Method for detecting abrasive exposure height of an electroplated grinding wheel

By using ultra-depth-of-field microscopy and image processing technology, stable and batch detection of the abrasive exposure height of electroplated grinding wheels has been achieved, solving the problems of instability and low efficiency of existing detection methods, and is applicable to electroplated grinding wheels with complex morphologies.

CN115775342BActive Publication Date: 2026-02-06ZHENGZHOU RES INST FOR ABRASIVES & GRINDING CO LTD
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Patent Information

Application Number
CN202211703621.7
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-12-23
Publication Date
2026-02-06
Estimated Expiration
2042-12-23

AI Technical Summary

Technical Problem

Existing testing methods cannot perform batch testing of the abrasive exposure height of electroplated grinding wheels, and the test results are unstable and inefficient. In particular, for superhard materials such as electroplated diamond grinding wheels, contact testing is prone to damaging the probe, while non-contact testing is greatly affected by subjective factors.

Method used

By employing a super depth-of-field microscope for continuous imaging, combined with image focusing depth synthesis and grayscale processing, and identifying abrasive and binder through binarization and feature segmentation, the exposed height of abrasive is automatically obtained, enabling 3D reconstruction and batch detection.

Benefits of technology

It enables stable and batch testing of the abrasive exposure height of electroplated grinding wheels, improves testing efficiency, reduces human error, and is suitable for electroplated grinding wheels with complex morphologies.

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Abstract

The application provides a method for detecting the exposed height of abrasive grains of an electroplated grinding wheel, comprising the following steps: S1, generating an image sequence of the micro-morphology of the surface of the electroplated grinding wheel; S2, performing image focus depth synthesis processing on the image sequence obtained in step S1 to obtain a two-dimensional fusion image and a three-dimensional reconstruction image of the micro-morphology of the surface of the electroplated grinding wheel; S3, performing binaryzation processing on the two-dimensional fusion image obtained in step S2 to obtain the position information of the abrasive grain size, position and binder region around the abrasive grain in the image; S4, obtaining the top height of the abrasive grain and the average height of the binder region around the abrasive grain; S5, obtaining the exposed height of the abrasive grain and marking the exposed height in the binary image BW The application can realize stable detection and automatic batch detection of all abrasive grains in the field of view, and effectively solves the problems of unstable detection results and low detection efficiency of the traditional detection method.
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Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of single-layer abrasive wheel surface morphology detection, and particularly relates to a method for detecting abrasive exposure height of an electroplated grinding wheel. BACKGROUND

[0002] The electroplated grinding wheel is deposited with abrasives on the surface of the grinding wheel base body through a metal bonding agent, and belongs to a single-layer abrasive wheel. Compared with multi-layer abrasive wheels such as ceramic grinding wheels and resin grinding wheels, the electroplated grinding wheel has the advantages of large chip space, high grinding efficiency and good sharpness, and is widely used in precision grinding of workpieces in the fields of aerospace, electronic devices and mold manufacturing.

[0003] During grinding, the electroplated grinding wheel mainly removes materials through the interaction between the abrasives exposed on the surface of the bonding agent and the workpiece. Therefore, the abrasive exposure height of the grinding wheel is crucial to the performance of the grinding tool. If the abrasive exposure height is too low, the sharpness of the grinding wheel will be reduced, and even the workpiece will be burned. If the abrasive exposure height is too high, the bonding agent will not have enough holding force, which will cause the abrasives to easily fall off and wear, and reduce the service life of the grinding wheel. Only when the abrasive exposure height is moderate, can the performance of the grinding tool and the processing effect be ensured. Therefore, the detection of the abrasive exposure height of the electroplated grinding wheel can effectively predict the grinding performance of the grinding wheel, and has important significance for improving the grinding capacity of the grinding wheel and improving the grinding quality of the workpiece.

[0004] At present, the detection methods of abrasive exposure height mainly include contact detection and non-contact detection. For the electroplated grinding wheel, especially the superhard material grinding wheel such as the electroplated diamond grinding wheel, the contact detection method is easy to damage the probe, and is limited by the shape and size of the probe, so it cannot detect the complex morphology of the surface of the electroplated grinding wheel. The common non-contact detection methods, such as optical microscope method and super-depth microscope method, need to manually measure each abrasive, and the selection of measurement points and the selection of reference are affected by subjective factors, which leads to unstable detection results, and cannot achieve batch detection for multiple abrasives in the field of view, so the detection efficiency is low. SUMMARY

[0005] In view of the technical problems that the existing detection methods cannot perform batch detection on the abrasive exposure height and have low efficiency, the application provides a method for detecting the abrasive exposure height of an electroplated grinding wheel, which effectively solves the problems of unstable detection results and low detection efficiency of the traditional detection methods.

[0006] In order to achieve the above purpose, the technical scheme of the application is as follows: a method for detecting the abrasive exposure height of an electroplated grinding wheel, comprising the following steps:

[0007] S1: using a super-depth microscope to continuously shoot the micro-morphology of the electroplated grinding wheel surface, and generating an image sequence I of the micro-morphology of the electroplated grinding wheel surface;

[0008] S2: performing image focus depth synthesis processing on the image sequence I obtained in step S1, to obtain a two-dimensional fusion image M and a three-dimensional reconstruction image H of the micro-morphology of the electroplated grinding wheel surface;

[0009] S3: performing binaryzation processing on the two-dimensional fusion image M obtained in step S2, to obtain a binaryzation image BW, performing feature segmentation on the binaryzation image BW, identifying the abrasive and the binder, and obtaining the abrasive particle size, position, and position information of the binder region around the abrasive in the image;

[0010] S4: combining the abrasive position information, the position information of the binder region around the abrasive in the image in step S3, and the three-dimensional reconstruction image H obtained in step S2, to obtain the top height of the abrasive and the average height of the binder region around the abrasive;

[0011] S5: subtracting the average height of the binder region around the abrasive from the top height of the abrasive obtained in step S4, to obtain the exposed height of the abrasive, and marking the exposed height in the binary image BW.

[0012] The method for generating the image sequence I of the micro-morphology of the electroplated grinding wheel surface in step S1 is: controlling the super-depth lens to continuously shoot the surface of the grinding wheel from bottom to top at equal intervals, the shooting interval being Δh, and the shooting process starting from a complete defocus state and ending when the lens is again completely defocused, to obtain partially focused images between the two completely defocused positions, performing n times of shooting on the electroplated grinding wheel, and generating the image sequence I consisting of n images {I1, I2, I3…In}. n} respectively represent each image shot. n

[0013] The method for obtaining the two-dimensional fusion image M and the three-dimensional reconstruction image H of the micro-morphology of the electroplated grinding wheel surface in step S2 is:

[0014] S2.1: performing gray scale processing on each image in the image sequence I={I1, I2, I3…In}, converting the three-dimensional matrix of the original image into a two-dimensional matrix of the gray scale image, to obtain a gray scale image sequence Igray={Igray1, Igray2, Igray3…Igrayn}, Igray1, Igray2, Igray3…Igrayn respectively represent the gray scale image of the image I1, I2, I3…I n n n n

[0015] ​​​​​S2.2: calling the imfilter command in matlab to filter the gray image sequence Igray = {Igray1, Igray2, Igray3... Igray n} to remove the noise points in the image and obtain the filtered image sequence G = {G1, G2, G3... G n};

[0016] S2.3: analyzing the pixel point G n (x, y) in each image in the filtered image sequence G = {G1, G2, G3... G n}, and calculating the focus evaluation function value F n (x, y) of the pixel point by using the improved Laplace operator.

[0017] S2.4: taking the image number n as the horizontal coordinate and the focus function evaluation value F n (x, y) as the vertical coordinate, drawing the F-n curve of each pixel point, and when the focus function evaluation value F is the largest, the corresponding horizontal coordinate k is obtained, which indicates that the pixel point is focused in G k . All the pixel points with the largest focus evaluation function value F are extracted to obtain the full-focus two-dimensional fusion image M.

[0018] S2.5: Gaussian fitting is performed on the F-n curve to obtain the continuously changing F'-n' curve, the horizontal coordinate k' when F' is the largest for each pixel point is extracted, and then the height index matrix H_index is obtained, the height value of the corresponding pixel point is h = (k'-1) x Δh, and the three-dimensional reconstruction image H is obtained by combining the height index matrix H_index and the height value h, and Δh is the shooting interval.

[0019] The filtering method in step S2.1 includes Gaussian filtering, mean filtering, and median filtering.

[0020] The improved Laplace operator in step S2.3 is shown in formula (1):

[0021]

[0022] wherein x and y represent the coordinates of the pixel point G n (x, y) in the image G n , s represents a variable step size, N represents the window size F n (x, y) is the focus function evaluation value, f(x, y) represents the Laplace operation value of the pixel point G n (x, y), F n (x, y) is the improved Laplace operation value, and here F n (x, y) represents the focus evaluation function value of the pixel point.

[0023] The information of the abrasive particle size, the location of the abrasive, and the location of the binder region around the abrasive in the image is obtained in step S3:

[0024] S3.1: The locations with value 1 in the binary image BW represent abrasives, and the locations with value 0 represent binders.

[0025] S3.2: The bwlabel command in matlab is called to find all eight-connected regions in the binary image BW, and the region is labeled as an abrasive. The marking matrix L and the number of connected regions num are obtained by the bwlabel command. Each abrasive in the marking matrix L has a marking value i, i = 1…num. The logical matrix logic1 represents the location information of each abrasive, that is, the locations of all marking values i in the marking matrix L. The locations of the abrasives are represented by value 1 in the logical matrix logic1, and the binders and other abrasive regions are represented by 0.

[0026] S3.3: The regionprops command in matlab is called to obtain the center of mass coordinates center(x, y) of each connected region in the marking matrix L. The center of mass coordinates center(x, y) of each abrasive are set as the coordinates of the center of mass.

[0027] S3.4: The find command is called to obtain the row index matrix hang and the column index matrix lie of each connected region in the marking matrix L. The abrasive particle size d = max(max(hang)-min(hang), max(lie)-min(lie)) is obtained.

[0028] S3.5: In the marking matrix L, the abrasive location is expanded by d / 2, and the locations of all elements with value 0 in this region, that is, the locations of the binder regions around the abrasives, are represented by the logical matrix logic2.

[0029] The method for marking the exposed height in the binary image BW in step S3 is as follows: according to the center of mass coordinates position center(x, y) of each abrasive obtained in step S3.2, the height value of each abrasive is calculated and marked in the binary image BW.

[0030] The method for obtaining the top height of the abrasive and the average height of the binder region around the abrasive in step 4 is as follows: in the three-dimensional reconstruction image H, all height values in the location logic1 are sorted, and the average of the top 5 values represents the top height of the abrasive. The average of all height values in the location logic2 represents the average height of the binder region around the abrasive.

[0031] The application realizes three-dimensional reconstruction of the micro-morphology of the electroplated grinding wheel by coupling the depth synthesis technology and the gray scale and binarization processing technology, using the height information and the gray scale information of the image, and realizes stable detection by automatically selecting the abrasive top and the binder height measurement datum, and can realize automatic batch detection of all abrasives in the field of view, effectively solving the problems of unstable detection results and low detection efficiency of the traditional detection method. BRIEF DESCRIPTION OF DRAWINGS

[0032] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0033] Figure 1 The flowchart of the present application.

[0034] Figure 2 The two-dimensional fusion image of the present application.

[0035] Figure 3 The three-dimensional reconstruction image of the present application.

[0036] Figure 4 The binary image of the present application.

[0037] Figure 5 The height mark image of the present application. DETAILED DESCRIPTION

[0038] The technical solutions in the embodiments of the present application will be described clearly and completely with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0039] As shown in Figure 1 A method for detecting the abrasive exposed height of an electroplated grinding wheel, comprising the following steps:

[0040] S1: The microscopic morphology of the electroplated grinding wheel surface is continuously photographed by using a super-depth microscope to generate an image sequence I of the microscopic morphology of the electroplated grinding wheel surface. The method for generating the image sequence I of the microscopic morphology of the electroplated grinding wheel surface is: controlling the super-depth lens to continuously photograph the grinding wheel surface from bottom to top at equal intervals, starting from a complete defocus state and ending at a complete defocus state again to obtain the partially focused images between the two complete defocus states, the lens magnification and the photographing interval Δh are adjusted according to the grain size of the grinding wheel, the electroplated grinding wheel is photographed n times, and the image sequence I is composed of n images {I1, I2, I3…I n When the abrasive grain size is 40 / 45#, the lens moving distance can be set to 650μm, the lens magnification is 150x, the photographing interval Δh is 10μm, and the image sequence I is composed of n=66 images {I1, I2, I3…I

[0041] S2: The image sequence I obtained in step S1 is subjected to image focus depth synthesis processing to obtain a two-dimensional fusion image M and a three-dimensional reconstruction image H of the microscopic morphology of the electroplated grinding wheel surface, as shown in Figure 2 and Figure 3 The specific steps are as follows:

[0042] S2.1: Each image in the image sequence I {I1, I2, I3…I n} is subjected to gray scale processing to convert the source image three-dimensional matrix into a gray scale image two-dimensional matrix to obtain a gray scale image sequence Igray {Igray1, Igray2, Igray3…Igray n};

[0043] S2.2: The imfilter command in matlab is called to filter the gray scale image sequence Igray {Igray1, Igray2, Igray3…Igray n} to remove noise points in the image to obtain a filtered image sequence G {G1, G2, G3…G n}, and the filtering algorithm includes Gaussian filtering, mean filtering, median filtering, etc., which can be selected according to the specific photographed image sequence;

[0044] S2.3: The pixel points G n (x, y) in each image in the image sequence G {G1, G2, G3…G n} are analyzed, and the improved Laplace operator is used to calculate the focus evaluation function value Fn(x, y) thereof, and the Laplace operator is shown in formula (1):

[0045]

[0046] Wherein, x, y represent the pixel points Gn (x, y) is the coordinate of the image G n s represents the variable step length, and N represents the window size. The improved Laplace operator is used for focus depth synthesis of the image sequence of the electroplated grinding wheel surface topography, and the image fusion quality is improved.

[0047] S2.4: Draw the F-n curve of each pixel point with the image number n as the horizontal coordinate and the focus function evaluation value F as the vertical coordinate. When the focus function evaluation value F is maximum, the corresponding horizontal coordinate k is obtained. The point k indicates that the pixel point in G k is focused. All pixel points with the maximum focus evaluation function value F are extracted to obtain the two-dimensional fusion image M.

[0048] S2.5: Gaussian fitting is performed on the F-n curve to obtain a continuously changing F'-n' curve. The horizontal coordinate k' when F' is maximum for each pixel point is extracted, and the height index matrix H_index is obtained. The height value of the corresponding pixel point is h=(k'-1) x Δh. Combined with the height index matrix H_index and the height value h, the three-dimensional reconstruction image H is obtained.

[0049] S3: As shown in Figure 4 , the two-dimensional fusion image M obtained in step S2 is subjected to binaryzation processing to obtain a binaryzation image BW. The binaryzation image BW is subjected to feature segmentation to identify the abrasive and the binder, and the abrasive particle size, position, and the position information of the binder region around the abrasive in the image are obtained. Specifically:

[0050] S3.1: The two-dimensional fusion image M is subjected to binaryzation processing to obtain a binaryzation image BW. The position with a value of 1 in the binaryzation image BW represents the abrasive, and the position with a value of 0 represents the binder.

[0051] S3.2: The bwlabel command in matlab is called to find all adjacent eight-pixel-point-connected regions in the binaryzation image BW, and the region is labeled as an abrasive. The label matrix L and the connected domain number num are obtained through the bwlabel command. Each abrasive in the label matrix has a label value i, i=1…num. The logic matrix logic1 represents the position information of each abrasive as the position of all label values i in the label matrix L. The value of 1 in logic1 is the position of the abrasive. The binder and other abrasive regions are represented by 0.

[0052] S3.3: The regionprops command in matlab is called to obtain the centroid coordinates center(x, y) of each connected region in the label matrix L. The centroid coordinates center(x, y) are set as the centroid position coordinates of each abrasive.

[0053] S3.4: calling find command to obtain the row index matrix hang and the column index matrix lie of each connected region in the mark matrix L, and obtaining the abrasive grain size d = max(max(hang)-min(hang), max(lie)-min(lie));

[0054] S3.5: in the mark matrix L, the abrasive position is enlarged by d / 2, and the positions of all elements with value 0 in the region, i.e. the positions of the binder region around the abrasive, are represented by the logic matrix logic2.

[0055] The present application can effectively identify the number, grain size and position information of the abrasive, and the position information of the binder by using the mark matrix to perform feature segmentation on the surface of the electroplated grinding wheel.

[0056] S4: combining the abrasive position information in step S3, the position information of the binder region around the abrasive in the image, and the three-dimensional reconstruction image H obtained in step S2. Performing logical multiplication operation on the three-dimensional reconstruction image H according to the logic matrix logic1 and logic2 respectively, i.e. obtaining the height information matrix H_moliao and H_jieheji of each abrasive and the binder around the abrasive. Taking the average of the five pixel points with the maximum value in H_moliao to represent the top height of each abrasive, and taking the average of the values of all pixel points in H_jieheji to represent the average height of the binder region around each abrasive. Taking the average height of the top five pixel points with the highest height and the average height of the binder region around the abrasive as the detection reference can weaken the influence of feature abnormal points on the detection result, and improve the detection accuracy.

[0057] S5: subtracting the average height of the binder region around the abrasive from the top height of the abrasive obtained in S4 can obtain the exposed height of the abrasive. According to the center coordinate position center(x, y) of each abrasive obtained in step S3.2, the height value of each abrasive is marked in the binary image BW, and the obtained height marking image is as shown in Figure 5 .

[0058] The detection method and detection reference proposed by the present application can ignore the surface shape of the grinding wheel, and are suitable for complex profile grinding wheels such as flat grinding wheels and arc surface grinding wheels. Meanwhile, the detection method proposed by the present application can realize batch detection of the exposed height of the abrasive.

[0059] The above only describes the preferred embodiments of the present application, and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for detecting the abrasive exposure height of an electroplated grinding wheel, characterized in that, Includes the following steps: S1: The microstructure of the electroplated grinding wheel surface is continuously photographed using an ultra-depth-of-field microscope to generate image sequence I of the microstructure of the electroplated grinding wheel surface. S2: Perform image focusing depth synthesis processing on the image sequence I obtained in step S1 to obtain a two-dimensional fused image M and a three-dimensional reconstructed image H of the micro-morphology of the electroplated grinding wheel surface; S3: Binarize the two-dimensional fused image M obtained in step S2 to obtain a binarized image BW. Perform feature segmentation on the binarized image BW to identify the abrasive and the binder, and obtain the abrasive particle size, position, and position information of the binder area around the abrasive in the image. S4: Combine the abrasive position information from step S3, the position information of the binder region around the abrasive in the image, and the three-dimensional reconstructed image H obtained in step S2 to obtain the top height of the abrasive and the average height of the binder region around the abrasive. S5: Subtract the top height of the abrasive obtained in step S4 from the average height of the bonding agent area around the abrasive to obtain the exposed height of the abrasive, and mark the exposed height in the binary image BW. The method for obtaining the two-dimensional fused image M and the three-dimensional reconstructed image H of the microstructure of the electroplated grinding wheel surface in step S2 is as follows: S2.1: For the image sequence I = {I1, I2, I3…I…} n Each image in the sequence is processed to grayscale, transforming the original three-dimensional image matrix into a two-dimensional grayscale image matrix, resulting in a grayscale image sequence Igray = {Igray1, Igray2, Igray3…Igray}. n }, Igray1, Igray2, Igray3…Igray n Representing images I1, I2, I3…I n grayscale image; S2.2: Use the `imfilter` command in MATLAB to process the grayscale image sequence Igray = {Igray1, Igray2, Igray3…Igray}. n The image is filtered to remove noise points, resulting in a filtered image sequence G = {G1, G2, G3…G}. n }; S2.3: For the filtered image sequence G = {G1, G2, G3…G…} n The pixel G in each image in} n The analysis is performed on (x,y), and the focusing evaluation function value F is calculated using the improved Laplace operator. n (x,y); S2.4: Focusing function evaluation value F with image index n as the x-axis. n Using (x, y) as the ordinate, plot the Fn curve for each pixel. The x-coordinate k corresponds to the point where the focus function evaluation value F is maximized. Point k indicates that the pixel is at the G... k The image is focused, and the pixel with the largest focus evaluation function value F is extracted to obtain the fully focused two-dimensional fused image M; S2.5: Perform Gaussian fitting on the Fn curve to obtain the continuously changing F'-n' curve. Extract the horizontal coordinate k' of each pixel when F' is at its maximum, and then obtain the height index matrix H_index. The height value of the corresponding pixel is h = (k'-1) × Δh. Combine the height index matrix H_index and the height value h to obtain the three-dimensional reconstructed image H, where Δh is the shooting distance. The improved Laplace operator described in step S2.3 is shown in equation (1): (1) Where x and y represent pixel G n (x, y) in the image G n In the coordinates, s represents the variable step size, N represents the window size, and f(x,y) represents the pixel point G. n The Laplace value of (x,y), F n (x, y) are the improved Laplace operation values, here represented by F. n (x,y) represents the focus evaluation function value of the pixel; Step S3 involves obtaining the abrasive particle size, the location of the abrasive, and the location information of the bonding agent region surrounding the abrasive in the image. S3.1: In the binary image BW, the position with a value of 1 represents the abrasive, and the position with a value of 0 represents the binder; S3.2: Use the bwlabel command in MATLAB to find all 8-connected regions in the binary image BW, label each region as an abrasive particle, and obtain the label matrix L and the number of connected regions num using the bwlabel command. Each abrasive particle in the label matrix L has a label value i, i = 1...num. The position information of each abrasive particle is represented by the logical matrix logic1, which is the position of all elements of the label value i in the label matrix L. The position of the abrasive particle is the value of 1 in the logical matrix logic1. The bonding agent and other abrasive particle regions are represented by 0. S3.3: Use the regionprops command in MATLAB to obtain the centroid coordinates center(x,y) of each connected region in the label matrix L. Let center(x,y) be the centroid position coordinates of each abrasive particle. S3.4: Call the find command to obtain the row index matrix hang and column index matrix lie of each connected region in the label matrix L, and obtain the abrasive particle size d = max(max(hang)-min(hang), max(lie)-min(lie)). S3.5: In the marking matrix L, the abrasive positions are enlarged by d / 2 times at equal intervals. The positions of all elements with a value of 0 in this region, i.e. the positions of the bonding agent regions around the abrasive, are represented by the logic matrix logic2.

2. The method for detecting the abrasive exposure height of an electroplated grinding wheel according to claim 1, characterized in that, The method for generating the image sequence I of the microstructure of the electroplated grinding wheel surface in step S1 is as follows: A super depth-of-field lens is controlled to continuously capture images of the grinding wheel surface from bottom to top at equal intervals, with an interval of Δh. The capturing process begins from a completely out-of-focus state and ends at another completely out-of-focus state to obtain partially focused images between the two completely out-of-focus positions. The electroplated grinding wheel is captured n times to generate the image sequence I, consisting of n images {I1, I2, I3…I…}. n The structure consists of I1, I2, I3…I n Each of the images taken represents a separate image.

3. The method for detecting the abrasive exposure height of an electroplated grinding wheel according to claim 1 or 2, characterized in that, The filtering methods described in step S2.1 include Gaussian filtering, mean filtering, and median filtering.

4. The method for detecting the abrasive exposure height of an electroplated grinding wheel according to claim 3, characterized in that, The method for marking the exposed height in the binary image BW in step S3 is as follows: based on the centroid coordinate position center(x,y) of each abrasive particle obtained in step S3.2, mark the calculated height value of each abrasive particle in the binary image BW.

5. The method for detecting the abrasive exposure height of an electroplated grinding wheel according to claim 4, characterized in that, The method for obtaining the top height of the abrasive and the average height of the bonding agent region surrounding the abrasive in step 4 is as follows: In the three-dimensional reconstructed image H, sort all height values ​​in the logic matrix logic1, take the average of the 5 largest values ​​to represent the top height of the abrasive; and take the average of all height values ​​in the logic matrix logic2 to represent the average height of the bonding agent region surrounding the abrasive.

Citation Information

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