A method for calculating wear amount of guide pair running-in process based on fractal theory and test data

Abstract

The present application relates to a kind of based on fractal theory and test data's guide rail pair running-in process wear amount calculation method, including step 1, on the basis of Weierstrass-Mandelbrot (W-M) function, the contact model of guide rail pair test sample contact surface micro asperity is established, according to the area distribution law of micro asperity on the surface of mechanical part, the contact area of micro asperity is calculated;Step 2, wear test is carried out, the fractal dimension (D) and characteristic scale coefficient (G) of sample contact surface are detected, the contact load and maximum contact area of micro asperity are calculated, and the specific stage of elastic-plastic deformation of micro asperity in contact process is distinguished;Step 3, suppose that micro asperity of contact surface is all hemispherical, in actual wear process, the wear amount on entire contact surface is calculated according to the formula of each elastic-plastic deformation stage.

Description

Technical Field

[0001] This invention relates to the field of guide rail pair friction and wear calculation, and in particular to a method for calculating the wear amount during the running-in process of guide rail pairs based on fractal theory and experimental data. Background Technology

[0002] A rolling guide pair is a rolling guiding device consisting of a guide rail with raceways, a slider, rolling elements that circulate between the slider and the guide rail, a return mechanism, and sealing end caps. The rolling elements continuously circulate between the slider and the guide rail, allowing the load platform to move linearly along the guide rail with high precision. Because it can achieve micron-level positioning accuracy, it is widely used in machine tools where the working parts require uniform movement, sensitive motion, and high positioning accuracy. During operation, the guide pair experiences wear, resulting in loss of accuracy, reduced rigidity, and decreased reliability. Therefore, studying the wear of the guide pair is crucial to ensuring its accuracy and the precise and reliable operation of the machine tool.

[0003] Currently, many scholars have explored the application of fractal theory in tribology.

[0004] Zhou et al.'s paper, "A new model for the preload degradation of linear rolling guide," uses fractal theory to calculate the actual contact area in establishing a preload loss model for linear rolling guide pairs, deriving a formula for calculating the wear depth of the guide pair, and verifying it through experiments. However, the paper has several drawbacks. First, using preload to indirectly represent wear depth is inaccurate and indirect. First, the magnitude of preload includes not only changes in wear depth but also deformation of the rolling elements, randomness of contact points, and other factors. Second, it fails to distinguish between elastic and plastic deformation during the contact process of micro-protrusions. Third, due to the large size and weight of linear rolling guide pairs, the amount of wear cannot be directly detected, and changes in wear during the running-in process cannot be detected.

[0005] In their study, "A modeling method for predicting the precision loss of the preload double-nut ball screw induced by raceway wear based on fractal theory," Jiajia Zhao et al. introduced fractal theory into the characterization of the wear surface of the ball screw and nut raceway. They used the structure function method to process the contour data of the wear surface, obtaining the fractal dimension and characteristic scale coefficient, which are independent of the measurement instrument resolution. The wear volume of the raceway was then calculated using these fractal parameters. Wenjun Gong et al.'s study, "Adhesion-fatigue dual-mode wear model for fractal surfaces in AISI1045 cylinder-plane contact pairs," applied fractal theory to the friction and wear research of slide valves. They uniquely represented the wear surface using the fractal dimension (D) and characteristic scale coefficient (G) as parameters. By distinguishing the critical diameter between adhesive wear and fatigue wear, they established a dual-mode wear model of adhesive fatigue, which was verified through (cylinder-plane pair) experiments. Neither of these similar papers considered the difference in wear amounts between elastoplastic contacts.

[0006] The patent CN201710247319.8, "Method for Calculating Wear of Spur Gears," published by Zhu Lisha et al., calculates the wear depth and wear amount at each tooth position by considering the surface pressure and sliding velocity at the meshing point of the spur gear, based on the Archard friction and wear model. The patent CN202210776652.9, "Image Processing-Based Bearing Wear Detection Method and System," published by Li Haiyan et al., acquires surface images of bearing wear, uses template image blocks to traverse and match the images of the surface to be tested, and defines images with a similarity greater than a preset similarity threshold as wear areas, while others are not considered wear areas. Neither of these patents uses fractal theory to calculate wear amount, nor does it analyze the elastoplastic contact stage in detail.

[0007] In summary, existing technologies for calculating guideway wear have the following limitations:

[0008] (1) The elastic deformation and plastic deformation during the contact process of micro-protrusions were not distinguished, resulting in a large gap between the theoretical assumptions and the actual contact situation.

[0009] (2) Using the preload of the guide rail pair to indirectly represent the wear depth or wear amount is not accurate or direct enough, because the magnitude of the preload includes not only the change in wear depth, but also other factors such as the deformation of the rolling elements and the randomness of the contact points.

[0010] (3) Since the rolling linear guide pair is large in volume and heavy in weight, the wear amount cannot be directly detected. The accuracy of the guide pair friction and wear prediction model has not been verified by direct experiment. Summary of the Invention

[0011] This invention provides a method for calculating the wear amount during the running-in process of a guide rail pair, based on fractal theory and experimental data, targeting the contact wear surfaces within the guide rail pair.

[0012] The technical solution adopted by this invention to solve the above problems is: a method for calculating the wear amount of guide rail pairs during the running-in process based on fractal theory and experimental data, including the following steps.

[0013] Step 1: Based on the Weierstrass-Mandelbrot function, establish a micro-protrusion contact model for the guide rail pair contact surface. The contact between two rough surfaces is equivalent to the contact between one rough surface and another rigid surface. The following assumptions are made: 1. The rough surface is isotropic and has fractal characteristics; 2. When analyzing the micro-contact process, work hardening caused by material deformation, changes in hardness depth, and friction between micro-protrusions are ignored. The contact area 'a' of the micro-protrusions is calculated based on the area distribution law of the micro-protrusions on the surface of the mechanical part.

[0014] Step 2: Conduct a wear and break-in test, measure the fractal dimension D and characteristic scale coefficient G of the contact surface of the test sample, and calculate the maximum contact area a of the micro-protrusions in combination with the contact load F. l Determine which stage of elastoplastic deformation the micro-protrusion is in during the contact process;

[0015] Step 3: Set all micro-protrusions on the contact surface to be hemispherical. In the actual wear process, calculate the wear amount on the entire contact surface according to the formulas for each stage of elastic-plastic deformation.

[0016] As one of the embodiments of this application, in step 1, the area distribution law of the micro-protrusions on the surface of the mechanical part is based on the area distribution law of islands in the ocean discovered by Mandelbrot, and is used to calculate the contact area a of the micro-protrusions. (Refer to Majumdar A, Tien C L. Fractional characterization and simulation of rough surfaces[J]. Wear, 1990, 136(2):313-327.)

[0017] Furthermore, in step 1, Majumdar and Bhushan have proven that the spatial frequency of the profile curve satisfies γ. -n=l, substituting this expression into the Weierstrass-Mandelbrot(WM) function yields

[0018]

[0019] In the formula, l is the sampling length in meters (m); G is the characteristic scale coefficient in meters (m).

[0020] The maximum height δ of the roughness peak before deformation of the micro-convex body was obtained as follows:

[0021] δ=G D-1 l 2-D

[0022] The radius of curvature R of the peak before deformation of the micro-convex body is expressed in meters.

[0023]

[0024] Using Hertz theory of elastic contact, the critical deformation δe for elastic deformation of the micro-convex body is obtained, and the relationship between the deformation δe and the normal load p is as follows:

[0025]

[0026] Where E is the equivalent elastic modulus of the two contact surface materials, which can be calculated by the following formula:

[0027]

[0028] E1 and E2 are the elastic moduli of the two contact surface materials, with the unit being Pa; ν1 and ν2 are the Poisson's ratios of the two contact surface materials, which are dimensionless.

[0029] According to Hertz theory

[0030]

[0031] Where, σ s K is the yield strength of the softer material in the contact surface. f It is the coefficient of friction of the contact surfaces, which can be calculated by the following formula:

[0032]

[0033] In the formula, μ is the friction coefficient;

[0034] Combining the above four equations, we can obtain the critical deformation δe at which the micro-protrusions on the contact surface begin to yield.

[0035]

[0036] When the deformation of the micro-protrusion δ = δ eAt this point, the critical value between elastic deformation and plastic deformation is obtained, and the critical elastic contact area a is obtained. e for

[0037]

[0038] Where φ=σ s ×E -1 Indicates material properties;

[0039] When the deformation of the micro-protrusion δ = 110δ e At this point, the micro-protrusion enters the stage of complete plastic deformation, and the deformation of the micro-protrusion is in δ. e ~110δ e The period between these two stages is known as the elasto-plastic deformation stage. The relationship between the critical elastic contact area and the critical plastic contact area is as follows:

[0040]

[0041] The critical plastic contact area a is obtained p

[0042]

[0043] When the deformation of the micro-protrusion δ > δ e , that is, a<a e Plastic deformation occurs; when the deformation of the micro-protrusion δ < δ e , that is, a>a e Elastic deformation occurs.

[0044] As one embodiment of this application, the area distribution function n(a) of the micro-protrusion contact point in the method is:

[0045]

[0046] Where Ψ represents the domain expansion factor of the contact size distribution, which is related to the fractal dimension:

[0047] Ψ (2-D) / 2 -(1+Ψ -(2-D) / D )=(2-D) / D

[0048] The actual contact area Ar of the friction pair is:

[0049]

[0050] In the formula, n(a)da represents the number of micro-protrusions on the rough surface with an area between a and a+da.

[0051] As one embodiment of this application, in step 2, the contact load of the micro-protrusion is calculated, taking into account the change in the maximum contact surface caused by the elastic deformation and plastic deformation of the micro-protrusion, and the entire wear stage is divided into two types:

[0052] When the contact area a of the micro-protrusion is greater than a e At this time, the micro-protrusion undergoes elastic deformation, and the elastic contact load at this point is...

[0053]

[0054] In the formula, a e It is the critical elastic contact area of ​​the micro-convex body, in meters. 2 E is the equivalent elastic modulus, in Pa; R is the radius of the peak of the micro-convexity, in meters; δ is the deformation of the micro-convexity, in meters; G is the characteristic scale coefficient, in meters; D is the fractal dimension, dimensionless.

[0055] When the contact area of ​​the micro-protrusion a ≤ a e At this time, the micro-protrusion is in the plastic deformation stage, and the normal load of the plastic deformation is...

[0056] F p =kσ s a

[0057] Where k is a variable related to hardness H and yield strength σ. s The relevant factor H = kσ s σ s Hardness H and yield strength σ s The unit is Pa.

[0058] The contact load F of the micro-forehead is the normal load on the contact surface. The maximum contact area a of the micro-forehead can be obtained by inverse solving the above equation. l .

[0059] The above two equations describe the load on a single micro-protrusion with a contact area of ​​*a*. Combining this with the area distribution function of the micro-protrusion, the load on the entire contact surface is obtained as follows:

[0060] (1) When a l ≥a e At that time, a l This represents the maximum contact area of ​​the micro-protrusion. The micro-protrusion undergoes both plastic and elastic deformation, and the total contact load F on the entire surface is...

[0061] When D≠1.5

[0062]

[0063] When D=1.5

[0064]

[0065] In the formula, Ψ represents the domain expansion factor of the contact size distribution, which is related to the fractal dimension D, and Ar is the actual contact area of ​​the friction pair, in meters.2 ;

[0066] (2) When a l <a e The micro-protrusions only undergo plastic deformation, and the contact load on the entire contact surface is...

[0067]

[0068] Specifically, in step 3, assuming that all micro-protrusions on the contact surface are hemispherical, the contact area of ​​the spherical peak is...

[0069]

[0070] During the wear process, relative sliding occurs at the contact points. When the sliding distance at the contact points is l, l = a 0.5 The amount of wear V(a) generated during this time is

[0071]

[0072] The wear volume on the entire contact surface is

[0073]

[0074] The above formula assumes that there is only one micro-protrusion on each contact surface. For all micro-protrusions, the total moving distance l1 of the friction pair when V-shaped wear debris is generated is:

[0075]

[0076] In actual wear processes, not all micro-protrusions undergo wear. Here, a wear probability coefficient λ is introduced. When the movement distance of the friction pair is S (in meters), the wear amount on the entire contact surface is...

[0077]

[0078] As one of the embodiments of this application, in step 2, a wear running-in test is conducted using a wear running-in test bench: the contact form, contact stress, roughness and hardness of the rolling guide pair are simulated by the mutual grinding contact of the test specimens. The test specimens include an upper specimen and a lower specimen. The upper specimen is a mutual grinding specimen, and the lower specimen is a test specimen. Both are designed as annular specimens. The upper specimen and the lower specimen are fitted with an interference fit so that they are in close contact during the test. The upper specimen is installed on the upper rotating shaft, and the lower specimen is installed on the lower rotating shaft, so that the upper specimen and the lower specimen roll relative to each other. The friction and wear generated by the relative rolling are used to simulate the contact wear between the rolling elements and the raceway of the guide pair during the running-in process. By periodically detecting and measuring the contour data of the test specimen surface after the interval, the fractal dimension D and characteristic scale coefficient G are calculated using the structure function method. The wear amount within the measurement interval is then calculated and compared with the wear amount obtained by actual weighing.

[0079] Ideally, during the wear and break-in test, the maximum contact stress of the test specimen was set to be consistent with the maximum contact stress between the rolling elements and the raceway during actual operation of the guide rail pair.

[0080] Preferably, the upper sample material is set as the rolling element material, and the circular surface of the upper sample is designed with two arc-shaped convex surfaces to simulate the rolling element; the lower sample material is set as the raceway material, and the circular surface of the lower sample is designed with two arc-shaped concave surfaces corresponding to the two arc-shaped convex surfaces of the upper sample to simulate the raceway. The upper sample and the lower sample make grinding contact through the two arc-shaped convex surfaces and the two arc-shaped concave surfaces.

[0081] Ideally, a preliminary test should be conducted before the wear and break-in test. The purpose of the preliminary test is to determine the cutoff condition and measurement interval. The roughness of the raceway when the guide rail pair loses its accuracy is used as the benchmark. The number of rotations of the lower shaft corresponding to the lower sample reaching the same roughness is used as the cutoff condition of the test. The measurement interval is determined according to the duration of the preliminary test.

[0082] Preferably, the test specimen is weighed before the wear and break-in test. During the wear and break-in test, the weight of the test specimen is recorded after each measurement interval, and the wear amount during that measurement interval is calculated. The profile data is measured using a surface roughness meter. The structure function method treats the surface profile with fractal properties as a time series z(x), and this time series satisfies the following structure function for its sampled data:

[0083] S(τ) = <[z(x+τ)-z(x)] 2 >=Cτ 4-2D

[0084] In the above formula:

[0085] [z(x+τ)-z(x)] 2 —The arithmetic mean of the differences;

[0086] C is a constant;

[0087] τ — An arbitrary value for the data interval, i.e., the sampling interval;

[0088] D – Fractal dimension;

[0089] As shown above, the structure function S(τ) is a power function of τ. S(τ) can be calculated from the profile curve z(x). Taking the logarithm of both sides of the above equation, we plot the discrete point relationship between lg(S) and lg(τ) on logarithmic coordinates. Then, we obtain a linear fitting curve. Let the slope of the fitting curve be m and the intercept be n. Then, the fractal dimension and characteristic scaling coefficient of the profile curve are respectively:

[0090]

[0091]

[0092] Compared with the prior art, the advantages of the present invention are as follows:

[0093] (1) The changes in the maximum contact surface caused by the elastic deformation and plastic deformation of the micro-protrusion are taken into account. The entire wear stage is divided into two stages and calculation formulas are given for each stage, which improves the calculation accuracy of the theoretical wear of the guide rail pair.

[0094] (2) Test specimens (upper specimen and lower specimen) are used instead of guide rail pairs. During the running-in wear test, the wear amount can be calculated and measured directly multiple times to monitor the entire wear process.

[0095] (3) The contact radius of the sample is consistent with that of the rolling elements (steel balls) and raceway inside the guide rail pair, the maximum contact stress is consistent, and the contact stress distribution is consistent, so as to ensure that the contact mechanical state of the wear test sample is consistent with that of the guide rail pair when it is working. Attached Figure Description

[0096] Figure 1 This is a schematic diagram of micro-protrusion contact;

[0097] Figure 2 Here is a flowchart of the running-in wear test;

[0098] Figure 3 This is a cross-sectional view of a linear guide pair;

[0099] Figure 4 The diagram shows the running-in wear test results for the upper and lower samples.

[0100] Figure 5 for Figure 4 Side view of the structure shown;

[0101] Figure 6 This is a diagram showing the change in fractal dimension during the wear process in the embodiment;

[0102] Figure 7 It is a comparison between the test values ​​and theoretical calculation values ​​of wear in the implementation case;

[0103] Figure 1 In the diagram, R represents the radius of curvature of the peak of the micro-protrusion, in meters; δ represents the maximum height of the rough peak before deformation of the micro-protrusion, in meters; l is the sampling length; and l' is the contact length of the micro-protrusion after deformation, in meters. Detailed Implementation

[0104] The present invention will be further described in detail below with reference to the embodiments. The embodiments are exemplary and intended to explain the present invention, but should not be construed as limiting the present invention.

[0105] Combination Figure 2 This invention provides a method for calculating the wear amount during the running-in process of guide rail pairs based on fractal theory and experimental data, comprising the following steps:

[0106] Step 1: Based on the Weierstrass-Mandelbrot(WM) function, establish a contact model of the micro-protrusions on the guide rail pair contact surface. Calculate the contact area 'a' of the micro-protrusions according to the area distribution law of the micro-protrusions on the surface of the mechanical part. A schematic diagram of the micro-protrusion contact is shown below. Figure 1 As shown. Majumdar and Bhushan have proven that the spatial frequency of the profile curve satisfies γ. -n =l, substituting into the above formula ((WM) function) yields

[0107]

[0108] In the formula, l is the sampling length in meters (m); G is the characteristic scale coefficient in meters (m).

[0109] The maximum height δ of the roughness peak before deformation of the micro-convex body can be obtained.

[0110] δ=G D-1 l 2-D

[0111] The radius of curvature R of the peak before deformation of the micro-convex body is

[0112]

[0113] In the formula, l is the sampling length in meters (m); G is the characteristic scale coefficient in meters (m).

[0114] Using Hertz theory of elastic contact, the critical deformation δe for elastic deformation of the micro-convex body is obtained, and the relationship between the deformation δe and the normal load is as follows:

[0115]

[0116] Where E is the equivalent elastic modulus of the two contact surface materials, which can be calculated by the following formula:

[0117]

[0118] E1 and E2 are the elastic moduli of the two contacting surface materials, in Pa; ν1 and ν2 are the Poisson's ratios of the two contacting surface materials, dimensionless.

[0119] According to Hertz theory

[0120]

[0121] Where, σs K is the yield strength of the softer material in the contact surface. f It is the coefficient of friction of the contact surfaces, which can be calculated by the following formula:

[0122]

[0123] In the formula, μ is the friction coefficient.

[0124] Combining the above four equations, we can obtain the critical deformation δe at which the micro-protrusions on the contact surface begin to yield.

[0125]

[0126] When the deformation of the micro-protrusion δ = δ e At this point, the critical value between elastic deformation and plastic deformation is obtained, and the critical elastic contact area a is obtained. e for

[0127]

[0128] Where φ=σ s ×E -1 Indicates material properties.

[0129] When the deformation of the micro-protrusion δ = 110δ e At this point, the micro-protrusion enters the stage of complete plastic deformation, and the deformation of the micro-protrusion is in δ. e ~110δ e The period between these two stages is known as the elasto-plastic deformation stage. The relationship between the critical elastic contact area and the critical plastic contact area is as follows:

[0130]

[0131] The critical plastic contact area a is obtained p

[0132]

[0133] When the deformation of the micro-protrusion δ > δ e , that is, a<a e Plastic deformation occurs; when the deformation of the micro-protrusion δ < δ e , that is, a>a e Elastic deformation occurs. From the above analysis, it can be seen that during the contact process of the micro-protrusions, as the contact area increases, the micro-protrusions first undergo plastic deformation, and then elastic deformation. This is because when the microscopic peaks of the two surfaces first come into contact, due to the small radius of curvature, the contact point is in a plastic contact state, the contact area increases, and some of the pressure is released, after which it enters an elastic contact state.

[0134] The area distribution function n(a) of the contact points of the micro-convex body is:

[0135]

[0136] Where Ψ represents the domain expansion factor of the contact size distribution, which is related to the fractal dimension:

[0137] Ψ (2-D) / 2 -(1+Ψ -(2-D) / D )=(2-D) / D

[0138] The actual contact area Ar of the friction pair is:

[0139]

[0140] In the formula, n(a)da represents the number of micro-protrusions on the rough surface with an area between a and a+da.

[0141] Step 2: Measure the fractal dimension (D) and characteristic scale coefficient (G) of the contact surface, and calculate the maximum contact area a of the micro-protrusion based on the contact load F of the micro-protrusion. l Identify which stage of elastoplastic deformation the micro-protrusion is in during the contact process.

[0142] When the contact area a of the micro-protrusion is greater than a e The micro-protrusion undergoes elastic deformation, and the elastic contact load at this time is:

[0143]

[0144] When the contact area a of the micro-protrusion is less than a e The micro-protrusion is in the plastic deformation stage, at which time the normal load of plastic deformation is

[0145] F p =kσ s a

[0146] Where k is a variable related to hardness H and yield strength σ. s The relevant factor H = kσ s Hardness H and yield strength σ s The unit is Pa.

[0147] The contact load of the micro-protrusion is the normal load on the sample. The maximum contact area 'a' of the micro-protrusion can be obtained by inverse solving the above equation. l .

[0148] The above two equations describe the load on a single micro-protrusion with a contact area of ​​*a*. Combining this with the area distribution function of the contact point, the load on the entire contact surface is obtained as follows:

[0149] 1. When a l >a e At this time, the micro-protrusion undergoes both plastic and elastic deformation, and the total contact load F on the entire surface is...

[0150] When D≠1.5

[0151]

[0152] When D=1.5

[0153]

[0154] 2. When a l ≤a e The micro-protrusions only undergo plastic deformation, and the contact load on the entire contact surface is...

[0155]

[0156] Step 3: Assuming that all micro-protrusions on the contact surface are hemispherical, calculate the wear amount on the entire contact surface according to the formulas for each stage of elastic-plastic deformation during the actual wear process.

[0157] Assuming that all micro-protrusions on the contact surface are hemispherical, then the contact area of ​​the spherical peak is:

[0158]

[0159] During the wear process, relative sliding occurs at the contact points. When the contact points slide a distance l (l = a) 0.5 The wear amount V(a) generated at time ) is

[0160]

[0161] The wear volume on the entire contact surface is

[0162]

[0163] The above formula assumes that there is only one micro-protrusion on each contact surface. For all micro-protrusions, the total moving distance l1 of the friction pair when V-shaped wear debris is generated is:

[0164]

[0165] In actual wear processes, not all micro-protrusions undergo wear. Here, a wear probability coefficient λ is introduced. When the movement distance of the friction pair is S, the wear amount on the entire contact surface is...

[0166]

[0167] A friction and wear test was designed. The surface contour data of the test sample was periodically measured at intervals. The fractal dimension D and characteristic scale coefficient G were calculated using the structure function method. The basic principle of the structure function method is: if the surface contour with fractal properties is considered as a time series z(x), then the structure function of the sampled data of this time series satisfies the following:

[0168] S(τ) = <[z(x+τ)-z(x)] 2 >=Cτ 4-2D

[0169] In the above formula:

[0170] [z(x+τ)-z(x)] 2 —The arithmetic mean of the differences;

[0171] C is a constant;

[0172] τ — An arbitrary value for the data interval, i.e., the sampling interval;

[0173] D – Fractal dimension;

[0174] As shown above, the structure function S(τ) is a power function of τ. S(τ) can be calculated from the profile curve z(x). Taking the logarithm of both sides of the above equation, we plot the relationship between lg(S) and lg(τ) on logarithmic coordinates (discrete points). Then, we obtain a linear fitting curve. Let the slope of the fitting curve be m and the intercept be n. Then, the fractal dimension and characteristic scale coefficient of the profile curve are respectively:

[0175]

[0176]

[0177] Fractal theory can characterize worn surfaces. This invention proposes a method for calculating the wear amount during the running-in process of guide rail pairs based on fractal theory and experimental data. It is found that the wear amount decreases as the fractal dimension and material property coefficient increase; however, the wear amount also increases as the characteristic scale coefficient increases.

[0178] Example 1

[0179] In this embodiment, a running-in wear test was conducted on the 50Mn2 (national standard 3077) material provided by Jiangyin Xingcheng Special Steel Co., Ltd.

[0180] 1. Test specimen

[0181] In designing the test specimen, it is necessary to simulate the contact form, contact stress, and parameters such as raceway roughness and hardness of the rolling linear guide pair; the machinability of the specimen also needs to be considered; the upper specimen is made of ball material, and the lower specimen is made of guide material. If it is necessary to study the wear between the ball and the slider, the lower specimen can be made of slider material. The test specimen is as follows: Figure 4 , 5 As shown.

[0182] 2. Test parameters

[0183] The test force was 120N, calculated based on 10% of the rated dynamic load of the simulated guide rail pair under actual working conditions and the principle of equal maximum contact stress. The test speed was 200r / min, and oil lubrication was used.

[0184] 3. Determination of test cutoff conditions

[0185] Before conducting the friction and wear test, a preliminary test is performed. The purpose of the preliminary test is to determine the cutoff condition and measurement interval. During the operation of the rolling linear guide pair, wear mainly occurs on the slider raceway. In this test, the roughness of the slider raceway when the rolling linear guide pair loses its accuracy is used as the benchmark. The number of rotations of the lower shaft of the friction and wear testing machine corresponding to the lower sample reaching the same roughness is used as the cutoff condition of the test, and the measurement interval is determined according to the duration of the preliminary test.

[0186] 4. Experimental Procedure

[0187] (1) Before the test, all sample parts that had come into contact with the lubricant were cleaned with an ultrasonic cleaner.

[0188] (2) Record the weight of the test specimen before the test using an electronic balance, then install the upper and lower specimens on the rotating shaft, install the grinding specimen on the upper shaft, and install the test specimen on the lower shaft.

[0189] (3) On the MMS-2A testing machine, after selecting the appropriate friction torque range and speed range, turn on the friction and wear testing machine and carry out the test;

[0190] (4) Record the changes in wear during the test. The wear was measured using a precision electronic balance at 10-hour intervals. The sample was cleaned with an ultrasonic cleaner before each measurement. The profile data of the sample surface was measured every 10 hours, and the fractal dimension D and characteristic scale coefficient G were calculated (the profile data was measured using a portable surface roughness meter, and the fractal dimension and characteristic scale coefficient were calculated using the structure function method in step 3). The load applied in the test was used as the contact load of the micro-protrusion, and the maximum contact area a was calculated. l The wear amount within those 10 hours was calculated.

[0191] (5) When the predetermined test cutoff condition is reached, remove the sample and end the test.

[0192] Comparison of the wear amount measured by the experiment with the wear amount calculated by theory, for example Figure 5 As shown, the minimum error is 20.59%, the average error is 29.34%, and the theoretical calculation results are good.

Claims

1. A method for calculating wear during the running-in process of a guide rail pair based on fractal theory and experimental data, characterized by comprising the following steps: Step 1: Based on the Weierstrass-Mandelbrot function, establish a micro-protrusion contact model for the guide rail pair contact surface. The contact between two rough surfaces is equivalent to the contact between one rough surface and another rigid surface, and the following assumptions are made:

1. Rough surfaces are isotropic and have fractal characteristics; 2. When analyzing the micro-contact process, work hardening caused by material deformation, changes in hardness depth, and friction between micro-protrusions are ignored; the contact area 'a' of the micro-protrusions is calculated based on the area distribution law of the micro-protrusions on the surface of the mechanical part. The spatial frequency and wavelength of the profile curve satisfy γ -n =l, substituting into the Weierstrass-Mandelbrot function, we get: ， In the formula l G is the sampling length, in meters; G is the characteristic scale coefficient, in meters. The maximum height δ of the roughness peak before deformation of the micro-convex body is obtained as follows: δ=G D-1 l 2-D , The radius of curvature R of the peak before deformation of the micro-convexity, in meters: ， Using Hertz theory of elastic contact, the critical deformation δe for elastic deformation of the micro-convex body is obtained. The deformation δe is related to the normal load. p The relationship is: ， in, E is the equivalent elastic modulus of the materials of the two contact surfaces, which can be calculated by the following formula: ， E 1 , E 2 It is the elastic modulus of the materials of the two contacting surfaces, in Pa; ν 1 , ν 2 It is the Poisson's ratio of the two contacting surface materials, and is dimensionless. According to Hertz theory , in, σ s K is the yield strength of the softer material in the contact surface. ƒ It is the coefficient of friction of the contact surfaces, which can be calculated by the following formula: ， In the formula μ It is the coefficient of friction; Combining the above four equations, we can obtain the critical deformation δe at which the micro-protrusions on the contact surface begin to yield: ， When the deformation of the micro-protrusion δ = δ e At this point, the critical value between elastic deformation and plastic deformation is obtained, and the critical elastic contact area is determined. a e for: ， Where φ=σ s ×E -1 Indicates material properties; When the deformation of the micro-protrusion δ = 110δ e At this point, the micro-protrusion enters the stage of complete plastic deformation, and the deformation of the micro-protrusion is in δ. e ~110δ e The period between these two phases is known as the elasto-plastic deformation stage. The relationship between the critical elastic contact area and the critical plastic contact area is as follows: ， Obtain the critical plastic contact area a p ， When the deformation of the micro-protrusion ,Right now Plastic deformation occurs; when the deformation of the micro-protrusion... ,Right now Elastic deformation occurs; Step 2: Conduct a wear and break-in test, measure the fractal dimension D and characteristic scale coefficient G of the contact surface of the test sample, and calculate the maximum contact area of ​​the micro-protrusions in combination with the contact load F. To determine whether the micro-protrusion is in the stage of elastoplastic deformation during the contact process; Step 3: Set all micro-protrusions on the contact surface to be hemispherical. In the actual wear process, calculate the wear amount on the entire contact surface according to the formulas for each stage of elastic-plastic deformation.

2. The method according to claim 1, characterized in that: In step 1, the area distribution pattern of the micro-protrusions on the surface of the mechanical part is based on the area distribution pattern of islands in the ocean discovered by Mandelbrot, and is used to calculate the contact area a of the micro-protrusions.

3. The method according to claim 1, characterized in that: The area distribution function n(a) of the contact points of the micro-convex body is: ， Where Ψ represents the domain expansion factor of the contact size distribution, which is related to the fractal dimension: P (2-D) / 2 -(1+Ψ -(2-D) / D )=(2-D) / D, The actual contact area Ar of the friction pair is: ， In the formula, n(a)da represents the number of micro-protrusions on the rough surface with an area between a and a+da.

4. The method according to claim 1, characterized in that: In step 2, the contact load of the micro-protrusion is calculated, taking into account the change in the maximum contact surface caused by the elastic and plastic deformation of the micro-protrusion, and the entire wear stage is divided into two types: When the contact area a of the micro-protrusion is greater than a e At this time, the micro-protrusion undergoes elastic deformation, and the elastic contact load at this point is: ， In the formula, a e It is the critical elastic contact area of ​​the micro-convex body, in meters. 2 ; E is the equivalent elastic modulus, in Pa; R is the radius of the peak of the micro-convexity, in meters (m). δ is the deformation of the micro-convexity, in meters (m); G It is the characteristic scaling coefficient, in meters (m). D is the fractal dimension, which is dimensionless; When the contact area of ​​the micro-protrusion At this time, the micro-protrusion is in the plastic deformation stage, and the normal load of the plastic deformation is: F p =kσ s a, Where k is a variable related to hardness H and yield strength. σ s The relevant factor H = kσ s σ s Hardness H and yield strength σ s The unit is Pa; the contact load F of the micro-protrusion is the normal load on the contact surface, and the maximum contact area a of the micro-protrusion can be obtained by inverse solution of the above formula. l ; The above two formulas describe the contact area as a The load on a single micro-protrusion, combined with the area distribution function of the micro-protrusion, yields the load on the entire contact surface as follows: (1) When a l ≥a e At that time, a l This represents the maximum contact area of ​​the micro-protrusion. The micro-protrusion undergoes both plastic and elastic deformation. The total contact load F on the entire surface is: When D≠1.5, ， When D = 1.5, ， In the formula, Ψ represents the domain expansion factor of the contact size distribution, which is related to the fractal dimension D, and Ar is the actual contact area of ​​the friction pair, in meters. 2 ; (2) When The micro-protrusions only undergo plastic deformation, and the contact load on the entire contact surface is: 。 5. The method according to claim 1, characterized in that: In step 3, Assuming that all micro-protrusions on the contact surface are hemispherical, the contact area of ​​the spherical peaks is: ， During the wear process, relative sliding occurs at the contact points. When the contact points slide a certain distance... l , l = a 0.5 The amount of wear V(a) generated during this time is: ， The wear volume across the entire contact surface is: ， The above formula assumes that there is only one micro-protrusion on each contact surface. For all micro-protrusions, the total moving distance l1 of the friction pair when V-shaped wear debris is generated is: ， In actual wear processes, not all micro-protrusions undergo wear. Here, a wear probability coefficient λ is introduced. When the movement distance of the friction pair is S (in meters), the wear amount on the entire contact surface is: 。 6. The method according to claim 1, characterized in that: In step 2, a wear running-in test is conducted using a wear running-in test bench. The wear contact of the test specimens is used to simulate the contact form, contact stress, raceway roughness, and hardness of the rolling guide pair. The test specimens include an upper specimen and a lower specimen. The upper specimen is the wear specimen, and the lower specimen is the test specimen. Both are designed as annular specimens. The upper and lower specimens are fitted with an interference fit to ensure close contact between them during the test. The upper specimen is installed on the upper rotating shaft, and the lower specimen is installed on the lower rotating shaft, causing the upper and lower specimens to roll relative to each other. The friction and wear generated by the relative rolling are used to simulate the contact wear between the rolling elements and the raceway during the running-in process of the guide pair. By periodically measuring the contour data of the test specimen surface after the measurement interval, the fractal dimension D and characteristic scale coefficient G are calculated using the structure function method. The wear amount within the measurement interval is then calculated.

7. The method according to claim 6, characterized in that: During the wear and break-in test, the maximum contact stress of the test specimen was set to be consistent with the maximum contact stress between the rolling elements and the raceway in the actual operation of the guide rail pair.

8. The method according to claim 6, characterized in that: The upper sample material is set as the rolling element material, and two convex arc surfaces are designed on the circular surface of the upper sample to simulate the rolling element; the lower sample material is set as the raceway material, and two concave arc surfaces are designed on the circular surface of the lower sample to simulate the raceway, corresponding to the two convex arc surfaces of the upper sample. The upper and lower samples make friction contact through the two convex arc surfaces and the two concave arc surfaces.

9. The method according to claim 6, characterized in that: Before the wear and break-in test, a preliminary test is conducted. The purpose of the preliminary test is to determine the cutoff condition and measurement interval. The roughness of the raceway when the guide rail pair loses its accuracy is used as the benchmark. The number of rotations of the lower shaft when the lower sample reaches the same roughness is used as the cutoff condition of the test. The measurement interval is determined according to the duration of the preliminary test.

10. The method according to claim 6, characterized in that: Before the wear-break-in test, the test specimen was weighed. During the wear-break-in test, the weight of the test specimen was recorded after each measurement interval, and the wear amount within that measurement interval was calculated. The profile data was measured using a surface roughness meter. The structure function method treats the fractal surface profile as a time series z(x), and this time series satisfies the following structure function for its sampled data: ， In the above formula: [z(x+τ)-z(x)] 2 —The arithmetic mean of the differences; C is a constant; τ — An arbitrary value for the data interval, i.e., the sampling interval; D – Fractal dimension; As shown above, the structure function S(τ) is a power function of τ. S(τ) can be calculated from the profile curve z(x). Taking the logarithm of both sides of the above equation, we plot the discrete point relationship between lg(S) and lg(τ) on logarithmic coordinates. Then, we obtain a linear fitting curve. Let the slope of the fitting curve be m and the intercept be n. Then, the fractal dimension and characteristic scaling coefficient of the profile curve are respectively: 。

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