CN114564827A - Characterization and modeling method for three-dimensional topography of surface of diamond parallel grinding wheel - Google Patents
Characterization and modeling method for three-dimensional topography of surface of diamond parallel grinding wheel Download PDFInfo
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Abstract
The invention discloses a method for representing and modeling three-dimensional topography of a diamond parallel grinding wheel surface, which comprises the following steps of representing abrasive particle density and edge height, and then carrying out randomized modeling on the orientation, the edge height, the axial position and the circumferential position of abrasive particles in sequence according to measurement results, wherein the method comprises the following steps: characterizing the density of the abrasive particles by a complex shape method and a Laser Scanning Confocal Microscope (LSCM); representing the abrasive particle edge-projecting height by adopting a complex method and a laser scanning confocal microscope to obtain statistical distribution of the abrasive particle edge-projecting height; performing randomized modeling of the orientation of the abrasive particles; performing randomized modeling on the abrasive particle edge height and the axial position according to the statistical distribution of the abrasive particle edge height; performing randomized modeling of the circumferential position of the abrasive particles; and judging the interference between the to-be-added abrasive particles and the existing abrasive particles on the surface of the grinding wheel, and adding the abrasive particles one by one until the measured abrasive particle density is reached. The method breaks through the limitation of a characterization instrument on the size of the grinding wheel, and realizes high-precision modeling of the surface appearance of the grinding wheel.
Description
Technical Field
The invention belongs to the technical field of diamond parallel grinding wheels, and particularly relates to a characterization and modeling method for three-dimensional topography of the surface of a diamond parallel grinding wheel.
Background
The ultra-precise hard and brittle material optical element is a key component of a laser nuclear fusion device, a high-resolution earth observation system, a large-scale astronomical telescope, a microelectronic technology, consumer electronics and the like, and subsurface damage is one of key factors for limiting the service performance of the optical element. The hard and brittle material optical element generally needs to be processed by adopting a diamond grinding wheel grinding method, and the shape and the cutting height of diamond abrasive particles on the surface of the grinding wheel, namely the height value of the abrasive particle protruding out of a binding agent, and the abrasive particle density (namely the number of the abrasive particles in unit surface area) have important influence on the generation of subsurface damage during grinding. Therefore, the representation and modeling of the three-dimensional appearance of the surface of the diamond grinding wheel are significant for realizing the simulation of the grinding process, further optimizing the grinding process and designing and preparing the grinding wheel.
In the prior art, the microscopic morphology of the grinding wheel is generally measured by methods such as contact measurement, laser triangulation, Scanning Electron Microscopy (SEM), optical microscopy and replica method. The accuracy of contact measurement is limited by the size of the probe and the deformation caused by the contact force. The laser triangulation method has high measurement speed, can be used for in-situ detection of the three-dimensional shape of the grinding wheel, but has limited horizontal resolution. The SEM and the optical microscope are two-dimensional measuring methods, and can directly measure the grinding wheel, so that the measuring result is reliable, but the size of the measured grinding wheel is limited by a measuring instrument. The magnification of the SEM can be adjusted from several times to several tens of thousands of times, and the SEM has large depth of field, so that the SEM is suitable for measuring the shape, the microscopic wear appearance, the stacking density and the like of the abrasive particles. The optical microscope is more suitable for measuring the number of dynamic abrasive particles of the diamond grinding wheel and the wear platform area of the abrasive particles due to smaller depth of field. The copying method is not limited by the specification of a measuring instrument, and the shape of the grinding wheel can be copied by stamping a lead belt or a polymer. However, when the abrasive grain density and the cutting height of the surface of the grinding wheel are measured by the imprinting method, a high-precision evaluation procedure is yet to be developed.
In the prior art, when geometric modeling is performed on the surface topography of a diamond grinding wheel, in order to simulate random distribution of the spatial positions of abrasive grains, the abrasive grains are regularly arranged according to a body-centered cube or a simple cube, and then the positions of the abrasive grains are randomly moved on the premise of ensuring that the abrasive grains do not interfere with each other. In recent years, researchers have also randomized abrasive grain positions by ball packing to achieve higher efficiency and degree of randomization. For single abrasive diamond wheels, the radial position of the abrasive grain is typically simulated using the concept of the height of the edge of the abrasive grain, and prior studies have assumed that the height of the edge is a constant value, such as a certain percentage of the grain size, or follows a normal distribution. The latter assumption is closer to the experimental results, but it is often assumed that the mean and standard deviation of the normal distribution are proportional to the size of the abrasive particles, with deviations from the actual situation.
Disclosure of Invention
The invention aims to provide a method for representing and modeling the three-dimensional topography of the surface of a diamond parallel grinding wheel, so as to break through the limitation of a representation instrument on the size of the grinding wheel and realize high-precision modeling of the surface topography of the grinding wheel.
In order to achieve the purpose, the invention adopts the following technical scheme:
a three-dimensional appearance characterization and modeling method for the surface of a diamond parallel grinding wheel comprises the steps of firstly characterizing the density of abrasive particles and the edge height, and then sequentially performing randomized modeling on the orientation, the edge height, the axial position and the circumferential position of the abrasive particles according to measurement results, wherein the method comprises the following steps:
the method comprises the following steps: characterizing the density of the abrasive particles by a complex shape method and a Laser Scanning Confocal Microscope (LSCM);
step two: representing the abrasive particle edge-projecting height by adopting a complex method and a laser scanning confocal microscope to obtain statistical distribution of the abrasive particle edge-projecting height;
step three: performing randomized modeling of the orientation of the abrasive particles;
step four: according to the statistical distribution of the abrasive grain exposure heights, performing randomized modeling on the abrasive grain exposure heights and the axial positions;
step five: performing randomized modeling of the circumferential position of the abrasive particles;
step six: and judging the interference between the abrasive particles to be added and the existing abrasive particles on the surface of the grinding wheel, and adding the abrasive particles one by one until the measured abrasive particle density is reached.
The further improvement of the invention is that in the first step, silica gel is adopted to imprint and copy the appearance of the grinding wheel, and then a laser scanning confocal microscope is used to observe the polymer complex to obtain the density of the abrasive particles; firstly, carrying out filtering processing on three-dimensional data measured by a laser scanning confocal microscope to remove burrs in an image; then, performing statistical analysis on the data to set upper and lower thresholds of height, adopting a gray color map, and setting upper and lower limits of the color map as the upper and lower thresholds so as to enhance the contrast between abrasive particles and a binding agent in an image and improve the accuracy of abrasive particle counting; and finally, measuring three areas uniformly distributed on the circumference of the grinding wheel, wherein each area is respectively used for measuring a plurality of sub-areas, and obtaining the average value and the standard deviation of the abrasive particle density.
The invention has the further improvement that in the second step, the laser scanning confocal microscope is adopted to measure the grinding wheel complex to obtain the edge height of the abrasive particles;the specific steps of extracting the abrasive grain edge height according to LSCM measurement data are as follows: (1) filtering the measured image by adopting a median filter with a set template size, and removing salt and pepper noise on the image to obtain a measured image; (2) manually selecting the vertex of a polygon in Matlab to obtain a bonding agent area of the grinding wheel; (3) subtracting the fitting plane of the binding agent area from the filtered image, thereby performing tilt correction on the measured image, and adjusting the average height value of the binding agent area to be 0 to obtain a corrected image; (4) selecting a point with the minimum z value in the abrasive particle area on the image, wherein the z value of the point corresponds to the edge height value of the abrasive particles; measuring multiple regions of the surface of the grinding wheel, drawing a statistical histogram of the abrasive particle edge height, assuming the statistical histogram to obey a distribution function according to the shape of the statistical histogram, and then adopting chi2Fitting tests performed hypothesis testing on the distribution function.
A further improvement of the invention is that the template size of the median filter is 5 x 5 pixels.
The further improvement of the invention is that in the third step, when the randomized modeling of the abrasive particle orientation is carried out, the origin O of the coordinate system is positioned at the geometric center of the grinding wheel, and the y axis is aligned with the axis of the grinding wheel; at the beginning, the geometric center of the abrasive grain is positioned at the origin of coordinates; randomizing the orientation, the cutting height, the axial position and the circumferential position of the abrasive particles in sequence to move the abrasive particles to the surface of the grinding wheel to obtain a geometric model of the grinding wheel; the direction of the abrasive particles on the grinding wheel is completely random, so that the orientation of each simulated abrasive particle is randomized; each vertex of the abrasive grain is rotated by a random angle value along the x-axis, the y-axis and the z-axis in sequence:
in the formula:
and
-the abrasive grain vertex coordinate vectors before and after orientation randomization, i.e. abrasive grain center to vertex vectors, respectively; rx、RyAnd Rz-a rotation matrix along the x-axis, y-axis and z-axis, respectively; the matrix form of the above formula is:
in the formula: α, β and γ, which are the angles of rotation along the x, y and z axes, respectively, obey a uniform distribution between 0 and 2 π, i.e.:
α,β,γ～U(0,2π) (3)。
the further improvement of the invention is that in the fourth step, when the randomized modeling of the abrasive grain exposure height and the axial position is carried out according to the statistical distribution of the abrasive grain exposure height, in order to establish a grinding wheel model, the geometric center of the abrasive grain is converted to the surface of the grinding wheel from the origin of coordinates, namely the geometric center of the grinding wheel; the distribution of the abrasive particles on the surface of the grinding wheel is completed by two steps: (1) randomizing the abrasive particle edge-projecting height and the axial position, and realizing the randomizing by translating each vertex coordinate of the abrasive particles; (2) randomizing the circumferential position of the abrasive particles, wherein the randomizing is realized by the rotation transformation of each vertex coordinate of the abrasive particles around the y axis; to achieve randomization of abrasive grain stand-off height and axial position, the following translation transformation is used:
in the formula:
-coordinate vectors of the translated abrasive grain vertices; t-translation matrix; the matrix form of this formula is:
in the formula: t is tx、tyAnd tzRespectively areTranslation along the x-axis, y-axis, and z-axis, wherein:
in the formula: r-nominal radius of grinding wheel; delta R is the height of the abrasive particle center protruding out of the bonding agent, and is the shape error of the abrasive particle base body, the shape, the size and the radial size variation of the edge-projecting height of the abrasive particle; Δ x and Δ z — coordinate variation amount of mounting eccentricity, misalignment error, and vibration with the grinding wheel; when the grinding wheel only has installation eccentricity with the eccentricity being e, the delta x is equal to e, and the delta z is equal to 0;
the height of the abrasive grain center protruding out of the bond refers to the distance from the abrasive grain center to the bond surface, namely:
ΔR＝hp-hc (7)
in the formula: h ispThe edge height of the abrasive particles, namely the distance between the highest point of the abrasive particles and the surface of the bonding agent, is randomly generated according to the edge height distribution parameters; h iscThe distance between the highest point of the abrasive particles and the center of the abrasive particles in the radial direction of the grinding wheel is obtained by calculating the coordinates of each top point of the abrasive particles;
since the positions of the abrasive grains in the axial direction are completely random, the width of the grinding wheel is assumed to be WgThen the coordinates of the center of the abrasive particle in the y direction obey the following uniform distribution:
in a further improvement of the present invention, in the fifth step, when performing the randomization modeling of the circumferential position of the abrasive grains, the randomization of the circumferential position of the abrasive grains is performed by rotating the abrasive grains around the y-axis:
in the formula:
-the coordinate vector of the vertex after randomization of the circumferential position of the abrasive particles; ry，1-a rotation matrix around the y-axis, the matrix form of equation (9) being:
in the formula: beta is a1-the phase of the grinding grain in the xz plane with respect to the grinding wheel axis; obviously, beta1Obey a uniform distribution between 0 and 2 pi, namely:
β1～U(0,2π) (11)。
the further improvement of the invention is that in the sixth step, the specific implementation method is as follows: the problem of interference between two abrasive particles is simplified into the problem of interference between the minimum external ball, wherein the sufficient conditions for interference between the abrasive particles 1 and 2 are as follows:
d1,2＜R1+R2 (12)
in the formula: r1And R2-the minimum circumscribed spherical radius of each of the two abrasive grains; d1,2-the distance between the centers of the two abrasive grains, expressed as:
according to the following constant inequality, sufficient conditions and necessary conditions for abrasive particle interference are obtained, so that the judgment efficiency of abrasive particle interference is improved:
let | Δ x | + | Δ y | + | Δ z | ═ d ', if d' < R1+R2Then the two abrasive grains interfere with each other; if it is
The two abrasive grains do not interfere; if neither of these conditions is trueIf yes, d is calculated1,2Then, whether interference occurs is judged according to the formula (14);
let the characteristic that the grinding wheel abrasive grain density is C0Then the number N of the abrasive grains is C0Product of surface area of grinding wheel:
N＝C0·2πRWg (15)
if the interference exists between a certain abrasive particle and other abrasive particles, the random position of the abrasive particle is determined again until the abrasive particle does not interfere with all abrasive particles generated previously; repeating the process until the quantity of the abrasive particles reaches a given value N, wherein the abrasive particle density at the moment reaches the abrasive particle density obtained by characterization; and finally, drawing a geometric model of the abrasive particles according to each vertex of the abrasive particles, and superposing the geometric models of all the abrasive particles on the surface of a binding agent to obtain a three-dimensional geometric model of the surface appearance of the grinding wheel.
Compared with the prior art, the invention has at least the following beneficial technical effects:
(A) the invention provides a method for measuring the abrasive particle density and the exposure height of the surface of a diamond grinding wheel based on a complex shape method and a laser confocal microscope, and the size of the measured grinding wheel is not influenced by the measuring range of an instrument;
(B) when the surface appearance of the diamond grinding wheel is represented, high-precision measurement of the surface abrasive particle density and the edge height can be realized only by adopting a material of silica gel and an instrument of a laser confocal microscope, and the method has the advantages of convenience in operation and low cost;
(C) in the three-dimensional modeling method for the surface topography of the grinding wheel, the exposure height of the abrasive particles obeys the statistical distribution obtained by actual measurement, and the transverse distribution of the abrasive particles is completely randomized, so that the method has the advantage of high modeling precision.
Drawings
FIG. 1 is a flow chart of characterization and modeling of three-dimensional topography of a diamond parallel grinding wheel surface.
Fig. 2 is a diagram of the D301 abrasive grain protrusion height extraction process according to the present invention, in which the measurement range is 640 μm, where fig. 2(a) is a filtered measurement image, fig. 2(b) is a manual binder selection area, fig. 2(c) is a selected binder area, and fig. 2(D) is a calibration of the measurement image with the binder area as a reference.
Fig. 3 shows a statistical histogram of the abrasive grain sharpening height D301 and a normal curve obtained by fitting.
FIG. 4 is a schematic coordinate system of a grinding wheel model.
FIG. 5 is a graph showing the simulation and actual measurement results of the surface topography of the D301 grinding wheel with the measurement range of 2560 μm × 2560 μm, wherein FIG. 5(a) is the simulation result and FIG. 5(b) is the actual measurement result.
Detailed Description
The following embodiments of the present invention are provided, and it should be noted that the present invention is not limited to the following embodiments, and all equivalent changes based on the technical solutions of the present invention are within the protection scope of the present invention.
According to the technical scheme, the method for characterizing and modeling the appearance of the diamond abrasive particles is provided in the embodiment, as shown in fig. 1, the characterization of the density and the edge height of the abrasive particles is firstly carried out, and then the randomized modeling is carried out on the orientation, the edge height, the axial position and the circumferential position of the abrasive particles in sequence according to the measurement results. The method specifically comprises the following steps:
the method comprises the following steps: abrasive particle density was characterized using a replica method and Laser Scanning Confocal Microscopy (LSCM).
This example will be described by taking an electroplated diamond parallel grinding wheel with abrasive grain size of D301 as an example. The appearance of the grinding wheel is imprinted and copied by silica gel, and then the polymer replica is observed by a laser scanning confocal microscope. The D301 grinding wheel was measured with a 5X objective over a measurement range of 2560 μm. Firstly, filtering three-dimensional data measured by a laser scanning confocal microscope to remove burrs in an image. Then, the data is subjected to statistical analysis to set upper and lower threshold values of the height, a gray color map is adopted, and upper and lower limits of the color map are set as the upper and lower threshold values, so that the contrast between abrasive particles (with smaller height and darker gray) and a binder (with higher height and lighter gray) in the image is enhanced, and the accuracy of abrasive particle counting is improved. Three areas evenly distributed on the circumference of the D301 grinding wheel were measured, 5 sub-areas were measured for each area, and the measured abrasive grain density was 9.37±0.60/mm2。
Step two: and (3) representing the abrasive particle edge-projecting height by adopting a complex method and a laser scanning confocal microscope to obtain the statistical distribution of the abrasive particle edge-projecting height.
The complex is measured by a laser scanning confocal microscope to obtain the edge height of the abrasive particles. The magnification of the microscope needs to be carefully chosen to ensure measurement accuracy. If the objective lens magnification is too large, large measurement deviations will occur in the area of the complex that is in contact with the side of the abrasive particle, since the side of the abrasive particle is steeper. For the above reasons, the abrasive grain exposure height of the D301 grinding wheel was measured using a 20 × objective lens.
As shown in fig. 2, the step of extracting the height of the edge of the abrasive grain according to the LSCM measurement data is: (1) filtering the measurement image by using a median filter with a template size of 5 × 5 pixels, and removing salt and pepper noise on the image to obtain a measurement image as shown in fig. 2 (a); (2) obtaining the bonding agent area of the grinding wheel by manually selecting the vertex of the polygon in Matlab, as shown in FIG. 2(b) and FIG. 2 (c); (3) subtracting the fitting plane of the binder region from the filtered image to perform tilt correction on the measured image, and adjusting the average height value of the binder region to 0, resulting in a corrected image as shown in fig. 2 (d); (4) and selecting the point with the minimum z value in the abrasive particle area on the image, wherein the z value of the point corresponds to the edge height value of the abrasive particles.
The statistical histogram of the abrasive grain sharpening height shown in fig. 3 fits well with the fitted normal distribution curve, so it can be assumed that it follows a normal distribution, and then χ is used2The fitting test method performed a hypothesis test on the distribution of the abrasive grain protrusion height of the D301 grinding wheel. The mean and variance of the distribution were 124.03 μm and 32.10 μm, respectively.
Step three: randomized modeling of abrasive grain orientation was performed.
Fig. 4 is a coordinate system of the grinding wheel model, and the origin O of the coordinate system is located at the geometric center of the grinding wheel, and the y-axis is aligned with the grinding wheel axis. Initially, the geometric center of the abrasive particle is at the origin of coordinates. The orientation, the cutting height, the axial position and the circumferential position of the abrasive particles are randomized in sequence, so that the abrasive particles can be moved to the surface of the grinding wheel, and a geometric model of the grinding wheel is obtained. This step performs a randomized modeling of the orientation of the abrasive grain.
The direction of the abrasive grain on the wheel is completely random, so it is necessary to randomize the orientation of each simulated abrasive grain. Each vertex of the abrasive grain is rotated by a random angle value along the x-axis, the y-axis and the z-axis in sequence:
in the formula:
and
-the abrasive grain vertex coordinate vectors before and after orientation randomization (i.e. abrasive grain center-to-vertex vectors), respectively; rx、RyAnd Rz-rotation matrices along the x-axis, y-axis and z-axis, respectively. The matrix form of this formula is:
in the formula: α, β and γ, which are the angles of rotation along the x, y and z axes, respectively, obey a uniform distribution between 0 and 2 π, i.e.:
α,β,γ～U(0,2π)
step four: and performing randomized modeling on the abrasive grain edge height and the axial position according to the statistical distribution of the abrasive grain edge height.
In order to establish a grinding wheel model, the geometric center of the abrasive grain needs to be transformed from the origin of coordinates (i.e., the geometric center of the grinding wheel) to the surface of the grinding wheel. The transformation is related to factors such as the shape, size, shape error and mounting error of the grinding wheel. The distribution of the abrasive particles on the surface of the grinding wheel is completed by two steps: (1) randomizing the abrasive particle edge-projecting height and the axial position, and realizing the randomizing by translating each vertex coordinate of the abrasive particles; (2) the randomization of the circumferential position of the abrasive particles is realized by the rotation transformation of the vertex coordinates of the abrasive particles around the y-axis. This step carries out the randomization modeling of the abrasive grain sharpening height and axial position.
Randomization of abrasive grain stand-off height and axial position was achieved by the following translation transformation:
in the formula:
-coordinate vectors of the vertices of the translated abrasive grains; t-translation matrix. The matrix form of this formula is:
in the formula: t is tx、tyAnd tz-translation along the x-axis, y-axis and z-axis, respectively, wherein:
in the formula: r-nominal radius of grinding wheel; delta R is the height of the abrasive particle center protruding out of the bonding agent, and is the radial size variation quantity related to the shape error of the grinding wheel base body, the shape, the size and the edge height of the abrasive particle and other factors; Δ x and Δ z — the amount of coordinate variation related to factors such as mounting eccentricity, misalignment, and vibration of the grinding wheel.
The height of the abrasive grain center protruding out of the bond refers to the distance from the abrasive grain center to the bond surface, namely:
ΔR＝hp-hc
in the formula: h ispThe cutting height of the abrasive particles, namely the distance between the highest point of the abrasive particles and the surface of the bonding agent, is randomly generated according to the normal distribution parameter measured in the step two; h iscIn the radial direction of the grinding wheel between the highest point of the abrasive grain and the centre of the abrasive grainThe distance can be calculated from the coordinates of each vertex of the abrasive particle.
Since the positions of the abrasive grains in the axial direction are completely random, the width of the grinding wheel is assumed to be WgThen the coordinates of the center of the abrasive particle in the y direction obey the following uniform distribution:
step five: randomized modeling of the circumferential position of the abrasive particles was performed.
Randomization of the circumferential position of the abrasive particles can be achieved by rotating the abrasive particles about the y-axis:
in the formula:
-the coordinate vector of the vertex after randomization of the circumferential position of the abrasive particles; ry，1-a rotation matrix around the y-axis. The matrix form of the above formula is:
in the formula: beta is a1-the phase of the grinding grain in the xz plane with respect to the grinding wheel axis. Obviously, beta1Obey a uniform distribution between 0 and 2 pi, i.e.:
β1～U(0,2π)
step six: and judging the interference between the abrasive particles to be added and the existing abrasive particles on the surface of the grinding wheel, and adding the abrasive particles one by one until the measured abrasive particle density is reached.
The problem of interference between two abrasive particles is simplified into the problem of interference between the minimum external ball. The sufficient conditions for interference between the abrasive grains 1 and 2 are:
d1,2＜R1+R2
in the formula: r1And R2-the minimum circumscribed spherical radius of each of the two abrasive grains; d1,2-the distance between the centers of the two abrasive grains, expressed as:
according to the following constant inequality, sufficient conditions and necessary conditions for abrasive particle interference can be obtained, thereby improving the judgment efficiency of abrasive particle interference:
let | Δ x | + | Δ y | + | Δ z | ═ d ', if d' < R1+R2Then the two abrasive grains interfere with each other; if it is
The two abrasive particles do not interfere. If both conditions are not satisfied, d is calculated1,2Then, whether the interference exists is judged according to the formula.
The measured abrasive grain density of the grinding wheel is C0Then the number N of the abrasive grains is C0Product of surface area of grinding wheel:
N＝C0·2πRWg
if there is interference between a particular abrasive particle and other abrasive particles, its random position is re-determined until the abrasive particle does not interfere with all previously generated abrasive particles. The above process is repeated until the number of abrasive grains reaches a given value N, at which point the abrasive grain density reaches the measured abrasive grain density. And finally, drawing a geometric model of the abrasive particles according to each vertex of the abrasive particles, and superposing the geometric models of all the abrasive particles on the surface of a bonding agent to obtain a three-dimensional geometric model of the surface appearance of the grinding wheel, as shown in fig. 5. The result shows that the positions, the directions and the edge-projecting heights of the abrasive particles on the surface of the simulated grinding wheel are random, and the abrasive particle density and the abrasive particle size between the simulated grinding wheel and the actually measured grinding wheel are consistent.
Although the invention has been described in detail hereinabove with respect to a general description and specific embodiments thereof, it will be apparent to those skilled in the art that modifications or improvements may be made thereto based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.
Claims (8)
1. A three-dimensional appearance characterization and modeling method for a diamond parallel grinding wheel surface is characterized by comprising the following steps of firstly characterizing the density of abrasive particles and the edge height, and then sequentially performing randomized modeling on the orientation, the edge height, the axial position and the circumferential position of the abrasive particles according to measurement results:
the method comprises the following steps: characterizing the density of the abrasive particles by a complex shape method and a Laser Scanning Confocal Microscope (LSCM);
step two: representing the abrasive grain edge height by adopting a complex shape method and a laser scanning confocal microscope to obtain statistical distribution of the abrasive grain edge height;
step three: performing randomized modeling of the orientation of the abrasive particles;
step four: performing randomized modeling on the abrasive particle edge height and the axial position according to the statistical distribution of the abrasive particle edge height;
step five: carrying out randomized modeling on the circumferential position of the abrasive particles;
step six: and judging the interference between the abrasive particles to be added and the existing abrasive particles on the surface of the grinding wheel, and adding the abrasive particles one by one until the measured abrasive particle density is reached.
2. The characterization and modeling method for the three-dimensional topography of the surface of the diamond parallel grinding wheel according to claim 1, wherein in the first step, the topography of the grinding wheel is imprinted and copied by silica gel, and then a polymer complex is observed by a laser scanning confocal microscope to obtain the density of abrasive particles; firstly, carrying out filtering processing on three-dimensional data measured by a laser scanning confocal microscope to remove burrs in an image; then, performing statistical analysis on the data to set upper and lower thresholds of height, adopting a gray color map, and setting upper and lower limits of the color map as the upper and lower thresholds so as to enhance the contrast between abrasive particles and a binding agent in an image and improve the accuracy of abrasive particle counting; and finally, measuring three areas uniformly distributed on the circumference of the grinding wheel, wherein each area is respectively used for measuring a plurality of sub-areas, and obtaining the average value and the standard deviation of the abrasive particle density.
3. The characterization and modeling method for the three-dimensional topography of the surface of the diamond parallel grinding wheel according to claim 1, wherein in the second step, a laser scanning confocal microscope is adopted to measure the grinding wheel complex to obtain the cutting height of the abrasive particles; the specific steps of extracting the abrasive grain exposure height according to LSCM measurement data are as follows: (1) filtering the measured image by adopting a median filter with a set template size, and removing salt and pepper noise on the image to obtain a measured image; (2) manually selecting the vertex of a polygon in Matlab to obtain a bonding agent area of the grinding wheel; (3) subtracting the fitting plane of the binding agent area from the filtered image, thereby performing tilt correction on the measured image, and adjusting the average height value of the binding agent area to be 0 to obtain a corrected image; (4) selecting a point with the minimum z value in the abrasive particle area on the image, wherein the z value of the point corresponds to the edge height value of the abrasive particles; measuring multiple regions on the surface of the grinding wheel, drawing a statistical histogram of the abrasive grain exposure height, assuming the statistical histogram obeys a certain distribution function according to the shape of the statistical histogram, and then adopting chi2Fitting tests performed hypothesis testing on the distribution function.
4. The characterization and modeling method for three-dimensional topography of the surface of a diamond parallel grinding wheel according to claim 1, wherein the template size of the median filter is 5 x 5 pixels.
5. The characterization and modeling method for the three-dimensional topography of the surface of the diamond parallel grinding wheel according to claim 1, wherein in the third step, when the randomized modeling of the orientation of the abrasive particles is performed, the origin O of the coordinate system is located at the geometric center of the grinding wheel, and the y-axis is aligned with the axis of the grinding wheel; at the beginning, the geometric center of the abrasive particles is positioned at the origin of coordinates; randomizing the orientation, the cutting height, the axial position and the circumferential position of the abrasive particles in sequence to move the abrasive particles to the surface of the grinding wheel to obtain a geometric model of the grinding wheel; the direction of the abrasive particles on the grinding wheel is completely random, so that the orientation of each simulated abrasive particle is randomized; each vertex of the abrasive grain is rotated by a random angle value along the x-axis, the y-axis and the z-axis in sequence:
in the formula:
and
-the abrasive grain vertex coordinate vectors before and after orientation randomization, i.e. abrasive grain center to vertex vectors, respectively; rx、RyAnd Rz-a rotation matrix along the x-axis, y-axis and z-axis, respectively; the matrix form of the above formula is:
in the formula: α, β and γ, which are the angles of rotation along the x, y and z axes, respectively, obey a uniform distribution between 0 and 2 π, i.e.:
α,β,γ～U(0,2π) (3)。
6. the characterization and modeling method for the three-dimensional topography of the surface of the diamond parallel grinding wheel according to claim 1, wherein in the fourth step, when the randomized modeling of the cutting height and the axial position of the abrasive particles is performed according to the statistical distribution of the cutting height of the abrasive particles, in order to establish a grinding wheel model, the geometric center of the abrasive particles is transformed from the origin of coordinates, namely the geometric center of the grinding wheel, to the surface of the grinding wheel; the distribution of the abrasive particles on the surface of the grinding wheel is completed by two steps: (1) randomization of the height and axial position of the abrasive particle exposure is realized by translation of each vertex coordinate of the abrasive particle; (2) randomizing the circumferential position of the abrasive particles, wherein the randomizing is realized by the rotation transformation of each vertex coordinate of the abrasive particles around the y axis; to achieve randomization of abrasive grain exposure height and axial position, the following translation transformation is implemented:
in the formula:
-coordinate vectors of the translated abrasive grain vertices; t-translation matrix; the matrix form of this formula is:
in the formula: t is tx、tyAnd tz-translation along the x-axis, y-axis and z-axis, respectively, wherein:
in the formula: r is the nominal radius of the grinding wheel; delta R is the height of the abrasive particle center protruding out of the bonding agent, and is the shape error of the abrasive particle base body, the shape, the size and the radial size variation of the edge-projecting height of the abrasive particle; Δ x and Δ z — coordinate variation amount of mounting eccentricity, misalignment error and vibration with the grinding wheel; when the grinding wheel only has installation eccentricity with the eccentricity e, the delta x is equal to e, and the delta z is equal to 0;
the height of the abrasive particle center protruding out of the binder refers to the distance from the abrasive particle center to the binder surface, namely:
ΔR＝hp-hc (7)
in the formula: h ispBy sharpening abrasive particlesThe height, namely the distance between the highest point of the abrasive particles and the surface of the bonding agent, is randomly generated according to the distribution parameters of the height of the cutting edge; h iscThe distance between the highest point of the abrasive particles and the center of the abrasive particles in the radial direction of the grinding wheel is obtained by calculating the coordinates of each top point of the abrasive particles;
since the positions of the abrasive grains in the axial direction are completely random, the width of the grinding wheel is assumed to be WgThen the coordinates of the center of the abrasive particle in the y direction obey the following uniform distribution:
7. the characterization and modeling method for the three-dimensional topography of the surface of the diamond parallel grinding wheel according to claim 1, wherein in the fifth step, when performing the randomized modeling of the circumferential position of the abrasive particles, the randomization of the circumferential position of the abrasive particles is realized by rotating the abrasive particles around the y-axis:
in the formula:
-the coordinate vector of the vertex after randomization of the circumferential position of the abrasive particles; r isy，1-a rotation matrix around the y-axis, the matrix form of equation (9) being:
in the formula: beta is a1-the phase of the grinding grain in the xz plane with respect to the grinding wheel axis; obviously, beta1Obey a uniform distribution between 0 and 2 pi, i.e.:
β1～U(0,2π) (11)。
8. the characterization and modeling method for the three-dimensional topography of the surface of the diamond parallel grinding wheel according to claim 1, wherein in the sixth step, the specific implementation method is as follows: the problem of interference between two abrasive particles is simplified into the problem of interference between the minimum external sphere, wherein the sufficient conditions of interference between the abrasive particles 1 and 2 are as follows:
d1,2＜R1+R2 (12)
in the formula: r1And R2-the minimum circumscribed spherical radius of each of the two abrasive grains; d1,2-the distance between the centers of the two abrasive grains, expressed as:
according to the following constant inequality, sufficient conditions and necessary conditions for abrasive particle interference are obtained, so that the judgment efficiency of abrasive particle interference is improved:
let | Δ x | + | Δ y | + | Δ z | ═ d ', if d' < R1+R2Then the two abrasive grains interfere with each other; if it is
The two abrasive grains do not interfere; if both conditions are not satisfied, d is calculated1,2Then, whether interference occurs is judged according to the formula (14);
let the characteristic that the grinding wheel abrasive grain density is C0Then the number N of the abrasive grains is C0Product of surface area of grinding wheel:
N＝C0·2πRWg (15)
if the interference exists between a certain abrasive particle and other abrasive particles, the random position of the abrasive particle is determined again until the abrasive particle does not interfere with all abrasive particles generated previously; repeating the process until the quantity of the abrasive particles reaches a given value N, wherein the abrasive particle density at the moment reaches the abrasive particle density obtained by characterization; and finally, drawing a geometric model of the abrasive particles according to each vertex of the abrasive particles, and superposing the geometric models of all the abrasive particles on the surface of a binding agent to obtain a three-dimensional geometric model of the surface appearance of the grinding wheel.
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