Wear prediction method considering friction coefficient difference

Abstract

The invention discloses a friction coefficient difference-considered wear prediction method, which comprises the following steps of: firstly, obtaining a stable friction coefficient and an evolution law through friction wear tests with different loads and frequencies; secondly, establishing a universal friction coefficient model which comprises a stable friction coefficient model and an evolution model of the friction coefficient along with the cycle number; thirdly, based on an energy method and in combination with the friction coefficient model, an energy wear model considering the friction coefficient difference is established; then, through a UMESHMOTION user subprogram and a loop jump technology, dynamic prediction of the wear depth is achieved in finite element simulation; and finally, verifying the accuracy of model prediction through a test. The dynamic change of the friction coefficient along with the load, the frequency and the cycle index can be accurately reflected, the application range of the energy wear model is expanded, the wear prediction precision under the complex working condition is remarkably improved, and the method has important theoretical significance and engineering application value.

Description

Technical Field

[0001] The present invention relates to the technical field of friction and wear prediction simulation, and in particular to a wear prediction method taking friction coefficient differences into consideration. Background Art

[0002] In engineering, wear is an inevitable phenomenon when materials in contact move relative to each other. This is particularly true in key components such as mechanical structures, bearings, and gears. Wear can increase contact gaps, affecting the structure's vibration characteristics and even threatening its operational safety. Therefore, accurately predicting and controlling the wear behavior of structures during the design phase is of great engineering significance.

[0003] Traditional wear prediction models are primarily based on the Archard wear equation, which states that the wear rate is proportional to the contact pressure load and surface hardness, with the proportionality constant (Archard wear coefficient) determined empirically. While the Archard equation is simple and easy to use, its limitation lies in its failure to account for changes in the friction coefficient during the wear process. In actual operating conditions, the friction coefficient can vary significantly with load, frequency, number of cycles, and other conditions, thus affecting the calculated wear amount. Existing wear prediction methods typically assume the friction coefficient is a constant, ignoring the dynamic characteristics of the friction coefficient as it changes with operating conditions, resulting in significant deviations between the predicted results and the actual situation.

[0004] To overcome this shortcoming, the energy wear method was proposed. This method calculates the wear loss as proportional to the work done by surface friction and takes into account the influence of the friction coefficient on the wear loss. However, existing energy wear methods still fail to fully incorporate the dynamic evolution of the friction coefficient as it changes with load, frequency, number of cycles, and other operating conditions, resulting in insufficient prediction accuracy under complex operating conditions. In particular, under high load, high frequency, or long-term cycling conditions, changes in the friction coefficient have a particularly significant impact on the wear loss, and existing methods struggle to accurately reflect this change.

[0005] Therefore, there is an urgent need for a wear prediction method that can account for variations in friction coefficient. By establishing a quantitative relationship between the friction coefficient and operating parameters such as load, frequency, and number of cycles, combined with energy wear methods, this method can accurately predict wear behavior under complex operating conditions. This present invention addresses this issue, aiming to address the prior art's inadequate consideration of the dynamic variations in friction coefficient and provide a more accurate and adaptable wear prediction method. Summary of the Invention

[0006] The purpose of this section is to summarize some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the abstract and title of this application to avoid obscuring the purpose of this section, the abstract and the title of the invention, and such simplifications or omissions should not be used to limit the scope of the present invention.

[0007] Therefore, in order to solve the above technical problems, the present invention provides the following technical solution: a wear prediction method considering the difference in friction coefficient, the specific steps are as follows:

[0008] S1: Friction and wear test of contacting materials:

[0009] Conduct friction and wear tests on the test materials at different loads and frequencies to obtain the stable friction coefficient, friction coefficient evolution law, and wear rate under different working conditions;

[0010] S2: Establishment of friction coefficient model:

[0011] Based on the experimental data, a universal friction coefficient model is established, including a stable friction coefficient model and a friction coefficient evolution model with the number of cycles;

[0012] S3: Establishment of energy wear model considering the difference in friction coefficient:

[0013] Combining the friction coefficient models under different working conditions, an energy wear model considering the difference in friction coefficient is established;

[0014] S4: Implementation of wear prediction considering differences in friction coefficients:

[0015] Based on the energy wear model that takes into account the difference in friction coefficient and the evolution law of the friction coefficient during the wear process, the wear depth prediction is achieved through the UMESHMOTION user subroutine;

[0016] S5: Model Validation:

[0017] The established model is used to predict the wear depth of the friction contact pair under different working conditions, and the accuracy of the model prediction is verified through friction and wear tests.

[0018] As a preferred solution of the wear prediction method considering friction coefficient differences of the present invention, the method for establishing the universal friction coefficient model in step S2 is as follows:

[0019] S21: Establish a stable friction coefficient model;

[0020] The stable friction coefficient μ0 changes with the change of load conditions. Specifically, the stable friction coefficient μ0 decreases with the increase of normal load and the increase of friction frequency, and has an exponential relationship with the linear speed.

[0021] The expression of the stable friction coefficient μ0 is:

[0022] μ0∝exp(-cv);

[0023] In the above formula, v is the friction linear velocity, c is a constant;

[0024] The friction linear velocity v is expressed by the frequency and friction stroke as follows: v = 2A·f, where A is the friction stroke and f is the friction frequency.

[0025] The stable friction coefficient μ0 has a hyperbolic relationship with the normal load. At this time, the expression of the stable friction coefficient μ0 is:

[0026] μ0∝P -b ;

[0027] Where P is the normal load and b is the exponential constant to be determined;

[0028] Therefore, the final expression of the stable friction coefficient model is:

[0029] μ0=a·P -b exp(-cv)=a·P -b exp(-2cAf);

[0030] In the above formula, constants a, b, and c are obtained through experimental fitting;

[0031] S22: Establish a model for the evolution of friction coefficient with cycle number;

[0032] Specifically, the test results show that the evolution of the friction coefficient increases approximately exponentially with the increase of the cycle number N. Therefore, based on the test results, an exponential fitting is performed on the friction coefficient and the cycle number to obtain the evolution model of the friction coefficient with the cycle number, which is expressed as follows:

[0033]

[0034] In the above expression, μ(N) is the friction coefficient at the Nth cycle, and m and n are obtained through experimental fitting.

[0035] As a preferred solution of the wear prediction method considering the difference in friction coefficients of the present invention, in step S3, the method for constructing the energy wear model considering the difference in friction coefficients is as follows:

[0036] S31: Determine the energy wear coefficient;

[0037] In the energy wear method, the amount of wear is proportional to the work done by the surface friction, and its expression is:

[0038] V=α∑Ed ;

[0039] Among them, ∑E d is the dissipated accumulated friction work; α is the wear coefficient of the energy method;

[0040] The wear coefficient α of the energy method can be obtained by the ratio of volume wear rate to friction coefficient, and its expression is:

[0041]

[0042] In the above formula, μ0 is the friction coefficient at stable state;

[0043] K is the volume wear coefficient, which is obtained by fitting the wear volume of the friction and wear test;

[0044] S32: Establish a wear model that takes into account the difference in friction coefficient;

[0045] The expression of the wear model considering the difference in friction coefficient is:

[0046]

[0047] Substituting the expression of the friction coefficient model applicable to different working conditions into the calculation formula of the energy-based wear amount, a wear model that considers the change of friction coefficient under different load conditions is obtained. The calculation formula of the expanded energy wear model is as follows:

[0048]

[0049] Based on the original model, this wear model is extended to calculate the wear amount under different normal loads and different frequencies.

[0050] As a preferred embodiment of the wear prediction method considering the difference in friction coefficients of the present invention, in step S4, the wear depth prediction method considering the difference in friction coefficients includes the following specific steps:

[0051] S41: In the finite element simulation, the contact setting uses the friction formula of the penalty function to simulate the tangential behavior of the contact surface. Based on the established evolution model of the friction coefficient with the number of cycles, the friction coefficient is modified in each analysis step using Python scripts;

[0052] S42: To effectively simulate wear depth, the cycle-jumping technique has been successfully used in wear simulations. Using the cycle-jumping technique, it is assumed that the wear depth increases linearly within a certain number of cycles ΔN. The wear depth Δh(x) of the nodes within the corresponding ΔN micro-motion cycles can be simulated in one analysis step using the following formula:

[0053]

[0054] Where Δh(x) is the total wear depth in n time periods, q(x,i) and s(x,i) represent the shear stress and slip distance of the contact surface node numbered x at the i-th moment, respectively;

[0055] S43: The wear process is simulated by using node motion and element shape change. The wear process also occurs gradually. After wear occurs, the coordinates of the upper and lower specimens in the constrained finite element model are changed according to the following formula within the framework of the UMESHMOTION user subroutine and adaptive mesh. The calculation formula is as follows:

[0056] y 1,j (x) = y 1,j-1 (x)-Δh 1,j (x);

[0057] y 2,j (x) = y 2,j-1 (x)+Δh 2,j (x);

[0058] Among them, y 1,j (x), y 2,j (x) are the ordinates of the nodes numbered x on the contact surfaces of the upper and lower specimens of the finite element model at the jth analysis step, and y 1,j-1 (x), y 2,j-1 (x) are the ordinates of the upper and lower specimen nodes at the j-1th analysis step, Δh 1,j (x), Δh 2,j (x) are the wear depths of the nodes numbered x on the contact surfaces of the lower and upper specimens calculated by the above step S42 in the jth analysis step.

[0059] As a preferred solution of the wear prediction method considering friction coefficient differences of the present invention, in step S5, the model verification method includes:

[0060] Use the established model to predict the wear depth under different working conditions;

[0061] The accuracy of the model prediction is verified through friction and wear tests to ensure the consistency between the model and the test results.

[0062] As a preferred solution of the wear prediction method considering the difference in friction coefficient described in the present invention, the method is applicable to wear prediction under different normal loads, frequencies and number of cycles, and the accuracy of the model is verified by experimental data.

[0063] Beneficial effects of the present invention:

[0064] 1. This paper uses friction and wear testing to obtain friction coefficient data under different loads, frequencies, and cycle numbers, and establishes a stable friction coefficient model and a friction coefficient evolution model with cycle number. These models accurately reflect the dynamic characteristics of the friction coefficient as it changes with operating conditions, overcoming the constant friction coefficient assumption in existing methods and significantly improving the accuracy of wear prediction.

[0065] 2. Building on the traditional energy wear model, this paper introduces a dynamic model that accounts for the variation of the friction coefficient with operating conditions, expanding the application scope of the energy wear model. By incorporating the friction coefficient model into the energy wear calculation, it can more accurately predict wear under varying loads, frequencies, and cycle times, making it suitable for wear prediction under complex operating conditions.

[0066] 3. The present invention realizes dynamic prediction of wear depth in finite element simulation through UMESHMOTION user subroutine and loop jump technology; this method can simulate the gradual change of contact surface morphology during wear and update the coordinates of contact surface nodes through adaptive mesh technology to ensure the accuracy and reliability of simulation results.

[0067] 4. The present invention adopts cycle skipping technology to linearize the wear depth of multiple micro-motion cycles in one analysis step, significantly improving the calculation efficiency. At the same time, the friction coefficient is dynamically adjusted through Python scripts to achieve efficient simulation of wear behavior under complex working conditions.

[0068] 5. The accuracy of the model prediction was verified by friction and wear tests to ensure the consistency between the model prediction results and the test data; this verification process proves the reliability and practicality of this method in actual engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive effort. Among them:

[0070] Figure 1 It is the workflow diagram of the present invention.

[0071] Figure 2 It is a schematic diagram of the three-dimensional finite element model of the present invention.

[0072] Figure 3 Schematic diagram of constraints and loads of the three-dimensional finite element model of the present invention.

[0073] Figure 4 This is a load displacement amplitude change trend diagram during the loading process of the present invention. DETAILED DESCRIPTION

[0074] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0075] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0076] Secondly, the term "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in various places throughout this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive of other embodiments.

[0077] Reference Figures 1 to 4 , which is an embodiment of the present invention, provides a wear prediction method that takes into account the difference in friction coefficient. This model and application method can effectively predict the wear amount of two friction pairs and has important engineering significance. The specific steps are as follows:

[0078] 1. Offline stage

[0079] 1) Friction and wear test of material contact pairs:

[0080] Conduct friction and wear tests on the test materials at different loads and frequencies to obtain the stable friction coefficient, friction coefficient evolution law, and wear rate under different working conditions;

[0081] 2) Establishment of friction coefficient model and energy wear model:

[0082] Based on the stable friction coefficient and friction coefficient evolution law obtained from the experiment, a universal friction coefficient model was established, including a stable friction coefficient model and a friction coefficient evolution model with the number of cycles. Based on the wear model of the energy method, combined with the friction coefficient models under different working conditions, an energy wear model that takes into account the differences in friction coefficient was established.

[0083] 3) Programming implementation of wear model:

[0084] The wear model was written using Fortran language and based on the UMESHMOTION user subroutine, so that the wear depth of each node could be represented by the movement rule of the adaptive grid in the simulation calculation.

[0085] 2. Online stage

[0086] 1) Establishment and loading settings of finite element model:

[0087] As attached Figure 2 As shown in the attached figure, establish the finite element model required for calculation, input material parameters and set the analysis step; Figure 3 As shown in the figure, a fixed constraint is applied to the bottom surface of the lower specimen, a normal load P is applied to the top of the upper specimen, and a reciprocating displacement load U is applied to the right end of the upper specimen. In the first analysis step, a normal load P is applied to the upper specimen, and then the normal load remains constant. Starting from the second analysis step, a displacement load U is applied to the right side of the upper specimen to complete the meshing of the model.

[0088] 2) Contact settings and dynamic adjustment of friction coefficient:

[0089] In ABAQUS software, the penalty function friction formula is used to simulate the tangential behavior of the contact surface in each analysis step. Based on the established friction coefficient evolution model, the friction coefficient of each analysis step is dynamically adjusted using Python commands.

[0090] 3) Wear depth calculation and stress redistribution in contact area:

[0091] In each incremental step of each analysis step, ABAQUS calculates the wear depth based on the energy wear model that takes into account the difference in friction coefficients. It changes the shape of the contact area by constraining node movement to achieve stress redistribution in the contact area.

[0092] In the energy wear method, the amount of wear is proportional to the work done by the surface friction, and its expression is:

[0093]

[0094] Where K is the volume wear coefficient, P is the normal load, A is the friction stroke, and f is the friction frequency; ∑E d To dissipate the accumulated friction work, constants a, b, and c will be obtained through experimental fitting;

[0095] The local wear depth of each contact point on the contact surface is calculated by applying the local energy wear method to the entire contact interface. The expression of the local wear model is as follows:

[0096]

[0097] Where Δh(x) is the total wear depth in n time periods, q(x,i) and s(x,i) are the shear stress and slip distance of the contact surface node numbered x at the i-th moment, respectively. This allows the wear depth of each node in the contact area to be calculated in the finite element method in any time period.

[0098] A micro-motion cycle can be simulated in one analysis step. The above equation is discretized. Assuming that each analysis step has n simulation increments, the total wear depth in one analysis step can be approximately expressed as:

[0099]

[0100] Where Δh(x) is the wear depth of the contact surface node numbered x in one fretting cycle, and Δs(x,i) is the relative slip distance of the contact surface node numbered x at the i-th moment.

[0101] 4) Cycle skipping technology and wear process simulation:

[0102] Cycle skipping has been successfully used in energy-based wear methods. To effectively simulate wear depth, this method uses a cycle skipping technique, assuming that the wear depth increases linearly within a certain number of cycles ΔN. The wear depth Δh(x) of a node within the corresponding ΔN fretting cycles can be simulated as follows:

[0103]

[0104] The "Arbitrary Lagrangian-Eulerian adaptive meshing" framework provided by ABAQUS gradually improves mesh quality without changing the number and connectivity of existing mesh elements and nodes, making it suitable for simulating wear problems.

[0105] The wear process is simulated by node motion and element shape change, and the wear process occurs gradually. When wear occurs, the coordinates of the constrained test piece and the micro-motion pad are updated according to the following formula under the UMESHMOTION user subroutine and adaptive mesh framework:

[0106] y 1,j (x) = y 1,j-1 (x)-Δh 1,j (x);

[0107] y 2,j (x) = y 2,j-1 (x)+Δh 2,j (x);

[0108] Where y 1,j (x), y 2,j (x) are the ordinates of the nodes numbered x on the contact surfaces of the lower and upper specimens at the jth analysis step, and y 1,j-1 (x), y 2,j-1 (x) are the ordinates of the node numbered x on the contact surface of the lower and upper specimens at the j-1th analysis step, Δh1,j (x), Δh 2,j (x) are the wear depths of the nodes numbered x on the contact surfaces of the lower and upper specimens calculated by the above formula at the jth analysis step;

[0109] 5) Iterative calculation and wear morphology acquisition:

[0110] Repeat the calculations from step 2) to step 4) until the set number of cycles is reached to obtain the contact surface morphology after wear.

[0111] The present invention establishes a dynamic model in which the friction coefficient changes with load, frequency, and number of cycles. By combining the dynamic model of the friction coefficient with the energy wear method, the application scope of the wear prediction model is expanded; through the UMESHMOTION user subroutine and cycle jumping technology, dynamic prediction of wear depth and updating of contact surface morphology are achieved.

[0112] The present invention can accurately predict the wear depth under different loads, frequencies and numbers of cycles, providing an important basis for the design and optimization of mechanical structures; especially under high load, high frequency or long cycle conditions, the prediction accuracy of the present invention is significantly better than existing methods, and has important engineering application value.

[0113] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A wear prediction method considering friction coefficient differences, characterized by: The specific steps are as follows: S1: Conduct friction and wear tests on the test material under different loads and frequencies to obtain the stable friction coefficient, friction coefficient evolution law and wear rate under different working conditions; S2: Based on the stable friction coefficient and friction coefficient evolution law obtained from the experiment, a universal friction coefficient model is established; S3: Wear model based on energy method, considering the friction coefficient model under different working conditions, and establishing an energy wear model considering the difference in friction coefficient; S4: Based on the energy wear model that takes into account the difference in friction coefficient, dynamic prediction of wear depth is achieved in finite element simulation through the UMESHMOTION user subroutine combined with the cycle jumping technology; S5: Verify the consistency between the wear depth predicted by the model and the test results.

2. The wear prediction method considering friction coefficient differences according to claim 1, wherein: The method for establishing the universal friction coefficient model in step S2 is as follows: S21: Establish a stable friction coefficient model; the stable friction coefficient μ0 changes with the change of load conditions. Specifically: the stable friction coefficient μ0 decreases with the increase of normal load and the increase of friction frequency, and has an exponential relationship with the linear speed; the expression of the stable friction coefficient μ0 is: μ0∝exp(-cv); In the above formula, v is the friction linear velocity, c is a constant; The friction linear velocity v is expressed by the frequency and friction stroke as follows: v = 2A·f, where A is the friction stroke and f is the friction frequency. The stable friction coefficient μ0 has a hyperbolic relationship with the normal load. At this time, the expression of the stable friction coefficient μ0 is: μ0∝P -b ; Where P is the normal load and b is the exponential constant to be determined; Therefore, the expression of the stable friction coefficient model is: μ0=a·P -b ·exp(-cv)=a·P -b ·exp(-2cAf); In the above formula, constants a, b, and c are obtained through experimental fitting; S22: Establishing an evolution model of the friction coefficient with the number of cycles; specifically, the friction coefficient increases approximately exponentially with the increase of the number of cycles N. By performing exponential fitting on the friction coefficient and the number of cycles, an evolution model of the friction coefficient with the number of cycles is obtained, and its expression is: In the above expression, μ(N) is the friction coefficient at the Nth cycle, and m and n are obtained through experimental fitting.

3. The wear prediction method considering friction coefficient differences according to claim 2, wherein: In step S3, the method for constructing the energy wear model considering the difference in friction coefficient is as follows: S31: Determine the energy wear coefficient; In the energy wear method, the amount of wear is proportional to the work done by the surface friction, and its expression is: V=α∑E d ; Among them, ∑E d is the dissipated accumulated friction work; α is the wear coefficient of the energy method; The wear coefficient α of the energy method is obtained by the ratio of volume wear rate to friction coefficient, and its expression is: In the above formula, μ0 is the friction coefficient at stable state; K is the volume wear coefficient, which is obtained by fitting the wear volume of the friction and wear test; S32: Establish a wear model that takes into account the difference in friction coefficient; The expression of the wear model considering the difference in friction coefficient is: Substituting the expression of the friction coefficient model applicable to different working conditions into the calculation formula of the energy-based wear amount, a wear model that considers the change of friction coefficient under different load conditions is obtained. The calculation formula of the expanded energy wear model is as follows: Based on the original model, this wear model is extended to calculate the wear amount under different normal loads and different frequencies.

4. The wear prediction method considering friction coefficient differences according to claim 3, wherein: In step S4, the method for predicting the wear depth considering the difference in friction coefficient includes the following specific steps: S41: In the finite element simulation, the penalty function friction formula is used to simulate the contact surface behavior, and the friction coefficient is dynamically adjusted according to the friction coefficient evolution model through Python script; S42: Using cycle skipping technology, the wear depth increases linearly within ΔN cycles. The calculation formula is as follows: Where Δh(x) is the total wear depth in n time periods, q(x,i) and s(x,i) represent the shear stress and slip distance of the contact surface node numbered x at the i-th moment, respectively; S43: When wear occurs, the ordinates of the nodes on the contact surfaces of the upper and lower specimens are updated using the UMESHMOTION subroutine and adaptive mesh technology. The calculation formula is as follows: y 1,j (x)=y 1,j-1 (x)-Δh 1,j (x); y 2,j (x)=y 2,j-1 (x)+Δh 2,j (x); Among them, y 1,j (x), y 2,j (x) are the ordinates of the upper and lower sample nodes at the jth analysis step, y 1,j-1 (x), y 2,j-1 (x) are the ordinates of the upper and lower specimen nodes at the j-1th analysis step, Δh 1,j (x), Δh 2,j (x) is the wear depth calculated in the jth analysis step.

5. The wear prediction method considering friction coefficient differences according to claim 4, characterized in that: In step S5, the model verification method includes: Use the established model to predict the wear depth under different working conditions; The accuracy of the model prediction is verified through friction and wear tests to ensure the consistency between the model and the test results.

6. The wear prediction method considering friction coefficient differences according to any one of claims 1 to 5, characterized in that: The method is applicable to wear prediction under different normal loads, frequencies and cycle numbers, and the accuracy of the model is verified by experimental data.

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