CN114564827B - Three-dimensional shape characterization and modeling method for diamond parallel grinding wheel surface - Google Patents
Three-dimensional shape characterization and modeling method for diamond parallel grinding wheel surface Download PDFInfo
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Abstract
The invention discloses a method for representing and modeling the three-dimensional morphology of the surface of a diamond parallel grinding wheel, which comprises the steps of firstly representing the density of abrasive particles and the height of an outlet blade, and then carrying out randomized modeling on the azimuth, the height of the outlet blade, the axial position and the circumferential position of the abrasive particles according to a measurement result, and comprises the following steps: characterizing abrasive particle density by adopting a complex forming method and a laser scanning confocal microscope LSCM; characterizing the height of the abrasive grain cutting edge by adopting a complex shape method and a laser scanning confocal microscope, and obtaining the statistical distribution of the height of the abrasive grain cutting edge; carrying out random modeling on the abrasive particle orientation; carrying out randomized modeling on the height of the abrasive grain cutting edge and the axial position according to the statistical distribution of the height of the abrasive grain cutting edge; carrying out randomized modeling on circumferential positions of abrasive particles; and judging 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 invention breaks through the limitation of the characterization instrument on the size of the grinding wheel, and realizes the high-precision modeling of the surface morphology of the grinding wheel.
Description
Technical Field
The invention belongs to the technical field of diamond parallel grinding wheels, and particularly relates to a method for representing and modeling three-dimensional morphology of a diamond parallel grinding wheel surface.
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 astronomical telescope, a microelectronic technology, consumer electronic equipment and the like, and subsurface damage is one of key factors limiting the service performance of the optical element. The optical element made of the hard and brittle material is generally processed by adopting a diamond grinding wheel grinding method, and the shape of diamond abrasive particles on the surface of the grinding wheel, the height of the cutting edge, namely the height value of the protruding bonding agent of the abrasive particles, and the abrasive particle density (namely the number of the abrasive particles in unit surface area) have important influences on the generation of subsurface damage during grinding. Therefore, the realization of the representation and modeling of the three-dimensional morphology of the diamond grinding wheel surface has important significance for realizing the simulation of the grinding process, and further optimizing the grinding process and the design and preparation of the grinding wheel.
In the prior art, the microscopic morphology of the grinding wheel is generally measured by adopting a contact measurement method, a laser triangulation method, a Scanning Electron Microscope (SEM), an optical microscope, a multiplexing method and the like. 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 measuring speed, can be used for in-situ detection of the three-dimensional morphology of the grinding wheel, but has limited horizontal resolution. SEM and optical microscope are two-dimensional measurement methods, and can directly measure the grinding wheel, so that the measurement 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 between a plurality of times and tens of thousands of times, and the SEM has a large depth of field, so the SEM is suitable for measuring the shape, microscopic wear morphology, bulk density and the like of abrasive particles. The optical microscope is more suitable for measuring the number of dynamic abrasive particles and the area of a wearing platform of the abrasive particles of the diamond grinding wheel due to the smaller depth of field. The shaping method is not limited by the specification of the measuring instrument, and lead bands or polymers can be adopted to imprint and copy the shape of the grinding wheel. However, in measuring the abrasive grain density and the blade height on the surface of the grinding wheel by the embossing method, there is still a need to develop a high-precision evaluation step.
In the prior art, when geometric modeling is performed on the surface morphology of the diamond grinding wheel, in order to simulate random distribution of the spatial positions of abrasive particles, the abrasive particles are often arranged regularly according to a body-centered cube or a simple cube, and then the positions of the abrasive particles are randomly moved on the premise of ensuring that the abrasive particles do not interfere with each other. In recent years, a learner also randomizes the positions of abrasive particles by using a sphere stacking method, thereby obtaining higher efficiency and randomization degree. For diamond grinding wheels with single-layer abrasive, the position of the abrasive grain in the radial direction is generally simulated by using the concept of the height of the abrasive grain out of the edge, and previous studies have assumed that the height of the edge is a constant value, such as a certain percentage of the abrasive grain size, or obeys 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 shape of the surface of a diamond parallel grinding wheel, which breaks through the limitation of a representing instrument on the size of the grinding wheel and realizes high-precision modeling of the shape of the surface of the grinding wheel.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the method comprises the steps of firstly carrying out characterization of abrasive particle density and blade height, and then carrying out randomized modeling on the azimuth, the blade height, the axial position and the circumferential position of the abrasive particles according to a measurement result, wherein the method comprises the following steps:
step one: characterizing abrasive particle density by adopting a complex forming method and a laser scanning confocal microscope LSCM;
step two: characterizing the height of the abrasive grain cutting edge by adopting a complex shape method and a laser scanning confocal microscope, and obtaining the statistical distribution of the height of the abrasive grain cutting edge;
step three: carrying out random modeling on the abrasive particle orientation;
step four: carrying out randomized modeling on the height of the abrasive grain cutting edge and the axial position according to the statistical distribution of the height of the abrasive grain cutting edge;
step five: carrying out randomized modeling on circumferential positions of abrasive particles;
step six: and judging 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.
In the first step, the shape of the grinding wheel is stamped and copied by adopting silica gel, and then the polymer complex is observed by using a laser scanning confocal microscope to obtain the abrasive particle density; firstly, filtering three-dimensional data measured by a laser scanning confocal microscope to remove burrs in an image; then, carrying out statistical analysis on the data to set an upper threshold value and a lower threshold value of the height, adopting a gray color chart, and setting the upper limit and the lower limit of the color chart as the upper threshold value and the lower threshold value so as to enhance the contrast between abrasive particles and a bonding 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, and respectively measuring a plurality of sub-areas in each area to obtain the average value and standard deviation of the abrasive particle density.
In the second step, a laser scanning confocal microscope is adopted to measure the grinding wheel complex to obtain the blade height of the abrasive particles; the specific steps for extracting the height of the abrasive grain outlet edge according to LSCM measurement data are as follows: (1) Filtering the measurement image by adopting a median filter with a set template size, and removing salt and pepper noise on the image to obtain the measurement image; (2) Manually selecting the vertexes of the polygons in Matlab to obtain a binding agent area of the grinding wheel; (3) Subtracting the fitting plane of the bonding agent region from the filtered image, so as to perform inclination correction on the measured image, and adjusting the average height value of the bonding agent region to 0 to obtain a corrected image; (4) Selecting a point with the smallest z value in the abrasive particle area on the image, wherein the z value of the point corresponds to the blade height value of the abrasive particle; measuring multiple regions of the surface of the grinding wheel, drawing a statistical histogram of the height of the cutting edge of the grinding wheel, assuming that the statistical histogram obeys a certain distribution function according to the shape of the statistical histogram, and adopting χ 2 The fitting test method performs hypothesis testing on the distribution function.
A further improvement of the invention is that the median filter has a template size of 5 x 5 pixels.
In the third step, when carrying out random modeling of the abrasive particle orientation, setting an origin O of a coordinate system to be positioned at the geometric center of the grinding wheel, and aligning a y axis with the axis of the grinding wheel; at the beginning, the geometric center of the abrasive particles is positioned at the origin of coordinates; the direction, the blade outlet height, the axial position and the circumferential position of the abrasive particles are randomized sequentially, 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; the direction of the abrasive particles on the grinding wheel is completely random, so that the orientation of each simulated abrasive particle is randomized; rotating each vertex of the abrasive particle by a random angle value along the x-axis, the y-axis and the z-axis sequentially:
wherein:and->-the vertex coordinate vectors of the abrasive particles before and after the orientation randomization, i.e. the vectors from the center to the vertices of the abrasive particles, respectively; r is R x 、R y And R is z -rotation matrices along x-axis, y-axis and z-axis, respectively; the matrix form of the above is:
wherein: alpha, beta and gamma, the rotation angles along the x-axis, y-axis and z-axis, respectively, obey a uniform distribution between 0 and 2 pi, i.e.:
α,β,γ～U(0,2π) (3)。
in the fourth step, according to the statistical distribution of the height of the abrasive grain cutting edge, when carrying out the randomizing modeling of the height of the abrasive grain cutting edge and the axial position, in order to establish a grinding wheel model, the geometric center of the abrasive grain is transformed from a coordinate origin, namely the geometric center of the grinding wheel, to the surface of the grinding wheel; the distribution of abrasive particles on the surface of the grinding wheel is completed by two steps: (1) Randomizing the height and axial position of the abrasive grain outlet edge, and translating the coordinates of each vertex of the abrasive grain; (2) Randomizing the circumferential positions of abrasive particles, wherein the randomizing is realized by rotating and transforming coordinates of each vertex of the abrasive particles around a y axis; to achieve randomization of the height and axial position of the abrasive grain out of the blade, this is achieved by the following translational transformation:
wherein:-a coordinate vector of the vertex of the translated abrasive particle; t-translation matrix; the matrix form of this formula is:
wherein: t is t x 、t y And t z -translation along x-axis, y-axis and z-axis, respectively, wherein:
wherein: r is the nominal radius of the grinding wheel; Δr—the height of the abrasive grain center protruding out of the bond, is the radial dimension variation with the shape error of the grinding wheel matrix, the shape, size and the blade height of the abrasive grain; Δx and Δz—the amount of coordinate variation eccentric to the mounting of the grinding wheel, misalignment errors, and vibrations; when the grinding wheel has only the mounting eccentricity of the eccentricity amount e, Δx=e, Δz=0;
the height of the center of the abrasive particle protruding from the bond is the distance from the center of the abrasive particle to the surface of the bond, i.e.:
ΔR＝h p -h c (7)
wherein: h is a p The height of the abrasive grain from the surface of the bonding agent, namely the distance between the highest point of the abrasive grain and the surface of the bonding agent, is randomly generated according to the distribution parameters of the height of the abrasive grain from the surface of the bonding agent; h is a c The 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 calculated by the coordinates of each vertex 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 W g The coordinates of the center of the abrasive grain in the y-direction obey the following uniform distribution:
in the fifth step, when the circumferential position of the abrasive particle is modeled in a randomized manner, the circumferential position of the abrasive particle is randomized by rotating the abrasive particle around the y axis:
wherein:-a coordinate vector of the vertex after randomizing the circumferential position of the abrasive particles; r is R y，1 -a rotation matrix about the y-axis, the matrix form of formula (9) being:
wherein: beta 1 -phase of abrasive particles relative to the wheel axis in xz-plane; obviously, beta 1 Obeying a uniform distribution between 0 and 2 pi, i.e.:
β 1 ～U(0,2π) (11)。
the invention further improves that in the step six, the specific implementation method is as follows: the interference problem between two abrasive particles is simplified into the interference problem between the minimum externally connected balls, wherein the interference between the abrasive particles 1 and 2 is as follows:
d 1,2 ＜R 1 +R 2 (12)
wherein: r is R 1 And R is 2 -the minimum outer sphere radius of two abrasive particles respectively; d, d 1,2 -the distance between the centers of two abrasive particles, expressed as:
the sufficient condition and the necessary condition of the interference of the abrasive grains are obtained according to the following constant inequality, thereby improving the judging efficiency of the interference of the abrasive grains:
let |Δx|+|Δy|+|Δz|=d ', if d' < R 1 +R 2 Interference between the two abrasive particles; if it isThe two abrasive particles do not interfere; if neither of these conditions is satisfied, then calculate d 1,2 Then, whether interference exists or not is judged according to a formula (14);
let the abrasive grain density of the grinding wheel reached by the representation be C 0 The number of abrasive grains N is C 0 Product of surface area of grinding wheel:
N＝C 0 ·2πRW g (15)
if interference exists between one abrasive particle and other abrasive particles, the random position of the abrasive particle is redetermined until the abrasive particle does not interfere with all the abrasive particles generated before; repeating the process until the number of the abrasive particles reaches a given value N, and the abrasive particle density at the moment reaches the abrasive particle density obtained by characterization; and finally, drawing geometric models of the abrasive particles according to the vertexes of the abrasive particles, and overlapping the geometric models of all the abrasive particles with the surface of the bonding agent to obtain the three-dimensional geometric model of the surface morphology 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 grain density and the blade height on the surface of a diamond grinding wheel based on a complex forming method and a laser confocal microscope, wherein the size of the measured grinding wheel is not influenced by the measuring range of an instrument;
(B) When the surface morphology of the diamond grinding wheel is characterized, the high-precision measurement of the surface abrasive particle density and the blade height is realized only by adopting a material such as silica gel and 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 morphology of the grinding wheel, the height of the abrasive grain out of the blade is subject to statistical distribution obtained by actual measurement, and the transverse distribution of the abrasive grain is completely randomized, so that the method has the advantage of high modeling precision.
Drawings
FIG. 1 is a flow chart for representing and modeling the three-dimensional morphology of the surface of a diamond parallel grinding wheel.
Fig. 2 is a diagram of an extraction step of the height of the exit edge of the D301 abrasive grain according to the present invention, wherein the measurement range is 640 μm, and fig. 2 (a) is a filtered measurement image, fig. 2 (b) is a manual selection of a binder region, fig. 2 (c) is a selected binder region, and fig. 2 (D) is a correction of the measurement image based on the binder region.
Fig. 3 is a statistical histogram of the D301 abrasive grain exit height and a normal curve fitted thereto.
Fig. 4 is a schematic diagram of the coordinate system of the grinding wheel model.
FIG. 5 is a graph showing simulation and actual measurement results of the surface morphology of the D301 grinding wheel in the measurement range of 2560 μm×2560 μm, wherein FIG. 5 (a) shows the simulation results and FIG. 5 (b) shows the actual measurement results.
Detailed Description
The following specific embodiments of the present invention are provided, and it should be noted that the present invention is not limited to the following specific embodiments, and all equivalent changes made on the basis of the technical solutions of the present application fall within the protection scope of the present invention.
According to the technical scheme, the embodiment provides a diamond abrasive particle morphology characterization and modeling method, as shown in fig. 1, firstly, the characterization of abrasive particle density and blade height is performed, and then the random modeling is performed on the orientation, blade height, axial position and circumferential position of the abrasive particles according to the measurement result. The method specifically comprises the following steps:
step one: the abrasive particle density was characterized using a replica method and a Laser Scanning Confocal Microscope (LSCM).
This example illustrates a parallel electroplated diamond wheel having an abrasive grain size D301. And (3) embossing and copying the shape of the grinding wheel by adopting silica gel, and then observing the polymer complex by using a laser scanning confocal microscope. The D301 grinding wheel was measured using a 5 x objective lens over a 2560 μm measurement range. Firstly, filtering processing is carried out on three-dimensional data measured by a laser scanning confocal microscope, and burrs in an image are removed. And then, carrying out statistical analysis on the data to set an upper threshold value and a lower threshold value of the height, adopting a gray color chart, and setting the upper limit and the lower limit of the color chart as the upper threshold value and the lower threshold value so as to enhance the contrast between abrasive particles (smaller in height and darker in gray) and binding agents (higher in height and brighter in gray) in the image and improve the accuracy of abrasive particle counting. Three regions uniformly distributed on the circumference of the D301 grinding wheel are measured, 5 sub-regions are measured in each region, and the measured abrasive particle density is 9.37+/-0.60/mm 2 。
Step two: and (3) characterizing the height of the abrasive particle cutting edge by adopting a complex shape method and a laser scanning confocal microscope, and obtaining the statistical distribution of the height of the abrasive particle cutting edge.
The complex is measured using a laser scanning confocal microscope to obtain the exit edge height of the abrasive particles. The magnification of the microscope needs to be carefully chosen to ensure measurement accuracy. If the magnification of the objective lens is too large, a large measurement deviation will occur in the region of the complex body in contact with the abrasive particle side surface, because the abrasive particle side surface is relatively steep. For the above reasons, the abrasive grain exit height of the D301 grinding wheel was measured using a 20 x objective lens.
As shown in fig. 2, the step of extracting the height of the abrasive grain outlet edge from the LSCM measurement data is: (1) Filtering the measured image by adopting a median filter with the template size of 5 multiplied by 5 pixels, and removing salt and pepper noise on the image to obtain a measured image as shown in fig. 2 (a); (2) Manually selecting the vertexes of the polygon in Matlab to obtain a bonding agent area of the grinding wheel, as shown in fig. 2 (b) and 2 (c); (3) Subtracting the fitting plane of the binder region from the filtered image, thereby performing tilt correction on the measured image, and adjusting the average height value of the binder region to 0, to obtain a corrected image as shown in fig. 2 (d); (4) A point on the image is selected where the z value in the abrasive particle area is the smallest, the z value of the point corresponding to the exit height value of the abrasive particle.
The statistical histogram of the height of the abrasive grain output edge shown in FIG. 3 fits well with the normal distribution curve obtained by fitting, so it can be assumed that it follows the normal distribution, and then χ is used 2 The fit test method performs hypothesis test on the distribution of the abrasive grain outlet heights of the D301 grinding wheel. The mean and variance of the distribution were 124.03 μm and 32.10 μm, respectively.
Step three: randomizing modeling of the orientation of the abrasive particles was performed.
Fig. 4 is a coordinate system of the grinding wheel model, where 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. At the beginning, the geometric center of the abrasive particle is located at the origin of coordinates. The abrasive particles can be moved to the surface of the grinding wheel by randomizing the azimuth, the blade outlet height, the axial position and the circumferential position of the abrasive particles, so that the geometric model of the grinding wheel is obtained. The step is to conduct random modeling of the abrasive particle orientation.
The direction of the abrasive grains on the grinding wheel is completely random, so that the orientation of each simulated abrasive grain needs to be randomized. Rotating each vertex of the abrasive particle by a random angle value along the x-axis, the y-axis and the z-axis sequentially:
wherein:and->-vertex coordinate vectors of the abrasive particles (i.e. the vectors of the abrasive particle center to vertex) before and after the orientation randomization, respectively; r is R x 、R y And R is z -rotational moments along the x-axis, y-axis and z-axis, respectivelyAn array. The matrix form of this formula is:
wherein: alpha, beta and gamma, the rotation angles along the x-axis, y-axis and z-axis, respectively, obey a uniform distribution between 0 and 2 pi, i.e.:
α,β,γ～U(0,2π)
step four: and carrying out randomized modeling on the height of the abrasive particle outlet and the axial position according to the statistical distribution of the height of the abrasive particle outlet.
In order to build a grinding wheel model, the geometric center of the abrasive grain needs to be transformed from the origin of coordinates (i.e., the grinding wheel geometric center) to the grinding wheel surface. The transformation is related to factors such as the shape, size, shape error, and installation error of the grinding wheel. The distribution of abrasive particles on the surface of the grinding wheel is completed by two steps: (1) Randomizing the height and axial position of the abrasive grain outlet edge, and translating the coordinates of each vertex of the abrasive grain; (2) Randomization of the circumferential position of the abrasive particles is achieved by rotational transformation of the coordinates of each vertex of the abrasive particles about the y-axis. The step is to conduct randomized modeling of the height of the abrasive grain outlet edge and the axial position.
Randomization of the height and axial position of the abrasive grain exit edge is achieved by the following translational transformation:
wherein:-a coordinate vector of the vertex of the translated abrasive particle; t-translation matrix. The matrix form of this formula is:
wherein: t is t x 、t y And t z -translation along x-axis, y-axis and z-axis, respectively, wherein:
wherein: r is the nominal radius of the grinding wheel; Δr—the height of the abrasive grain center protruding out of the bond, is the radial dimension variation related to the shape error of the grinding wheel matrix, the shape, size, and height of the abrasive grain; Δx and Δz—the amount of coordinate variation associated with the mounting eccentricity of the grinding wheel, misalignment errors, vibrations, and the like.
The height of the center of the abrasive particle protruding from the bond is the distance from the center of the abrasive particle to the surface of the bond, i.e.:
ΔR＝h p -h c
wherein: h is a p The height of the abrasive grain from the surface of the bonding agent, namely the distance between the highest point of the abrasive grain and the surface of the bonding agent, is randomly generated according to the normal distribution parameters measured in the step two; h is a c The distance between the highest point of the abrasive particles and the center of the abrasive particles in the radial direction of the grinding wheel can be calculated by the coordinates of each vertex 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 W g The coordinates of the center of the abrasive grain in the y-direction obey the following uniform distribution:
step five: randomizing 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:
wherein:-a coordinate vector of the vertex after randomizing the circumferential position of the abrasive particles; r is R y，1 -a rotation matrix around the y-axis. The matrix form of the above is:
wherein: beta 1 -phase of abrasive particles relative to the wheel axis in xz plane. Obviously, beta 1 Obeying a uniform distribution between 0 and 2 pi, i.e.:
β 1 ～U(0,2π)
step six: and judging 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 interference problem between two abrasive particles is reduced to the interference problem between the smallest outer balls. The conditions for interference between abrasive grain 1 and abrasive grain 2 are:
d 1,2 ＜R 1 +R 2
wherein: r is R 1 And R is 2 -the minimum outer sphere radius of two abrasive particles respectively; d, d 1,2 -the distance between the centers of two abrasive particles, expressed as:
sufficient conditions and necessary conditions for the interference of abrasive grains can be obtained according to the following constant inequality, thereby improving the judging efficiency of the interference of abrasive grains:
let |Δx|+|Δy|+|Δz|=d ', if d' < R 1 +R 2 Interference between the two abrasive particles; if it isThe two abrasive particles do not interfere. If neither of these conditions is satisfied, then calculate d 1,2 And then judging whether interference exists according to the above formula.
Let the measured abrasive grain density of the grinding wheel be C 0 The number of abrasive grains N is C 0 Product of surface area of grinding wheel:
N＝C 0 ·2πRW g
if there is interference between one abrasive particle and other abrasive particles, the random position is redetermined until the abrasive particle does not interfere with all the abrasive particles generated before. Repeating the above process until the number of the abrasive particles reaches a given value N, and the abrasive particle density reaches the measured abrasive particle density. Finally, drawing geometric models of the abrasive particles according to the vertexes of the abrasive particles, and overlapping the geometric models of all the abrasive particles with the surface of the bonding agent to obtain the three-dimensional geometric model of the surface morphology of the grinding wheel, as shown in fig. 5. The result shows that the positions, the directions and the blade-out 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.
While the invention has been described in detail in the foregoing general description and with reference to specific embodiments thereof, it will be apparent to one skilled in the art that modifications and improvements can be made thereto. Accordingly, such modifications or improvements may be made without departing from the spirit of the invention and are intended to be within the scope of the invention as claimed.
Claims (4)
1. The method is characterized in that firstly, the representation of abrasive particle density and blade height is carried out, and then, the random modeling is carried out on the azimuth, the blade height, the axial position and the circumferential position of the abrasive particles according to the measurement result, and the method comprises the following steps:
step one: characterizing abrasive particle density by adopting a complex forming method and a laser scanning confocal microscope LSCM;
step two: characterizing the height of the abrasive grain cutting edge by adopting a complex shape method and a laser scanning confocal microscope, and obtaining the statistical distribution of the height of the abrasive grain cutting edge;
step three: carrying out random modeling on the abrasive particle orientation; setting an origin O of a coordinate system to be positioned at the geometric center of the grinding wheel, and aligning a y axis with the axis of the grinding wheel; at the beginning, the geometric center of the abrasive particles is positioned at the origin of coordinates; the direction, the blade outlet height, the axial position and the circumferential position of the abrasive particles are randomized sequentially, 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; the direction of the abrasive particles on the grinding wheel is completely random, so that the orientation of each simulated abrasive particle is randomized; rotating each vertex of the abrasive particle by a random angle value along the x-axis, the y-axis and the z-axis sequentially:
wherein:and->-the vertex coordinate vectors of the abrasive particles before and after the orientation randomization, i.e. the vectors from the center to the vertices of the abrasive particles, respectively; r is R x 、R y And R is z -rotation matrices along x-axis, y-axis and z-axis, respectively; the matrix form of the above is:
wherein: alpha, beta and gamma, the rotation angles along the x-axis, y-axis and z-axis, respectively, obey a uniform distribution between 0 and 2 pi, i.e.:
α,β,γ～U(0,2π) (3)
step four: carrying out randomized modeling on the height of the abrasive grain cutting edge and the axial position according to the statistical distribution of the height of the abrasive grain cutting edge; according to the statistical distribution of the height of the abrasive grain cutting edge, when carrying out randomized modeling of the height of the abrasive grain cutting edge and the axial position, in order to establish a grinding wheel model, the geometric center of the abrasive grain is transformed from a coordinate origin, namely the geometric center of the grinding wheel, to the surface of the grinding wheel; the distribution of abrasive particles on the surface of the grinding wheel is completed by two steps: (1) Randomizing the height and axial position of the abrasive grain outlet edge, and translating the coordinates of each vertex of the abrasive grain; (2) Randomizing the circumferential positions of abrasive particles, wherein the randomizing is realized by rotating and transforming coordinates of each vertex of the abrasive particles around a y axis; to achieve randomization of the height and axial position of the abrasive grain out of the blade, this is achieved by the following translational transformation:
wherein:-a coordinate vector of the vertex of the translated abrasive particle; t-translation matrix; the matrix form of this formula is:
wherein: t is t x 、t y And t z -translation along x-axis, y-axis and z-axis, respectively, wherein:
wherein: r is the nominal radius of the grinding wheel; Δr—the height of the abrasive grain center protruding out of the bond, is the radial dimension variation with the shape error of the grinding wheel matrix, the shape, size and the blade height of the abrasive grain; Δx and Δz—the amount of coordinate variation eccentric to the mounting of the grinding wheel, misalignment errors, and vibrations; when the grinding wheel has only the mounting eccentricity of the eccentricity amount e, Δx=e, Δz=0;
the height of the center of the abrasive particle protruding from the bond is the distance from the center of the abrasive particle to the surface of the bond, i.e.:
ΔR＝h p -h c (7)
wherein: h is a p The height of the abrasive grain from the surface of the bonding agent, namely the distance between the highest point of the abrasive grain and the surface of the bonding agent, is randomly generated according to the distribution parameters of the height of the abrasive grain from the surface of the bonding agent; h is a c -the highest point of the abrasive grain and the center of the abrasive grainThe distance between the two points in the radial direction of the grinding wheel is calculated by 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 W g The coordinates of the center of the abrasive grain in the y-direction obey the following uniform distribution:
step five: carrying out randomized modeling on circumferential positions of abrasive particles; randomization of the circumferential position of the abrasive particles is achieved by rotating the abrasive particles about the y-axis:
wherein:-a coordinate vector of the vertex after randomizing the circumferential position of the abrasive particles; r is R y，1 -a rotation matrix about the y-axis, the matrix form of formula (9) being:
wherein: beta 1 -phase of abrasive particles relative to the wheel axis in xz-plane; obviously, beta 1 Obeying a uniform distribution between 0 and 2 pi, i.e.:
β 1 ～U(0,2π) (11)
step six: judging 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 specific implementation method comprises the following steps: the interference problem between two abrasive particles is simplified into the interference problem between the minimum externally connected balls, wherein the interference between the abrasive particles 1 and 2 is as follows:
d 1,2 ＜R 1 +R 2 (12)
wherein: r is R 1 And R is 2 -the minimum outer sphere radius of two abrasive particles respectively; d, d 1,2 -the distance between the centers of two abrasive particles, expressed as:
the sufficient condition and the necessary condition of the interference of the abrasive grains are obtained according to the following constant inequality, thereby improving the judging efficiency of the interference of the abrasive grains:
let |Δx|+|Δy|+|Δz|=d ', if d' < R 1 +R 2 Interference between the two abrasive particles; if it isThe two abrasive particles do not interfere; if neither of these conditions is satisfied, then calculate d 1,2 Then, whether interference exists or not is judged according to a formula (14);
let the abrasive grain density of the grinding wheel reached by the representation be C 0 The number of abrasive grains N is C 0 Product of surface area of grinding wheel:
N＝C 0 ·2πRW g (15)
if interference exists between one abrasive particle and other abrasive particles, the random position of the abrasive particle is redetermined until the abrasive particle does not interfere with all the abrasive particles generated before; repeating the process until the number of the abrasive particles reaches a given value N, and the abrasive particle density at the moment reaches the abrasive particle density obtained by characterization; and finally, drawing geometric models of the abrasive particles according to the vertexes of the abrasive particles, and overlapping the geometric models of all the abrasive particles with the surface of the bonding agent to obtain the three-dimensional geometric model of the surface morphology of the grinding wheel.
2. The method for representing and modeling the three-dimensional morphology of the surface of a diamond parallel grinding wheel according to claim 1, wherein in the first step, silica gel is adopted to imprint and copy the morphology of the grinding wheel, and then a laser scanning confocal microscope is used to observe a polymer complex to obtain the abrasive particle density; firstly, filtering three-dimensional data measured by a laser scanning confocal microscope to remove burrs in an image; then, carrying out statistical analysis on the data to set an upper threshold value and a lower threshold value of the height, adopting a gray color chart, and setting the upper limit and the lower limit of the color chart as the upper threshold value and the lower threshold value so as to enhance the contrast between abrasive particles and a bonding 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, and respectively measuring a plurality of sub-areas in each area to obtain the average value and standard deviation of the abrasive particle density.
3. The method for representing and modeling the three-dimensional morphology 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 blade height of the grinding particles; the specific steps for extracting the height of the abrasive grain outlet edge according to LSCM measurement data are as follows: (1) Filtering the measurement image by adopting a median filter with a set template size, and removing salt and pepper noise on the image to obtain the measurement image; (2) Manually selecting the vertexes of the polygons in Matlab to obtain a binding agent area of the grinding wheel; (3) Subtracting the fitting plane of the bonding agent region from the filtered image, so as to perform inclination correction on the measured image, and adjusting the average height value of the bonding agent region to 0 to obtain a corrected image; (4) Selecting a point with the smallest z value in the abrasive particle area on the image, wherein the z value of the point corresponds to the blade height value of the abrasive particle; measuring multiple regions of the surface of the grinding wheel, drawing a statistical histogram of the height of the cutting edge of the grinding wheel, assuming that the statistical histogram obeys a certain distribution function according to the shape of the statistical histogram, and adopting χ 2 The fitting test method performs hypothesis testing on the distribution function.
4. The method for characterizing and modeling the three-dimensional topography of a surface of a diamond parallel grinding wheel according to claim 1, wherein the template size of the median filter is 5 x 5 pixels.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106446403A (en) * | 2016-09-22 | 2017-02-22 | 北京航空航天大学 | Virtual grinding wheel simulation method based on randomly distributed multiple abrasive particles |
| CN107657661A (en) * | 2017-10-10 | 2018-02-02 | 湖南科技大学 | A kind of three-dimensional modeling method of parallel skive surface topography |
| CN112276683A (en) * | 2020-10-28 | 2021-01-29 | 沈阳工业大学 | Method for predicting surface appearance of abrasive belt grinding screw curved surface |
| WO2021169357A1 (en) * | 2020-02-29 | 2021-09-02 | 华南理工大学 | Grinding wheel grinding performance classification method based on diamond abrasive grain crystal face directionality |
-
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106446403A (en) * | 2016-09-22 | 2017-02-22 | 北京航空航天大学 | Virtual grinding wheel simulation method based on randomly distributed multiple abrasive particles |
| CN107657661A (en) * | 2017-10-10 | 2018-02-02 | 湖南科技大学 | A kind of three-dimensional modeling method of parallel skive surface topography |
| WO2021169357A1 (en) * | 2020-02-29 | 2021-09-02 | 华南理工大学 | Grinding wheel grinding performance classification method based on diamond abrasive grain crystal face directionality |
| CN112276683A (en) * | 2020-10-28 | 2021-01-29 | 沈阳工业大学 | Method for predicting surface appearance of abrasive belt grinding screw curved surface |
Non-Patent Citations (1)
| Title |
|---|
| 氧化铝砂轮地貌的量化评价及数学建模;言兰;融亦鸣;姜峰;;机械工程学报(17);全文 * |
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