METHOD FOR DETERMINING INITIATION POSITION OF FRETTING FATIGUE CRACKS

Abstract

The present disclosure relates to a method for determining initiation positions of fretting fatigue cracks. The processed inner circular hole test workpiece is placed on a stage of an optical microscope, wherein the inner hole surface to be measured is perpendicular to the scanning beam direction of the microscope; measurement is performed along the real contact orientation between the inner hole surface of the inner circular hole test workpiece and the pin shaft. From the measured surface morphology and profile image, rectangular target areas with a coverage rate of 75%˜90%, and the amplitude distribution function, surface skewness and surface kurtosis values of the respective surface profiles are extracted from the target areas. By comparing the positive/negative of and the magnitude of the skewness and kurtosis values measured in the target areas, the side where the initiation position of fretting fatigue cracks is located can be determined.

Claims

1. A method for determining initiation position of fretting fatigue cracks, comprising: In Step 1, classifying features of a processed inner circular hole test workpiece (1), constructing a coordinate system O—X.sub.cY.sub.cZ.sub.c (4) of the inner circular hole test workpiece (1), cutting off a sample (101) from the inner circular hole test workpiece (1), and rotating the coordinate system O—X.sub.cY.sub.cZ.sub.c of the inner circular hole test workpiece (1) clockwise by 45 degrees around an OZ.sub.c axis to construct a coordinate system O—X.sub.sY.sub.sZ.sub.s (5) of the sample (101), so as to determine an inner hole surface (102), an inner hole axis (103), planes of symmetry (104) and a measurement and placement plane (105) mating with a pin shaft (2) on the sample (101), wherein the planes of symmetry (104) pass through the inner hole axis (103) and are parallel to an Y.sub.s—O—Z.sub.s plane of the coordinate system O—X.sub.sY.sub.sZ.sub.s (5) of the sample (101); In Step 2, establishing an optical microscope coordinate system O.sub.w—X.sub.wY.sub.wZ.sub.w (3), and measuring a surface morphology and profile of the sample (101); In Step 3, according to the distribution of surface morphology and profile in Step 2, a first target area (102a) and a second target area (102b) are respectively selected on both sides of the planes of symmetry (104), and amplitude distribution functions APD.sub.L and APD.sub.R, the surface skewness R.sub.skL and R.sub.skR, the surface kurtosis values R.sub.kuL and R.sub.kuR of respective surface profiles are extracted from the first target area (102a) and the second target area (102b); (4) Defining a comparison set of surface skewness and surface kurtosis values as shown in formula (I):
N.sub.u={max(R.sub.skL,R.sub.skR)}∪{max(R.sub.kuL,R.sub.kuR)}  (I) In formula (I), N.sub.u is a marking for noting a comparison set of large skewness values and large kurtosis values on both sides of the first target area (102a) and the second target area (102b); R.sub.skL and R.sub.skR are respectively skewness values (accounting to two decimal places) of surface texture parameters of the first target area (102a) and the second target area (102b), and R.sub.kuL and R.sub.kuR are respectively kurtosis values (accounting to two decimal places) of surface texture parameters of the first target area (102a) and the second target area (102b), wherein max refers to the larger one among the two; (5) Determining the side where the fretting fatigue crack initiation position is located, wherein it is determined according to formula (II) below for the fretting fatigue crack initiation position corresponding to the surface texture parameters, for which the crack initiates at the side with larger skewness and kurtosis: $\begin{array}{cc}L=\{\begin{array}{c}\mathrm{Left},N_u=\left\{R_{\mathrm{skL}},R_{\mathrm{kuL}}\right\}\\ \mathrm{Right},N_u=\left\{R_{\mathrm{skR}},R_{\mathrm{kuR}}\right\}\\ \mathrm{Left},N_u=\left\{R_{\mathrm{skL}},R_{\mathrm{kuR}}\right\}\mathrm{and}{R}_{\mathrm{kuR}}+3<\frac{R_{\mathrm{skL}}}{\sigma }\underset{i=1}{\overset{n}{.Math.}}\left(x_i-\stackrel{\_}{x}\right)\\ \mathrm{Right},N_u=\left\{R_{\mathrm{skL}},R_{\mathrm{kuR}}\right\}\mathrm{and}{R}_{\mathrm{kuR}}+3>\frac{R_{\mathrm{skL}}}{\sigma }\underset{i=1}{\overset{n}{.Math.}}\left(x_i-\stackrel{\_}{x}\right)\\ \mathrm{Left},N_u=\left\{R_{\mathrm{skR}},R_{\mathrm{kuL}}\right\}\mathrm{and}{R}_{\mathrm{kuL}}+3>\frac{R_{\mathrm{skR}}}{\sigma }\underset{i=1}{\overset{n}{.Math.}}\left(x_i-\stackrel{\_}{x}\right)\\ \mathrm{Right},N_u=\left\{R_{\mathrm{skR}},R_{\mathrm{kuL}}\right\}\mathrm{and}{R}_{\mathrm{kuL}}+3<\frac{R_{\mathrm{skR}}}{\sigma }\underset{i=1}{\overset{n}{.Math.}}\left(x_i-\stackrel{\_}{x}\right)\end{array}& \left(\mathrm{II}\right)\end{array}$ In formula (II), L is a marking that notes the initiation position of fretting fatigue cracks, x.sub.i is a i data point measured in the target area, n is a number of total data points measured in the target area, x is an average value of data measured in the target area side, and σ is a standard deviation of data values measured in the target area, wherein the first target area (102a) corresponds to a crack initiation position on the left side, and the second target area (102b) corresponds to a crack initiation position on the right side.

2. The method for determining initiation position of fretting fatigue cracks according to claim 1, wherein the Step 1 comprises: the inner circular hole test workpiece (1) is a plate-shaped structural specimen with a uniform thickness, a peripheral profile surface shaped like a symmetrical octagon, and a cylindrical through hole along the thickness direction is arranged at the symmetrical center of the workpiece $\stackrel{\mathrm{uuu}}{{\mathrm{OZ}}_s}.$ before measurement, by passing across a cylindrical through hole axis (103), a quarter volume of the inner circular hole test workpiece (1) is cut off from the workpiece, along two planes of symmetry perpendicular to each other, X.sub.c—O—Z.sub.c and Y.sub.c—O—Z.sub.c, as a sample (101); wherein the sample (101) includes a measurement and placement plane (105), as well as an inner hole surface (102) to be measured.

3. The method for determining initiation position of fretting fatigue cracks according to claim 1, wherein the Step 2 comprises: 201: With the measurement and placement plane (105) acting as the placement plane, the sample 101 is placed on a stage of an optical microscope such as a white light interferometer or a laser confocal microscope; By adjusting the sample (101) based on the sample coordinate system O—X.sub.sY.sub.sZ.sub.s (5), the inner hole axis (103) of the inner hole surface (102) to be measured to be parallel to the X.sub.w axis of the microscope coordinate system (3), and the microscope scanning beam (302) irradiates the bottom position at center of the inner hole surface (102) to be measured, so as to ensure that the inner hole surface (102) to be measured is perpendicular to the direction in which the microscope scanning beam (302) is located; Measurement is performed along the real contact orientation between the inner hole surface (102) of the inner circular hole test workpiece (1) and the pin shaft (2), so that a scanning path (303) of the microscope is perpendicular to the inner hole axis (103), in order to measure the surface morphology and profile image of the inner hole surface (102) of the sample (101).

4. The method for determining initiation position of fretting fatigue cracks according to claim 1, wherein the first target area (102a) and the second target area (102b) are rectangular, and the morphological coverage of the first target area (102a) and the second target area (102b) ranges from 75% to 90%.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to illustrate the embodiments of the present disclosure or in the prior art more clearly, the accompanying drawings required in the embodiments or prior art will be briefly introduced below. Apparently, the drawings in the following description are only some embodiments of the present disclosure, and those of ordinary skills in the art may obtain other drawings according to these drawings without creative work.

[0022] FIG. 1 is a schematic diagram of the contact between a pin shaft and an inner circular hole test workpiece;

[0023] FIG. 2 is a schematic diagram of the surface morphology and profile measurement method according to the present disclosure;

[0024] FIG. 3 is a schematic diagram of target area selection for extracting a surface profile amplitude distribution function, surface skewness and surface kurtosis values according to the present disclosure;

[0025] FIG. 4 is a flow chart of the method in the present disclosure;

[0026] FIG. 5 is a schematic diagram of target area selection for extracting a surface profile amplitude distribution function, surface skewness and surface kurtosis values according to an embodiment in the present disclosure;

[0027] FIG. 6 is a comparison diagram of numerical results of surface profile amplitude distribution function, surface skewness and surface kurtosis according to an embodiment of the present disclosure;

[0028] FIG. 7 shows the fretting fatigue crack propagation path obtained by testing in an embodiment of the present disclosure;

[0029] The reference numerals in the figures include: 1 inner circular hole test workpiece, 101 sample, 102 inner hole surface, 102a first target area, 102b second target area, 103 inner hole axis, 104 plane of symmetry, 105 measurement and placement plane, 2 pin shaft, 3 microscope coordinate system, 301 microscope scanning lens, 302 microscope scanning beam, 303 microscope scanning path, 4 test workpiece coordinate system, 5 sample coordinate system, and 6 fatigue load.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0030] Technical schemes in the embodiments of the present disclosure will be described clearly and completely with reference to the accompanying drawings thereof. Apparently, the embodiments described herein are only part of, not all of, embodiments in the present disclosure. Based on the embodiments of the present disclosure, all other embodiments obtained by those of ordinary skills in the art without creative work belong to the scope claimed by the present disclosure.

[0031] (1) Feature Division on Inner Circular Hole Test Workpiece 1

[0032] The inner circular hole test workpiece 1 is a plate-shaped structural specimen with a uniform thickness, a peripheral profile surface shaped like a symmetrical octagon, and a cylindrical through hole along the thickness direction is arranged at the symmetrical center of the workpiece. A coordinate system 4 is established for the inner circular hole test workpiece 1, and, by passing across a cylindrical through the hole axis, a quarter volume of the inner circular hole test workpiece sample is cut off from the workpiece, along two planes of symmetry perpendicular to each other, X.sub.c—O—Z.sub.e and Y.sub.c—O—Z.sub.c, as a sample 101. The coordinate system 4 is rotated clockwise by 45 degrees around the OZ.sub.c axis to construct a sample coordinate system 5, so as to determine an inner hole surface 102, an inner hole axis 103, planes of symmetry 104 and a measurement and placement plane 105 mating with a pin shaft 2 on the sample 101, wherein the planes of symmetry 104 pass through the inner hole axis 103 and are parallel to an Y.sub.s—O—Z.sub.s plane of the sample coordinate system 5.

[0033] (2) Measurement of Surface Morphology and Profile of Inner Hole Surface

[0034] An optical microscope related coordinate system 3 is established, and the surface morphology and profile of the sample 101 is measured. With and the placement plane 105, the sample 101 is placed on a stage of an optical microscope such as a white light interferometer or a laser confocal microscope. By adjusting the sample 101 based on the sample coordinate system 5, the inner hole axis 103 of the inner hole surface 102 to be measured is parallel to the X.sub.w axis of the microscope coordinate system 3, and the microscope scanning beam 302 irradiates the bottom position at center of the inner hole surface 102 to be measured, so as to ensure that the inner hole surface 102 to be measured is perpendicular to the direction in which the microscope scanning beam 302 is located. Measurement is performed along the real contact orientation between the inner hole surface of the inner circular hole test workpiece 1 and the pin shaft 2, so that a scanning path 303 of the microscope is perpendicular to the inner hole axis 103, in order to measure the surface morphology and profile image of the inner hole surface 102 of the sample 101.

[0035] (3) Target Area Selection

[0036] On the measured image of the surface morphology and profile, a rectangular first target area 102a and a rectangular second target area 102b with a coverage of 75%˜90% are symmetrically selected on each side relative to the planes of symmetry 104 passing through the inner hole axis 103, which covers the morphology information of the whole inner hole surface to be measured to a greater extent, and also eliminates possible processing defects in the peripheral boundary area of the sample and the interference caused by unmeasurable curved surface areas. The amplitude distribution functions APD.sub.L and APD.sub.R, the surface skewness R.sub.skL and R.sub.skR, the surface kurtosis values R.sub.kuL and R.sub.kuR of respective surface profiles are extracted from the target area 102a and 102b.

[0037] (4) Defining the Comparison Set of Surface Skewness and Surface Kurtosis Values, as Shown in Formula (I):

N.sub.u={max(R.sub.skL,R.sub.skR)}∪{max(R.sub.kuL,R.sub.kuR)}  (I)

[0038] In formula (I), N.sub.u is a marking that notes a comparison set of large skewness values and large kurtosis values on both left sides and right sides; R.sub.skL and R.sub.skR are respectively skewness values (accounting to two decimal places) of surface texture parameters of the first target area 102a and the second target area 102b, and R.sub.kuL a R.sub.kuR are respectively kurtosis values (accounting to two decimal places) of surface texture parameters of the first target area 102a and the second target area 102b, wherein max refers to the larger one among the two.

[0039] (5) Determining the initiation position of fretting fatigue cracks

[0040] By comparing the magnitude of the skewness and kurtosis values measured in the first target area and the second target area according to formula (I), it is determined according to formula (II) below for the fretting fatigue crack initiation position corresponding to the surface texture parameters, for which the cracks initiate at the side with larger skewness and kurtosis values.

[00002]$\begin{array}{cc}L=\{\begin{array}{c}\mathrm{Left},N_u=\left\{R_{\mathrm{skL}},R_{\mathrm{kuL}}\right\}\\ \mathrm{Right},N_u=\left\{R_{\mathrm{skR}},R_{\mathrm{kuR}}\right\}\\ \mathrm{Left},N_u=\left\{R_{\mathrm{skL}},R_{\mathrm{kuR}}\right\}\mathrm{and}{R}_{\mathrm{kuR}}+3<\frac{R_{\mathrm{skL}}}{\sigma }\underset{i=1}{\overset{n}{.Math.}}\left(x_i-\stackrel{\_}{x}\right)\\ \mathrm{Right},N_u=\left\{R_{\mathrm{skL}},R_{\mathrm{kuR}}\right\}\mathrm{and}{R}_{\mathrm{kuR}}+3>\frac{R_{\mathrm{skL}}}{\sigma }\underset{i=1}{\overset{n}{.Math.}}\left(x_i-\stackrel{\_}{x}\right)\\ \mathrm{Left}\mathrm{or}\mathrm{right},N_u=\left\{R_{\mathrm{skL}},R_{\mathrm{kuR}}\right\}\mathrm{and}{R}_{\mathrm{kuR}}+3=\frac{R_{\mathrm{skL}}}{\sigma }\underset{i=1}{\overset{n}{.Math.}}\left(x_i-\stackrel{\_}{x}\right)\\ \mathrm{Left},N_u=\left\{R_{\mathrm{skR}},R_{\mathrm{kuL}}\right\}\mathrm{and}{R}_{\mathrm{kuL}}+3>\frac{R_{\mathrm{skR}}}{\sigma }\underset{i=1}{\overset{n}{.Math.}}\left(x_i-\stackrel{\_}{x}\right)\\ \mathrm{Right},N_u=\left\{R_{\mathrm{skR}},R_{\mathrm{kuL}}\right\}\mathrm{and}{R}_{\mathrm{kuL}}+3<\frac{R_{\mathrm{skR}}}{\sigma }\underset{i=1}{\overset{n}{.Math.}}\left(x_i-\stackrel{\_}{x}\right)\\ \mathrm{Left}\mathrm{or}\mathrm{right},N_u=\left\{R_{\mathrm{skR}},R_{\mathrm{kuL}}\right\}\mathrm{and}{R}_{\mathrm{kuL}}+3=\frac{R_{\mathrm{skR}}}{\sigma }\underset{i=1}{\overset{n}{.Math.}}\left(x_i-\stackrel{\_}{x}\right)\end{array}& \left(\mathrm{II}\right)\end{array}$

[0041] In formula (II), L is a marking that notes the initiation position of fretting fatigue cracks, x.sub.i is a i data point measured in the target area, n is a number of total data points measured in the target area, x is an average value of data measured in the target area side, and σ is a standard deviation of data values measured in the target area. In addition, in formula (2), when

[00003]$N_u=\left\{R_{\mathrm{skL}},R_{\mathrm{kuR}}\right\}\begin{array}{c}•\\ •\\ •\\ \\ \end{array}{R}_{\mathrm{kuR}}+3=\frac{R_{\mathrm{skL}}}{\sigma }\underset{i=1}{\overset{n}{.Math.}}\left(x_i-\stackrel{\_}{x}\right)\mathrm{or}{N}_u=\left\{R_{\mathrm{skR}}{,}_{\mathrm{kuL}}\right\}\begin{array}{c}•\\ •\\ •\\ \\ \end{array}{R}_{\mathrm{kuL}}+3=\frac{R_{\mathrm{skR}}}{\sigma }\underset{i=1}{\overset{n}{.Math.}}\left(x_i-\stackrel{\_}{x}\right),$

it is possibly not able to completely determine whether fretting fatigue cracks originate on the left side or the right side. However, there is very little probability that N.sub.u satisfy such cases. During actual workpiece machining, surface texture parameter relations satisfying these two cases rarely exist for machined surfaces. In order to make the relation a closed loop, the conditions of the two minimum probability events mentioned above are also listed in formula (2) as well.

[0042] Before the measurement, all samples 101 cut off from the test workpiece 1 should be put into ultrasonic cleaning equipment for cleaning to remove residual oil, particles, and dust on its surface.

[0043] By texture parameters such as surface skewness and kurtosis, a dependence relationship is directly established between the initiation position of fretting fatigue cracks on the surface and surface texture parameters, which gives targeted instruction on the process design of surface enhancement and protection treatment in order to obtain the surface texture features with the best fretting fatigue resistance.

[0044] Specific Embodiments Include:

[0045] Taking the test workpiece 1 with a circular hole diameter of φ12.2 mm as an example, six different groups of machined inner hole surfaces 102 are obtained through six different milling parameters, and the test workpieces are numbered as #1˜#6. Using the method proposed by the present disclosure. The surface morphology of the inner hole surface 102 is measured along the plane of symmetry 104, as shown in FIG. 5. On this basis, the target areas 102a and 102b are demarcated according to the area coverage rate of 80%, and their surface skewness and kurtosis values are extracted and listed in Table 1, with the results being shown in FIG. 6.

TABLE-US-00001 TABLE 1 Skewness and Kurtosis values of circular hole surfaces of different test workpieces Test Skewness value: Kurtosis value: workpieces Left side Right side Left side Right side #1 0.33 −0.21 6.93 6.35 #2 0.13 −0.13 4.66 4.63 #3 0.30 −0.21 4.71 3.73 #4 0.52 0.42 6.60 6.24 #5 0.13 0.05 3.41 3.37 #6 0.09 −0.09 7.29 7.02

[0046] By substituting the numerical values into formula (I) and formula (II), it is found that the skewness value and kurtosis value on the left side are both larger than those on the right side in the measurement target areas 102a and 102b of the inner hole surface 102, so it can be determined that fretting fatigue cracks all initiate on the left side. By combining this result with the crack propagation path (see FIG. 7) obtained by fretting fatigue testing under a fatigue load 6, it is found that the tested results are consistent with the predicted results, namely, fretting fatigue cracks always initiate on the side with larger skewness value and kurtosis value, and eventually propagate and result in fatigue failure of the test workpieces.

[0047] The embodiments described above are only preferred embodiments of the present disclosure, but not an exhaustive list of feasible implementations of the present disclosure. For those of ordinary skill in the art, any obvious changes made without departing from the principle and spirit of the present disclosure should be considered to be included in the claimed scope of the claims of the present disclosure.