Diamond grinding wheel surface topography geometric modeling based on discrete element method
Through the three-dimensional parametric geometric modeling method of diamond grinding wheel surface morphology based on discrete unit method, the problem of three-dimensional surface morphology modeling of grinding wheel in grinding processing is solved, and the grinding simulation efficiency and accuracy are improved.
Patent Information
- Application Number
- CN202510044852.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-10
- Publication Date
- 2025-05-09
AI Technical Summary
During the grinding process, it is difficult for the prior art to accurately model and simulate the three-dimensional surface morphology of the grinding wheel, resulting in insufficient grinding simulation efficiency and accuracy.
The three-dimensional parametric geometric modeling method of diamond grinding wheel surface morphology is adopted based on the discrete unit method. By measuring the grinding wheel geometric dimensions, generating discrete element particle models, calculating the average abrasive particle spacing, defining a single abrasive model and establishing a virtual grid, the accurate model of the three-dimensional geometric morphology of the grinding wheel is achieved.
The accuracy and simulation speed of the grinding wheel model in grinding simulation are improved, providing better support for grinding process optimization and grinding wheel design.
Smart Images
Figure CN119962001A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of grinding wheel surface morphology simulation, in particular to a grinding wheel three-dimensional parameterized geometric modeling method based on discrete element method. Background Art
[0002] In the grinding process, it is difficult to observe and analyze the grinding process experimentally due to the large number of abrasive particles, irregular geometric shapes, high grinding speed, small and inconsistent grinding depth, etc. Therefore, many scholars at home and abroad have introduced simulation technology into the research of grinding process to study high-speed, complex and difficult-to-observe grinding processes. Therefore, the characterization and modeling of the three-dimensional morphology of the diamond grinding wheel surface is of great significance for realizing the simulation of the grinding process and optimizing the grinding process and the design and preparation of the grinding wheel.
[0003] A very important task in grinding simulation is grinding wheel modeling. Establishing an accurate grinding wheel model is the first problem that needs to be solved in various grinding simulation studies. Grinding is a complex processing method with strong randomness, and this randomness is largely determined by the randomness of the grinding wheel surface topography. Therefore, only by establishing a grinding wheel model that is relatively close to the actual grinding wheel can subsequent grinding simulation work be accurately performed. In recent years, the discrete element method has been applied in grinding simulation. In terms of grinding wheel modeling, the discrete element method is used to establish a three-dimensional discrete element model of the grinding wheel. The final grinding wheel model is mainly characterized by discrete element particles. The present invention provides a grinding wheel surface morphology modeling based on discrete element simulation, and optimizes the calculation method of abrasive particle arrangement, which can effectively improve the simulation speed and efficiency, and bring great convenience to the simulation work. Summary of the invention
[0004] The present invention proposes a three-dimensional parametric geometric modeling method for the surface morphology of a diamond grinding wheel based on a discrete element method. The method comprises the following steps: Step 1: Measure the geometric dimensions of the diamond grinding wheel and define the geometric model dimensions of the grinding wheel; Step 2: Generate a discrete element grinding wheel model in the EDEM software, and use bonding bonds to bond the particles to establish an initial grinding wheel model; Step 3: Calculate the average spacing of the abrasive grains based on the surface morphology of the grinding wheel and the particle size of the grinding wheel; Step 4: Define a single abrasive grain model, divide the grinding wheel geometry model into grids, and establish a cube virtual grid; Step 5: Initially position the center plane of the abrasive grain at each vertex of the outer surface of the virtual grid, and the abrasive grain moves within the virtual grid; Step 6: Generate polygonal abrasive particles in the EDEM software, establish a rectangular binder matrix, define its plane on the coordinate plane of the center of the sphere circumscribed by the abrasive, bond the abrasive and the binder matrix through the Bonding key, and form a three-dimensional geometric morphology model of the grinding wheel; Step 7: According to the actual abrasive edge height, move the abrasive to meet the conditions and determine the three-dimensional geometric morphology model of the grinding wheel.
[0005] In the above-mentioned diamond grinding wheel surface morphology geometric modeling based on discrete element method, in step 1, a diamond cup grinding wheel with a grain size of D20 is selected, and by measuring its geometric dimensions, a grinding wheel with a center hole diameter of 20 mm, a grinding wheel outer diameter of 100 mm, and a grinding wheel working diameter of 10 mm is established.
[0006] In the above-mentioned diamond grinding wheel surface morphology geometric modeling based on discrete element method, in the step 2, EDEM software is used, the particle parameters are set in the Bulk Material part of the software, and Volume is established in the Geometries part to make the discrete element particles form a three-dimensional geometric model of the grinding wheel. In Physics, the contact condition is selected as Bonding contact model key to form the grinding wheel matrix, and the initial model of the grinding wheel is established.
[0007] In the above-mentioned diamond grinding wheel surface morphology geometric modeling based on discrete element method, in the step three, the surface morphology of the diamond grinding wheel is observed, and the diamond abrasive grains with a grinding wheel concentration of 100% and a grain size of D20 correspond to a diamond abrasive grain size range of 20um-30um.
[0008] In the above-mentioned diamond grinding wheel surface morphology geometric modeling based on discrete element method, in step three, the actual diamond surface morphology is observed by a super depth of field microscope system. In order to eliminate the influence of random factors, four areas A, B, C, and D are selected on the grinding wheel surface for observation. The number of abrasive grains in different observation areas and their corresponding area areas are counted respectively to obtain the abrasive grain area density on the surface of the diamond grinding wheel with a particle size of D20.
[0009] In the above-mentioned diamond grinding wheel surface morphology geometric modeling based on discrete element method, in the step three, the average spacing a of the abrasive grains is calculated according to the abrasive grain area density on the grinding wheel surface and the grinding wheel grain size.
[0010] Assume that the abrasive particles are evenly distributed in the area, where the side length of the small rectangle is a (average spacing between abrasive particles). Then, on the a×a area, the number of abrasive particles is 1, that is, the area density of abrasive particles on the a×a area is 1 / a. 2 Based on the experimentally measured abrasive area density, the average spacing a can be calculated.
[0011] In the above-mentioned diamond grinding wheel surface morphology geometric modeling based on the discrete element method, in the step 4, the surface morphology of the grinding wheel is observed by an ultra-depth of field microscope, and the three-dimensional morphology information of the abrasive is obtained after image binarization processing. The shape of the abrasive is simplified and set to a polyhedron. By cutting a regular tetrahedron, polyhedral abrasives with different shapes are obtained, with a total of 5 types.
[0012] The first model is a regular tetrahedron with a side length of S. Subsequently, 1 / 8 of the side length S of the regular tetrahedron is cut in turn at the four vertices of the regular tetrahedron to obtain abrasive particles with different numbers of faces. As the cutting step n (0, 1, 2, 3, 4) increases, the abrasive particles gradually transform into regular octahedrons.
[0013] In the above-mentioned diamond grinding wheel surface morphology geometric modeling based on discrete element method, in step 4, the actual diameter of the polyhedron abrasive grain is replaced by the diameter of its circumscribed sphere.
[0014] The relationship between the side length S and the radius R of the circumscribed sphere of a regular tetrahedral abrasive grain with step length n=0 is: Where: R is the radius of the circumscribed sphere of the abrasive particle; S is the length of one side of the abrasive particle
[0015] For the polyhedral abrasive grains with step length n=1, 2, 3, the circumscribed sphere radius of the polyhedral abrasive grains is obtained by subtracting the circumscribed sphere radius R1 of the cut small regular tetrahedron from the circumscribed sphere radius R of the initial regular tetrahedron, so the circumscribed sphere radius R can be calculated by the side length S.
[0016] In the above-mentioned diamond grinding wheel surface morphology geometric modeling based on discrete element method, in the step 4, the grinding wheel geometric model is virtual meshed to divide the grinding wheel ring into multiple cubes.
[0017] Under initial conditions, the abrasive particles are arranged in a uniform position in space, and the distance a between two abrasive particles at this concentration is calculated based on the average diameter of the abrasive particles. The calculated average distance a between the abrasive particles is used as the side length, and the average particle size D of the abrasive particles is used as the real grid spacing, thereby dividing it into multiple cells.
[0018] In the above-mentioned diamond grinding wheel surface morphology geometric modeling based on discrete element method, in the step 5, the center of the circumscribed sphere of the abrasive grains is located on the grid surface, and the random arrangement of the abrasive grains is achieved by adjusting the coordinates of the center of the circumscribed sphere of the abrasive grains.
[0019] Assume that the origin O of the coordinate system is located at the geometric center of the abrasive grain on the grinding wheel, and the geometric center of the circumscribed sphere of the abrasive grain is located at the origin of the coordinate system; the direction of the abrasive grain on the grinding wheel is completely random, and the position and posture of each simulated abrasive grain is randomized.
[0020] In the process of randomizing the positions of the two abrasive particles, in order to avoid the overlap of the abrasive particles during the random arrangement process, each abrasive particle is confined to a grid area of a certain size, and the coordinates of the center of the circumscribed sphere are randomly changed within the area. The interference problem between the two abrasive particles is simplified to the interference problem between their minimum circumscribed spheres, where the necessary and sufficient conditions for the interference between abrasive particles 1 and 2 are: D<R1+R2 Where: R1 and R2 are the circumscribed sphere radii of the two abrasive particles; D is the average particle size of the two abrasive particles.
[0021] In the above-mentioned diamond grinding wheel surface morphology geometric modeling based on discrete element method, in step six, in order to characterize the characteristic parameters of the grinding wheel surface morphology, it is necessary to define the grinding wheel bond plane and determine the plane height of the bond matrix in order to determine the edge height of the abrasive.
[0022] The grinding wheel surface is considered as a rigid body, and the randomness of the edge height is achieved by the random posture of the abrasive grain. Here, the binder matrix plane can be determined as the surface where the coordinates of the center of the circumscribed sphere of the abrasive grain are located.
[0023] For actual grinding wheels, considering the holding strength of the bond matrix on the abrasive grains, the exposed edge height of the surface abrasive grains will not exceed 1 / 3 of their equivalent particle size. When the exposed edge height of the diamond abrasive grains exceeds 1 / 3 of their particle size, they are prone to break and fall off during high-speed rotation and cutting. Therefore, the maximum exposed edge height of the abrasive grains on the grinding wheel surface is taken. h nax =d g / 3 Where: h max ——The maximum height of the abrasive grains on the grinding wheel surface; d g ——mean diameter of abrasive particles;
[0024] NX 12.0 software is used to create the three-dimensional abrasive grains of the grinding wheel polygon, and the user programming formula is as follows: S=25*4 / sqrt(6) n=0(1,2,3,4) x=S / 8*n a=sin((S / 2*tan(30)) / (S*sin(60))) Where S is the side length of the abrasive grain of the regular tetrahedron grinding wheel; n is the step length of the abrasive grain sectioning; x is the side length of the abrasive grain sectioning; a is the draft angle of the abrasive grain.
[0025] By changing the sectioning step n (0, 1, 2, 3, 4) through the NX 12.0 software operation page, abrasive particles with different numbers of faces can be obtained. As the sectioning step n increases, the abrasive particles gradually transform into regular octahedrons.
[0026] In the EDEM software, select Tools to form the polyhedron abrasive model into a New Template in turn, and finally establish the particle bonding model.
[0027] An area of 279.2 × 279.2 μm was taken from the D20 grinding wheel, and a virtual grinding wheel surface with 8 × 8 × 1 polyhedral abrasives was randomly distributed.
[0028] A cubic binder matrix is established in the EDEM software, and a particle Factory is added on this basis to define the coincidence of the square matrix plane with the coordinate plane of the center of the abrasive circumscribed sphere.
[0029] The virtual grid parameters corresponding to the D20 grinding wheel are calculated, and the random coordinate parameters of the center of the circumscribed sphere of the abrasive, the random sectioning step n of the abrasive (abrasives of different shapes), and the random rotation angles α, β, and γ corresponding to the abrasive are set in the 8×8×1 virtual grid through the EDEM software.
[0030] In the EDEM software, different random step sizes n of initial position parameters and rotation angles of abrasive particles are set on the cube binder matrix Factory to achieve random posture.
[0031] The plane is determined on the coordinate plane of the center of the sphere circumscribed by the abrasive grains, and then the abrasive grains are bonded to the binder matrix through the Bonding key to form a three-dimensional geometric morphology model of the grinding wheel. BRIEF DESCRIPTION OF THE DRAWINGS
[0032] Figure 1 This is the flow chart of EDEM’s diamond wheel surface topography geometry modeling.
[0033] Figure 2 This is a schematic diagram of diamond grinding wheel EDEM.
[0034] Figure 3 This is a schematic diagram of the D20 single abrasive modeling method.
[0035] Figure 4 This is a schematic diagram of the calculation of the equivalent diameter of a single abrasive grain of D20.
[0036] Figure 5 This is a schematic diagram of the cube mesh division of the D20 grinding wheel.
[0037] Figure 6 It is a schematic diagram of the random distribution of random abrasive grains of the D20 grinding wheel.
[0038] Figure 7 This is the three-dimensional surface morphology modeling diagram of D20 sand. DETAILED DESCRIPTION
[0039] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.
[0040] like Figure 1 Shown is a technical roadmap for three-dimensional modeling of the surface morphology of a diamond grinding wheel based on a discrete element method, which includes the following steps.
[0041] Step 1: Measure the geometric dimensions of the diamond grinding wheel and define the geometric model dimensions of the grinding wheel.
[0042] Grinding wheel model: The diamond cup grinding wheel used in the present invention has a center hole diameter of 20 mm, a grinding wheel outer diameter of 100 mm, and a grinding wheel working diameter of 10 mm. The grinding wheel surface morphology modeling mainly analyzes the surface morphology of the working layer, so the grinding wheel simulation shape is determined to be a ring with an outer diameter of 100 mm and a thickness of 10 mm, such as Figure 2 shown.
[0043] Abrasive grain model: The actual diamond surface morphology was observed using an ultra-depth three-dimensional microscope system. In order to eliminate the influence of random factors, four areas A, B, C, and D were selected on the grinding wheel surface for observation, and the number of abrasive grains distributed in each area was counted. In order to solve the problem of the mixing of the colors of the binder and the diamond abrasive grains in the diamond surface morphology observed by the ultra-depth microscope system, the original image was processed by grayscale, grayscale enhancement, and binarization, and the number of abrasive grains in different observation areas and their corresponding area areas were counted respectively to obtain the abrasive grain area density on the surface of the diamond grinding wheel with a particle size of D20.
[0044] By performing the above image processing on the surface observation image of the above-mentioned D20 grinding wheel, the number of abrasive grains in different observation areas is counted respectively. According to the experimental observation results, the area size of 160×122μm2 is selected on the grinding wheel D20, and the number of abrasive grains in the four areas A, B, C, and D is 17, 15, 17, and 15, and the average value is 16. The area density of the abrasive grains can be calculated by dividing the average number of abrasive grains in the selected area by the area of the area, and the area density of the abrasive grains on the surface of the resin bond diamond grinding wheel with a particle size of D20 is calculated to be 820mm-2.
[0045] Step 3: Calculate the average spacing between abrasive grains based on the grinding wheel surface topography measurement and grinding wheel grain size.
[0046] Assume that the abrasive particles are evenly distributed in the area, where the side length of the small rectangle is a (average spacing between abrasive particles). Then, on the a×a area, the number of abrasive particles is 1, that is, the area density of abrasive particles on the a×a area is 1 / a. 2 According to the abrasive area density measured in the previous experiment, the average spacing a can be calculated. According to the calculation, the average spacing of the abrasive grains on the surface of the resin-bonded diamond grinding wheel with a particle size of D20 is 0.0349 mm.
[0047] Step 4: Define the single abrasive model, mesh the grinding wheel geometry model, and establish a cube virtual grid.
[0048] The surface morphology of the grinding wheel was observed through an ultra-depth of field microscope. The three-dimensional morphology information of the abrasive was obtained after image binarization processing. The shape of the abrasive was simplified and set to a polyhedron. By cutting the regular tetrahedron, polyhedral abrasives with different shapes were obtained, with a total of 5 types.
[0049] The first model is a regular tetrahedron with a side length of S. Then, at the four vertices of the regular tetrahedron, small regular tetrahedrons with a controlled side length of X (X = n × S / 8) are established for segmentation. By changing the segmentation step n (0, 1, 2, 3, 4), abrasive particles with different numbers of faces can be obtained. As the segmentation step n increases, the abrasive particles gradually transform into regular octahedrons, such as Figure 3 shown.
[0050] Before performing random modeling of the polyhedral abrasive grain pose, the actual diameter of the polyhedral abrasive grain needs to be replaced by the diameter of its circumscribed sphere, such as Figure 4 shown.
[0051] The relationship between the side length S and the radius R of the circumscribed sphere of a regular tetrahedral abrasive grain with step length n=0 is: Where: R is the radius of the circumscribed sphere of the abrasive particle; S is the length of one side of the abrasive particle
[0052] For polyhedral abrasive particles with step length n=1, 2, 3, 4, the circumscribed sphere radius of the polyhedral abrasive particles is obtained by subtracting the circumscribed sphere radius R1 of the small regular tetrahedron from the circumscribed sphere radius R of the initial regular tetrahedron, so that the circumscribed sphere radius R can be calculated by the side length S. When n=1, When n=2, When n=3, When n=4,
[0053] The D20 grit grinding wheel selected in this paper has a corresponding abrasive particle size range of 20 to 30 μm, and the average value is 25 μm as the equivalent particle size of the abrasive. The corresponding initial regular tetrahedron side length S = 40.8 μm is calculated by the formula.
[0054] The present invention adopts a virtual grid method to realize the random distribution of the positions of abrasive particles with random postures on a binder matrix.
[0055] The schematic diagram of the random distribution of abrasive particles using the virtual grid method is shown in the figure. Figure 5 As shown, the centers of the circumscribed spheres of the abrasive particles are all located on the grid surface. a is the average spacing between the abrasive particles measured in the above-mentioned grinding wheel surface observation experiment, which is also equal to the side length of the dotted grid. The coordinates of the centers of the abrasive particles are randomly distributed in the solid grid with a side length of L. The spacing between the solid grids is D, which is consistent with the average equivalent particle size (circumscribed sphere diameter) of the abrasive particles, so that the overlap of the abrasive particles can be avoided. It is easy to know that the side length L of the solid grid is equal to the difference between the side length a of the dotted grid and the spacing D of the solid grid. Since the corresponding average spacing a between the abrasive particles and the average equivalent particle size D of D20 are known, the corresponding side length L of the solid grid can be calculated.
[0056] Step 5: Initially position the center plane of the abrasive grain at each vertex of the outer surface of the virtual grid, and the abrasive grain position moves within the virtual grid.
[0057] Assume that the origin O of the coordinate system is located at the geometric center of the abrasive grain on the grinding wheel, and the geometric center of the circumscribed sphere of the abrasive grain is located at the origin of the coordinate system; the direction of the abrasive grain on the grinding wheel is completely random, and the position and posture of each simulated abrasive grain is randomized.
[0058] Each vertex of the abrasive particle is rotated by a random angle along the x-axis, y-axis and z-axis in sequence.
[0059] Taking the tetrahedral abrasive as an example, at the original spherical center coordinate system O-XYZ of the abrasive, it is rotated by angles α, γ, and β in the range of [0,0.5π] around the coordinate axes X, Y, and Z respectively.
[0060] Step 6: Generate polygonal abrasive particles in the EDEM software, establish a rectangular binder matrix, define its plane as the coordinate plane of the center of the sphere circumscribed by the abrasive, bond the abrasive to the binder matrix through the Bonding key, and form a three-dimensional geometric morphology model of the grinding wheel.
[0061] For actual grinding wheels, considering the holding strength of the bond matrix on the abrasive grains, the exposed edge height of the surface abrasive grains will not exceed 1 / 3 of their equivalent particle size. When the exposed edge height of the diamond abrasive grains exceeds 1 / 3 of their particle size, they are prone to break and fall off during high-speed rotation and cutting. Therefore, the maximum exposed edge height of the abrasive grains on the grinding wheel surface is taken. h nax =dg / 3 Where: h max ——The maximum height of the abrasive grains on the grinding wheel surface; d g ——Average diameter of abrasive particles
[0062] NX 12.0 software is used to create the three-dimensional abrasive grains of the grinding wheel polygon, and the user programming formula is as follows: n=0(1,2,3,4) x=S / 8*n a=sin((S / 2*tan(30)) / (S*sin(60))) In the formula: S is the side length of the tetrahedral grinding wheel; n is the step length of the abrasive cutting; x is the side length of the abrasive cutting; a is the draft angle of the abrasive
[0063] By changing the sectioning step n (0, 1, 2, 3, 4) through the NX 12.0 software operation page, abrasive particles with different numbers of faces can be obtained. As the sectioning step n increases, the abrasive particles gradually transform into regular octahedrons.
[0064] In the EDEM software, select Tools to form the polyhedron abrasive model into a New Template in turn, and finally establish the particle bonding model.
[0065] An area of 279.2 × 279.2 μm was taken from the D20 grinding wheel, and a virtual grinding wheel surface with 8 × 8 × 1 polyhedral abrasives was randomly distributed.
[0066] A rectangular binder matrix is established in the EDEM software, and a particle Factory is added on this basis to define the rectangular matrix plane to coincide with the coordinate plane of the center of the abrasive circumscribed sphere.
[0067] The virtual grid parameters corresponding to the D20 grinding wheel are calculated, and the random coordinate parameters of the center of the circumscribed sphere of the abrasive, the random sectioning step n of the abrasive (abrasives of different shapes), and the random rotation angles α, β, and γ corresponding to the abrasive are set in the 8×8×1 virtual grid through the EDEM software.
[0068] In the EDEM software, different random step lengths n of initial position parameters and rotation angles of abrasive particles are set on the rectangular binder matrix Factory to achieve random postures, such as Figure 6 shown.
[0069] The plane is determined on the coordinate plane of the center of the abrasive sphere. Then, the abrasive is bonded to the binder matrix through the Bonding key to form a three-dimensional geometric morphology model of the grinding wheel, such as Figure 7 shown.
Claims
1. The geometric modeling of the diamond grinding wheel surface morphology based on the discrete element method includes the following steps: Step 1: Measure the geometric dimensions of the diamond grinding wheel and define the geometric model dimensions of the grinding wheel; Step 2: Generate a discrete element grinding wheel model in the EDEM software, and use bonding bonds to bond the particles to establish an initial grinding wheel model; Step 3: Calculate the average spacing between the abrasive grains based on the abrasive grain morphology measurement on the grinding wheel surface and the grinding wheel grain size; Step 4: Define the single abrasive grain model of the grinding wheel, divide the grinding wheel geometric model into grids, and establish a cube virtual grid; Step 5: Initially position the center plane of the abrasive grain at each vertex of the outer surface of the virtual grid, and the abrasive grain moves within the virtual grid; Step 6: Generate polygonal abrasive particles in the EDEM software, establish a rectangular binder matrix, define its plane on the coordinate plane of the center of the sphere circumscribed by the abrasive, bond the abrasive and the binder matrix through the Bonding key, and form a three-dimensional geometric morphology model of the grinding wheel; Step 7: According to the actual abrasive edge height, move the abrasive to meet the conditions and determine the three-dimensional geometric morphology model of the grinding wheel.
2. According to the diamond grinding wheel surface morphology geometric modeling based on discrete element method as claimed in claim 1, in step 1, by measuring the geometric dimensions of a real diamond cup grinding wheel, a three-dimensional geometric model with a center hole diameter of 20 mm, a grinding wheel outer diameter of 100 mm, and a grinding wheel working diameter of 10 mm is established.
3. According to the diamond grinding wheel surface morphology geometric modeling based on discrete element method as claimed in claim 1, EDEM software is used in step 2, particle parameters are set in the Bulk Material part of the software, Volume is established in the Geometries part so that discrete particles form a three-dimensional geometric model of the grinding wheel, and the contact condition is selected as Bonding contact model key in Physics to form a grinding wheel matrix, and an initial model of the grinding wheel is established.
4. According to the diamond grinding wheel surface morphology geometric modeling based on discrete element method as claimed in claim 1, the surface morphology of the diamond grinding wheel is observed in step 3, and the diamond abrasive grains with a grinding wheel concentration of 100% and a grain size of D20 correspond to a diamond abrasive grain size range of 20um-30um.
5. According to the geometric modeling of the surface morphology of the diamond grinding wheel based on the discrete element method as claimed in claim 1, in step three, the actual diamond surface morphology is observed by a super depth of field microscope system. In order to eliminate the influence of random factors, four areas A, B, C, and D are selected on the grinding wheel surface for observation. The number of abrasive grains in different observation areas and their corresponding area areas are counted respectively to obtain the abrasive grain area density on the surface of the diamond grinding wheel with a particle size of D20.
6. According to the geometric modeling of the surface morphology of diamond grinding wheel based on discrete element method as claimed in claim 1, in step 3, the average spacing a of the abrasive grains is calculated according to the abrasive grain area density and the grain size of the grinding wheel; if it is assumed that the abrasive grains are equidistantly distributed in the region, where the side length of the small rectangle is a (average spacing of the abrasive grains), then on the a×a area, the number of abrasive grains is 1, that is, the abrasive grain area density on the a×a area is 1 / a 2 Based on the abrasive area density measured in the above experiment, the average spacing a can be calculated.
7. According to the geometric modeling of the surface morphology of a diamond grinding wheel based on the discrete element method as described in claim 1, in step 4, the surface morphology of the grinding wheel is observed through an ultra-depth of field microscope, and the three-dimensional morphology information of the abrasive is obtained after image binarization processing. The shape of the abrasive is simplified and set to a polyhedron. By cutting a regular tetrahedron, polyhedral abrasives with different shapes are obtained. There are 5 types in total, among which the first model is a regular tetrahedron with a side length of S; then, at the four vertices of the regular tetrahedron, small regular tetrahedrons with a controlled side length of X (X=n×S / 8) are established for cutting; by changing the cutting step length n (0, 1, 2, 3, 4), abrasives with different numbers of faces can be obtained, and as the cutting step length n increases, the abrasive particles gradually transform into regular octahedrons.
8. According to the geometric modeling of diamond grinding wheel surface morphology based on discrete element method in claim 1, in step 4, the actual diameter of the polyhedral abrasive grain is replaced by the diameter of its circumscribed sphere. For a regular tetrahedral abrasive grain with a step length n=0, the relationship between its side length S and the radius R of the circumscribed sphere is: For polyhedral abrasives with step lengths n=1, 2, and 3, the circumscribed sphere radius of the polyhedral abrasive is obtained by subtracting the circumscribed sphere radius R1 of the small regular tetrahedron from the circumscribed sphere radius R of the initial regular tetrahedron, so that the circumscribed sphere radius R can be calculated by the side length S.
9. According to the geometric modeling of the surface morphology of a diamond grinding wheel based on the discrete element method as described in claim 1, in step 4, the cup-type grinding wheel geometric model is virtually meshed, and the grinding wheel ring is divided into a plurality of cubes. Under initial conditions, the abrasive particles are arranged in space in a uniform position, and the spacing A between two abrasive particles at the concentration is calculated based on the average diameter of the abrasive particles. The calculated average spacing A between the abrasive particles is used as the side length, and the average particle size D of the abrasive particles is used as the real grid spacing, thereby dividing it into a plurality of cells.
10. According to the geometric modeling of the surface morphology of a diamond grinding wheel based on the discrete element method in claim 1, in step 5, the center of the circumscribed sphere of the abrasive grain is located on the grid surface, and the random arrangement of the abrasive grains is achieved by adjusting the coordinates of the center of the circumscribed sphere of the abrasive grain. In this process, in order to avoid the overlap of the abrasive grains during the random arrangement process, each abrasive grain is confined to a grid area of a certain size, and the coordinates of the center of the circumscribed sphere are randomly changed within the area.
11. According to the geometric modeling of the surface morphology of a diamond grinding wheel based on the discrete element method as described in claim 1, in step six, an area of 279.2×279.2 μm is taken on the abrasive grain size D20 grinding wheel, and a polyhedral abrasive virtual grinding wheel surface of 8×8×1 is randomly distributed; the virtual grid parameters corresponding to the D20 grinding wheel are calculated, and the random coordinate parameters of the center of the circumscribed sphere of the abrasive, the random sectioning step n of the abrasive (abrasive grains of different shapes) and the random rotation angles α, β, γ corresponding to the abrasive grains, and the random parameters of the abrasive grains are set in the 8×8×1 square matrix through the EDEM software.
12. According to the geometric modeling of the surface morphology of a diamond grinding wheel based on the discrete element method as described in claim 1, in step six, a cubic binder matrix is established, and its plane is defined as the coordinate plane of the center of the sphere circumscribed by the abrasive, and the abrasive is bonded to the binder matrix through the Bonding key, thereby forming a three-dimensional abrasive model.
13. According to the geometric modeling of the surface morphology of the diamond grinding wheel based on the discrete element method as described in claim 1, in step seven, the surface morphology of the grinding wheel is observed to obtain the cutting edge height of the abrasive grains, and then the position of the tetrahedral abrasive grains is translated to be consistent with the actual cutting edge height of the abrasive grains, and finally a three-dimensional geometric morphology model of the diamond cup-shaped stone grinding wheel is generated.