A wear prediction method considering friction coefficient difference

Abstract

The application discloses a wear prediction method considering friction coefficient difference, and comprises the following steps: firstly, obtaining stable friction coefficients and evolution rules through friction and wear tests under different loads and frequencies; secondly, establishing a universal friction coefficient model, including a stable friction coefficient model and an evolution model of friction coefficients with cycle numbers; thirdly, based on an energy method, combining the friction coefficient model, and establishing an energy wear model considering friction coefficient difference; then, through a UMESHMOTION user subroutine and a cycle jump technology, realizing dynamic prediction of wear depth in finite element simulation; finally, verifying the accuracy of model prediction through tests. The application can accurately reflect dynamic changes of friction coefficients with loads, frequencies and cycle numbers, expands the application range of the energy wear model, significantly improves the wear prediction precision under complex working conditions, and has important theoretical significance and engineering application value.

Description

Technical Field

[0001] This invention relates to the field of friction and wear prediction simulation technology, and in particular to a wear prediction method that takes into account differences in friction coefficients. Background Technology

[0002] In the engineering field, wear is an unavoidable phenomenon in the relative motion of material contact pairs. Especially in critical components such as mechanical structures, bearings, and gears, wear leads to an increase in contact gaps, which in turn affects the vibration characteristics of the structure and may even threaten the service safety of the mechanism. Therefore, accurate prediction and control of the wear performance 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 its proportionality constant (Archard wear coefficient) determined empirically. While the Archard equation is simple and easy to use, its limitation lies in failing to consider the changes in the friction coefficient during the wear process. In actual working conditions, the friction coefficient changes significantly with variations in load, frequency, and cycle number, thus affecting the calculated wear amount. Existing wear prediction methods typically assume a constant friction coefficient, neglecting the dynamic characteristics of friction coefficient changes with working conditions, leading to significant deviations between predicted results and actual conditions.

[0004] To overcome this deficiency, the energy-based wear method has been proposed. This method proportionally links the amount of wear to the work done by surface friction and considers the influence of the friction coefficient on the amount of wear. However, existing energy-based wear methods still fail to fully incorporate the dynamic evolution of the friction coefficient with variations in load, frequency, and cycle number, resulting in insufficient prediction accuracy under complex operating conditions. Particularly under high load, high frequency, or long-term cycling conditions, the impact of changes in the friction coefficient on the amount of wear is particularly significant, and existing methods struggle to accurately reflect this variation.

[0005] Therefore, there is an urgent need for a wear prediction method that can take into account differences in friction coefficients. By establishing a quantitative relationship between the friction coefficient and operating parameters such as load, frequency, and cycle number, and combining this with energy-based wear methods, accurate prediction of wear behavior under complex operating conditions can be achieved. This invention is proposed against this backdrop, aiming to address the problem that the dynamic changes in the friction coefficient are not fully considered in existing technologies, and to provide a more accurate and adaptable wear prediction method. Summary of the Invention

[0006] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

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

[0008] S1: Friction and wear test of material contact pairs:

[0009] Friction and wear tests were conducted on the material under different loads and frequencies to obtain the stable friction coefficient, the evolution law of the friction coefficient, and the wear rate under different working conditions.

[0010] S2: Establishment of the friction coefficient model:

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

[0012] S3: Establishment of an energy wear model considering differences in friction coefficients:

[0013] By combining friction coefficient models under different working conditions, an energy wear model considering the differences in friction coefficients is established.

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

[0015] Based on the energy wear model that considers the difference in friction coefficient, and combined with the evolution law of friction coefficient during the wear process, the wear depth is predicted through the UMESHMOTION user subroutine.

[0016] S5: Model Validation

[0017] The established model was used to predict the wear depth of frictional contact pairs under different working conditions, and the accuracy of the model prediction was verified by friction and wear tests.

[0018] As a preferred embodiment of the wear prediction method considering friction coefficient differences described in this 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 load conditions. Specifically, the stable friction coefficient μ0 decreases with the increase of normal load and friction frequency, and has an exponential relationship with linear velocity.

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

[0022] μ0∝exp(-cv);

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

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

[0025] The stable friction coefficient μ0 exhibits a hyperbolic relationship with the normal load. Therefore, the expression for the stable friction coefficient μ0 is:

[0026] μ0∝P -b ;

[0027] Where P is the normal load and b is an undetermined exponential constant;

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

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

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

[0031] S22: Establish an evolution model of the friction coefficient with the number of cycles;

[0032] Specifically, the experimental results show that the friction coefficient increases approximately exponentially with the increase of the number of cycles N. Therefore, based on the experimental results, an exponential fit is performed on the friction coefficient and the number of cycles to obtain the evolution model of the friction coefficient with the number of cycles, the expression of which is:

[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 embodiment of the wear prediction method considering friction coefficient differences described in this invention, in step S3, the method for constructing the energy wear model considering friction coefficient differences is as follows:

[0036] S31: Determine the energy wear coefficient;

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

[0038] V=α∑Ed ;

[0039] Where, ∑E d α represents the accumulated frictional work dissipated; α is the wear coefficient of the energy method.

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

[0041]

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

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

[0044] S32: Establish a wear model that considers differences in friction coefficients;

[0045] The expression for the wear model considering differences in friction coefficients is as follows:

[0046]

[0047] Substituting the expressions of the established friction coefficient models applicable to different working conditions into the energy-based wear calculation formula, we obtain a wear model that considers the variation of friction coefficient under different loads. The extended calculation formula of the energy-based wear model is as follows:

[0048]

[0049] This wear model extends the original model to calculate wear under different normal loads and frequencies.

[0050] As a preferred embodiment of the wear prediction method considering friction coefficient differences according to the present invention, step S4, the method for predicting wear depth considering friction coefficient differences includes the following specific steps:

[0051] S41: In finite element simulation, the contact settings use the friction formula of the penalty function to simulate the tangential behavior of the contact surface, and based on the established evolution model of the friction coefficient with the number of cycles, the friction coefficient of each analysis step is modified using a Python script.

[0052] S42: To effectively simulate wear depth, the cyclic skip technique has been successfully used for wear simulation calculations. The cyclic skip technique assumes 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 over n time periods, and q(x,i) and s(x,i) represent the shear stress and slip distance of the contact surface node numbered x at time i, respectively.

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

[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) represents the ordinate of the node numbered x on the contact surface of the upper and lower specimens in the finite element model at the j-th analysis step, respectively. 1,j-1 (x), y 2,j-1 (x) represents the ordinate of the upper and lower specimen nodes in the (j-1)th analysis step, respectively, and Δh 1,j (x), Δh 2,j (x) represents the wear depth of the node numbered x on the contact surface of the lower and upper samples, calculated by step S42 above in the j-th analysis step.

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

[0060] The established model is used to predict the wear depth under different working conditions;

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

[0062] As a preferred embodiment of the wear prediction method considering the difference in friction coefficient described in this invention, 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.

[0063] The beneficial effects of this invention are:

[0064] 1. This invention obtains friction coefficient data under different loads, frequencies, and cycle numbers through friction and wear tests, and establishes a stable friction coefficient model and an evolution model of the friction coefficient with the number of cycles. These models can accurately reflect the dynamic characteristics of the friction coefficient changing with working conditions, overcome the assumption that the friction coefficient is constant in existing methods, and significantly improve the accuracy of wear prediction.

[0065] 2. This invention introduces a dynamic model of friction coefficient variation with operating conditions into the traditional energy wear model, thus expanding the application scope of the energy wear model. By substituting the friction coefficient model into the energy wear calculation, the wear amount under different loads, frequencies, and cycle numbers can be predicted more accurately, making it suitable for wear prediction under complex operating conditions.

[0066] 3. This invention achieves dynamic prediction of wear depth in finite element simulation through the UMESHMOTION user subroutine and loop jump technology. This method can simulate the gradual change of the contact surface morphology during the wear process and update the coordinates of the contact surface nodes through adaptive mesh technology, ensuring the accuracy and reliability of the simulation results.

[0067] 4. This invention employs a cyclic skipping technique to linearize the wear depth of multiple micro-motion cycles in a single analysis step, significantly improving computational efficiency. Simultaneously, by dynamically adjusting the friction coefficient using a Python script, it achieves efficient simulation of wear behavior under complex working conditions.

[0068] 5. The present invention verifies the accuracy of the model prediction through friction and wear tests, ensuring the consistency between the model prediction results and the experimental data; this verification process proves the reliability and practicality of the method in actual engineering applications. Attached Figure Description

[0069] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments 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. Wherein:

[0070] Figure 1 This is a flowchart of the process of the present invention.

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

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

[0073] Figure 4 This is a graph showing the trend of load displacement amplitude during the loading process of the present invention. Detailed Implementation

[0074] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0075] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0076] Secondly, the term "one embodiment" or "embodiment" as used 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 different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0077] Reference Figures 1-4 As an embodiment of the present invention, a wear prediction method considering the difference in friction coefficients is provided. This model and application method can effectively predict the wear of two friction pairs, which has important engineering significance. The specific steps are as follows:

[0078] 1. Offline Phase

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

[0080] Friction and wear tests were conducted on the material under different loads and frequencies to obtain the stable friction coefficient, the evolution law of the friction coefficient, and the wear rate under different working conditions.

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

[0082] Based on the stable friction coefficient and the evolution law of friction coefficient obtained from experiments, a universal friction coefficient model is established, including a stable friction coefficient model and a friction coefficient evolution model with the number of cycles; based on the wear model of energy method, combined with the friction coefficient model under different working conditions, an energy wear model considering the difference of friction coefficient is established.

[0083] 3) Programming implementation of the wear model:

[0084] Using the Fortran language, a wear model was written based on the UMESHMOTION user subroutine, which represents the wear depth of each node in the simulation calculation through the adaptive mesh movement rule.

[0085] 2. Online Phase

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

[0087] As attached Figure 2 As shown, establish the finite element model required for the calculation, input material parameters, and set the analysis steps; as attached. Figure 3 As shown, 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 mesh generation of the model.

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

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

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

[0091] In each incremental step of each analysis step, the ABAQUS software calculates the wear depth based on an energy wear model that takes into account the difference in friction coefficients. By constraining node movement to change the shape of the contact area, the stress in the contact area is redistributed.

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

[0093]

[0094] Where K is the volumetric wear coefficient, P is the normal load, A is the friction stroke, and f is the friction frequency; ∑E d The constants a, b, and c, representing the accumulated frictional work dissipated, will be obtained through experimental fitting.

[0095] By applying the local energy wear method to the entire contact interface, the local wear depth at each contact point on the contact surface is calculated; the expression for the local wear model is as follows:

[0096]

[0097] In the formula, Δh(x) is the total wear depth over n time periods, and q(x,i) and s(x,i) are the shear stress and slip distance of the contact surface node numbered x at time i, respectively. Thus, the wear depth of each node in the contact area can be calculated in any time period in the finite element method.

[0098] A micro-motion cycle can be simulated within one analysis step. Discretizing the above equation, and assuming each analysis step has n simulation increments, the total wear depth within one analysis step can be approximated as:

[0099]

[0100] In the formula, Δh(x) is the wear depth of the contact surface node numbered x in one micro-motion cycle, and Δs(x,i) is the relative slip distance of the contact surface node numbered x at time i.

[0101] 4) Cyclic jump technology and wear process simulation:

[0102] Cyclic skipping techniques have been successfully applied to energy-based wear methods. To effectively simulate wear depth, this method employs cyclic skipping techniques, assuming that 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 as follows:

[0103]

[0104] The "Arbitrary Lagrangian-Eulerian adaptive meshing" framework provided by ABAQUS can gradually improve the mesh quality without changing the original mesh cell and node number and connection relationship, and is suitable for simulation of wear problems.

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

[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] In the formula, y 1,j (x), y 2,j (x) represents the ordinate of the node numbered x on the contact surface of the lower and upper samples at the j-th analysis step, respectively. 1,j-1 (x), y 2,j-1 (x) represents the ordinate of the node numbered x on the contact surface of the lower and upper samples in the (j-1)th analysis step, and Δh1,j (x), Δh 2,j (x) represents the wear depth of node x on the contact surface of the lower and upper samples, calculated by the above formula in the j-th analysis step;

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

[0110] Repeat steps 2) to 4) until the set number of cycles is reached to obtain the morphology of the worn contact surface.

[0111] This invention establishes a dynamic model of the friction coefficient as a function of load, frequency, and number of cycles. By combining the dynamic friction coefficient model with the energy wear method, the application scope of the wear prediction model is expanded. Through the UMESHMOTION user subroutine and the loop jump technique, dynamic prediction of wear depth and updating of contact surface morphology are realized.

[0112] This invention can accurately predict the wear depth under different loads, frequencies and 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 this invention is significantly better than existing methods, and it 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 it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A wear prediction method considering differences in friction coefficients, characterized in that: The specific steps are as follows: S1: Conduct friction and wear tests on the material under test with 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 its evolution law obtained from experiments, a universal friction coefficient model is established, the expression of which is: ； In the above expression, The friction coefficient is the coefficient of friction in the Nth cycle. To stabilize the friction coefficient, its expression is: , For normal load, The exponent constant is to be determined. For friction stroke, The friction frequency, It is a constant. The results were obtained through experimental fitting. S3: Wear model based on energy method, considering friction coefficient models under different working conditions, establishes an energy wear model that takes into account the difference in friction coefficient, the expression of which is: ； in, This refers to the accumulated frictional work that is dissipated. Where is the wear coefficient of the energy method, and K is the volumetric wear coefficient; S4: Based on the energy wear model that considers the difference in friction coefficient, the wear depth is dynamically predicted in finite element simulation by combining the UMESHMOTION user subroutine with the loop jump technique. Among them, the cyclic skipping technique, in The wear depth increases linearly within each cycle, calculated using the following formula: ； in, Let be the total wear depth over n time periods. , Let x represent the shear stress and slip distance of the contact surface node numbered x at time i, respectively. Let x be the relative sliding distance of the contact surface node at time i. S5: Verify the consistency between the wear depth predicted by the model and the experimental results.

2. The wear prediction method considering friction coefficient differences as described in claim 1, characterized in that: The method for establishing the universal friction coefficient model in step S2 is as follows: S21: Establish a stable friction coefficient model; stable friction coefficient It varies with the load conditions; specifically: the stable friction coefficient. It decreases with increasing normal load and friction frequency, and exhibits an exponential relationship with linear velocity; the stable friction coefficient The expression is: ； In the above formula, Let be the friction linear velocity. It is a constant; Among them, the friction linear velocity Expressed using frequency and friction stroke: In this formula, For friction stroke, The friction frequency; Stable coefficient of friction The coefficient of friction exhibits a hyperbolic relationship with the normal load; in this case, the stable friction coefficient... The expression is: ； in, For normal load, The exponent constant is to be determined. Therefore, the expression for the stable friction coefficient model is: ； In the above formula, the constant The results were obtained through experimental fitting. S22: Establish 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 an exponential fit on the friction coefficient and the number of cycles, the evolution model of the friction coefficient with the number of cycles is obtained, and its expression is: ； In the above expression, The friction coefficient is the coefficient of friction in the Nth cycle. The results were obtained through experimental fitting.

3. The wear prediction method considering the difference in friction coefficient as described in claim 2, characterized in that: 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-based wear method, the amount of wear is directly proportional to the work done by surface friction, and its expression is: ； in, This refers to the accumulated frictional work that is dissipated. The wear coefficient for the energy method; Wear coefficient of energy method It is obtained by the ratio of volumetric wear rate to friction coefficient, and its expression is: ； In the above formula, The coefficient of friction when at rest; K is the volumetric wear coefficient, which is obtained by fitting the wear volume calculation through friction and wear test; S32: Establish a wear model that considers differences in friction coefficients; The expression for the wear model considering differences in friction coefficients is as follows: ； Substituting the expressions of the established friction coefficient models applicable to different working conditions into the energy-based wear calculation formula, we obtain a wear model that considers the variation of friction coefficient under different loads. The extended calculation formula of the energy-based wear model is as follows: ； This wear model extends the original model to calculate wear under different normal loads and frequencies.

4. The wear prediction method considering the difference in friction coefficient as described in claim 3, characterized in that: In step S4, the method for predicting wear depth considering differences in friction coefficients includes the following specific steps: S41: In finite element simulation, the penalty function friction formula is used to simulate the behavior of the contact surface, and the friction coefficient is dynamically adjusted according to the friction coefficient evolution model through Python script; S42: Employs a cyclic skipping technique, in The wear depth increases linearly within each cycle, calculated using the following formula: ； in, Let be the total wear depth over n time periods. , Let x represent the shear stress and slip distance of the contact surface node numbered x at time i, respectively. S43: After wear occurs, the ordinates of the nodes on the contact surface of the upper and lower samples are updated using the UMESHMOTION subroutine and adaptive mesh technology. The calculation formula is as follows: ； ； in, , These are the ordinates of the upper and lower sample nodes at the j-th analysis step, respectively. , These represent the ordinates of the upper and lower specimen nodes in the (j-1)th analysis step, respectively. , The wear depth is calculated in the j-th analysis step.

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

6. The wear prediction method considering the difference in friction coefficient as described in 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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