CN108188480B - Abrasive particle parameter optimization design method for saw blade with abrasive particle parametric arrangement - Google Patents

Abrasive particle parameter optimization design method for saw blade with abrasive particle parametric arrangement Download PDF

Info

Publication number
CN108188480B
CN108188480B CN201810046403.8A CN201810046403A CN108188480B CN 108188480 B CN108188480 B CN 108188480B CN 201810046403 A CN201810046403 A CN 201810046403A CN 108188480 B CN108188480 B CN 108188480B
Authority
CN
China
Prior art keywords
saw blade
abrasive
abrasive particle
parameters
workpiece
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201810046403.8A
Other languages
Chinese (zh)
Other versions
CN108188480A (en
Inventor
黄国钦
崔长彩
尹方辰
方从富
黄辉
徐西鹏
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Huaqiao University
Original Assignee
Huaqiao University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Huaqiao University filed Critical Huaqiao University
Priority to CN201810046403.8A priority Critical patent/CN108188480B/en
Publication of CN108188480A publication Critical patent/CN108188480A/en
Application granted granted Critical
Publication of CN108188480B publication Critical patent/CN108188480B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23D—PLANING; SLOTTING; SHEARING; BROACHING; SAWING; FILING; SCRAPING; LIKE OPERATIONS FOR WORKING METAL BY REMOVING MATERIAL, NOT OTHERWISE PROVIDED FOR
    • B23D61/00—Tools for sawing machines or sawing devices; Clamping devices for these tools
    • B23D61/02—Circular saw blades
    • B23D61/028—Circular saw blades of special material
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23D—PLANING; SLOTTING; SHEARING; BROACHING; SAWING; FILING; SCRAPING; LIKE OPERATIONS FOR WORKING METAL BY REMOVING MATERIAL, NOT OTHERWISE PROVIDED FOR
    • B23D65/00—Making tools for sawing machines or sawing devices for use in cutting any kind of material
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Mechanical Engineering (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • General Engineering & Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Polishing Bodies And Polishing Tools (AREA)

Abstract

The invention discloses a method for optimally designing abrasive particle parameters of a saw blade with parameterized abrasive particle arrangement, which comprises the following steps of: (1) setting abrasive particle cutting thickness distribution according to a processing result, giving a set sawing amount, and initializing saw blade surface abrasive particle parameters; (2) calculating the abrasive particle cutting thickness distribution of the saw blade surface abrasive particle parameters and the saw cutting amount, and calculating the abrasive particle cutting thickness distribution; (3) and (3) comparing the abrasive particle cutting thickness distribution calculated in the step (2) with the target abrasive particle cutting thickness distribution set in the step (1), if the difference between the abrasive particle cutting thickness distribution and the target abrasive particle cutting thickness distribution is too large, adjusting the sawing amount of the abrasive particles, and repeating the steps (2) and (3) until the difference between the abrasive particle cutting thickness distribution calculated in the step (3) and the abrasive particle cutting thickness distribution set in the step (1) meets a set standard, and stopping calculation, wherein the abrasive particle parameters on the surface of the saw blade are the optimal results. (4) Saw blade preparation is performed based on the preferred result saw blade abrasive grain parameters. The saw blade is adopted for processing, and the expected processing purpose can be effectively achieved.

Description

Abrasive particle parameter optimization design method for saw blade with abrasive particle parametric arrangement
Technical Field
The invention relates to the field of saw cutting, in particular to a method for optimally designing abrasive particle parameters of a saw blade with parameterized abrasive particle arrangement.
Background
Sawing is the main processing means for cutting parts and is an important component of advanced manufacturing technology. The control of the sawing process and the accurate prediction of the processing result are of great importance to the efficient precision sawing processing technology. The sawing process is a processing mode in which a plurality of abrasive particles respectively realize micro-cutting under the holding of a bonding agent, and further macroscopically remove workpiece materials. In other words, the sawing process is a macro-level removal of material from the tool, which is actually done microscopically by cutting each abrasive particle. Therefore, the cutting thickness value of each abrasive particle is always a key control quantity of the sawing process and the sawing result.
Currently, the maximum undeformed chip thickness of a single abrasive grain is mainly adopted by the industry as the cutting thickness of each abrasive grain for designing the saw blade. However, the maximum undeformed chip thickness of a single abrasive grain is assumed to be based on an ideal state that all abrasive grains on the surface of the saw blade are uniformly distributed and have consistent size, shape and edge-projecting height. In other words, it is assumed that the amount of cut per abrasive particle on the saw blade is uniform. However, it is known that there are many abrasive grains on the surface of the saw blade and the height, size and shape of the edge of the saw blade are not uniform, that is, the cutting thickness of the abrasive grains on the surface of the saw blade is not uniform in the actual machining process. This is also the root cause of the large deviation from expectations that are often encountered when controlling the sawing process with maximum undeformed chip thickness of a single abrasive grain. In fact, the industry has also found that the method for calculating the maximum undeformed chip thickness of a single abrasive grain has the principle assumption defect. Also because of this, the industry has also begun to find better solutions for the cut thickness of the abrasive particles. The American Markin teaches that the three-dimensional randomness of the abrasive particles on the surface of the saw blade is simplified into the non-uniform and unequal abrasive particle distribution in the plane (the plane vertical to the axial direction of the saw blade), and further, a solving formula of the cutting thickness of the abrasive particles in the plane is provided, but the essence is only to consider the plane (namely, the two-dimensional randomness).
In summary, the existing saw blade shape design using the cutting thickness of single abrasive particle, especially the parameters of the abrasive particle on the surface of the saw blade, are obviously not correct. Therefore, it is particularly urgent to find a more reasonable saw blade design method, and particularly, to find a method that can perform a reverse-thrust design from a machining result and can more closely approach the actual interference cutting depth of the abrasive particles and the workpiece.
Disclosure of Invention
The invention aims to solve the problem that the optimization design of the parameters of the abrasive particles on the surface of the saw blade cannot be carried out by taking a machining result as a constraint at present, and provides a method for optimizing and designing the parameters of the abrasive particles of the saw blade with parameterized abrasive particles.
A method for optimally designing abrasive particle parameters of a saw blade with parameterized abrasive particle arrangement comprises the following steps:
(1) setting target abrasive particle cutting thickness distribution according to a machining result, giving a set sawing amount, and initializing saw blade surface abrasive particle parameters;
(2) calculating the abrasive particle cutting thickness distribution of the abrasive particle parameters on the surface of the saw blade and the sawing amount, and calculating the cutting depth of each abrasive particle and the interference to obtain the abrasive particle 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), if the difference between the abrasive particle cutting thickness distribution and the abrasive particle cutting thickness distribution is too large, adjusting the parameters of the abrasive particles on the surface of the saw blade, and repeating the steps (2) and (3) 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 smaller than a set standard value, stopping calculation, wherein the parameters of the abrasive particles on the surface of the saw blade adjusted for the last time are the optimal design result;
(4) and preparing the saw blade according to the optimal saw blade surface abrasive grain parameters to obtain the optimal design saw blade.
In one embodiment, the abrasive grain thickness cut distribution is the depth each abrasive grain on the saw blade surface cuts into the workpiece during the sawing process.
In one embodiment, the sawing dosage includes a sawing speed, a sawing depth and a feeding speed.
In one embodiment, the abrasive particle parameters include a position parameter of the abrasive particles on the saw blade, a height parameter, and an abrasive particle size.
In an embodiment, the setting criterion in step (3) is used to measure the coincidence condition of the two curves, and includes one or more of standard deviation, similarity, error, average value, and coincidence degree, and the value of the setting criterion is determined according to actual requirements.
In one embodiment, the abrasive grain cut thickness distribution calculation of step (2) includes the following A, B, C, D calculation process:
A. modeling a saw blade: the abrasive grain parameters of the saw blade surface are expressed as a matrix Gjk}p×qThe p x q matrix is a matrix with p rows and q columns, namely the surface of the saw blade is composed of elements G formed by combining p rows of abrasive particles in the axial direction and q columns of abrasive particles in the circumferential directionjkI 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 GjkOn sawPosition coordinate of the sheet in the circumferential direction, ZjkDenotes abrasive grain GjkIn the position coordinates of the axial direction of the saw blade, the distance between two adjacent rows is a transverse distance delta w, and the position distance between two adjacent rows is a tangential distance delta X; dg andjkdenotes the particle diameter of the abrasive grains, hjkRepresenting the exit edge height of the abrasive particles; (ii) a
B. 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 (saw blade width) of the saw blade, 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 flat sawing, the saw blade is moved at a 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 grain outlet edge height of the saw blade in the axial direction are determined; x is0、y0Is a coordinate in an XYZ coordinate system of the center of the saw blade, and theta is 2lg/ds，lgIs the initial position of the abrasive particles in the circumferential direction of the saw blade, lg＝Xjk，dsIs the diameter of the saw blade, ap、 vw、vsIs a sawing parameter, i.e. sawing dosage, where apIs the sawing depth vwIs the workpiece feed speed, vsIs the sawing blade linear speed, t is the processing time.
Further coupling the shape of the abrasive particles with the movement track of the spherical center of the abrasive particles to obtain the saw blade surface saw bladeYiyike abrasive grain GjkEquation 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: 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 (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 the grain G from the numerical model of the saw bladejkAbrasive 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
Figure GDA0002300570400000031
And is compared with the initial height value stored in the workpiece array WBy comparison, if
Figure GDA0002300570400000033
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
Figure GDA0002300570400000034
At the same time will
Figure GDA0002300570400000035
Stored in a temporary array WtIn combination with each other
Figure GDA0002300570400000036
Replacement of
Figure GDA0002300570400000037
Then storing in an array W;
④ changing the j and k values, repeating the above ①②③ steps to obtain the saw blade surface abrasive grain matrix { G }jk}p×qThe interference depth of all the abrasive particles and all the vertical lines on the plane u is correspondingly stored in the matrix hmaxG jk}p×qAnd obtaining the cutting thickness distribution of the abrasive particles.
In one embodiment, the initialized blade surface abrasive grain parameters are generated by a distribution function, specifically { G }jk}p×qAbrasive grain diameter dg ofjkThe height h of the edge is obtained from the distribution function of the grain diameter of the abrasive grainsjkFrom the distribution function of the height of the edge of the abrasive grain, the position coordinate Z of the abrasive grainjk＝k·Δw，XjkAnd alpha is an included angle between the distribution row of the abrasive particles on the saw blade and the axial direction of the saw blade, delta w is the transverse spacing of the abrasive particles on the saw blade, and delta X is the tangential spacing of the abrasive particles on the saw blade.
In one embodiment, the distribution function includes at least one of a weibull distribution function, a skewed distribution function, a rayleigh distribution function, an exponential distribution function, a polynomial distribution function, and a normal distribution function.
Advantages of the invention
(1) The depth of the abrasive particles on the surface of the saw blade cutting and cutting into a workpiece in the sawing process is measured by adopting abrasive particle cutting thickness distribution, and the method is more accurate, reasonable and effective than the method of using one abrasive particle cutting thickness value (the maximum cutting thickness of a single abrasive particle) after adopting an ideal assumption in the prior art.
(2) The method for solving the cutting thickness distribution of the abrasive particles does not assume the ideal situation of the saw blade, and the like, and the required cutting thickness distribution can be closer to the actual processing process.
(3) The target abrasive particle thickness cutting distribution is set by taking the machining result as constraint, and then the parameters of the abrasive particles on the surface of the saw blade are optimized, so that the saw blade designed by the optimized parameters can quickly and effectively reach the expected machining result when in use, a large amount of time, labor, material resources, financial resources and the like consumed by adjusting the 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 saw blade.
FIG. 3 is a schematic representation of the interference of abrasive particles with a workpiece (parallel to the XY plane).
FIG. 4 is a schematic view of workpiece dispersion and its interference with abrasive particles (parallel to the XY plane);
FIG. 5 shows the calculated thickness of all the abrasive grains on the surface of the saw blade in step (2) (one calculation thereof)
Fig. 6 shows the blade profile according to the calculation. (a) Saw blade processing stone (b) made local abrasive grain arrangement indication
Detailed Description
The first embodiment is as follows:
in this embodiment, the saw blade surface is performed with the aim of obtaining high machining efficiencyAnd (5) optimally designing abrasive particle parameters. The workpiece is G603 granite, and the processing efficiency is 1200m2And s. The user gives the set sawing quality (sawing speed v)sAt 45m/s, feed speed vw6m/min, sawing depth ap10 mm).
(1) Setting a target abrasive grain cut thickness distribution according to the processing result, as shown in distribution 1 of fig. 1; setting the sawing amount by adopting a user set value; initializing saw blade surface abrasive particle parameters, wherein the abrasive particle size and the blade height are normally distributed, and the parameters are as follows: particle size N (550,0.25), land height N (67,0.15), Δ w ═ 1.5mm, Δ X ═ 3mm.
(2) Calculating the abrasive particle cutting thickness distribution of the saw blade surface abrasive particle parameters and the saw cutting amount, and calculating the abrasive particle cutting thickness distribution; the method comprises the following steps:
A. modeling a saw blade: the abrasive grain parameters of the saw blade surface are expressed as a matrix Gjk}p×qP × q means that the matrix is a p-row and q-column matrix, i.e., the surface of the saw blade is composed of a combination of p rows of abrasive grains in the axial direction and q columns of abrasive grains in the circumferential direction, 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 saw blade, ZjkDenotes abrasive grain GjkIn the position coordinates of the axial direction of the saw blade, the distance between two adjacent rows is a transverse distance delta w, and the position distance between two adjacent rows is a tangential distance delta X; dg andjkdenotes the particle diameter of the abrasive grains, hjkIndicating the height of the edge of the abrasive grain;
in the first calculation, a normal distribution function (particle size N (550,0.25) and edge height N (67, 0.15)) was used for { G }jk}p×qIn the saw blade surface abrasive grain parameter initialization, specifically { Gjk}p×qAbrasive grain diameter dg ofjkThe height h of the edge is obtained from the distribution function of the grain diameter of the abrasive grainsjkFrom the distribution function of the height of the edge of the abrasive grain, the position coordinate Z of the abrasive grainjk＝k·Δw，XjkAlpha is the included angle between the abrasive grain distribution row on the saw blade and the axial direction of the saw blade, delta w is the transverse spacing of the abrasive grains on the saw blade,Δ X is the tangential spacing of the abrasive particles on the saw blade, see FIG. 2.
B. Calculating the trace of the abrasive particle contour point, namely fixing a coordinate system XYZ on a working table, wherein the X direction is the translation direction of a workpiece, the Z direction is consistent with the axial direction (saw blade width) direction of a saw blade, 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 flat sawing, the saw blade is moved at a speed vsRotate at a speed vwMoving relative to the workpiece; referring to FIG. 3, abrasive grain G at time tjkThe motion trajectory equation of the sphere center in the XYZ coordinate system is as follows:
Figure GDA0002300570400000051
Figure GDA0002300570400000052
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 grain outlet edge height of the saw blade in the axial direction are determined; x is0、y0Is a coordinate in an XYZ coordinate system of the center of the saw blade, and theta is 2lg/ds，lgIs the initial position of the abrasive particles in the circumferential direction of the saw blade, lg＝Xjk，dsIs the diameter of the saw blade, ap、 vw、vsIs a sawing parameter, i.e. sawing dosage, where apIs the sawing depth vwIs the workpiece feed speed, vsIs the sawing blade linear speed, t is the processing time.
Further coupling the shape of the abrasive particles with the movement track of the spherical center of the abrasive particles to obtain any abrasive particle G on the surface of the saw bladejkEquation 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. 4, 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 the grain G from the numerical model of the saw bladejkAbrasive 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
Figure GDA0002300570400000061
And is compared with the initial height value stored in the workpiece array WCompared withIf, if
Figure GDA0002300570400000063
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
Figure GDA0002300570400000064
At the same time will
Figure GDA0002300570400000065
Stored in a temporary array WtIn combination with each other
Figure GDA0002300570400000066
Replacement of
Figure GDA0002300570400000067
Then storing in an array W;
④ transforming j and k values, repeating the above ①②③ steps to obtain the matrix G of the abrasive grains on the surface of the saw bladejk}p×qThe depth of interference of all abrasive particles in (c) with all vertical lines on the plane u, and the corresponding existence matrix { h }maxG jk}p×qThe distribution of the cut thickness of the abrasive grains is obtained, and the values are graphically shown in FIG. 5, thereby obtaining a distribution 2 on the distribution diagram 1 of the cut thickness of the abrasive grains.
(3) Comparing the calculated abrasive grain cutting thickness distribution (2) with the target abrasive grain cutting thickness distribution (1), and if the difference between the calculated abrasive grain cutting thickness distribution and the target abrasive grain cutting thickness distribution exceeds a set standard value (the set standard used in the embodiment is an error, and the value is 10%), adjusting the abrasive grain parameter { G on the surface of the saw blade in the step (2) }jk}p×qAnd (3) repeating the steps (2) and (3) until 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 less than 10%, stopping calculating the distribution (3) shown in the figure 1, and at the moment, stopping calculating the abrasive grain parameter matrix { G on the surface of the saw bladejk}p×qThe preferred results are given as median values, shown in FIG. 1.
(4) Saw blade preparation using preferred saw blade surface abrasive grain parameters to obtain a saw blade of preferred design, as shown in FIG. 6The normal distribution N (375,0.15) and the edge height of the abrasive grains are weibull distribution W (2, 0.7,0.95), Δ W is 1.7mm, and Δ X is 4.5mm. By adopting the saw blade and the sawing consumption (sawing speed vs is 45m/s, feeding speed vf is 6m/min and sawing depth is 10mm), G603 granite is sawed, the sawing efficiency can be easily achieved to 1200m under the condition of low sawing force and low sawing power consumption2And/s, the user is very satisfied.
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 (7)

1. A method for optimally designing abrasive particle parameters of a saw blade with parameterized abrasive particle arrangement comprises the following steps:
(1) setting target abrasive particle cutting thickness distribution according to a machining result, giving a set sawing amount, and initializing saw blade surface abrasive particle parameters;
(2) calculating the abrasive particle cutting thickness distribution of the abrasive particle parameters on the surface of the saw blade and the sawing amount, and calculating the interference depth between each abrasive particle and the workpiece, namely the depth of each abrasive particle in cutting into the workpiece to obtain the abrasive particle cutting thickness distribution; wherein, the calculation of the abrasive particle cutting thickness distribution comprises the following A, B, C, D calculation processes:
A. modeling a saw blade: the abrasive grain parameters of the saw blade surface are expressed as a matrix Gjk}p×qThe p × q matrix is a matrix with p rows and q columns, namely the surface of the saw blade is formed by combining abrasive grains with p rows in the axial direction and abrasive grains with q columns in the circumferential direction, namely the total abrasive grains on the saw blade are p × q; 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, Gjk＝{Xjk,Zjk,dgjk,hjk}；XjkDenotes abrasive grain GjkPosition coordinate in the circumferential direction of the saw blade, ZjkDenotes abrasive grain GjkIn the position coordinates of the axial direction of the saw blade, the distance between two adjacent rows is a transverse distance delta w, and the position distance between two adjacent rows is a tangential distance delta X; dg andjkdenotes the particle diameter of the abrasive grains, hjkRepresenting the exit edge height of the abrasive particles;
B. 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 saw blade, 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 flat sawing, the saw blade is moved at a 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:
Figure FDA0002302273950000011
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 grain outlet edge height of the saw blade in the axial direction are determined; x is the number of0、y0Is a coordinate in an XYZ coordinate system of the center of the saw blade, and theta is 2lg/ds，lgIs the initial position of the abrasive particles in the circumferential direction of the saw blade, lg＝Xjk，dsIs the diameter of the saw blade, ap、vw、vsIs a sawing parameter, i.e. sawing dosage, where apIs the sawing depth vwIs the workpiece feed speed, vsThe linear speed of a saw blade is saw cutting, and t is processing time;
further coupling the shape of the abrasive particles with the movement track of the spherical center of the abrasive particles to obtain any abrasive particle G on the surface of the saw bladejkEquation 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: 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 (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 the grain G from the numerical model of the saw bladejkAbrasive 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 obtainAnd is compared with the initial height value stored in the workpiece array W
Figure FDA0002302273950000022
By comparison, ifDescription 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
Figure FDA0002302273950000024
At the same time will
Figure FDA0002302273950000025
Stored in a temporary array WtIn combination with each other
Figure FDA0002302273950000026
Replacement of
Figure FDA0002302273950000027
Then storing in an array W;
④ changing the j and k values, repeating the above ①②③ steps to obtain the saw blade surface abrasive grain matrix { G }jk}p×qThe interference depth of all the abrasive particles and all the vertical lines on the plane u is correspondingly 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), if the difference between the abrasive particle cutting thickness distribution and the abrasive particle cutting thickness distribution is too large, adjusting the parameters of the abrasive particles on the surface of the saw blade, and repeating the steps (2) and (3) 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 smaller than a set standard value, stopping calculation, wherein the parameters of the abrasive particles on the surface of the saw blade adjusted for the last time are the optimal design result;
(4) and preparing the saw blade according to the optimal saw blade surface abrasive grain parameters to obtain the optimal design saw blade.
2. The method for optimally designing the abrasive grain parameters of the abrasive grain parametric configuration saw blade as claimed in claim 1, wherein: the abrasive particle thickness cutting distribution is the depth of each abrasive particle on the surface of the saw blade cutting into a workpiece during sawing.
3. The method for optimally designing the abrasive grain parameters of the abrasive grain parametric configuration saw blade as claimed in claim 1, wherein: the sawing dosage comprises sawing speed, sawing depth and feeding speed.
4. The method for optimally designing the abrasive grain parameters of the abrasive grain parametric configuration saw blade as claimed in claim 1, wherein: the abrasive particle parameters comprise position parameters of abrasive particles on the saw blade, height parameters and abrasive particle diameters, and the position parameters comprise tangential position parameters and transverse position parameters.
5. The method for designing the abrasive grain parameter of the parameterized saw blade according to any one of claims 1 to 4, wherein: the set standard in the step (3) 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, and the value of the set standard is determined according to actual requirements.
6. The method of claim 1, wherein the initial saw blade surface abrasive grain parameters are generated by a distribution function, { Gjk}p×qAbrasive grain diameter dg ofjkThe height h of the edge is obtained from the distribution function of the grain diameter of the abrasive grainsjkFrom the distribution function of the height of the edge of the abrasive grain, the position coordinate Z of the abrasive grainjk＝k·Δw，XjkAnd alpha is an included angle between the distribution row of the abrasive particles on the saw blade and the axial direction of the saw blade, delta w is the transverse spacing of the abrasive particles on the saw blade, and delta X is the tangential spacing of the abrasive particles on the saw blade.
7. The method of claim 6, wherein the distribution function comprises at least one of a weibull distribution function, a skewed distribution function, a rayleigh distribution function, an exponential distribution function, a polynomial distribution function, and a normal distribution function.
CN201810046403.8A 2018-01-17 2018-01-17 Abrasive particle parameter optimization design method for saw blade with abrasive particle parametric arrangement Active CN108188480B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810046403.8A CN108188480B (en) 2018-01-17 2018-01-17 Abrasive particle parameter optimization design method for saw blade with abrasive particle parametric arrangement

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810046403.8A CN108188480B (en) 2018-01-17 2018-01-17 Abrasive particle parameter optimization design method for saw blade with abrasive particle parametric arrangement

Publications (2)

Publication Number Publication Date
CN108188480A CN108188480A (en) 2018-06-22
CN108188480B true CN108188480B (en) 2020-01-17

Family

ID=62590067

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810046403.8A Active CN108188480B (en) 2018-01-17 2018-01-17 Abrasive particle parameter optimization design method for saw blade with abrasive particle parametric arrangement

Country Status (1)

Country Link
CN (1) CN108188480B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108247554A (en) * 2018-01-17 2018-07-06 华侨大学 A kind of wheel face abrasive grain parameter preferred design method that thick distribution constraint is cut based on abrasive grain

Family Cites Families (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0342528A3 (en) * 1988-05-19 1991-04-17 Fortuna-Werke Maschinenfabrik GmbH Method of grinding the cams of a camshaft
CN1281377C (en) * 2003-10-15 2006-10-25 南京航空航天大学 Technological method of single-layer soldered diamond consolidated abrasive tool with optimized configuration
TWI321503B (en) * 2007-06-15 2010-03-11 Univ Nat Taiwan Science Tech The analytical method of the effective polishing frequency and number of times towards the polishing pads having different grooves and profiles
CN102773808B (en) * 2012-07-16 2015-03-25 南京航空航天大学 Optimization method for topography of soldering diamond-impregnated grinding wheel of high-speed railway track plate
CN106272118B (en) * 2016-10-13 2018-09-18 江苏理工学院 Ultrasonic vibration aided grinding grinding wheel abrasive grain placement strategy and abrasive grain cut thick method for establishing model
CN108247554A (en) * 2018-01-17 2018-07-06 华侨大学 A kind of wheel face abrasive grain parameter preferred design method that thick distribution constraint is cut based on abrasive grain

Also Published As

Publication number Publication date
CN108188480A (en) 2018-06-22

Similar Documents

Publication Publication Date Title
Zhang et al. Modeling and simulation of the distribution of undeformed chip thicknesses in surface grinding
CN108214307B (en) Grinding wheel dressing amount optimal selection design method based on abrasive particle thickness cutting distribution control
Darafon et al. 3D metal removal simulation to determine uncut chip thickness, contact length, and surface finish in grinding
CN108247434B (en) Abrasive particle cutting thickness distribution solving method and use method thereof in grinding process design
CN112276683B (en) Method for predicting surface appearance of abrasive belt grinding screw curved surface
CN107451382B (en) Control method for surface appearance of high-speed cutting workpiece
Fang et al. Study on geometrical patterns of textured fixed-abrasive pads in sapphire lapping based on trajectory analysis
CN108188480B (en) Abrasive particle parameter optimization design method for saw blade with abrasive particle parametric arrangement
Novoselov et al. Patterns of removing material in workpiece-grinding wheel contact area
Chen et al. Kinematic simulation of surface grinding process with random cBN grain model
Cai et al. Dynamic grinding force model for carbide insert peripheral grinding based on grain element method
Fomin Microgeometry of surfaces after profile milling with the use of automatic cutting control system
CN108897955A (en) A kind of high speed internal screw thread grinding force calculation method considering lead angle and abrasive grain overlap coefficient
Bagaber et al. Sustainable optimization of dry turning of stainless steel based on energy consumption and machining cost
Wang et al. Simulation and experimental study of the ground surface topography of GH4169 by grains arrayed brazed diamond wheels
CN108334673B (en) Grinding consumption design method based on abrasive particle cutting thickness distribution constraint
Uhlmann et al. Increasing the productivity and quality of flute grinding processes through the use of layered grinding wheels
Rabiey et al. Simulation of workpiece surface roughness after flat grinding by electroplated wheel
CN108247554A (en) A kind of wheel face abrasive grain parameter preferred design method that thick distribution constraint is cut based on abrasive grain
Dittrich et al. Parametric grinding wheel model for material removal simulation of tool grinding processes
CN108573091B (en) Method for designing waveform edge of cutter
CN107953258B (en) Method for predicting maximum thickness of undeformed chips in grinding
CN113656903B (en) Evaluation and control method for cutting residual stress of diamond abrasive particles
CN106670991B (en) A kind of pattern preferred method of concretion abrasive phyllotaxy abrasive disk
Pralea et al. Study of the Milling Tools When Machining X37CrMoV5-1 after Heat Treatment

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant