A high-temperature high-frequency fretting fatigue life prediction method for surface integrity evolution

Abstract

The application relates to a high-temperature high-frequency fretting fatigue life prediction method of surface integrity evolution, and belongs to the field of fretting fatigue life prediction methods. A fretting contact simulation model of a fretting fatigue sample with a real surface topography is established, high-temperature mechanical property parameters and surface residual stress stable values of the fretting fatigue sample are introduced, surface topography evolution in the fretting contact simulation process is realized by combining a surface hardness evolution law, a wear rate evolution model and a self-adaptive grid technology, a high-frequency vibration influence factor is introduced to correct a damage parameter model, and the fretting fatigue life corresponding to the damage parameter and the fretting fatigue damage at the current iteration step are calculated. The damage threshold is used as a criterion for iteration termination, surface topography evolution is used as a damage transmission medium to perform step-by-step iteration, and the total fretting fatigue life is obtained. The application can effectively improve the accuracy and engineering applicability of the fretting fatigue life prediction, and has good popularization and application value.

Description

Technical Field

[0001] This invention belongs to the field of fretting fatigue life prediction methods, and relates to a high-temperature, high-frequency fretting fatigue life prediction method based on surface integrity evolution. Background Technology

[0002] During the service life of aero-engines, the turbine disk tenon joint structure is subjected to the coupled effects of centrifugal force, thermal load, aerodynamic load, and vibration load over a long period of time. In whole-disk tests of multiple engine models, it was found that the complex service environment and the evolution of the surface integrity of the machined surface in the contact area of ​​the turbine disk tenon groove accelerate the accumulation of damage in this contact area, promote the premature initiation of cracks at the tenon groove, and thus cause fretting fatigue failure of the tenon joint structure, ultimately leading to fatigue failure of the turbine disk.

[0003] High-temperature loads and high-frequency vibrations have a significant impact on fretting fatigue life prediction. High temperatures and high-frequency vibrations reduce the mechanical properties of materials. Furthermore, the coupling effect of these two factors leads to the evolution of the surface integrity in the tenon-groove contact area. High temperatures reduce surface hardness and relax residual compressive stress, increasing the fretting wear rate, exacerbating fatigue crack initiation and propagation, and reducing fretting fatigue life. The evolution of the surface morphology after fretting wear alters the contact stress distribution and stress concentration, further increasing or inhibiting fretting wear, thus making the fretting fatigue life uncertain. If the effects of high temperature, high-frequency vibration, and surface integrity evolution are not comprehensively considered in fretting fatigue life prediction, the prediction results are prone to being either conservative or aggressive, thereby affecting the accuracy of the fretting fatigue life prediction.

[0004] To better predict the fretting fatigue life of tenons and mortises, environmental variables or surface integrity parameters are typically incorporated into classic fretting fatigue damage models. Therefore, this paper proposes a fretting fatigue life prediction method that simultaneously considers surface integrity parameters and high-temperature, high-frequency vibration. This method is of great significance for studying the influence of surface integrity on fretting fatigue and for establishing and validating life prediction models.

[0005] Currently, there are some patented technologies for the study of fretting fatigue at the tenon joint of turbine blades, but there are still certain limitations.

[0006] Chinese invention patent CN202110291467.6 discloses "A fretting fatigue life prediction model and method considering surface roughness." This technology introduces a wear coefficient factor related to surface roughness to characterize the influence of initial surface roughness on fretting fatigue behavior, thus considering surface morphology factors. However, during fretting fatigue testing, the contact surface morphology continuously evolves with wear, and its evolution law is difficult to accurately obtain and quantify. Therefore, this patent does not further establish a fretting contact model that includes the surface morphology evolution characteristics. Chinese invention patent CN202110117449.6 discloses "A fretting fatigue life prediction method considering wear effects under spectral loading." This technology introduces an energy wear model into the fretting fatigue life prediction framework, but the evolution law of surface hardness at high temperatures is difficult to obtain, causing this patent to fail to consider the influence of surface hardness evolution under high-temperature conditions on fretting fatigue behavior. Chinese invention patent CN202411090806.4 discloses an "Efficient Prediction Model for Fretting Fatigue Life Considering Surface Condition." This technology comprehensively considers factors such as residual stress after relaxation and stabilization, fretting wear, and initial stress concentration factor. However, this model still relies on surface parameters in the initial or stable state and does not further consider the influence of surface morphology and surface hardness evolution during fretting fatigue on contact behavior and fatigue life. Furthermore, because high-frequency vibration loading conditions are difficult to achieve under experimental conditions, and the frequency influence coefficient during high-frequency vibration is difficult to accurately obtain through experimental or theoretical methods, none of the aforementioned patented technologies consider the impact of high-frequency vibration on fretting fatigue life. Summary of the Invention

[0007] To overcome the shortcomings of the prior art, the present invention provides a high-temperature and high-frequency fretting fatigue life prediction method based on surface integrity evolution, which can fully consider the influence of high temperature, high frequency and surface integrity evolution on fretting fatigue life. The surface integrity evolution includes: surface hardness evolution, surface residual stress evolution and surface morphology evolution, and the selection of processing technology and process parameters for serving and supporting tenon and mortise components.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A method for predicting high-temperature, high-frequency fretting fatigue life based on surface integrity evolution includes the following steps:

[0010] Step 1: Extract the surface morphology parameters of the fretting fatigue specimen, establish a finite element geometric model of the fretting fatigue specimen with a realistic surface morphology, and establish a fretting contact simulation model through the tangential fit between the fretting fatigue specimen and the fretting pad; details are as follows:

[0011] Step 1.1: Obtain the surface morphology of the fretting fatigue specimen using a white light interferometer, output the Z-coordinate parameters of the fretting fatigue specimen surface morphology to a .txt file, and establish a finite element geometric model of the fretting fatigue specimen with a real surface morphology by using the coordinate mapping method in Comsol software to obtain the Z-coordinate parameters in the .txt file.

[0012] Step 1.2: Define the length direction of the fretting fatigue specimen as the axial direction and the direction perpendicular to the length direction of the fretting fatigue specimen as the normal direction. Apply a high-frequency vibration normal load P to the fretting pad and an axial load Q to the fretting fatigue specimen to establish a fretting contact simulation model.

[0013] Step 2: Based on the high-temperature mechanical properties of the fretting fatigue specimens, the evolution law of surface residual stress is obtained. By calculating the stable value of surface residual stress, the evolution law of surface hardness of the fretting fatigue specimens is obtained. The high-temperature wear rate model is then modified based on the Archard model; the details are as follows:

[0014] Step 2.1: Conduct high-temperature tensile tests on the fretting fatigue specimens at high temperatures to obtain their high-temperature mechanical properties, including yield strength, tensile strength, elastic modulus, and Poisson's ratio.

[0015] Step 2.2: By conducting surface residual stress relaxation tests at different test time points, the variation law of surface residual stress over time is obtained, that is, the evolution law of surface residual stress is obtained, as shown in formula (1):

[0016] (1)

[0017] Where t represents the test time; σ res (t) represents the surface residual stress at time t; σ0 represents the initial surface residual stress; B represents the material constant; Q represents the activation energy; R represents the gas molar constant; T represents the absolute temperature; D represents the material constant.

[0018] Based on the variation law of surface residual stress with time, as the test time increases, the surface residual stress gradually decreases and reaches t=t balance When a stable value is reached, t=t balance Substituting into formula (1), the stable value of surface residual stress σ is calculated. res,balance ; where t balance This indicates the time required for the residual stress to stabilize.

[0019] Step 2.3: By conducting surface hardness evolution tests at different test time points, the surface hardness variation law over time is obtained, i.e., the surface hardness evolution law is obtained, as shown in formula (2):

[0020] (2)

[0021] Where HV(t) represents the surface hardness at time t, HV0 represents the initial surface hardness, a represents the pre-exponential factor, and m represents a constant; A constant power representing time.

[0022] Step 2.4: Based on the surface hardness evolution law in Step 2.3, the wear rate k is corrected to obtain its high-temperature wear rate evolution model; specifically as follows:

[0023] The traditional Archard model is shown in formula (3). Based on formula (4), the wear rate k of the fretting fatigue sample surface is calculated. In this invention, the surface hardness evolution law obtained in step 2.3 is used to replace HV0 with HV(t) to modify formula (4), and the modified high-temperature wear rate model is shown in formula (5):

[0024] (3)

[0025] (4)

[0026] (5)

[0027] Where k represents the wear rate, k(t) represents the wear rate at time t, V represents the wear volume, P represents the contact pressure, and s represents the sliding distance.

[0028] Step 3: Create material properties based on the high-temperature mechanical properties of the fretting fatigue specimens from Step 2.1; add the stable value of surface residual stress from Step 2.2 as prestress to the fretting contact simulation model established in Step 1.2; and establish a fretting contact simulation model considering surface morphology evolution based on the high-temperature wear rate model obtained in Step 2.4 and adaptive mesh technology, introducing a high-frequency vibration influence factor (1+f) d The damage parameter model is modified, and then the fretting fatigue life prediction model is modified to calculate fretting fatigue damage; specifically:

[0029] Step 3.1: Based on the high-temperature mechanical properties obtained in Step 2.1, establish ABAQUS material properties that consider the high-temperature mechanical properties of the fretting fatigue specimen, and add them to the fretting contact simulation model established in Step 1.2.

[0030] Step 3.2, apply prestress to the t=t obtained in step 2.2. balance The surface residual stress stability value σ at time t res,balance Add it to the micro-motion contact simulation model established in step 1.2.

[0031] Step 3.3, based on the high-temperature wear rate model in Step 2.4, calculate the wear depth, perform node offsetting using adaptive meshing technology, and then establish a micro-motion contact simulation model considering surface morphology evolution; specifically:

[0032] Step 3.3.1: In the fretting contact simulation model in step 1.2, set the adaptive mesh element set SET1 for the contact area between the fretting pad and the fretting fatigue specimen, and set the node set corresponding to the element in element set SET1 to SET2.

[0033] Step 3.3.2: Using the high-temperature wear rate model k(t) modified in step 2.4, calculate the wear depth Δh(x,i). Use adaptive mesh technology to offset the nodes of the fretting fatigue specimen SET2 in the fretting contact simulation model to establish a fretting contact simulation model of the surface morphology evolution of the contact area.

[0034] Step 3.4, using the high-frequency vibration influence factor (1+ ) and damage parameter SWT res,HV Multiply to obtain the corrected damage parameter SWT, which takes into account the influence of high-frequency vibration factors. res,HV,f The formula is as follows:

[0035] (6)

[0036] (7)

[0037] Where f represents the vibration frequency, and d represents the frequency influence coefficient. This represents the dimensionless frequency influence factor. Indicates the maximum normal stress. SWT represents the maximum normal strain. res,HV SWT represents the damage parameter that takes into account surface hardness and residual surface stress. res,HV,f This represents the damage parameters that take into account surface hardness, surface residual stress, and high-frequency vibration.

[0038] Step 3.5, based on the fretting fatigue life prediction model (8), combined with steps 3.1 to 3.4, the modified fretting fatigue life prediction model is as follows:

[0039] (8)

[0040] (9)

[0041] in, E represents the fatigue strength coefficient, b represents the elastic modulus, and N represents the fatigue strength index. f This represents the total fretting fatigue life. denoted by , where c represents the fatigue ductility coefficient and c represents the fatigue ductility factor.

[0042] Step 3.6, calculate the total fretting fatigue damage D, using the following formula:

[0043] (10)

[0044] Where D represents fretting fatigue damage.

[0045] Step 4: After analyzing the fretting contact simulation model established in Step 3.4 using ABAQUS, calculate the fretting fatigue life using formula (9) and the fretting fatigue damage using formula (10). When the damage does not exceed the damage threshold, perform node offset according to the wear depth and update the nodes of the finite element geometric model of the fretting fatigue specimen. If the fretting fatigue damage exceeds the damage threshold, calculate the total fretting fatigue life. The specific iterative steps are as follows:

[0046] Step 4.1: To reduce computation time, the iteration step is increased by ΔN times. The fretting contact simulation model is analyzed using ABAQUS. After the calculation is completed, the fretting fatigue life N under step 1 is calculated using formula (11). f1 Then, the fretting fatigue damage D1 under step 1 is calculated using formula (12);

[0047] (11)

[0048] (12)

[0049] Among them, SWT(1) res,HV,f This represents the damage parameters in step 1. This represents the maximum normal stress in step 1. N represents the maximum normal strain in step 1. f1 D represents the fretting fatigue life corresponding to the damage parameters in step 1, D1 represents the fretting fatigue damage in step 1, ΔN represents the iteration amplification factor, and D r This represents the damage threshold.

[0050] Step 4.2, compare D1 and D r When D1 is not less than D r When D1 is less than D, terminate the iteration and calculate the total fretting fatigue life; r At that time, based on the wear evolution law, the wear depth Δh(x,1) is calculated, node offset is performed, and node coordinate y1(x) is updated, so as to update the surface morphology of the finite element geometric model and the fretting contact simulation model of the fretting fatigue specimen.

[0051] (13)

[0052] (14)

[0053] Where x represents the node number, Δh(x,1) represents the wear depth of the x-th node in step 1, q(x,1) represents the contact stress of the x-th node in step 1, Δs(x,1) represents the slip distance increment of the x-th node in step 1, y2(x) represents the node coordinates after step 1 iteration, and y1(x) represents the initial node coordinates.

[0054] After reanalyzing the micro-motion contact simulation model using ABAQUS, the maximum normal stress in step 2 was calculated. and maximum normal strain The fretting fatigue life N in step 2 is calculated using formula (15). f2 Then, the fretting fatigue damage D2 in step 2 is calculated using formula (16);

[0055] (15)

[0056] (16)

[0057] Among them, SWT(2) res,HV,f This represents the damage parameters in step 2. This represents the maximum normal stress in step 2. N represents the maximum normal strain in step 2. f2 D1 represents the fretting fatigue life corresponding to the damage parameter in step 2, and D2 represents the fretting fatigue damage in step 2.

[0058] Step 4.3, compare D2 and D r When D2 is not less than D r When D2 is less than D, the iteration terminates and the total fretting fatigue life is calculated; r Based on the wear evolution law, Δh(x,2) is calculated, node offset is performed, and node coordinates y2(x) are updated, so as to update the surface morphology of the finite element geometric model and the fretting contact simulation model of the fretting fatigue specimen.

[0059] (17)

[0060] (18)

[0061] Where Δh(x,2) represents the wear depth of the x-th node in step 2, q(x,2) represents the contact stress of the x-th node in step 2, Δs(x,2) represents the slip distance increment of the x-th node in step 2, and y3(x) represents the node coordinates after step 2 iteration.

[0062] After reanalyzing the micro-motion contact simulation model using ABAQUS, the maximum normal stress in step 3 was calculated. and maximum normal strain The fretting fatigue life N in step 3 is calculated using formula (19). f3 Then, the fretting fatigue damage D3 in step 3 is calculated using formula (20);

[0063] (19)

[0064] (20)

[0065] Among them, SWT(3) res,HV,f This represents the damage parameters in step 3. This represents the maximum normal stress in step 3. N represents the maximum normal strain in step 3. f3 D3 represents the fretting fatigue life corresponding to the damage parameter in step 3, and D3 represents the fretting fatigue damage in step 3.

[0066] Step 4.4, compare D3 and D r When D3 is not less than D r When D3 is less than D, terminate the iteration and calculate the total fretting fatigue life; r Following the iterative steps 4.1 to 4.3, and based on the wear evolution pattern, calculate Δh(x,i-1), perform node offset, and update the node coordinates y. i-1 (x), thereby achieving the purpose of updating the surface morphology of the finite element geometric model and the fretting contact simulation model of the fretting fatigue specimen;

[0067] (twenty one)

[0068] (twenty two)

[0069] Where i represents the iteration step, Δh(x,i-1) represents the wear depth of the x-th node in the (i-1)-th step, q(x,i-1) represents the contact stress of the x-th node in the (i-1)-th step, Δs(x,i-1) represents the slip distance increment of the x-th node in the (i-1)-th step, and y i-1 (x) represents the node coordinates after the (i-2)th iteration, y i (x) represents the node coordinates after the (i-1)th iteration;

[0070] After reanalyzing the micro-motion contact simulation model using ABAQUS, the maximum normal stress at step i is calculated. and maximum normal strain The fretting fatigue life N in the i-th step is calculated using formula (23). fi Then, the fretting fatigue damage D in the i-th step is calculated using formula (24). i The total fretting fatigue damage D is calculated using formula (25), and D and D are compared. r When D exceeds D r The total fretting fatigue life N is calculated using formula (26). f ;

[0071] (twenty three)

[0072] (twenty four)

[0073] (25)

[0074] (26)

[0075] Where, SWT(i) res,HV,f This represents the damage parameter at step i. This represents the maximum normal stress at step i. It means that N fi Let represent the fretting fatigue life corresponding to the damage parameter in step i, and let Di represent the fretting fatigue damage in step i.

[0076] In summary, this invention provides a method for predicting high-temperature, high-frequency fretting fatigue life based on the evolution of surface integrity. By constructing a fretting contact simulation model that considers the evolution of surface integrity at the contact interface, this invention provides a unified description of the evolution laws of high temperature, high-frequency vibration, surface residual stress, surface hardness, and surface morphology, thereby improving the prediction accuracy of the fretting fatigue life prediction model. Compared with existing technologies, this invention effectively improves the accuracy and engineering applicability of fretting fatigue life prediction and has significant potential for widespread application.

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] (1) This invention utilizes the evolution of surface hardness, the evolution of surface residual stress and the evolution of surface morphology to enhance the prediction accuracy of fretting fatigue life, which helps to improve the processing technology of tenon and mortise.

[0079] (2) The present invention utilizes the high frequency vibration influence factor, so that the influence of high frequency vibration can be taken into account in the fretting fatigue life prediction process, thereby increasing the prediction accuracy.

[0080] (3) Based on the idea of ​​damage iteration, this invention considers the influence of the evolution of surface integrity parameters on fretting fatigue life. Attached Figure Description

[0081] Figure 1 This is a flowchart of a high-temperature, high-frequency fretting fatigue life prediction method for surface integrity evolution according to the present invention.

[0082] Figure 2 This is a schematic diagram of a micro-motion contact simulation model;

[0083] Figure 3 This is a schematic diagram of the normal load P from high-frequency vibration.

[0084] Figure 4 This is a schematic diagram of the axial load Q;

[0085] Figure 5 This is a schematic diagram of the coordinate offset of the fretting wear node. Detailed Implementation

[0086] The invention will be further described below with reference to the accompanying drawings.

[0087] This invention proposes a method for predicting fretting fatigue life. Based on simple finite element calculation, this method integrates the evolution of surface integrity, such as surface hardness evolution, surface residual stress evolution, and surface morphology evolution, and further introduces high-temperature mechanical properties and high-frequency vibration influence factors to improve the prediction accuracy of fretting fatigue life.

[0088] This embodiment provides a method for predicting high-temperature, high-frequency fretting fatigue life based on surface integrity evolution, such as... Figure 1 As shown, it includes the following steps:

[0089] Step 1: Extract the surface morphology parameters of the fretting fatigue specimen, establish a finite element geometric model of the fretting fatigue specimen with a realistic surface morphology, and establish a fretting contact simulation model through the tangential fit between the fretting fatigue specimen and the fretting pad, as detailed below:

[0090] Step 1.1: Obtain the surface morphology of the fretting fatigue specimen using a white light interferometer, and output the Z-coordinate parameters of the fretting fatigue specimen surface morphology to a .txt file. Then, use the coordinate mapping method in Comsol software to establish a finite element geometric model of the fretting fatigue specimen with a realistic surface morphology, as detailed below. Figure 2 The fretting fatigue specimen is shown in the image.

[0091] Step 1.2: Define the length direction of the fretting fatigue specimen as the axial direction and the direction perpendicular to the length direction of the fretting fatigue specimen as the normal direction. Apply a high-frequency vibration normal load P on the fretting pad, such as... Figure 3 As shown, an axial load Q is applied to the fretting fatigue specimen, as follows: Figure 4 As shown, a micro-motion contact simulation model is established, such as... Figure 2 As shown.

[0092] Step 2: Based on the high-temperature mechanical properties of the fretting fatigue specimens, the evolution law of surface residual stress is obtained. By calculating the stable value of surface residual stress, the evolution law of surface hardness of the fretting fatigue specimens is obtained. The high-temperature wear rate model is modified based on the Archard model, as follows:

[0093] Step 2.1: Conduct high-temperature tensile tests on the fretting fatigue specimens at high temperatures to obtain their high-temperature mechanical properties, including yield strength, tensile strength, elastic modulus, and Poisson's ratio.

[0094] Step 2.2: By conducting surface residual stress relaxation tests at different test time points, the variation law of surface residual stress over time is obtained, that is, the evolution law of surface residual stress is obtained, as shown in formula (1):

[0095] (1)

[0096] Where t represents the test time; σ res (t) represents the surface residual stress at time t; σ0 represents the initial surface residual stress; B represents the material constant; Q represents the activation energy; R represents the gas molar constant; T represents the absolute temperature; D represents the material constant.

[0097] Based on the variation law of surface residual stress with time, as the test time increases, the surface residual stress gradually decreases and reaches t=t balance When a stable value is reached, t=t balance Substituting into formula (1), the stable value of surface residual stress σ is calculated. res,balance ; where t balance This represents the time required for residual stress to stabilize.

[0098] Step 2.3: By conducting surface hardness evolution tests at different test time points, the surface hardness variation law over time is obtained, i.e., the surface hardness evolution law is obtained, as shown in formula (2):

[0099] (2)

[0100] Where HV(t) represents the surface hardness at time t, HV0 represents the initial surface hardness, a represents the pre-exponential factor, and m represents a constant; A constant power representing time;

[0101] Step 2.4: Based on the surface hardness evolution law in Step 2.3, the wear rate k is corrected to obtain its high-temperature wear rate evolution model, as follows:

[0102] The traditional Archard model is shown in formula (3). Based on formula (4), the wear rate k of the fretting fatigue sample surface is calculated. In this invention, the surface hardness evolution law obtained in step 2.3 is used to replace HV0 with HV(t) to modify formula (4), and the modified high temperature wear rate model k(t) is obtained, as shown in formula (5):

[0103] (3)

[0104] (4)

[0105] (5)

[0106] Where k represents the wear rate, k(t) represents the wear rate at time t, V represents the wear volume, P represents the contact pressure, and s represents the sliding distance;

[0107] Step 3: Create material properties based on the high-temperature mechanical properties of the fretting fatigue specimens from Step 2.1; add the stable value of surface residual stress from Step 2.2 as prestress to the fretting contact simulation model established in Step 1.2; and establish a fretting contact simulation model considering surface morphology evolution based on the high-temperature wear rate model obtained in Step 2.4 and adaptive mesh technology, introducing a high-frequency vibration influence factor (1+f) d The damage parameter model is modified, and then the fretting fatigue life prediction model is modified to calculate fretting fatigue damage; specifically:

[0108] Step 3.1: Based on the high-temperature mechanical properties obtained in Step 2.1, establish ABAQUS material properties that consider the high-temperature mechanical properties of the fretting fatigue specimen, and add them to the fretting contact simulation model established in Step 1.2.

[0109] Step 3.2, apply prestress to the t=t obtained in step 2.2. balance The surface residual stress stability value σ at time t res,balance Add it to the micro-motion contact simulation model established in step 1.2;

[0110] Step 3.3, based on the high-temperature wear rate model in Step 2.4, calculate the wear depth, perform node offsetting using adaptive meshing technology, and then establish a micro-motion contact simulation model considering surface morphology evolution; specifically:

[0111] Step 3.3.1: In the fretting contact simulation model in step 1.2, set the adaptive mesh element set SET1 for the contact area between the fretting pad and the fretting fatigue specimen, and set the node set corresponding to the element in element set SET1 to SET2.

[0112] Step 3.3.2: Using the high-temperature wear rate model k(t) modified in step 2.4, calculate the wear depth Δh(x,i), and use adaptive mesh technology to offset the nodes of the fretting fatigue specimen SET2 in the fretting contact simulation model to establish a fretting contact simulation model of the surface morphology evolution of the contact area.

[0113] Step 3.4, using the high-frequency vibration influence factor (1+f) d ) and damage parameter SWT res,HV Multiply to obtain the corrected damage parameter SWT, which takes into account the influence of high-frequency vibration factors. res,HV,f The formula is as follows:

[0114] (6)

[0115] (7)

[0116] Where f represents the vibration frequency, and d represents the frequency influence coefficient. This represents the dimensionless frequency influence factor. Indicates the maximum normal stress. SWT represents the maximum normal strain. res,HV SWT represents the damage parameter that takes into account surface hardness and residual surface stress. res,HV,f This represents damage parameters that take into account surface hardness, surface residual stress, and high-frequency vibration.

[0117] Step 3.5, based on the fretting fatigue life prediction model (8), combined with steps 3.1 to 3.4, the modified fretting fatigue life prediction model is as follows:

[0118] (8)

[0119] (9)

[0120] in, E represents the fatigue strength coefficient, b represents the elastic modulus, and N represents the fatigue strength index. f This represents the total fretting fatigue life. represents the fatigue ductility coefficient, and c represents the fatigue ductility factor;

[0121] Step 3.6, combine the N obtained in step 3.5 f The total fretting fatigue damage D is calculated using the following formula:

[0122] (10)

[0123] Where D represents fretting fatigue damage;

[0124] Step 4: After analyzing the fretting contact simulation model established in Step 3.4 using ABAQUS, calculate the fretting fatigue life using formula (9) and the fretting fatigue damage using formula (10). When the damage does not exceed the damage threshold, perform node offset according to the wear depth and update the nodes of the finite element geometric model of the fretting fatigue specimen. If the fretting fatigue damage exceeds the damage threshold, calculate the total fretting fatigue life. The specific iterative steps are as follows:

[0125] Step 4.1: To reduce computation time, the iteration step is increased by ΔN times. The fretting contact simulation model is analyzed using ABAQUS. After the calculation is completed, the fretting fatigue life N under step 1 is calculated using formula (11). f1 Then, calculate the fretting fatigue damage D1 in step 1 using formula (12), and compare D1 with D r :

[0126] (11)

[0127] (12)

[0128] Among them, SWT(1) res,HV,f This represents the damage parameters in step 1. This represents the maximum normal stress in step 1. N represents the maximum normal strain in step 1. f1 D represents the fretting fatigue life corresponding to the damage parameters in step 1, D1 represents the fretting fatigue damage in step 1, ΔN represents the iteration amplification factor, and D r Indicates the damage threshold;

[0129] Step 4.2, when D1 is less than D r At that time, based on the wear evolution law, the wear depth Δh(x,1) is calculated, node offset is performed, and the node coordinate y1(x) is updated. The schematic diagram of the fretting wear node coordinate offset is shown in the figure. Figure 5 As shown, this is to achieve the purpose of updating the surface morphology of the finite element geometric model and the fretting contact simulation model of the fretting fatigue specimen;

[0130] (13)

[0131] (14)

[0132] Where x represents the node number, Δh(x,1) represents the wear depth of the x-th node in step 1, q(x,1) represents the contact stress of the x-th node in step 1, Δs(x,1) represents the slip distance increment of the x-th node in step 1, y2(x) represents the node coordinates after step 1 iteration, and y1(x) represents the initial node coordinates.

[0133] After reanalyzing the micro-motion contact simulation model using ABAQUS, the maximum normal stress in step 2 was calculated. and maximum normal strain The fretting fatigue life N in step 2 is calculated using formula (15). f2 Then, calculate the fretting fatigue damage D2 in step 2 using formula (16), and compare D2 with D r ;

[0134] (15)

[0135] (16)

[0136] Among them, SWT(2) res,HV,f This represents the damage parameters in step 2. This represents the maximum normal stress in step 2. N represents the maximum normal strain in step 2. f2 D1 represents the fretting fatigue life corresponding to the damage parameters in step 2, and D2 represents the fretting fatigue damage in step 2.

[0137] Step 4.3, when D2 is less than D r Based on the wear evolution law, Δh(x,2) is calculated, node offset is performed, and node coordinates y2(x) are updated, so as to update the surface morphology of the finite element geometric model and the fretting contact simulation model of the fretting fatigue specimen.

[0138] (17)

[0139] (18)

[0140] Where Δh(x,2) represents the wear depth of the x-th node in step 2, q(x,2) represents the contact stress of the x-th node in step 2, Δs(x,2) represents the slip distance increment of the x-th node in step 2, and y3(x) represents the node coordinates after step 2 iteration;

[0141] After reanalyzing the micro-motion contact simulation model using ABAQUS, the maximum normal stress in step 3 was calculated. and maximum normal strain The fretting fatigue life N in step 3 is calculated using formula (19). f3 Then, calculate the fretting fatigue damage D3 in step 3 using formula (20), and compare D3 with D r ;

[0142] (19)

[0143] (20)

[0144] Among them, SWT(3) res,HV,f This represents the damage parameters in step 3. This represents the maximum normal stress in step 3. N represents the maximum normal strain in step 3. f3 D3 represents the fretting fatigue life corresponding to the damage parameter in step 3, and D3 represents the fretting fatigue damage in step 3.

[0145] Step 4.4, D3 is less than D r Following the iterative steps 4.1 to 4.3, and based on the wear evolution pattern, calculate Δh(x,i-1), perform node offset, and update the node coordinates y. i-1 (x), thereby achieving the purpose of updating the surface morphology of the finite element geometric model and the fretting contact simulation model of the fretting fatigue specimen;

[0146] (twenty one)

[0147] (twenty two)

[0148] Among them, SWT(3) res,HV,f This represents the damage parameters in step 3. This represents the maximum normal stress in step 3. N represents the maximum normal strain in step 3. f3 D3 represents the fretting fatigue life corresponding to the damage parameter in step 3, and D3 represents the fretting fatigue damage in step 3.

[0149] After reanalyzing the micro-motion contact simulation model using ABAQUS, the maximum normal stress at step i is calculated. and maximum normal strain The fretting fatigue life N in the i-th step is calculated using formula (23). fi Then, the fretting fatigue damage D in the i-th step is calculated using formula (24). i The total fretting fatigue damage D is calculated using formula (25), and D and D are compared. r When D exceeds D r The total fretting fatigue life N is calculated using formula (26). f ;

[0150] (twenty three)

[0151] (twenty four)

[0152] (25)

[0153] (26)

[0154] Where, SWT(i) res,HV,f This represents the damage parameter at step i. This represents the maximum normal stress at step i. It means that N fi D represents the fretting fatigue life corresponding to the damage parameter in step i. i This represents the fretting fatigue damage at step i.

[0155] The above embodiments are provided merely for the purpose of describing the present invention and are not intended to limit the scope of the invention. Various equivalent substitutions and modifications made without departing from the spirit and principles of the present invention should be included within the scope of the present invention.

Claims

1. A method for predicting high-temperature, high-frequency fretting fatigue life based on surface integrity evolution, characterized in that, The high-temperature, high-frequency fretting fatigue life prediction method includes the following steps: Step 1: Extract the surface morphology parameters of the fretting fatigue specimen, establish a finite element geometric model of the fretting fatigue specimen with a real surface morphology, and establish a fretting contact simulation model through the tangential fit between the fretting fatigue specimen and the fretting pad. Step 2: Based on the high-temperature test of the fretting fatigue specimen, obtain its high-temperature mechanical properties, obtain the evolution law of surface residual stress, calculate the stable value of surface residual stress, obtain the evolution law of surface hardness of the fretting fatigue specimen, and modify the high-temperature wear rate model based on the Archard model. Step 3: Create material properties based on the high-temperature mechanical properties of the fretting fatigue specimens in Step 2, add the stable value of surface residual stress as prestress to the fretting contact simulation model; establish a fretting contact simulation model that considers the evolution of surface morphology using the high-temperature wear rate model and adaptive mesh technology, introduce the high-frequency vibration influence factor to correct the damage parameter model, and then correct the fretting fatigue life prediction model to calculate fretting fatigue damage. Step 4: After analyzing the fretting contact simulation model, calculate the fretting fatigue life and fretting fatigue damage respectively. When the damage does not exceed the damage threshold, perform node offset according to the wear depth and update the nodes of the finite element geometric model of the fretting fatigue specimen. If the fretting fatigue damage exceeds the damage threshold, calculate the total fretting fatigue life.

2. The high-temperature, high-frequency fretting fatigue life prediction method based on surface integrity evolution according to claim 1, characterized in that, Step 1 is described in detail below: Step 1.1: Obtain the surface morphology of the fretting fatigue specimen using a white light interferometer, and establish a finite element geometric model of the fretting fatigue specimen with a real surface morphology. Step 1.2: Define the length direction of the fretting fatigue specimen as the axial direction and the direction perpendicular to the length direction of the fretting fatigue specimen as the normal direction. Apply a high-frequency vibration normal load P to the fretting pad and an axial load Q to the fretting fatigue specimen to establish a fretting contact simulation model.

3. The high-temperature, high-frequency fretting fatigue life prediction method based on surface integrity evolution according to claim 2, characterized in that, Step 2 is described in detail below: Step 2.1: Conduct high-temperature tensile tests on the fretting fatigue specimens at high temperatures to obtain their high-temperature mechanical properties, including yield strength, tensile strength, elastic modulus, and Poisson's ratio. Step 2.2: By conducting surface residual stress relaxation tests at different test time points, the variation law of surface residual stress over time is obtained, that is, the evolution law of surface residual stress is obtained, as shown in formula (1): （1） where t represents the test time; σ res (t) represents the surface residual stress at time t; σ0represents the initial surface residual stress; B represents a material constant; Q represents an activation energy; R represents a gas molar constant; T represents an absolute temperature; D represents a material constant; Based on the variation law of surface residual stress with time, as the test time increases, the surface residual stress gradually decreases and reaches t=t balance When a stable value is reached, t=t balance Substituting into formula (1), the stable value of surface residual stress σ is calculated. res,balance ; where t balance This represents the time required for residual stress to stabilize. Step 2.3: By conducting surface hardness evolution tests at different test time points, the surface hardness variation law over time is obtained, i.e., the surface hardness evolution law is obtained, as shown in formula (2): （2） Where HV(t) represents the surface hardness at time t, HV0 represents the initial surface hardness, a represents the pre-exponential factor, and m represents a constant; A constant power representing time; Step 2.4: Based on the surface hardness evolution law in Step 2.3, the wear rate k is corrected to obtain its high-temperature wear rate evolution model; specifically as follows: The traditional Archard model is shown in Equation (3). Based on Equation (4), the wear rate k of the fretting fatigue sample surface is calculated. Equation (4) is modified by replacing HV0 with HV(t), and the modified high-temperature wear rate model is shown in Equation (5). （3） （4） （5） Where k represents the wear rate, k(t) represents the wear rate at time t, V represents the wear volume, P represents the contact pressure, and s represents the sliding distance.

4. The high-temperature, high-frequency fretting fatigue life prediction method based on surface integrity evolution according to claim 3, characterized in that, Step 3 is described in detail below: Step 3.1: Based on the high-temperature mechanical properties obtained in Step 2.1, establish ABAQUS material properties that consider the high-temperature mechanical properties of the fretting fatigue specimen and add them to the fretting contact simulation model. Step 3.2, apply prestress to the t=t obtained in step 2.

2. balance The surface residual stress stability value σ at time t res,balance Add it to the micro-motion contact simulation model; Step 3.3: Based on the high-temperature wear rate model in Step 2.4, calculate the wear depth, perform node offset using adaptive meshing technology, and then establish a micro-motion contact simulation model that considers the evolution of surface morphology. Step 3.4, using the high-frequency vibration influence factor (1+ Damage parameter SWT considering surface hardness and residual surface stress res,HV Multiplying these values ​​yields the corrected damage parameter SWT, which takes into account surface hardness, residual surface stress, and high-frequency vibration. res ,HV,f The formula is as follows: （6） （7） Where f represents the vibration frequency, and d represents the frequency influence coefficient. This represents the dimensionless frequency influence factor. Indicates the maximum normal stress. SWT represents the maximum normal strain. res,HV SWT represents the damage parameter that takes into account surface hardness and residual surface stress. res,HV,f This represents damage parameters that take into account surface hardness, surface residual stress, and high-frequency vibration. Step 3.5, based on the fretting fatigue life prediction model (8), combined with steps 3.1 to 3.4, the modified fretting fatigue life prediction model is as follows: （8） （9） in, E represents the fatigue strength coefficient, b represents the elastic modulus, and N represents the fatigue strength index. f This represents the total fretting fatigue life. represents the fatigue ductility coefficient, and c represents the fatigue ductility factor; Step 3.6, calculate the total fretting fatigue damage D, using the following formula: （10） Where D represents fretting fatigue damage.

5. The high-temperature, high-frequency fretting fatigue life prediction method based on surface integrity evolution according to claim 4, characterized in that, Step 3.3 is as follows: Step 3.3.1: In the fretting contact simulation model in step 1.2, set the adaptive mesh element set SET1 for the contact area between the fretting pad and the fretting fatigue specimen, and set the node set corresponding to the element in element set SET1 to SET2. Step 3.3.2: Calculate the wear depth Δh(x,i) using the high-temperature wear rate model k(t) modified in step 2.

4. Then, use adaptive mesh technology to offset the nodes of the fretting fatigue specimen SET2 in the fretting contact simulation model to establish a fretting contact simulation model of the surface morphology evolution of the contact area.

6. The high-temperature, high-frequency fretting fatigue life prediction method based on surface integrity evolution according to claim 5, characterized in that, Step 4 is described in detail below: Step 4.1: The iteration step is amplified by ΔN times. The fretting contact simulation model is analyzed using ABAQUS. First, the fretting fatigue life N under step 1 is calculated using formula (11). f1 Then, the fretting fatigue damage D1 under step 1 is calculated using formula (12); （11） （12） in, This represents the damage parameters in step 1. This represents the maximum normal stress in step 1. N represents the maximum normal strain in step 1. f1 D represents the fretting fatigue life corresponding to the damage parameters in step 1, D1 represents the fretting fatigue damage in step 1, ΔN represents the iteration amplification factor, and D r Indicates the damage threshold; Step 4.2, compare D1 and D r When D1 is not less than D r When D1 is less than D, terminate the iteration and calculate the total fretting fatigue life; r At that time, based on the wear evolution law, the wear depth Δh(x,1) is calculated, node offset is performed, and node coordinates are updated, so as to update the surface morphology of the finite element geometric model and the fretting contact simulation model of the fretting fatigue specimen. （13） （14） Where x represents the node number, Δh(x,1) represents the wear depth of the x-th node in step 1, q(x,1) represents the contact stress of the x-th node in step 1, Δs(x,1) represents the slip distance increment of the x-th node in step 1, y2(x) represents the node coordinates after step 1 iteration, and y1(x) represents the initial node coordinates. After reanalyzing the micro-motion contact simulation model using ABAQUS, the maximum normal stress in step 2 was calculated. and maximum normal strain The fretting fatigue life N in step 2 is calculated using formula (15). f2 Then, the fretting fatigue damage D2 in step 2 is calculated using formula (16); （15） （16） Among them, SWT(2) res,HV,f This represents the damage parameters in step 2. This represents the maximum normal stress in step 2. N represents the maximum normal strain in step 2. f2 D1 represents the fretting fatigue life corresponding to the damage parameters in step 2, and D2 represents the fretting fatigue damage in step 2. Step 4.3, compare D2 and D r When D2 is not less than D r When D2 is less than D, the iteration terminates and the total fretting fatigue life is calculated; r Based on the wear evolution law, Δh(x,2) is calculated, node offset is performed, and node coordinates are updated, so as to update the surface morphology of the finite element geometric model and the fretting contact simulation model of the fretting fatigue specimen. （17） （18） Where Δh(x,2) represents the wear depth of the x-th node in step 2, q(x,2) represents the contact stress of the x-th node in step 2, Δs(x,2) represents the slip distance increment of the x-th node in step 2, and y3(x) represents the node coordinates after step 2 iteration; After reanalyzing the micro-motion contact simulation model using ABAQUS, the maximum normal stress in step 3 was calculated. and maximum normal strain The fretting fatigue life N in step 3 is calculated using formula (19). f3 Then, the fretting fatigue damage D3 in step 3 is calculated using formula (20); （19） （20） Among them, SWT(3) res,HV,f This represents the damage parameters in step 3. This represents the maximum normal stress in step 3. N represents the maximum normal strain in step 3. f3 D3 represents the fretting fatigue life corresponding to the damage parameter in step 3, and D3 represents the fretting fatigue damage in step 3. Step 4.4, compare D3 and D r When D3 is not less than D r When D3 is less than D, the iteration terminates and the total fretting fatigue life is calculated; r Iterate sequentially according to steps 4.1 to 4.3, calculate Δh(x,i-1) based on the wear evolution law, perform node offset, and update the node coordinate y. i-1 (x), thereby achieving the purpose of updating the surface morphology of the finite element geometric model and the fretting contact simulation model of the fretting fatigue specimen; （21） （22） Where i represents the iteration step, Δh(x,i-1) represents the wear depth of the x-th node in the (i-1)-th step, q(x,i-1) represents the contact stress of the x-th node in the (i-1)-th step, Δs(x,i-1) represents the slip distance increment of the x-th node in the (i-1)-th step, and y i-1 (x) represents the node coordinates after the (i-2)th iteration, y i (x) represents the node coordinates after the (i-1)th iteration; After reanalyzing the micro-motion contact simulation model using ABAQUS, the maximum normal stress at step i is calculated. and maximum normal strain The fretting fatigue life N in the i-th step is calculated using formula (23). fi Then, the fretting fatigue damage D in the i-th step is calculated using formula (24). i The total fretting fatigue damage D is calculated using formula (25), and D and D are compared. r When D exceeds D r The total fretting fatigue life N is calculated using formula (26). f ; （23） （24） （25） （26） Where, SWT(i) res,HV,f This represents the damage parameter at step i. This represents the maximum normal stress at step i. It means that N fi D represents the fretting fatigue life corresponding to the damage parameter in step i. i This represents the fretting fatigue damage at step i.

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