the contact stress, relative slip in each direction, and wear coefficient output from the local analysis operation. The wear amount of the coarse mesh nodes on each tooth surface of the complete spline pair is obtained by interpolation from the wear amount of the fine mesh nodes of its corresponding sub-model. Fine mesh nodes in a wear cycle The formula for calculating the current cyclic wear is as follows:

[0080] (3)

[0081] in, The wear coefficient is denoted as . For the first Contact stress of the frame. , For the first The relative slippage of the frame in two directions. This represents the total number of frames of the output field results within a single rotation cycle.

[0082] Example 10:

[0083] The main content of this embodiment is the same as any one of embodiments 1 to 9. In step S10), a wear jump method is used to accelerate the wear evolution process. First, the wear distribution within a representative cycle is calculated. Then, the wear increment scaling factor is determined based on the maximum wear increment allowed by a single geometric update. One numerical update represents multiple actual wear cycles, improving computational efficiency while ensuring the stability of wear iteration updates. If the global coarse mesh nodes... Corresponding to four fine mesh nodes The interpolation weights are respectively Then the coarse mesh nodes in the current loop The amount of wear is:

[0084] (4)

[0085] For both the complete spline pair geometry model and the local single-tooth pair geometry model, the wear distribution within a representative cycle is first calculated. Then, the wear amount of that cycle is amplified based on the maximum allowable wear increment. One numerical update represents multiple actual cycles. That is, the wear jump method is used to accelerate the wear evolution process and improve the efficiency of fretting wear iteration calculation. The main calculation formulas are as follows:

[0086] (5)

[0087] (6)

[0088] (7)

[0089] in, The maximum wear increment allowed for a single geometric update. Indicates the first The wear increment scaling factor in the next wear update, also known as the wear jump factor. and The first Fine mesh nodes after secondary wear update and coarse grid nodes The cumulative wear and tear.

[0090] Example 11:

[0091] This embodiment provides a method for evaluating double-sided fretting wear of an angularly misaligned involute spline pair, including the following steps:

[0092] S1) Using finite element analysis software, geometric models of internal and external spline single teeth are established using internal and external spline single teeth as modeling units, and the material properties of each single tooth model are defined.

[0093] S2) Assemble and position the internal and external spline single-tooth models to construct a simulation sub-model. Simultaneously, array the internal and external spline single-tooth models circumferentially to form a complete spline pair geometric model. After assembly and positioning, construct the global simulation model. It is worth noting that in this embodiment, the internal and external spline single-tooth models established in step S1) need to be assembled and positioned as independent simulation sub-models. Using the internal and external spline single-tooth models established in step S1) as basic units, a complete spline pair geometric model needs to be generated by circumferential arraying. After assembly and positioning, this model serves as the global simulation model.

[0094] S3) Structured mesh generation is performed on both the global simulation model and the sub-simulation models. A sparse structured mesh is used for the global simulation model, while a fine structured mesh is used for the sub-simulation models. This balances computational efficiency and simulation accuracy, reducing overall computational overhead while obtaining the displacement field distribution of the global model and achieving high-precision solution for the contact field variables of the sub-models.

[0095] S4) Calculate the maximum allowable misalignment angle of the spline pair relative motion under angular misalignment conditions.

[0096] S5) Establish simulation analysis steps for the global simulation model and simulation sub-models, including wear analysis steps and rotation analysis steps. The wear analysis step defines the double-sided fretting wear behavior, while the rotation analysis step characterizes the relative motion within a single rotation cycle. By performing tooth profile point set expansion around the rotation axis and skew transformation around the non-rotation axis on a set of paired teeth in space, the tooth profile interference is determined using the two-dimensional projection line segment intersection criterion. The skew angle at the first interference is the maximum allowable skew angle for the relative motion of the spline pair. The main calculation formula is as follows:

[0097] (1)

[0098] (2)

[0099] in, Let be the three-dimensional coordinates of the set of tooth profile points on one side of a pair of teeth in space. The tooth position angle about the axis of rotation. It is the deflection angle about the non-rotational axis.

[0100] S6) Based on the contact and motion characteristics of the spline pair under angular misalignment conditions, set the interaction properties, boundary conditions, and load conditions for the global simulation model and the sub-simulation model respectively.

[0101] S7) Create solution jobs for the global simulation model and the simulation sub-model respectively, and configure the corresponding user subroutine files. Two types of solution jobs need to be created for the global simulation model and the simulation sub-model: a global analysis job and a local analysis job. The corresponding global analysis UMESHMOTION subroutine files and local analysis UMESHMOTION subroutine files should be configured for each type of model respectively.

[0102] S8) Submit a global analysis job, define the displacement changes of each node on each tooth surface of the complete spline pair through a user subroutine, and solve to obtain the displacement field distribution of the global simulation model. Using the global analysis UMESHMOTION subroutine file, the displacement changes of all tooth surfaces and all nodes on the tooth surfaces of the inner and outer splines of the complete spline pair geometric model are defined to characterize the double-sided fretting wear behavior of the complete spline pair geometric model.

[0103] S9) Using the local displacement field from the global analysis job as boundary conditions, submit a local analysis job. Define the displacement changes of a single tooth on each node of the two tooth surfaces using a user subroutine, and calculate and output the contact stress and contact displacement field variables. Employ the local analysis UMESHMOTION subroutine file to define the displacement changes of a single tooth on all nodes on the inner and outer spline surfaces of the geometric model, thereby characterizing the bi-face fretting wear behavior of the single tooth on the geometric model. The local analysis job is based on the sub-model technology of the ABAQUS finite element analysis software, using the local displacement from the global analysis job as boundary conditions for solution calculation.

[0104] S10) Based on the contact stress and contact displacement results output in step S9), calculate the wear amount of each node on both tooth surfaces of the local single tooth pair and each node on each tooth surface of the complete spline pair under the current wear cycle, update the cumulative wear amount of each node, and then return to step S8) to enter the next wear cycle until the preset number of cycles is reached. The global analysis and local analysis are solved iteratively using ABAQUS finite element analysis software. After each wear cycle is completed, the total wear amount of each node on the tooth surface is updated and accumulated immediately.

[0105] Based on the contact stress and contact displacement results output by the local analysis operation, the wear amount of each node on the two tooth surfaces of the local single tooth pair geometric model under the current wear cycle is obtained. Fine mesh nodes in a wear cycle The formula for calculating the current cyclic wear is as follows:

[0106] (3)

[0107] in, The wear coefficient; For the first Contact stress of the frame; , For the first The relative slippage of the frame in two directions; This represents the total number of frames of the output field results within a single rotation cycle.

[0108] The wear amount of each tooth surface and node in the complete spline pair geometry model under the current wear cycle is obtained by interpolating the wear amount of the corresponding local single tooth pair node in the fine mesh geometry model. If the global coarse mesh node... Corresponding to four fine mesh nodes The interpolation weights are respectively Then the coarse mesh nodes in the current loop The amount of wear is:

[0109] (4)

[0110] For both the complete spline pair geometry model and the local single-tooth pair geometry model, the wear distribution within a representative cycle is first calculated. Then, the wear amount of that cycle is amplified based on the maximum allowable wear increment. One numerical update represents multiple actual cycles. That is, the wear jump method is used to accelerate the wear evolution process and improve the efficiency of fretting wear iteration calculation. The main calculation formulas are as follows:

[0111] (5)

[0112] (6)

[0113] (7)

[0114] in, The maximum wear increment allowed for a single geometry update; Indicates the first The wear increment scaling factor in the next wear update, i.e. the wear jump factor; and The first Fine mesh nodes after secondary wear update and coarse grid nodes The cumulative wear and tear.

[0115] Example 12:

[0116] This embodiment mainly shares the same content as any one of embodiments 1 to 11, but analyzes the evolution of double-sided fretting wear of ductile iron involute spline pairs under torque and angular misalignment conditions. Using ABAQUS finite element analysis software, a geometric model is established using individual teeth of the internal and external splines as modeling units. The preprocessing settings for the global and sub-models of the angular misalignment involute spline pair simulation are completed using ABAQUS finite element analysis software. Since both the internal and external spline materials in this embodiment are QT700-6, the same material parameters (elastic modulus) are defined for the individual tooth models of the internal and external splines in the material editing module. Poisson's ratio Complete spline pair geometry model, number of teeth. The mesh generation of the geometric model for the complete spline pair and the local single tooth is as follows: Figure 2 and Figure 3 As shown. In comparison, the mesh of the complete spline pair is relatively sparse, while the mesh of the local single tooth pair is finer. In this embodiment, the tooth profile data of the involute spline pair are extracted from the simulation sub-model. The calculation results show that the maximum allowable deflection angle of the relative motion of the involute spline pair is... In this embodiment, the step size of the rotation analysis step for both the global model and the sub-model of the involute spline pair is set to... This results in the involute spline pair having 12 discrete spatial positions within a single rotation cycle. In this embodiment, the contact surfaces of the inner and outer splines are set as mutually master-slave surfaces to simulate double-sided fretting wear. The interaction type of the tooth surface contact area is set to surface-to-surface contact, and the slip formula is finite slip. The contact tangential direction uses a penalty function algorithm, and the friction coefficient is set to 0.3. The contact normal direction uses a hard contact constraint model, allowing separation after contact. In this embodiment, the degree of freedom of the inner spline around the axis of rotation is released and a constraint is applied. Torque, external spline setting The discrete rotation sequence corresponding to the angular skew; and in accordance with the application requirements of ABAQUS sub-model technology, the corresponding boundary conditions are set for the sub-model.

[0117] Using ABAQUS finite element analysis software, the global and local analysis tasks are solved iteratively. In this embodiment, the wear coefficient... The maximum wear increment allowed in a single geometry update The wear cycle is 1, and the total wear amount of each node on the tooth surface is updated after each wear cycle is completed.

Claims

1. A method for evaluating double-sided fretting wear of an angularly misaligned involute spline pair, characterized in that, Includes the following steps: S1) Using finite element analysis software, the geometric models of the internal and external spline single teeth are established respectively, with the internal and external spline single teeth as modeling units, and the material properties of each single tooth model are defined. S2) Assemble and position the internal and external spline single-tooth models to construct the simulation sub-model; at the same time, array the internal and external spline single-tooth models along the circumferential direction to form a complete spline pair geometric model, and construct the global simulation model after completing the assembly and positioning. S3) Perform structured mesh generation on the global simulation model and the simulation sub-model respectively; S4) Calculate the maximum allowable misalignment angle of the spline pair relative motion under angular misalignment conditions; S5) Establish simulation analysis steps for the global simulation model and the simulation sub-model, including wear analysis step and rotation analysis step; wherein, the wear analysis step is used to define the double-sided fretting wear behavior, and the rotation analysis step is used to characterize the relative motion within a single rotation cycle; S6) Based on the contact and motion characteristics of the spline pair under the angular misalignment condition, set the interaction properties, boundary conditions and load conditions for the global simulation model and the sub-simulation model respectively. S7) Create solution jobs for the global simulation model and the sub-simulation model respectively, and configure the corresponding user subroutine files; S8) Submit a global analysis job, define the displacement changes of each node on each tooth surface of the complete spline pair through user subroutines, and solve to obtain the displacement field distribution of the global simulation model; S9) Using the local displacement field of the global analysis job as the boundary condition, submit the local analysis job, define the displacement change of a single tooth on each node of the two tooth surfaces through the user subroutine, and calculate and output the contact stress and contact displacement field variables. S10) Based on the contact stress and contact displacement results output in step S9), calculate the wear amount of each node on the two tooth surfaces of the local single tooth pair and each node on each tooth surface of the complete spline pair under the current wear cycle, update the cumulative wear amount of each node, and then return to step S8) to enter the next wear cycle until the preset number of cycles is reached.

2. The method for evaluating double-sided fretting wear of an angularly misaligned involute spline pair according to claim 1, characterized in that: In step S3), a sparse structured mesh is used for the global simulation model, and a fine structured mesh is used for the sub-simulation models, so as to achieve high-precision solution of the contact field variables of the sub-models while reducing the overall computational overhead.

3. The method for evaluating double-sided fretting wear of an angularly misaligned involute spline pair according to claim 1, characterized in that: In step S4), the tooth profile point set of paired teeth in space is expanded around the rotation axis and deflected around the non-rotation axis. The two-dimensional projection line segment intersection criterion is used to determine tooth profile interference. The deflection angle corresponding to the first interference is taken as the maximum allowable deflection angle for the relative motion of the spline pair. The coordinate calculation formula for the deflection transformation is: （1） （2） in, Let be the three-dimensional coordinates of the set of tooth profile points on one side of a pair of teeth in space. The tooth position angle about the axis of rotation. It is the deflection angle about the non-rotational axis.

4. The method for evaluating double-sided fretting wear of an angularly misaligned involute spline pair according to claim 1, characterized in that: In step S5), the step size of the rotation analysis step is set so that the spline pair has several discrete spatial positions within a single rotation cycle, so as to fully characterize the relative motion process within a rotation cycle.

5. The method for evaluating double-sided fretting wear of an angularly misaligned involute spline pair according to claim 1, characterized in that: In step S6), the inner and outer spline contact surfaces are set as master and slave surfaces to simulate double-sided fretting wear; the contact tangential direction uses a penalty function algorithm to define the friction behavior, and the contact normal direction uses a hard contact constraint model and allows separation after contact.

6. The method for evaluating double-sided fretting wear of an angularly misaligned involute spline pair according to claim 1, characterized in that: In step S6), adaptive mesh regions, adaptive mesh constraints, and adaptive mesh controls are defined for the tooth surface contact areas of the global simulation model and the simulation sub-model, respectively. In the adaptive mesh constraints, user-defined rules are used to define the mesh motion form to achieve dynamic updating of the tooth surface geometry during the wear process.

7. The method for evaluating double-sided fretting wear of an angularly misaligned involute spline pair according to claim 1, characterized in that: In step S7), the user subroutine file is the UMESHMOTION subroutine, and the global analysis job and the local analysis job are configured with independent UMESHMOTION subroutine files respectively.

8. The method for evaluating double-sided fretting wear of an angularly misaligned involute spline pair according to claim 1, characterized in that: In step S9), output variables are set, and contact-related field variables such as contact stress and contact displacement are output at the end of each unit time step.

9. The method for evaluating double-sided fretting wear of an angularly misaligned involute spline pair according to claim 1, characterized in that: In step S10), the current cyclic wear of each node on the two tooth surfaces of the local single tooth is calculated based on the contact stress, relative slip in each direction, and wear coefficient output from the local analysis operation; the wear of the coarse mesh nodes on each tooth surface of the complete spline pair is obtained by interpolation of the wear of the corresponding fine mesh nodes of the sub-model; Fine mesh nodes in a wear cycle The formula for calculating the current cyclic wear is as follows: （3） in, The wear coefficient; For the first Contact stress of the frame; , For the first The relative slippage of the frame in two directions; This represents the total number of frames of the output field results within a single rotation cycle.

10. The method for evaluating double-sided fretting wear of an angularly misaligned involute spline pair according to claim 1, characterized in that: In step S10), the wear jump method is used to accelerate the wear evolution process. First, the wear distribution in a representative cycle is calculated, and then the wear increment scaling factor is determined based on the maximum wear increment allowed by a single geometric update. One numerical update represents multiple actual wear cycles, which improves computational efficiency while ensuring the stability of wear iteration update. If global coarse grid nodes Corresponding to four fine mesh nodes The interpolation weights are respectively Then the coarse mesh nodes in the current loop The amount of wear is: （4） For both the complete spline pair geometry model and the local single-tooth pair geometry model, the wear distribution within a representative cycle is first calculated. Then, the wear amount of that cycle is amplified based on the maximum allowable wear increment. One numerical update represents multiple actual cycles. That is, the wear jump method is used to accelerate the wear evolution process and improve the efficiency of fretting wear iteration calculation. The main calculation formulas are as follows: （5） （6） （7） in, The maximum wear increment allowed for a single geometry update; Indicates the first The wear increment scaling factor in the next wear update, i.e. the wear jump factor; and The first Fine mesh nodes after secondary wear update and coarse grid nodes The cumulative wear and tear.

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