Virtual grinding wheel 3D landform reconstruction method based on matrix convolution operation

Abstract

The invention provides a virtual grinding wheel 3D landform reconstruction method based on matrix convolution operation. A digital filtering matrix and random matrix convolution mode is adopted to reconstruct a grinding wheel landform. The actual grinding wheel landform is collected through a 3D optical contourgraph, statistical analysis is conducted, and statistical parameters such as the average value, the standard deviation, the skewness and the kurtosis are adopted for conducting quantitative analysis on the distribution rule of grinding wheel landform height data. According to the method, the protruding abrasive particles on the surface of the grinding wheel are extracted, statistical analysis of the shapes of the abrasive particles is carried out, the statistical abrasive particles serve as a filtering function, convolution calculation is carried out on the filtering function and the random matrix, reconstruction of the random grinding wheel landform is achieved, and reconstruction of the virtual grinding wheel landform is carried out by taking the actually-collected grinding wheel landform as a reference. And for grinding wheel landforms in different wear stages, performing conversion calculation on the grinding wheel landform digital matrix by adopting Johnson conversion. According to the method, the problem of poor consistency between virtual grinding wheel landform reconstruction and actual grinding wheel landform is solved, and the accuracy of grinding wheel landform reconstruction is improved.

Description

Technical Field

[0001] The invention proposes a virtual grinding wheel topography reconstruction method, in particular to the randomness of the abrasive shape on the grinding wheel surface and the change of the abrasive shape in different wear stages, and belongs to the technical field of grinding processing. Background Art

[0002] The grinding wheel is composed of abrasive grains and a binder. The protrusion of abrasive grains on the surface of the grinding wheel has a certain randomness, among which the position, protrusion height and shape of the abrasive grains all have a certain randomness. In order to deepen the understanding of grinding behavior, virtual grinding wheels are often used in grinding simulation calculations to explore the interaction between abrasive grains and materials during grinding and the material removal mechanism. Grinding wheel topography plays a very important role in analyzing the grinding process and is the basis for simulation calculations of the grinding process [Wei L, Zhaohui D, Yuanyuan S, et al. Parametric evaluation and three-dimensional modelling for surfacetopography of grinding wheel [J]. International Journal of Mechanical Sciences, 2019, 155: 334-342]. Unfortunately, measuring the entire grinding wheel topography is a time-consuming and laborious task. However, the complete grinding wheel topography is required for the simulation of the grinding process. Therefore, most studies focus on virtual grinding wheel topography reconstruction [D.AD, AW, RBA survey of recent grinding wheel topography models [J]. International Journal of Machine Tools and Manufacture, 2005, 46 (3): 343-352] and use it for the simulation of the grinding process. Suto [Suto and T.Sala, Simulation of grinding process based on wheel surface characteristics, Journal of the Japan Society of Precision Engineering, 1979, 45 (535), 775-780] established an empirical model of the grinding process by measuring the number of active cutting edges and the wear area, but did not consider the size of the abrasive particles. Chen Xun [Xun C, WB R. Analysis and simulation of the grinding process. Part I: Generation of the grinding wheelsurface [J]. International Journal of Machine Tools and Manufacture, 1996, 36 (8): 871-882] constructed a virtual grinding wheel topography based on random numbers, assumed the shape of the abrasive particles to be spherical, and used the reconstructed virtual grinding wheel for simulation calculations of grinding wheel dressing and grinding processes.Li Haonan [Hao NL, Tian BY, Li DZ, et al. Analytical modeling of ground surface topography in monocrystalline silicon grinding considering the ductile-regime effect [J]. Archives of Civil and Mechanical Engineering, 2017, 17 (4): 880-893] In the study of the surface creation mechanism of monocrystalline silicon, the abrasive particles were assumed to be truncated cone shaped. To summarize the above studies, when constructing the virtual grinding wheel topography, the abrasive particles were assumed to be regular in shape. The reconstruction of the virtual grinding wheel topography was completed by statistically analyzing and summarizing the size, position and protrusion height of the abrasive particles on the actual grinding wheel surface.

[0003] During the grinding process, the topography of the grinding wheel at different grinding stages is not static, but a dynamic process. Regarding the study of grinding wheel topography at different grinding stages, Chen Xun [Xun C, WB R, BM, et al. Analysis and simulation of the grinding process. Part IV: Effects of wheel wear [J]. International Journal of Machine Tools and Manufacture, 1998, 38 (1): 41-49] found that the wear of the grinding wheel affects the quality and efficiency of grinding, and proposed that the grinding wheel has different topographic characteristics after dressing and wear. Akshit Choudhary [Akshit C, NR B. Influence of 3D topography on tribological behavior of grinding wheel [J]. Procedia Manufacturing, 2020, 48: 533-540] used a laser confocal microscope to collect the topography of the grinding wheel at different wear stages and found that as the grinding progressed, the density of the abrasive tip gradually decreased, and more abrasive particles came into contact with the workpiece by friction, which led to a gradual increase in the grinding force. Hwang[Hwang TW, Evans CJ, Malkin S. High Speed ​​Grinding of Silicon Nitride with Electroplastic Diamond Wheels, Part 2: Wheel Topography and Grinding Mechanisms[J]. Journal of Manufacturing Science and Engineering, 2000, 122(1): 42-50]'s research shows that compared with the normal distribution, the probability distribution curve of the abrasive protrusion height shows obvious skewness.Yao Peng [Peng Y, Yadong G, Takeshi M, et al. Investigation of wheel wear mechanisms during grinding optical glasses through statistical analysis of wheel topography [J]. Int. J. of Abrasive Technology, 2012, 5 (1): 33-47] measured the wheel topography of diamond grinding wheels at different stages of grinding optical glass and found that as grinding continued, the height of the abrasive protrusion gradually changed from a normal distribution to a skewed distribution, and used statistical parameters such as mean, standard deviation, skewness and kurtosis to describe the distribution characteristics of the abrasive protrusion height. Hamid Jamshidi [Jamshidi H, Gurtan M, Budak E. Identification of active number of grits and its effects on mechanics and dynamics of abrasive processes [J]. Journal of Materials Processing Tech., 2018, 273: 116-239] used extreme functions to describe the probability distribution of the abrasive protrusion height at different grinding stages.

[0004] Compared with the virtual grinding wheel reconstructed by assuming the abrasive particles to be of standard shape, the virtual grinding wheel topography reconstruction method proposed in the present invention can well represent the randomness of the abrasive particle size, position, protrusion height and shape, and realizes the change of the abrasive particle shape through Johnson transformation, which greatly improves the consistency between the virtual grinding wheel topography and the actual grinding wheel topography. Summary of the invention

[0005] Purpose of the invention: In view of the problem that the current virtual grinding wheel topography reconstruction is insufficient in expressing the randomness of abrasive particles, the present invention proposes a virtual grinding wheel 3D topography reconstruction method based on matrix convolution operation, which can fully express the randomness of the size, position, protrusion height and shape of the abrasive particles on the grinding wheel surface. The present invention provides a method for calculating the topography change of the grinding wheel at different wear stages, which realizes the change of the size, protrusion height and shape of the abrasive particles under the condition that the position of the abrasive particles remains unchanged by performing Johnson transformation on the digital matrix of the grinding wheel topography.

[0006] Technical solution: In order to achieve the purpose of the above invention, the present invention adopts the following technical solution:

[0007] A virtual grinding wheel 3D topography reconstruction method based on matrix convolution operation, the steps are as follows:

[0008] Step 1: Use a 3D profilometer to collect the grinding wheel topography and determine the grinding wheel topography characteristics.

[0009] Step 2: Use mean, standard deviation, skewness and kurtosis to quantitatively analyze and evaluate the distribution law of grinding wheel landform height data.

[0010] Step 3: extract the abrasive grains protruding from the surface of the grinding wheel, count the shapes of the extracted abrasive grains, and obtain the statistical results of the abrasive grain shapes.

[0011] Step 4: The abrasive shape matrix obtained by statistics is used as the convolution kernel to perform convolution calculation with the random matrix to obtain the grinding wheel topography with random characteristics, which can well describe the randomness of the abrasive size, position, protrusion height and shape.

[0012] Step 5. For the grinding wheel topography at different wear stages, the Johnson transformation is used to convert and calculate the grinding wheel topography digital matrix. Under the condition that the abrasive position remains unchanged, the abrasive size, protrusion height and shape are converted and calculated, which provides a new method for reconstructing the grinding wheel topography at different wear stages.

[0013] Step 6: Conduct grinding tests and surface morphology simulation calculations to verify the feasibility of the above-mentioned grinding wheel topography reconstruction method.

[0014] The beneficial effects of the present invention are:

[0015] (1) The present invention proposes a method for quantitative analysis and evaluation of grinding wheel topography, and uses statistical parameters (mean value, standard deviation, skewness and kurtosis) to analyze and evaluate the grinding wheel topography.

[0016] (2) In view of the problem that the abrasive grains on the grinding wheel surface are currently assumed to be regular in shape, which reduces the accuracy of the reconstruction of the virtual grinding wheel topography, the present invention uses a convolution method to reconstruct the grinding wheel topography, which can restore the randomness of the shape of the abrasive grains on the grinding wheel surface. A method for reconstructing random grinding wheel topography is proposed, which can well describe the randomness of the size, position, protrusion height and shape of the abrasive grains on the grinding wheel surface, and improve the consistency between the virtual grinding wheel topography and the actual grinding wheel topography.

[0017] (3) The present invention proposes a method for reconstructing the topography of a grinding wheel at different wear stages. Without changing the position of the abrasive grains, the size, protrusion height and shape of the abrasive grains are changed, providing a new method for reconstructing the topography of a grinding wheel at different wear stages.

[0018] In summary, the present invention aims at the problem of low accuracy of reconstruction of grinding wheel landforms, and reconstructs grinding wheel landforms by convolution of digital filter matrix and random matrix. Actual grinding wheel landforms are collected by Sensofar (3D optical profiler) and statistical analysis is performed, and statistical parameters such as mean value, standard deviation, skewness and kurtosis are used to quantitatively analyze the distribution law of grinding wheel landform height data. The abrasive grains protruding from the surface of the grinding wheel are extracted, and statistical analysis of the shape of the abrasive grains is performed. The abrasive grains after statistics are used as filter functions, and convolution calculations are performed with random matrices to achieve reconstruction of random grinding wheel landforms. The grinding wheel landforms actually collected are used as reference benchmarks to reconstruct virtual grinding wheel landforms. For grinding wheel landforms at different wear stages, Johnson conversion is used to convert and calculate the grinding wheel landform digital matrix. The present invention solves the problem of poor consistency between virtual grinding wheel landform reconstruction and actual grinding wheel landforms, and the feasibility of the method is verified by comparing grinding tests with simulation calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a schematic diagram of the diamond grinding wheel dressing process in Example 1;

[0020] Figure 2 is the actual grinding wheel topography image acquired by the 3D profilometer in Example 1;

[0021] Figure 3 is the statistical result of the actual grinding wheel landform height data in Example 1;

[0022] Figure 4 is the statistical calculation result of the actual grinding wheel topography height data in Example 1;

[0023] Figure 5 It is a schematic diagram of the contact state between the abrasive and the workpiece;

[0024] Figure 6 It is the actual grinding wheel topography abrasive grain extraction result;

[0025] Figure 7 is the actual wear particle statistical shape;

[0026] Figure 8 It is a schematic diagram of the convolution calculation process of the digital filter matrix;

[0027] Fig. 9 It is to reconstruct the virtual grinding wheel topography;

[0028] Fig.10 It is the abrasive grain extraction result of virtual grinding wheel topography;

[0029] Fig.11 It is a schematic diagram of Johnson transformation of grinding wheel landform;

[0030] Fig.12It is a schematic diagram of the experimental process of grinding GH4169;

[0031] Fig.13 These are the results of the grinding test and simulation calculation of GH4169; among them: (a) the grinding test result; (b) the simulation calculation result.

[0032] In the figure: 1. three-jaw chuck; 2. silicon carbide rod; 3. diamond grinding wheel; 4. grinding wheel spindle; 5. abrasive; 6. binder; 7. pits; 8. part where abrasive contacts material; 9. normal projection of part where abrasive contacts material; 10. tangential projection of part where abrasive contacts material; 11. GH4169 material; 12. microcrystalline corundum grinding wheel. DETAILED DESCRIPTION

[0033] The invention is further described in detail below with reference to the accompanying drawings and specific examples:

[0034] Example 1

[0035] A virtual grinding wheel topography reconstruction method comprises the following steps:

[0036] Step 1: Use a 3D profilometer to collect the grinding wheel topography and determine the grinding wheel topography characteristics. The grinding wheel dressing process and the actual grinding wheel topography collected are as follows: Figure 1 and Figure 2 The collected grinding wheel topography is used as the basis for reconstructing the virtual grinding wheel topography. The machine tool used in the diamond grinding wheel dressing test 3 is a STUDER S131 internal and external cylindrical grinder. Figure 1 In the process, the diamond grinding wheel 3 is fixed on the grinding wheel spindle 4, the silicon carbide rod 2 is fixed by means of a three-jaw chuck 1, the diamond grinding wheel and the silicon carbide rod rotate in opposite directions, and the grinding wheel dressing parameters are shown in Table 1:

[0037] Table 1 Grinding wheel dressing parameters

[0038]

[0039] The 3D morphology of the grinding wheel surface was characterized by sensorfar (3D optical profiler), and the sampling area size was 500×500μm. 2 , the spatial sampling interval is 0.5 μm, and the grinding wheel topography data consists of a 1000 × 1000 matrix, such as Figure 2 As shown, the surface of the grinding wheel is composed of protruding abrasive grains 5, bonding agent 6 and pits 7 formed by the falling of abrasive grains.

[0040] Step 2: Use mean value, standard deviation, skewness and kurtosis to quantitatively analyze and evaluate the distribution law of grinding wheel landform height data. The specific implementation steps are as follows:

[0041] The grinding wheel landform height data has a certain randomness. MATALB software is used to perform statistical analysis on the collected grinding wheel landform height data. The statistical results are as follows: Figure 3 Compared with the normal distribution, the grinding wheel landform data shows a certain deviation. In order to quantitatively analyze the grinding wheel landform height data, the statistical parameters mean, variance, skewness and kurtosis are used to describe the distribution law of the grinding wheel landform height data. The statistical calculation results of the grinding wheel landform are shown in Figure 4 shown.

[0042] The calculation formula of the average value ζ1 is shown in (1):

[0043]

[0044] Among them, h is the height of the grinding wheel landform, and n is the sum of statistical data.

[0045] The standard deviation ζ2 reflects the degree of aggregation of the data set, and the calculation formula is shown in (2):

[0046]

[0047] Skewness ζ3 is the standard third-order moment of sample data. Skewness ζ3 is a measure of the direction and degree of skewness of statistical data distribution and is a digital feature of the degree of asymmetry of statistical data distribution. The larger the absolute value of skewness ζ3 is, the greater the degree of skewness of the data set is. The calculation formula is shown in (3):

[0048]

[0049] Kurtosis ζ4 is the standard fourth-order moment of sample data. Kurtosis ζ4 is a statistic that describes the steepness of the distribution of all sample data in the population. The kurtosis of a normal distribution is 3. The calculation formula for kurtosis ζ4 is shown in (4):

[0050]

[0051] Step 3: The part where the abrasive contacts the workpiece material is irregular, such as Figure 5 The abrasive grains 5 protruding from the grinding wheel surface are extracted, as shown in FIG. Figure 6 As shown, statistical analysis is performed. When the statistical result is large enough, the shape of the abrasive particles has a certain degree of certainty. The abrasive particle shapes extracted are statistically analyzed to obtain the abrasive particle shape matrix, as shown in Figure 7 shown.

[0052] Step 4: The abrasive shape matrix obtained by statistics is used as the convolution kernel to perform convolution calculation with the random matrix to obtain the grinding wheel topography with randomness. The details are as follows:

[0053] (1) The reconstruction of the virtual grinding wheel is based on the statistical law of the grinding wheel topography height data to establish the virtual grinding wheel random topography. Convolution calculation can represent the characteristics of two functions, namely, the deterministic shape of the abrasive grain after statistics and the randomness of a single abrasive grain. The convolution process of the digital matrix is ​​as follows: Figure 8 As shown, the calculation formula is shown in formula (5):

[0054]

[0055] Wherein the matrix b represents the convolution kernel, is a digital filter matrix, the digital filter matrix of the present invention is the abrasive shape matrix obtained by statistics in the previous text, η is a random digital matrix, and h is a grinding wheel topography digital matrix.

[0056] (2) The virtual grinding wheel topography obtained by convolution calculation is as follows Fig. 9 As shown in the figure, the abrasive grains are extracted from the virtual grinding wheel topography to obtain the abrasive grain size, position, protrusion height and shape. Fig.10 shown.

[0057] Step 5: For the grinding wheel topography at different wear stages, Johnson transformation is used to convert and calculate the grinding wheel topography digital matrix to obtain the grinding wheel topography at different wear stages.

[0058] (1) With the gradual wear of the grinding wheel, the grinding wheel topography changes continuously at different grinding stages. The grinding wheel topography at different grinding stages obtained by Johnson transformation is shown in the figure below: Fig.11 As shown in Figure 6, the Johnson transformation changes the abrasive particle size, protrusion height and shape when the abrasive particle position is below the bottom edge. The general formula of the Johnson transformation is shown in formula (6):

[0059]

[0060] Where h is a normal random sequence, h' is a random sequence with specified skewness and kurtosis, γ and δ are shape parameters, ε is the center offset, and λ is the scale factor.

[0061] (2) For different non-normal random sequences, Johnson has different transformation forms, including the bounded system S B , unbounded system S U and the lognormal system S L There are three types. As shown in Table 2:

[0062] Table 2 Three types of Johnson transformation

[0063]

[0064] Step 6: Conduct GH4169 grinding test. The experimental device is as follows: Fig.12As shown, the machine tool used for the internal and external cylindrical grinding test is a STUDER S131 internal and external cylindrical grinder, and the microcrystalline corundum grinding wheel 12 is fixed on the grinding wheel spindle 4. The grinding wheel has a diameter of 20 mm, a width of 20 mm, and a grit size of 150 mesh. The GH4169 material 11 is fixed with the help of a three-jaw chuck 1. After the installation is completed, a circular runout instrument is used to detect the circular runout of the workpiece surface to be processed to ensure that it is within 3 μm, and the surface morphology of GH4169 is simulated and calculated to verify the feasibility of the above-mentioned grinding wheel topography reconstruction method. The experimental parameters are shown in Table 3:

[0065] Table 3 Grinding test parameters

[0066]

[0067] The surface morphologies obtained by experiment and simulation are shown in Fig.13 As shown, Figure (a) is the result of the grinding experiment; Figure (b) is the result of the simulation calculation. It can be seen that the surface roughness Sa obtained by the experiment and simulation are 0.713μm and 0.749μm respectively, the maximum difference in surface height Sz is 5.609μm and 5.353μm respectively, and the errors of Sa and Sz on the workpiece surface are 5.04% and 4.56% respectively. The difference in the surface morphology of the workpiece obtained by the experiment and the simulation calculation is slight, which is caused by the randomness of the abrasive grains on the surface of the grinding wheel. Based on the grinding test and simulation results of GH4169, the feasibility of the virtual grinding wheel topography reconstruction method proposed in the present invention is verified.

[0068] This embodiment does not impose any formal limitation on the shape, material, structure, etc. of the present invention. Any simple modification, equivalent change and modification made to the above embodiment based on the technical essence of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A virtual grinding wheel 3D topography reconstruction method based on matrix convolution operation, characterized in that: Here are the steps: Step 1: Use a 3D profilometer to collect the grinding wheel topography and determine the grinding wheel topography characteristics; Step 2: Use mean value, standard deviation, skewness and kurtosis to quantitatively analyze and evaluate the distribution law of grinding wheel landform height data; Step 3, extracting the abrasive grains protruding from the surface of the grinding wheel, and statistically analyzing the shapes of the extracted abrasive grains to obtain statistical results of the shapes of the abrasive grains; Step 4: The abrasive shape matrix obtained by statistics is used as a convolution kernel to perform convolution calculation with the random matrix to reconstruct the grinding wheel topography with random characteristics, which is used to describe the randomness of the abrasive size, position, protrusion height and shape; Step 5. For the grinding wheel topography at different wear stages, the Johnson transformation is used to convert and calculate the grinding wheel topography digital matrix. Under the condition that the abrasive position remains unchanged, the abrasive size, protrusion height and shape are converted and calculated to adapt to the reconstruction of the grinding wheel topography at different wear stages.

2. The method for reconstructing 3D topography of a virtual grinding wheel based on matrix convolution operation according to claim 1 is characterized in that: In step (2), MATALB software is used to perform statistical analysis on the collected grinding wheel topography height data; wherein, The calculation formula of the average value σ1 is shown in (1): Among them, h is the height of the grinding wheel landform, and n is the sum of statistical data; The standard deviation σ2 reflects the degree of aggregation of the data set, and the calculation formula is shown in (2): Skewness σ3 is the standard third-order moment of sample data. Skewness σ3 is a measure of the direction and degree of skewness of statistical data distribution and is a numerical feature of the degree of asymmetry of statistical data distribution. The larger the absolute value of skewness σ3 is, the greater the degree of skewness of the data set is. The calculation formula is shown in (3): Kurtosis σ4 is the standard fourth-order moment of sample data. Kurtosis σ4 is a statistic that describes the steepness of the distribution of all sample data in the population. The kurtosis of a normal distribution is 3. The calculation formula for kurtosis σ4 is shown in (4):

3. The method for reconstructing 3D topography of a virtual grinding wheel based on matrix convolution operation according to claim 1 is characterized in that: In step (4), the process of reconstructing and establishing the virtual grinding wheel random topography is as follows: (1) The convolution calculation represents the characteristics of two functions, namely, the determinism of the wear particle shape after statistics and the randomness of a single wear particle. The calculation formula of the digital matrix is ​​shown in formula (5): Wherein the matrix b represents the convolution kernel, is a digital filter matrix, the digital filter matrix of the present invention is the abrasive shape matrix obtained by the above statistics, η is a random digital matrix, and h is a grinding wheel topography digital matrix; (2) The virtual grinding wheel topography obtained by convolution calculation is used to extract abrasive particles, and the abrasive particle size, position, protrusion height and shape are obtained for grinding simulation calculation.

4. The method for reconstructing 3D topography of a virtual grinding wheel based on matrix convolution operation according to claim 1 is characterized in that: The specific process of step (5) is as follows: (1) With the gradual wear of the grinding wheel, the grinding wheel topography changes continuously at different grinding stages. The grinding wheel topography at different grinding stages is obtained by Johnson transformation. Johnson transformation changes the abrasive grain size, protrusion height and shape without changing the abrasive grain position. The general formula of Johnson transformation is shown in formula (6): Where h is a normal random sequence, h' is a random sequence with specified skewness and kurtosis, γ and δ are shape parameters, ε is the center offset, and λ is the scale factor; (2) For different non-normal random sequences, Johnson has different transformation forms, including the bounded system S B , unbounded system S U and the lognormal system S L Three types:

5. The method for reconstructing 3D topography of a virtual grinding wheel based on matrix convolution operation according to claim 1 is characterized in that: In step three, the abrasive particle shapes are statistically analyzed to obtain an abrasive particle shape matrix, and the process is as follows: (1) Query the diameter of the abrasive grains according to the grinding wheel model and calculate the size of the pixel area occupied by the abrasive grains. The calculation formula for the length of the pixel area occupied by the abrasive grains is shown in (7): Among them, n x 、n y Represents the length in the horizontal and vertical directions, d g Indicates the abrasive particle diameter, l b Represents the distance between adjacent pixels; (2) Obtain the position and height of the abrasive particle apex. The abrasive particle apex is the highest point of the abrasive particle, that is, the maximum value of the pixel area occupied by a single abrasive particle. The calculation formula is shown in (8): in, Indicates that the point is the vertex of the abrasive particle. In order to distinguish the vertex of the abrasive particle from other positions, I and J are used to represent the fixed point position of the abrasive particle. In order to eliminate the influence of the irregular shape of the binder on the shape of the abrasive, the vertex height of the abrasive should be greater than the height of the binder. The calculation formula is shown in (9): The calculation formula of wear particle location area is as follows: (3) Obtaining the shape of the abrasive particles. After the above steps, the vertex position (I, J) of the abrasive particles and the corresponding height value have been obtained. The calculation formula for extracting the shape of the abrasive particles is shown in (10): (4) The extracted abrasive particles are superimposed to obtain the average shape of the abrasive particles. The shape matrices of the extracted single abrasive particles are superimposed and averaged to obtain the average shape matrix of the abrasive particles. The calculation formula is shown in (11):

6. The method for reconstructing 3D topography of a virtual grinding wheel based on matrix convolution operation according to claim 1, characterized in that: In step three and step four, the abrasive grains in the reconstructed virtual grinding wheel topography are extracted, and the position, height and shape of the abrasive grains on the virtual grinding wheel surface are recorded and used for grinding simulation calculation to verify the feasibility of the method of reconstructing the grinding wheel topography.

Images