CN108214307B - Grinding wheel dressing amount optimal selection design method based on abrasive particle thickness cutting distribution control - Google Patents
Grinding wheel dressing amount optimal selection design method based on abrasive particle thickness cutting distribution control Download PDFInfo
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- CN108214307B CN108214307B CN201810046401.9A CN201810046401A CN108214307B CN 108214307 B CN108214307 B CN 108214307B CN 201810046401 A CN201810046401 A CN 201810046401A CN 108214307 B CN108214307 B CN 108214307B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B53/00—Devices or means for dressing or conditioning abrasive surfaces
- B24B53/06—Devices or means for dressing or conditioning abrasive surfaces of profiled abrasive wheels
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Abstract
The invention discloses a grinding wheel dressing amount optimal design method based on abrasive particle cut thickness distribution control, which comprises the following steps of: (1) giving a set abrasive particle parameter on the surface of the grinding wheel, giving a grinding amount, and setting the thickness cutting distribution of target abrasive particles according to a processing result; (2) after the abrasive particle parameters on the surface of the grinding wheel are virtually trimmed, abrasive particle cutting thickness distribution calculation is carried out on the abrasive particle parameters and the grinding consumption, and abrasive particle cutting thickness distribution is calculated; (3) and (3) comparing the abrasive grain cutting thickness distribution calculated in the step (2) with the target abrasive grain cutting thickness distribution set in the step (1), if the difference between the abrasive grain cutting thickness distribution and the target abrasive grain cutting thickness distribution is too large, adjusting the virtual trimming amount, and circulating the steps (2) and (3) again until the difference between the abrasive grain cutting thickness distribution calculated in the step (3) and the abrasive grain cutting thickness distribution set in the step (1) meets a set standard, and stopping calculation. The grinding wheel is trimmed by adopting the optimal trimming amount, and the trimmed grinding wheel is processed by combining the given grinding amount, so that the expected processing purpose can be effectively achieved.
Description
Technical Field
The invention relates to the field of grinding, in particular to a grinding wheel dressing amount optimal selection design method based on abrasive particle cut thickness distribution control.
Background
Grinding is the main processing means of high dimensional accuracy and high surface quality of parts and is an important component of advanced manufacturing technology. The control of the grinding process and the accurate prediction of the processing result are of great importance to the efficient and precise grinding processing technology. The grinding process is a processing mode that a plurality of abrasive grains respectively realize micro-cutting under the holding of a binding agent, and further macroscopically remove workpiece materials. In other words, the abrasive machining is the removal of material from the tool on a macroscopic level, which is actually done microscopically by cutting each abrasive particle. Therefore, the cut thickness value of each abrasive particle is always a key control quantity of the grinding process and the grinding result. Due to manufacturing problems, the heights of the abrasive particles on the surface of the grinding wheel are uneven, the cutting thickness of each abrasive particle is seriously influenced, and the processing quality is further influenced. In the grinding wheel dressing, the part with excessively high abrasive particles on the grinding wheel is ground by a dressing tool so as to obtain a grinding wheel surface with relatively consistent edge height. Obviously, the dressing of the grinding wheel is crucial to the grinding process, and how to select a reasonable dressing amount is the biggest problem of dressing of the grinding wheel.
How to select the dressing amount is mostly done in the industry by measuring the contour of the abrasive grains on the surface of the grinding wheel, then carrying out the dressing amount, then measuring again, and repeating the steps until the requirements are met. This method is obviously time consuming, labor intensive, inefficient, costly, and does not meet the machining result requirements, sometimes with inadequate dressing and sometimes over-dressing. Therefore, how to design the dressing amount of the grinding wheel based on the machining result has become the key point of urgent need in the industry. To realize the key point, a bridge of the abrasive particle parameters of the grinding wheel and the processing result needs to be found.
In the grinding research process, the industry mainly adopts the maximum undeformed chip thickness of a single abrasive particle as a bridge to carry out the grinding process design. However, the maximum undeformed chip thickness of a single abrasive particle is assumed to be based on an ideal state that all abrasive particles on the surface of the grinding wheel are uniformly distributed and have consistent size, shape and edge-projecting height. In other words, assuming that the cutting amount of each abrasive grain on the grinding wheel is uniform, the grinding wheel is ideal, and therefore, dressing is not necessary. This bridge is clearly not available for trim amount design.
In summary, the requirement of the industry cannot be met by simply designing the dressing amount of the grinding wheel from the high-performance angle of the abrasive grains on the surface of the grinding wheel. It is obviously particularly urgent to find a more reasonable grinding wheel dressing amount design, and particularly a dressing amount design method which can perform a back-stepping design from a machining result and can truly reflect the interference cutting depth condition of abrasive particles and a workpiece.
Disclosure of Invention
The invention aims to solve the problem that the dressing amount of a grinding wheel cannot be designed by taking a machining result as a constraint at present, and provides a grinding wheel dressing amount optimal design method based on abrasive particle cutting thickness distribution control.
The technical scheme of the invention is as follows:
a grinding wheel dressing amount optimal design method based on abrasive particle thickness cutting distribution control comprises the following steps:
(1) setting target abrasive particle cutting thickness distribution according to a processing result, giving a set abrasive particle parameter on the surface of the grinding wheel, giving a grinding amount, setting target abrasive particle cutting thickness distribution according to the processing result, and giving an initial value of a finishing amount;
(2) constructing a digital grinding wheel, virtually finishing the grinding wheel, calculating the abrasive grain cutting thickness distribution of the abrasive grain parameters and the grinding consumption of the virtually finished grinding wheel surface, and calculating the interference, namely the cutting depth, of each abrasive grain on the grinding wheel surface to obtain the abrasive grain cutting thickness distribution;
(3) comparing the abrasive particle cutting thickness distribution calculated in the step (2) with the abrasive particle cutting thickness distribution set in the step (1), adjusting the trimming amount if the difference between the abrasive particle cutting thickness distribution and the abrasive particle cutting thickness distribution exceeds a set standard value, and performing the step (2) and the step (3) again until the difference between the abrasive particle cutting thickness distribution calculated in the step (2) and the abrasive particle cutting thickness distribution set in the step (1) is less than the set standard value, stopping calculation, wherein the trimming amount adjusted in the step (2) for the last time is the optimal designed trimming amount;
(4) and (3) dressing the grinding wheel in the step (1) by adopting the optimal dressing amount, and grinding by matching with the grinding amount in the step (1) after dressing, so that the processing result in the step (1) can be efficiently obtained.
In an embodiment of the present invention, the machining result includes at least one of grinding efficiency, workpiece surface roughness, grinding force, grinding temperature, and degree of sub-surface damage of the ground workpiece.
In an embodiment of the present invention, the abrasive grain thickness cutting distribution is a depth of each abrasive grain cut into the workpiece on the surface of the grinding wheel during grinding.
In one embodiment of the invention, the grinding amount includes a grinding speed, a grinding depth and a feeding speed.
In an embodiment of the present invention, the abrasive particle parameters include a position parameter of the abrasive particle on the grinding wheel, a height parameter, and an abrasive particle diameter.
In an embodiment of the present invention, the setting criterion in step (3) is used to measure the coincidence condition of two curves, and includes one or more of a standard deviation, a similarity, an error, an average value, and a coincidence degree, and the value of the setting criterion is determined according to actual requirements.
In an embodiment of the present invention, the calculation of the cutting thickness distribution of the abrasive particles in the step (2) includes the following A, B, C, D, E calculation process:
A. constructing a digital grinding wheel: expressing the abrasive grain parameters of the surface of the grinding wheel into a matrix Gjk}p×qThe p x q is a matrix with p rows and q columns, namely, the excircle of the grinding wheel has p rows and q columns of abrasive particles distributed, and the element GjkI is more than or equal to 0 and less than or equal to p, k is more than or equal to 0 and less than or equal to q, Gjk＝{Xjk,Zjk,dgjk,hjk}；XjkDenotes abrasive grain GjkPosition coordinate in the circumferential direction of the grinding tool, ZjkDenotes abrasive grain GjkPosition coordinates in the axial direction of the grinding tool, dgjkDenotes the particle diameter of the abrasive grains, hjkRepresenting the exit edge height of the abrasive particles; leading the abrasive particle parameters of the grinding wheel surface given by a user into a matrix Gjk}p×q；
B. Virtually finishing the grinding wheel: in the matrix { Gjk}p×qFinding out the maximum value hmax of the edge height, and then subtracting the trimming amount dr from hmax to obtain a value which is the maximum value hdrmax of the edge height of the trimmed abrasive particles, namely hdrmax is hmax-dr; finally, it will be in the matrix { G }jk}p×qMedium abrasive grain GjkHeight h of the edgejkComparing the size with hdrmax if hjk<hdrmax, then h is notjkMaking any modification if hjkWhen the value is more than or equal to hdrmax, h isjkReplacing the value of hdrmax with hdrmax; varying the value of i, k, for the matrix { G }jk}p×qProcessing the edge height values of all the abrasive grains;
C. calculating the outline track of the abrasive particles: the X direction is the translation direction of the workpiece, the Z direction is consistent with the axial direction (width direction) of the grinding tool, the Y direction is the same as the normal direction of the working table, and the origin of the coordinate system is placed in the center of the working table; for face grinding, the grinding tool is set at speed vsRotate at a speed vwMoving relative to the workpiece; abrasive grain G at time tjkThe motion trajectory equation of the sphere center in the XYZ coordinate system is as follows:
zc(t)＝Zjk(c)
in the formula, xc(t)、yc(t)、zc(t) is abrasive grain GjkCoordinates of the center of sphere at time t, Z, in XYZ coordinate systemjk、dgjk、hjkRespectively represent abrasive grains GjkThe position coordinates, the grain diameter and the height of the exit edge of the abrasive grains in the axial direction of the abrasive tool; x is0、y0Is the coordinate in XYZ coordinate system of the center of the grinding tool, theta 2lg/ds，lgIs the initial position of the abrasive grain along the circumferential direction of the abrasive tool, lg＝Xjk，dsIs the diameter of the grinding tool, ap、vw、vsIs a grinding parameter, i.e. grinding quantity, where apIs the grinding depth vwIs the workpiece feed speed, vsIs the linear speed of the grinding wheel, t is the processing time;
further coupling the shape of the abrasive particles with the movement locus of the spherical center of the abrasive particles to obtain any abrasive particle G on the surface of the grinding wheeljkEquation of motion at any point (xg, yg, zg):
(xg-xc(t))2+(yg-yc(t))2+(zg-zc(t))2＝(dgjk)2(d)
D. workpiece dispersion: cutting the workpiece into n sections with the distance delta x perpendicular to the translation direction of the workpiece, wherein the distance delta x between the sections multiplied by n represents the length of the workpiece; each section is cut into m vertical lines with the distance delta z, the length of the line segments in the y-direction represents the height of the workpiece, and the distance delta z between the line segments multiplied by m represents the width of the workpiece; thus, the workpiece is scattered into n multiplied by m vertical line segments; after discretization, the workpiece can be represented by a two-dimensional array W, the height value of each vertical line is stored, the position of each line segment in the array is represented by subscripts u, v, u represents the position in the X direction, v represents the position in the Z direction, 0 < u < n,0 < v < m; coordinate x of the v-th vertical line on the u-th cross sectionuvAnd zuvExpressed as:
xuv＝u*Δx (e)
zuv＝v*Δz (f)
E. calculating the cutting thickness distribution of the abrasive particles: abrasive grain GjkThe interference depth with the nth vertical line of the u section can be obtained by the following steps:
① reading grain G from the grinding tool numerical modeljkAbrasive grain diameter d ofg jkHeight h of edgejkAbrasive grain axial position coordinate ZjkAnd circumferential initial position coordinate Xjk；
② for equation (a), let xc(t)＝xuvSolving the numerical solution of t by a Newton iteration method, substituting into the equation (b) to obtain yc(t)；
③ processing xc(t)、yc(t)、zc(t) substituting the equations (e) and (f) into the equation (d), and solving; if the equation is not solved, the abrasive grain G is illustratedjkThere is no intersection with the vertical line v; otherwise, solving the equation to obtain
And is compared with the initial height value stored in the workpiece array W
By comparison, if
Description of the abrasive grain GjkAbove the vertical line v, there is no contact with the vertical line v, otherwise, the abrasive grain G is foundjkHeight of vertical line v of cut, i.e. depth of cut
At the same time will
Stored in a temporary array WtIn combination with each other
Replacement of
Then storing in an array W;
④ transforming j and k values, repeating the above ①②③ steps to obtain abrasive grain matrix { G }on the surface of the grinding wheeljk}p×qThe interference depth of all the abrasive particles and all the vertical lines on the plane u is stored in the matrix hmaxG jk}p×qAnd obtaining the cutting thickness distribution of the abrasive particles.
In one embodiment of the invention, the abrasive grain parameters of the given grinding wheel surface are generated by a distribution function, in particular the grain diameter dg of the abrasive grainjkObtained from the grain size distribution of the abrasive grains; nominal position coordinate Z of abrasive grain on grinding wheel surfacenom jk＝w x Rand Z，Xnom jk＝ΔX·j+zjkTan (α), randZ is random with the value range of (0, 1), α is the included angle between the distribution row of the abrasive particles on the grinding wheel and the axial direction of the grinding wheel, and the offset Z of the Z-axis direction of the abrasive particles is expressed by a distribution functiondevAnd offset X in X-axis directiondevThen GjkActual position coordinate Z on the surface of the grinding wheeljkGrinding consumption design method based on abrasive particle cutting thickness distribution constraint + Zdev，Xjk＝ΔX·j+Zjk/tan(α)+Xdev。
In an embodiment of the invention, the distribution function includes at least one of a weibull function, a rayleigh distribution function, a skewed distribution function, an exponential function, a polynomial function, and a normal distribution function.
Advantages of the invention
(1) The depth of the abrasive particles cut into the workpiece on the surface of the grinding wheel in the grinding process is measured by adopting abrasive particle cut thickness distribution, and the method is more accurate, reasonable and effective than the method of using one abrasive particle cut thickness value (the maximum cut thickness of a single abrasive particle) after adopting an ideal assumption in the prior art.
(2) The method for solving the abrasive particle cutting thickness distribution does not assume the parameters of the abrasive particle size, the position distribution and the like of the grinding wheel to be ideal, and the like, and the calculated abrasive particle cutting thickness distribution can be closer to the actual processing process.
(4) The actual processing amount (namely the abrasive particle thickness cutting distribution) of the abrasive particles on the surface of the grinding wheel is controlled, so that the grinding wheel is more reasonable, more accurate and more advanced compared with the existing grinding wheel in consideration of abrasive particle parameters.
(3) The target abrasive particle thickness cutting distribution is set by taking the processing result as constraint, then the grinding wheel dressing amount is optimized, then the grinding wheel dressing is carried out by the optimized dressing amount, and then the grinding processing is carried out, so that the expected processing result can be quickly and effectively achieved, a large amount of time, labor, material resources, financial resources and the like consumed by adjusting the dressing process are avoided, and the intelligent manufacturing is really realized.
Drawings
The invention is further illustrated by the following figures and examples.
Fig. 1 is a cut thickness profile of abrasive particles. Wherein the distribution 1 is the target abrasive grain cut thickness distribution; the distribution 2 is a grinding particle cut thickness distribution obtained in the calculation process; distribution 3 is the final calculation result.
Fig. 2 is a schematic diagram of the position coordinates of the grinding wheel.
FIG. 3 is a graph of the height of the edge of an unfinished grinding wheel;
FIG. 4 is a graph of the height profile of the abrasive grain exposure of FIG. 4 through a virtual dressing wheel;
FIG. 5 is a schematic representation of the interference of abrasive particles with a workpiece (parallel to the XY plane).
FIG. 6 is a schematic view of workpiece dispersion and its interference with abrasive particles (parallel to the XY plane);
fig. 7 shows a comparison of the quality of the machined surface before and after the optimization design (a) the machined surface with the unoptimized grinding stock and (b) the machined surface with the optimized grinding stock.
Detailed Description
The first embodiment is as follows:
in the present embodiment, the grinding amount is optimally designed with the aim of obtaining good quality of the machined surface. The tool workpiece is No. 45 steel, the surface roughness Ra of the expected processing result is less than 0.4um, the abrasive particle parameters of the surface of the grinding wheel are given by a user, the granularity, the position and the edge height are normally distributed, and the parameters are as follows: the grain size N (550,0.25) and the land height N (0.1,0.4) were N (67, 0.15). Given machining dose as grinding speed vsAt 45m/s, feed speed vw20m/min, grinding depth ap Is 10 um; the preliminary estimate of the trimming amount is 50um
The specific optimization design process comprises the following steps:
(1) setting a target abrasive grain cut thickness distribution according to the processing result, as shown in distribution 1 of fig. 1; the given abrasive particle parameters of the grinding wheel adopt user given values, namely, the user has given abrasive particle parameters on the surface of the grinding wheel, the granularity, the position and the cutting height are all in normal distribution, and the parameters are as follows: the grain size N (550,0.25) and the cutting height N (0.1,0.4) are N (67, 0.15); grinding amount (grinding speed v)sAt 45m/s, feed speed vw20m/min, grinding depth ap10um), the trimming amount is initially 50 um.
(2) Constructing a digital grinding wheel, virtually finishing the grinding wheel, calculating the abrasive grain cutting thickness distribution of the abrasive grain parameters and the grinding consumption of the virtually finished grinding wheel surface, and calculating the interference, namely the cutting depth, of each abrasive grain on the grinding wheel surface to obtain the abrasive grain cutting thickness distribution; specifically, the method comprises the following A, B, C, D, E calculation process:
A. constructing a digital grinding wheel: representing the abrasive grains on the surface of the abrasive tool as a matrix Gjk}p×qThe p x q is a matrix with p rows and q columns, namely, the excircle of the grinding wheel has p rows and q columns of abrasive particles distributed, and the element GjkI is more than or equal to 0 and less than or equal to p, k is more than or equal to 0 and less than or equal to q, Gjk＝{Xjk,Zjk,dgjk,hjk}；XjkDenotes abrasive grain GjkPosition coordinate in the circumferential direction of the grinding tool, ZjkDenotes abrasive grain GjkPosition coordinates in the axial direction of the grinding tool, dgjkDenotes the particle diameter of the abrasive grains, hjkRepresenting the exit edge height of the abrasive particles;
Gjk}p×qthe abrasive grain parameters of the grinding wheel surface in the embodiment are generated by adopting a distribution function given by a user: in particular the grain size dg of the abrasive grainsjkObtained from the grain size distribution of the abrasive grains; nominal position coordinate Z of abrasive grain on grinding wheel surfacenom jk＝w x Rand Z，Xnom jk＝ΔX·j+zjkTan (α), randZ is random with the value range of (0, 1), α is the included angle between the distribution row of the abrasive particles on the grinding wheel and the axial direction of the grinding wheel, and the offset Z of the Z-axis direction of the abrasive particles is expressed by a distribution functiondevAnd offset X in X-axis directiondevThen GjkActual position coordinate Z on the surface of the grinding wheeljkGrinding consumption design method based on abrasive particle cutting thickness distribution constraint + Zdev，Xjk＝ΔX·j+Zjk/tan(α)+XdevSee FIG. 2, the calculated abrasive grain GjkParameter storage matrix Gjk}p×q(ii) a Repeating the steps to obtain the abrasive particle parameters to obtain an abrasive particle parameter matrix { G) corresponding to the given grinding wheeljk}p×q。
B. Virtually finishing the grinding wheel: in the matrix { Gjk}p×qIn this embodiment, the maximum value hmax of the cutting edge height is found, the distribution of the cutting edge height of the abrasive grains of the grinding wheel without dressing in this embodiment is as shown in fig. 3, hmax is 597um, and then a value obtained by subtracting the dressing amount dr (from the dressing initial value 75um in the first calculation) from hmax is the maximum value hdrmax of the cutting edge height of the abrasive grains after dressing, that is, hdrmax-dr is 597-50 um 547 um; finally, it will be in the matrix { G }jk}p×qMedium abrasive grain GjkHeight h of the edgejkComparing the size with hdrmax if hjk<hdrmax, then h is notjkMaking any modification if hjkWhen the value is more than or equal to hdrmax, h isjkReplacing the value of hdrmax with hdrmax; varying the value of i, k, for the matrix { G }jk}p×qThe edge height values of all the abrasive grains are processed.
B. Calculating the trace of the abrasive particle contour points: the X direction is the translation direction of the workpiece, the Z direction is consistent with the axial direction (width direction) of the grinding tool, the Y direction is the same as the normal direction of the working table, and the origin of the coordinate system is placed in the center of the working table; for face grinding, the grinding tool is set at speed vsRotate at a speed vwMoving relative to the workpiece; referring to FIG. 5, abrasive grain G at time tjkThe motion trajectory equation of the sphere center in the XYZ coordinate system is as follows:
zc(t)＝Zjk(c)
in the formula, xc(t)、yc(t)、zc(t) is abrasive grain GjkCoordinates of the center of sphere at time t, Z, in XYZ coordinate systemjk、dgjk、hjkRespectively represent abrasive grains GjkThe position coordinates, the grain diameter and the height of the exit edge of the abrasive grains in the axial direction of the abrasive tool; x is0、y0Is the coordinate in XYZ coordinate system of the center of the grinding tool, theta 2lg/ds，lgIs the initial position of the abrasive grain along the circumferential direction of the abrasive tool, lg＝Xjk，dsIs the diameter of the grinding tool, ap、vw、vsIs a grinding parameter, i.e. grinding quantity, where apIs the grinding depth vwIs the workpiece feed speed, vsIs the grinding wheel linear velocity and t is the machining time.
Further coupling the shape of the abrasive particles with the movement locus of the spherical center of the abrasive particles to obtain any abrasive particle G on the surface of the grinding wheeljkEquation of motion at any point (xg, yg, zg):
(xg-xc(t))2+(yg-yc(t))2+(zg-zc(t))2＝(dgjk)2(d)
C. workpiece dispersion: as in fig. 6, the workpiece is cut into n sections with a distance Δ x perpendicular to the direction of translation of the workpiece, the distance Δ x between the sections multiplied by n representing the length of the workpiece; each section is cut into m vertical lines with the distance delta z, the length of the line segments in the y-direction represents the height of the workpiece, and the distance delta z between the line segments multiplied by m represents the width of the workpiece; thus, the workpiece is scattered into n multiplied by m vertical line segments; after discretization, the workpiece can be represented by a two-dimensional array W, the height value of each vertical line is stored, the position of each line segment in the array is represented by subscripts u, v, u represents the position in the X direction, v represents the position in the Z direction, 0 < u < n,0 < v < m; coordinate x of the v-th vertical line on the u-th cross sectionuvAnd zuvExpressed as:
xuv＝u*Δx (e)
zuv＝v*Δz (g)
D. calculating the cutting thickness distribution of the abrasive particles: abrasive grain GjkThe interference depth with the nth vertical line of the u section can be obtained by the following steps:
① reading grain G from the grinding tool numerical modeljkAbrasive grain diameter d ofg jkHeight of emergence hjkAbrasive grain axial position coordinate Zjk(zc) And circumferential initial position coordinate Xjk；
② for equation (a), let xc(t)＝xuvSolving the numerical solution of t by a Newton iteration method, substituting into the equation (b) to obtain yc(t)；
③ processing xc(t)、yc(t)、zc(t) substituting the equations (e) and (f) into the equation (d), and solving; if the equation is not solved, the abrasive grain G is illustratedjkThere is no intersection with the vertical line v; otherwise, solving the equation to obtain
And is compared with the initial height value stored in the workpiece array W
By comparison, if
Description of the abrasive grain GjkAbove the vertical line v, there is no contact with the vertical line v, otherwise, the abrasive grain G is foundjkHeight of vertical line v of cut, i.e. depth of cut
At the same time will
Stored in a temporary array WtIn combination with each other
Replacement of
Then storing in an array W;
④ the value of j and k is converted, and the above ①②③ steps are repeated to obtain the abrasive grain { Φ } - { G } on the grinding wheel surfacejk}j×kThe interference depth of all the abrasive particles and all the vertical lines on the plane u is correspondingly stored in a matrix hmaxG jk}p×qAnd obtaining the cutting thickness distribution of the abrasive particles, and further obtaining the distribution 2 on the cutting thickness distribution diagram 1 of the abrasive particles.
(3) Comparing the abrasive grain cutting thickness distribution calculated in the step (2) with the target abrasive grain cutting thickness distribution set in the step (1), if the difference between the abrasive grain cutting thickness distribution calculated in the step (2) and the target abrasive grain cutting thickness distribution set in the step (1) is too large, changing the abrasive grain parameters on the surface of the grinding wheel, and repeating the steps (2) and (3) until the average error between the abrasive grain cutting thickness distribution calculated in the step (2) and the target abrasive grain cutting thickness distribution set in the step (1) is less than 5%, stopping calculation, wherein the dressing amount is a preferable result, the dressing amount is preferably 73um in the embodiment, and the distribution diagram of the corresponding abrasive grain cutting height is shown in fig. 4.
(4) And (3) dressing the grinding wheel by using the optimal grinding dosage (73um), and dressing the outer circle of the grinding wheel by using a diamond roller. Grinding the dressed grinding wheel at a grinding speed vs45m/s, feed speed vw20m/min grinding depth apThe No. 45 steel is ground for 10um, the roughness value of the obtained grinding surface is 0.37-0.43um, and compared with the expected machined roughness of 0.4um, the unilateral error is less than 10%, and the effect is very good. The dressing efficiency is more than 5 times higher than that of the traditional tentative dressing. Fig. 7 shows the difference in the measured results of the machined surface before and after dressing, and it is apparent that the surface quality of the ground workpiece after dressing is much improved.
The above description is only a preferred embodiment of the present invention, and therefore should not be taken as limiting the scope of the invention, which is defined by the appended claims and their equivalents. .
Claims (6)
1. A grinding wheel dressing amount optimal design method based on abrasive particle thickness cutting distribution control comprises the following steps:
(1) setting target abrasive particle cutting thickness distribution according to a processing result, giving a set abrasive particle parameter on the surface of the grinding wheel, giving a grinding amount, setting target abrasive particle cutting thickness distribution according to the processing result, and giving an initial value of a finishing amount;
(2) constructing a digital grinding wheel, virtually finishing the grinding wheel, calculating the abrasive particle cutting thickness distribution of the abrasive particle parameters and the grinding amount on the surface of the virtually finished grinding wheel, and calculating the interference between each abrasive particle on the surface of the grinding wheel and a workpiece, namely the cutting depth to obtain the abrasive particle cutting thickness distribution;
the calculation of the abrasive particle thickness cutting distribution comprises the following calculation processes of A, B, C, D, E:
A. constructing a digital grinding wheel: expressing the abrasive grain parameters of the surface of the grinding wheel into a matrix Gjk}p×qThe p x q is a matrix with p rows and q columns, namely, the excircle of the grinding wheel has p rows and q columns of abrasive particles distributed, and the element GjkJ is more than or equal to 0 and less than or equal to p, k is more than or equal to 0 and less than or equal to q, and G represent the kth row and the kth column of abrasive particles on the surface of the grinding tooljk＝{Xjk,Zjk,dgjk,hjk}；XjkDenotes abrasive grain GjkPosition coordinate in the circumferential direction of the grinding tool, ZjkDenotes abrasive grain GjkPosition coordinates in the axial direction of the grinding tool, dgjkDenotes the particle diameter of the abrasive grains, hjkRepresenting the exit edge height of the abrasive particles; give users toFixed grinding wheel surface abrasive particle parameter import matrix { Gjk}p×q；
B. Virtually finishing the grinding wheel: in the matrix { Gjk}p×qFinding out the maximum value hmax of the edge height, and then subtracting the trimming amount dr from hmax to obtain a value which is the maximum value hdrmax of the edge height of the trimmed abrasive particles, namely hdrmax is hmax-dr; finally, it will be in the matrix { G }jk}p×qMedium abrasive grain GjkHeight h of the edgejkComparing the size with hdrmax if hjk<hdrmax, then h is notjkMaking any modification if hjkWhen the value is more than or equal to hdrmax, h isjkReplacing the value of hdrmax with hdrmax; varying the value of j, k, for the matrix { Gjk}p×qProcessing the edge height values of all the abrasive grains;
C. calculating the outline track of the abrasive particles: the X direction is the translation direction of the workpiece, the Z direction is consistent with the axial direction of the grinding tool, namely the width direction of the grinding tool, the Y direction is the same as the normal direction of the working table, and the origin of the coordinate system is arranged in the center of the working table; for face grinding, the grinding tool is set at speed vsRotate at a speed vwMoving relative to the workpiece; abrasive grain G at time tjkThe motion trajectory equation of the sphere center in the XYZ coordinate system is as follows:
zc(t)＝Zjk(c)
in the formula, xc(t)、yc(t)、zc(t) is abrasive grain GjkCoordinates of the center of sphere at time t, Z, in XYZ coordinate systemjk、dgjk、hjkRespectively represent abrasive grains GjkThe position coordinates, the grain diameter and the height of the exit edge of the abrasive grains in the axial direction of the abrasive tool; x is the number of0、y0Is the coordinate in XYZ coordinate system of the center of the grinding tool, theta 2lg/ds，lgIs the initial position of the abrasive grain along the circumferential direction of the abrasive tool, lg＝Xjk，dsIs the diameter of the grinding tool, ap、vw、vsIs a grinding parameter, i.e. grinding quantity, where apIs the grinding depth vwIs the workpiece feed speed, vsIs the linear speed of the grinding wheel, t is the processing time;
further coupling the shape of the abrasive particles with the movement locus of the spherical center of the abrasive particles to obtain any abrasive particle G on the surface of the grinding wheeljkEquation of motion at any point (xg, yg, zg):
(xg-xc(t))2+(yg-yc(t))2+(zg-zc(t))2＝(dgjk)2(d)
D. workpiece dispersion: cutting the workpiece into n sections with the distance delta x perpendicular to the translation direction of the workpiece, wherein the distance delta x between the sections multiplied by n represents the length of the workpiece; each section is cut into m vertical lines with the distance delta z, the length of the line segments in the y direction represents the height of the workpiece, and the distance delta z between the line segments multiplied by m represents the width of the workpiece; thus, the workpiece is scattered into n multiplied by m vertical line segments; after discretization, the workpiece can be represented by a two-dimensional array W, the height value of each vertical line is stored, the position of each line segment in the array is represented by subscripts u, v, u represents the position in the X direction, v represents the position in the Z direction, 0 < u < n,0 < v < m; coordinate x of the v-th vertical line on the u-th cross sectionuvAnd zuvExpressed as:
xuv＝u*Δx (e)
zuv＝v*Δz (f)
E. calculating the cutting thickness distribution of the abrasive particles: abrasive grain GjkThe interference depth with the nth vertical line of the u section can be obtained by the following steps:
① reading grain G from the grinding tool numerical modeljkAbrasive grain diameter d ofg jkHeight h of edgejkAbrasive grain axial position coordinate ZjkAnd circumferential initial position coordinate Xjk；
② for equation (a), let xc(t)＝xuvThe value of t is obtained by Newton iteration methodSolving, substituting into equation (b), to obtain yc(t)；
③ processing xc(t)、yc(t)、zc(t) substituting the equations (e) and (f) into the equation (d), and solving; if the equation is not solved, the abrasive grain G is illustratedjkThere is no intersection with the vertical line v; otherwise, solving the equation to obtain
And is compared with the initial height value stored in the workpiece array W
By comparison, if
Description of the abrasive grain GjkAbove the vertical line v, there is no contact with the vertical line v, otherwise, the abrasive grain G is foundjkHeight of vertical line v of cut, i.e. depth of cut
At the same time will
Stored in a temporary array WtIn combination with each other
Replacement of
Then storing in an array W;
④ transforming j and k values, repeating the above ①②③ steps to obtain abrasive grain matrix { G }on the surface of the grinding wheeljk}p×qThe interference depth of all the abrasive particles and all the vertical lines on the plane u is stored in the matrix hmaxG jk}p×qObtaining the cutting thickness distribution of the abrasive particles;
(3) comparing the abrasive particle cutting thickness distribution calculated in the step (2) with the abrasive particle cutting thickness distribution set in the step (1), adjusting the trimming amount if the difference between the abrasive particle cutting thickness distribution and the abrasive particle cutting thickness distribution exceeds a set standard value, and performing the step (2) and the step (3) again until the difference between the abrasive particle cutting thickness distribution calculated in the step (2) and the abrasive particle cutting thickness distribution set in the step (1) is less than the set standard value, stopping calculation, wherein the trimming amount adjusted in the step (2) for the last time is the optimal designed trimming amount;
(4) and (3) dressing the grinding wheel in the step (1) by using the preferred dressing amount.
2. The method of claim 1, wherein the method comprises the following steps: the processing result comprises at least one of grinding efficiency, workpiece surface roughness, grinding force, grinding temperature and grinding workpiece subsurface damage degree.
3. The method of claim 1, wherein the method comprises the following steps: the abrasive particle thickness cutting distribution refers to the depth of each abrasive particle on the surface of the grinding wheel cutting into a workpiece during grinding.
4. The method of claim 1, wherein the method comprises the following steps: the grinding amount comprises grinding speed, grinding depth and feeding speed.
5. The method of claim 1, wherein the method comprises the following steps: the abrasive particle parameters comprise position parameters, height parameters and abrasive particle diameters of abrasive particles on the grinding wheel.
6. A method of designing a controlled dressing amount of a grinding wheel based on a cut-thickness distribution of abrasive grains according to any one of claims 1 to 5, wherein: and (3) setting a standard value, which is used for measuring the coincidence condition of the two curves and comprises one or more of standard deviation, similarity, error, average value and coincidence degree, wherein the value is determined according to actual requirements.
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