CN108188480B - A method for optimal design of abrasive grain parameters for a saw blade with abrasive grain parameterized arrangement - Google Patents

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

A method for optimal design of abrasive grain parameters for a saw blade with abrasive grain parameterized arrangement

technical field

The invention relates to the field of sawing, in particular to a method for optimal design of abrasive grain parameters of a saw blade for parameterized abrasive grain arrangement.

Background technique

Sawing is the main processing method for parts cutting and is an important part of advanced manufacturing technology. The control of the sawing process and the accurate prediction of the machining results are crucial to efficient precision sawing technology. Sawing processing is a processing method in which many abrasive particles realize micro-cutting under the control of binder, and then remove the workpiece material from the macroscopic level. In other words, sawing is the removal of material on the tool at the macro level, and at the micro level, it is actually done by each abrasive grain. Therefore, the cut thickness value per grain has always been a key control quantity for the sawing process and the sawing result.

At present, the industry mainly adopts the maximum undeformed chip thickness of a single abrasive particle as the cutting thickness of each abrasive particle to design the saw blade. However, the existing maximum undeformed chip thickness of a single abrasive grain is based on the ideal assumption that all abrasive grains on the surface of the saw blade are uniformly distributed and have the same size, shape, and cutting edge height. In other words, it is assumed that the cutting amount of each abrasive grain on the saw blade is uniform. However, as we all know, there are many abrasive grains on the surface of the saw blade, and the height, size and shape of the blade are not uniform, that is to say, the cutting thickness of the abrasive grains on the surface of the saw blade is not uniform in actual processing. This is also the fundamental reason why the maximum undeformed chip thickness of a single abrasive particle is often used to control the sawing process, which often deviates greatly from the expected. In fact, the industry has also found that the calculation method of the maximum undeformed chip thickness of a single abrasive particle has a principle assumption defect. Because of this, the industry has also begun to look for a better solution for the cutting thickness of abrasive grains. Professor Markin of the United States simplified the three-dimensional randomness of abrasive particles on the surface of the saw blade into a plane (the plane perpendicular to the axial direction of the saw blade) with uneven distribution of abrasive particles and unequal heights, and then proposed a solution formula for the cutting thickness of abrasive particles in the plane. , but the essence still only considers in-plane (ie, two-dimensional randomness).

To sum up, the existing use of single abrasive grain cutting thickness for saw blade topography design, especially the saw blade surface abrasive grain parameters, is obviously wrong. Therefore, it is very urgent to find a more reasonable design method of saw blade, especially the cutting depth that can be reversed from the machining results and can be closer to the real interference between the abrasive particles and the workpiece.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the problem that it is difficult to optimize the design of abrasive grain parameters on the saw blade surface with processing results as constraints, and to propose a method for optimal design of abrasive grain parameters of a saw blade with an abrasive grain parameterized arrangement.

A method for optimal design of abrasive grain parameters of a saw blade with abrasive grain parameterized arrangement, comprising the following steps:

(1) Set the target abrasive grain thickness distribution according to the processing results, give the set sawing amount, and initialize the abrasive grain parameters on the saw blade surface;

(2) Calculate the thickness distribution of abrasive grains on the surface of the saw blade with the abrasive grain parameters and the amount of sawing, and calculate the cutting depth of each abrasive grain and interference to obtain the thickness distribution of abrasive grains;

(3) Compare the abrasive grain thickness distribution calculated in step (2) with the abrasive grain cutting thickness distribution set in step (1). If the difference between the two is too large, adjust the abrasive grain parameters on the surface of the saw blade, and perform step ( Steps 2) and (3) are cycled until the difference between the abrasive grain thickness distribution calculated in step (2) and the abrasive grain thickness distribution set in step (1) is less than the set standard value, the calculation is stopped, and the last adjusted saw blade The surface abrasive parameters are the optimal design results;

(4) The saw blade is prepared based on the optimal abrasive grain parameters on the surface of the saw blade, and the optimal design saw blade is obtained.

In one embodiment, the thickness distribution of the abrasive particles is the depth of each abrasive particle on the surface of the saw blade cutting into the workpiece during sawing.

In one embodiment, the sawing amount includes sawing speed, sawing depth and feeding speed.

In one embodiment, the abrasive grain parameters include a position parameter, a height parameter, and a grain size of the abrasive grains on the saw blade.

In one embodiment, the set standard described in step (3) is used to measure the coincidence situation of the two curves, including one or more of standard deviation, similarity, error, average value, and coincidence degree, Its value is determined according to actual requirements.

In one embodiment, the calculation of the abrasive particle thickness distribution in step (2) includes the following A, B, C, and D calculation processes:

A. Saw blade modeling: The abrasive particle parameters on the saw blade surface are expressed as a matrix {G _jk } _p×q , p×q means that the matrix is a matrix of p rows and q columns, that is, the saw blade surface has p in the axial direction The combination of row abrasive grains and q columns of abrasive grains in the circumferential direction constitutes the element G _jk that represents the jth row and kth column of abrasive grains on the surface of the saw blade, 0≤i≤p, 0≤k≤q, G _jk ={X ^jk , Z ^jk ,dg ^jk ,h ^jk }; X ^jk represents the position coordinates of the abrasive grains G _jk in the circumferential direction of the saw blade, Z ^jk represents the position coordinates of the abrasive grains G _jk in the axial direction of the saw blade, and the spacing between two adjacent columns is The lateral spacing Δw, the position spacing of two adjacent rows is the tangential spacing ΔX; dg ^jk represents the particle size of the abrasive particles, and h ^jk represents the edge height of the abrasive particles;

B. Calculation of abrasive particle profile trajectory: the coordinate system XYZ is fixed on the worktable, the X direction is the translation direction of the workpiece, the Z direction is consistent with the axial (saw blade width) direction of the saw blade, and the Y direction is the same as the normal direction of the worktable surface. The origin of the coordinate system is placed at the center of the worktable; for plane sawing, the saw blade rotates at a speed v _s and moves relative to the workpiece at a speed v _w ; the motion trajectory equation of the abrasive particle G _jk ball center in the XYZ coordinate system at time t for:

z _c (t)=Z ^jk (c)

In the formula, x _c (t), y _c (t), z _c (t) are the coordinates of the center of the abrasive grain G _jk at time t in the XYZ coordinate system, and Z ^jk , dg ^jk , and h ^jk represent the abrasive grain G, respectively The position coordinates of _jk in the axial direction of the saw blade, the grain size of the abrasive grains and the height of the abrasive grains; , x ₀ , y ₀ are the coordinates in the XYZ coordinate system of the center of the saw blade, θ=2l _g /d _s , and l _g is the grinding wheel The initial position of the grain along the circumferential direction of the saw blade, l _g =X ^jk , d _s is the diameter of the saw blade, a _p , v _w , and v _s are the sawing parameters, that is, the amount of sawing, where a _p is the cutting depth, v _w is the workpiece feed rate, v _s is the linear speed of the saw blade, and t is the processing time.

Further, through the coupling between the shape of the abrasive grain and the trajectory of the center of the abrasive grain, the equation of motion of any point (xg, yg, zg) on any abrasive grain G _jk on the surface of the saw blade is obtained:

(xg-x _c (t)) ² +(yg-y _c (t)) ² +(zg-z _c (t)) ² =(dg ^jk ) ² (d)

C. Discrete workpiece: The workpiece is cut into n sections with a spacing of Δx and perpendicular to the translation direction of the workpiece. The spacing between the sections is multiplied by n to represent the length of the workpiece; each section is cut into m sections with a spacing of Δz. Vertical line, the length of the line segment in the y-direction represents the height of the workpiece, and the spacing between line segments Δz multiplied by m represents the width of the workpiece; in this way, the workpiece is discretized into n×m vertical line segments; after discretization, the workpiece can be used A two-dimensional array W represents, storing the height value of each vertical line, 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; the coordinates x _uv and z _uv of the v-th vertical line on the u-th section are expressed as:

x _uv =u*Δx (e)

z _uv = v*Δz (g)

D. Calculation of abrasive grain thickness distribution: The interference depth between abrasive grain G _jk and the v-th vertical line of the u-th section can be obtained through the following steps:

①Read out the abrasive particle diameter d _g ^jk , the exposed height h ^jk , the axial position coordinate Z ^jk (z _c ) and the circumferential initial position coordinate X ^jk of the abrasive particle G _jk from the numerical model of the saw blade;

②For equation (a), let x _c (t)=x _uv , obtain the numerical solution of t by the Newton iteration method, and substitute it into equation (b) to obtain y _c (t);

并与工件数组W中储存的初始高度值相比较，如果

说明磨粒G_jk在竖直线v的上方，与竖直线v没有接触，否则，求得磨粒G_jk切割竖直线v的高度即切深深度

同时将

储存在临时数组 W_t中，并用

替换

后储存在数组W中；③ Substitute x _c (t), y _c (t), z _c (t) and equations (e) and (f) into equation ( _d ) and solve; The line v has no intersection; otherwise, solve the equation to find

And with the initial height value stored in the workpiece array W In comparison, if

It means that the abrasive grains G _jk are above the vertical line v and have no contact with the vertical line v. Otherwise, the height of the vertical line v of the abrasive grains G _jk is obtained, that is, the depth of cut.

At the same time will

stored in the temporary array W _t , and used

replace

and then stored in the array W;

④Change the values of j and k, and repeat the above ①②③ steps to obtain the interference depth of all abrasive grains in the abrasive grain matrix {G _jk } _p×q on the saw blade surface and all vertical lines on the plane u, and store them in the matrix accordingly. {h _maxG ^jk } _p×q , that is, the cutting thickness distribution of abrasive grains is obtained.

In one embodiment, the initialized saw blade surface abrasive particle parameters are generated by a distribution function, specifically, the abrasive particle size dg ^jk in {G _jk } _p×q is obtained from the abrasive particle size distribution function, and the edge height h ^jk is obtained by the grinding The particle exit height distribution function is obtained, the position coordinates of the abrasive particles are Z ^jk =k·Δw, X ^jk =ΔX·j, α is the angle between the abrasive grain distribution column on the saw blade and the axial direction of the saw blade, and Δw is the abrasive grain on the saw blade. The lateral spacing of ΔX is the tangential spacing of abrasive grains 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 present invention

(1) The thickness distribution of abrasive grains is used to measure the cutting depth of the abrasive grains on the surface of the saw blade into the workpiece during the sawing process. ) to be more accurate, reasonable and effective.

(2) There is no assumption about idealization of the saw blade in the process of solving the method of abrasive grain thickness distribution, and the required thickness distribution is closer to the actual processing process.

(3) Set the target abrasive grain thickness distribution with the processing result as the constraint, and then optimize the abrasive grain parameters on the saw blade surface. The saw blade designed with the optimized parameters can quickly and effectively achieve the expected processing results when used, avoiding the It takes a lot of time, labor, material and financial resources to adjust the process to truly realize intelligent manufacturing.

Description of drawings

The present invention will be further described below with reference to the accompanying drawings and embodiments.

Figure 1 is a distribution diagram of the cut thickness of abrasive grains. Among them, distribution 1 is the target abrasive grain thickness distribution; distribution 2 is an abrasive grain thickness distribution obtained by the calculation process; distribution 3 is the final calculation result.

Figure 2 is a schematic diagram of the position coordinates of the saw blade.

FIG. 3 is a schematic diagram of the interference between the abrasive grains and the workpiece (parallel to the XY plane).

Fig. 4 is a schematic diagram of workpiece dispersion and its interference with abrasive particles (parallel to the XY plane);

Figure 5 shows the thickness of all abrasive grains on the surface of the saw blade calculated in step (2) (one of the calculations)

Figure 6 shows the topography of the saw blade based on the calculation. (a) The manufactured saw blade processing stone (b) The local abrasive grain arrangement of the manufactured saw blade

Detailed ways

Example 1:

In this embodiment, the optimal design of the abrasive grain parameters on the surface of the saw blade is carried out with the goal of obtaining high processing efficiency. The workpiece is G603 granite, and the processing efficiency is 1200m ² /s. The user gives the set sawing amount (sawing speed v _s = 45m/s, feed speed v _w = 6m/min, sawing depth a _p is 10mm).

(1) Set the target abrasive grain thickness distribution according to the processing results, as shown in distribution 1 in Figure 1; the given sawing amount adopts the value given by the user; initialize the abrasive grain parameters on the surface of the saw blade, and the abrasive grain size and the edge height are the same. It is a normal distribution, and its parameters are: particle size N (550, 0.25), blade height N (67, 0.15), Δw=1.5mm, ΔX=3mm.

(2) Calculate the thickness distribution of abrasive particles on the surface of the saw blade and the amount of sawing, and calculate the thickness distribution of abrasive particles; specifically:

A. Saw blade modeling: The abrasive particle parameters on the saw blade surface are expressed as a matrix {G _jk } _p×q , p×q means that the matrix is a matrix of p rows and q columns, that is, the saw blade surface has p in the axial direction The row abrasive grains and the circumferential direction are composed of q columns of abrasive grains. The element G _jk represents the jth row and kth column abrasive grains on the surface of the saw blade, 0≤i≤p, 0≤k≤q, G _jk = {X ^jk , Z ^jk , dg ^jk , h ^jk }; X ^jk represents the position coordinates of the abrasive grains G _jk in the circumferential direction of the saw blade, Z ^jk represents the position coordinates of the abrasive grains G _jk in the axial direction of the saw blade, and the distance between two adjacent columns is the lateral spacing Δw, and the position spacing of two adjacent rows is the tangential spacing ΔX; dg ^jk represents the particle size of the abrasive particles, and h ^jk represents the edge-out height of the abrasive particles;

In the first calculation, the normal distribution function (particle size N(550, 0.25), blade height N(67, 0.15)) is used to initialize the surface abrasive parameters of the saw blade in {G _jk } _p×q . is {G _jk } The abrasive particle size dg ^jk in _p×q is obtained from the abrasive particle size distribution function, the edge height h ^jk is obtained from the abrasive particle edge height distribution function, and the abrasive particle position coordinates Z ^jk = k·Δw, X ^jk = ΔX j, α is the angle between the abrasive grain distribution column on the saw blade and the axial direction of the saw blade, Δw is the lateral distance of the abrasive grains on the saw blade, ΔX is the tangential distance of the abrasive grains on the saw blade, see Figure 2 .

B. Calculation of abrasive particle contour point trajectory: the coordinate system XYZ is fixed on the worktable, the X direction is the translation direction of the workpiece, the Z direction is consistent with the axial (saw blade width) direction of the saw blade, and the Y direction is the same as the normal direction of the worktable surface , the origin of the coordinate system is placed at the center of the worktable; for plane sawing, the saw blade rotates at a speed v _s and moves relative to the workpiece at a speed v _w ; as shown in Figure 3, the center of the abrasive grain G _jk is in the XYZ coordinate system at time t The motion trajectory equation in is:

z _c (t)=Z ^jk (c)

In the formula, x _c (t), y _c (t), z _c (t) are the coordinates of the center of the abrasive grain G _jk at time t in the XYZ coordinate system, and Z ^jk , dg ^jk , and h ^jk represent the abrasive grain G, respectively The position coordinates of _jk in the axial direction of the saw blade, the grain size of the abrasive grains and the height of the abrasive grains; , x ₀ , y ₀ are the coordinates in the XYZ coordinate system of the center of the saw blade, θ=2l _g /d _s , and l _g is the grinding wheel The initial position of the grain along the circumferential direction of the saw blade, l _g =X ^jk , d _s is the diameter of the saw blade, a _p , v _w , and v _s are the sawing parameters, that is, the amount of sawing, where a _p is the cutting depth, v _w is the workpiece feed rate, v _s is the linear speed of the saw blade, and t is the processing time.

Further, through the coupling between the shape of the abrasive grain and the motion trajectory of the abrasive grain center, the equation of motion of any point (xg, yg, zg) on any abrasive grain G _jk on the surface of the saw blade is obtained:

(xg-x _c (t)) ² +(yg-y _c (t)) ² +(zg-z _c (t)) ² =(dg ^jk ) ² (d)

C. Discrete workpiece: As shown in Figure 4, the workpiece is cut into n sections with a spacing of Δx and perpendicular to the translation direction of the workpiece. The spacing between the sections is multiplied by n to represent the length of the workpiece; each section is cut into m strips A vertical line with a spacing of Δz, the length of the line segment in the y-direction represents the height of the workpiece, and the spacing between line segments Δz multiplied by m represents the width of the workpiece; in this way, the workpiece is discretized into n×m vertical line segments; discretization After that, the workpiece can be represented by a two-dimensional array W, which stores the height value of each vertical line. The position of each line segment in the array is represented by subscripts u and v, where u represents the position in the X direction, and v represents the position in the Z direction. , 0<u<n, 0<v<m; the coordinates x _uv and z _uv of the v-th vertical line on the u-th section are expressed as:

x _uv =u*Δx (e)

z _uv = v*Δz (g)

D. Calculation of abrasive grain thickness distribution: The interference depth between abrasive grain G _jk and the v-th vertical line of the u-th section can be obtained through the following steps:

①Read out the abrasive particle diameter d _g ^jk , the exposed height h ^jk , the axial position coordinate Z ^jk (z _c ) and the circumferential initial position coordinate X ^jk of the abrasive particle G _jk from the numerical model of the saw blade;

②For equation (a), let x _c (t)=x _uv , obtain the numerical solution of t by the Newton iteration method, and substitute it into equation (b) to obtain y _c (t);

并与工件数组W中储存的初始高度值相比较，如果

说明磨粒G_jk在竖直线v的上方，与竖直线v没有接触，否则，求得磨粒G_jk切割竖直线v的高度即切深深度

同时将

储存在临时数组W_t中，并用

替换

后储存在数组W中；③ Substitute x _c (t), y _c (t), z _c (t) and equations (e) and (f) into equation ( _d ) and solve; The line v has no intersection; otherwise, solve the equation to find

And with the initial height value stored in the workpiece array W In comparison, if

It means that the abrasive grains G _jk are above the vertical line v and have no contact with the vertical line v. Otherwise, the height of the vertical line v of the abrasive grains G _jk is obtained, that is, the depth of cut.

At the same time will

stored in the temporary array W _t , and used

replace

and then stored in the array W;

④Transform the values of j and k, and repeat the above ①②③ steps to obtain the abrasive grain matrix {G _jk } _p×q on the surface of the saw blade, the interference depth of all abrasive grains and all vertical lines on the plane u, and the corresponding existence matrix {h _maxG ^jk } _p×q , that is, the cutting thickness distribution of abrasive grains is obtained, and its value is shown in a graph as shown in Figure 5, and then the distribution 2 on the cutting thickness distribution of abrasive grains in Figure 1 is obtained.

(3) Compare the abrasive grain thickness distribution calculated in (2) with the target abrasive grain thickness distribution set in (1), if the difference between the two exceeds the set standard value (the set standard used in this embodiment is the error, value is 10%), then adjust the saw blade surface abrasive grain parameter {G _jk } _p×q in step (2), and repeat steps (2) and (3) until the abrasive cut thickness calculated in step (2) is reached. When the difference between the distribution and the target abrasive grain thickness distribution set in (1) is less than 10%, the distribution 3 shown in Figure 1, stop the calculation, at this time the saw blade surface abrasive grain parameter matrix {G _jk } _p×q The median value is the preferred result, shown in Figure 1.

(4) The saw blade is prepared by using the optimal abrasive parameters on the surface of the saw blade to obtain the optimally designed saw blade. As shown in Figure 6, the normal distribution of the abrasive particle size is N(375, 0.15), and the blade height is Weibull distribution. W(2, 0.7, 0.95), Δw=1.7 mm, ΔX=4.5 mm. Using this saw blade and sawing amount (saw cutting speed vs=45m/s, feed speed vf=6m/min, sawing depth is 10mm), G603 granite can be sawed at low cutting force and low In the case of sawing power consumption, the sawing efficiency of 1200m ² /s is easily achieved, and the user is very satisfied.

The above descriptions are only preferred embodiments of the present invention, so the scope of implementation of the present invention cannot be limited accordingly, that is, equivalent changes and modifications made according to the patent scope of the present invention and the contents of the description should still be covered by the present invention. within the range.

Claims (7)

1. A preferred design method for abrasive grain parameters of a saw blade with abrasive grain parameterized arrangement, comprising the following steps: (1) Set the target abrasive grain thickness distribution according to the processing results, give the set sawing amount, and initialize the abrasive grain parameters on the saw blade surface; (2) Calculate the thickness distribution of abrasive particles on the surface of the saw blade and the amount of sawing, and calculate the interference depth between each abrasive particle and the workpiece, which is the depth of each abrasive particle cutting into the workpiece, and obtain the thickness distribution of abrasive particles. ; Wherein, the described abrasive grain thickness distribution calculation includes the following A, B, C, D calculation processes: A. Saw blade modeling: The abrasive particle parameters on the saw blade surface are expressed as a matrix {G _jk } _p×q , p×q means that the matrix is a matrix of p rows and q columns, that is, the saw blade surface has p in the axial direction The row abrasive grains and the circumferential direction are composed of q columns of abrasive grains, that is, the total abrasive grains on the saw blade are p×q; the element G _jk represents the jth row and kth column of the saw blade surface. The abrasive grains, 0≤j≤ p, 0≤k≤q, G _jk = {X ^jk , Z ^jk , dg ^jk , h ^jk }; X ^jk represents the position coordinates of the abrasive grain G _jk in the circumferential direction of the saw blade, and Z ^jk represents the abrasive grain G _jk in the saw blade The position coordinates in the axial direction of the sheet, the spacing between two adjacent columns is the lateral spacing Δw, and the position spacing between two adjacent rows is the tangential spacing ΔX; dg ^jk represents the particle size of the abrasive particles, and h ^jk represents the edge height of the abrasive particles; B. Abrasive particle contour trajectory calculation: The coordinate system XYZ is fixed on the worktable, 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 worktable, and the origin of the coordinate system is placed at The center of the worktable is in the same position; for plane sawing, the saw blade rotates at a speed v _s and moves relative to the workpiece at a speed v _w ; the motion trajectory equation of the center of the abrasive particle G _jk in the XYZ coordinate system at time t is:

z _c (t)=z ^jk (c) In the formula, x _c (t), y _c (t), z _c (t) are the coordinates of the center of the abrasive grain G _jk at time t in the XYZ coordinate system, and Z ^jk , dg ^jk , and h ^jk represent the abrasive grain G, respectively The position coordinates of _jk in the axial direction of the saw blade, the particle size of the abrasive particles and the height of the abrasive particles; x ₀ , y ₀ are the coordinates in the XYZ coordinate system of the center of the saw blade, θ=2l _g /d _s , and l _g is the abrasive particle The initial position along the circumferential direction of the saw blade, l _g =X ^jk , d _s is the diameter of the saw blade, a _p , v _w , and v _s are the sawing parameters, that is, the amount of sawing, where a _p is the cutting depth, v _w is the workpiece feed rate, v _s is the linear speed of the saw blade, and t is the processing time; Further, through the coupling between the shape of the abrasive grain and the trajectory of the center of the abrasive grain, the equation of motion of any point (xg, yg, zg) on any abrasive grain G _jk on the surface of the saw blade is obtained: (xg-x _c (t)) ² +(yg-y _c (t)) ² +(zg-z _c (t)) ² =(dg ^jk ) ² (d) C. Discrete workpiece: The workpiece is cut into n sections with a spacing of Δx and perpendicular to the translation direction of the workpiece. The spacing between the sections is multiplied by n to represent the length of the workpiece; each section is cut into m sections with a spacing of Δz. Vertical line, the length of the line segment in the Y direction represents the height of the workpiece, and the distance between the line segments Δz multiplied by m represents the width of the workpiece; in this way, the workpiece is discretized into n×m vertical line segments; after discretization, the workpiece can be used as a The two-dimensional array W represents, stores the height value of each vertical line, 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; the coordinates x _uv and z _uv of the v-th vertical line on the u-th section are expressed as: x _uv =u*Δx (e) z _uv = v*Δz (g) D. Calculation of abrasive grain thickness distribution: The interference depth between abrasive grain G _jk and the v-th vertical line of the u-th section can be obtained through the following steps: ①Read out the abrasive particle diameter d _g ^jk , the exposed height h ^jk , the axial position coordinate Z ^jk (z _c ) and the circumferential initial position coordinate X ^jk of the abrasive particle G _jk from the numerical model of the saw blade; ②For equation (a), let x _c (t)=x _uv , obtain the numerical solution of t by the Newton iteration method, and substitute it into equation (b) to obtain y _c (t); ③ Substitute x _c (t), y _c (t), z _c (t) and equations (e) and (f) into equation ( _d ) and solve; The line v has no intersection; otherwise, solve the equation to find And with the initial height value stored in the workpiece array W

In comparison, if It means that the abrasive grains G _jk are above the vertical line v and have no contact with the vertical line v. Otherwise, the height of the vertical line v of the abrasive grains G _jk is obtained, that is, the depth of cut.

At the same time will

stored in the temporary array W _t , and used

replace

and then stored in the array W; ④Change the values of j and k, and repeat the above ①②③ steps to obtain the interference depth of all abrasive grains in the abrasive grain matrix {G _jk } _p×q on the saw blade surface and all vertical lines on the plane u, and store them in the matrix accordingly. {h _maxG ^jk } _p×q , that is, the cutting thickness distribution of abrasive grains is obtained; (3) Compare the abrasive grain thickness distribution calculated in step (2) with the abrasive grain cutting thickness distribution set in step (1). If the difference between the two is too large, adjust the abrasive grain parameters on the surface of the saw blade, and perform step ( Steps 2) and (3) are cycled until the difference between the abrasive grain thickness distribution calculated in step (2) and the abrasive grain thickness distribution set in step (1) is less than the set standard value, the calculation is stopped, and the last adjusted saw blade The surface abrasive parameters are the optimal design results; (4) The saw blade is prepared based on the optimal abrasive grain parameters on the surface of the saw blade, and the optimal design saw blade is obtained. 2. A kind of optimal design method of abrasive grain parameters of a kind of abrasive grain parameterized arrangement saw blade as claimed in claim 1, it is characterized in that: described abrasive grain thickness distribution is that each grain of saw blade surface grinds during sawing processing The grains are cut into the workpiece depth. 3 . The optimal design method for abrasive particle parameters of a saw blade with an abrasive particle parameterized arrangement according to claim 1 , wherein the sawing amount includes sawing speed, sawing depth and feed speed. 4 . 4. The optimal design method for abrasive grain parameters of a saw blade with abrasive grain parameterized arrangement as claimed in claim 1, characterized in that: the abrasive grain parameters include position parameters and height parameters of abrasive grains on the saw blade. , Abrasive particle size, the position parameters include tangential position parameters and transverse position parameters. 5. The optimal design method for abrasive grain parameters of a saw blade with an abrasive grain parameterized arrangement according to any one of claims 1 to 4, characterized in that: the setting standard described in step (3) is used for Measure the coincidence of two curves, including one or more of standard deviation, similarity, error, average, and coincidence, and the value is determined according to actual requirements. 6 . The optimal design method for abrasive grain parameters of a saw blade with an abrasive grain parameterized arrangement according to claim 1 , wherein the initialized saw blade surface abrasive grain parameters are generated by a distribution function, {G _jk } _p×q The abrasive particle size dg ^jk is obtained from the abrasive particle size distribution function, the edge height h ^jk is obtained from the abrasive particle edge height distribution function, and the abrasive position coordinates Z ^jk = k · Δw, X ^jk = ΔX · j, α is The angle between the abrasive grain distribution column on the saw blade and the axial direction of the saw blade, Δw is the lateral spacing of the abrasive grains on the saw blade, and ΔX is the tangential spacing of the abrasive grains on the saw blade. 7. The optimal design method for abrasive particle parameters of a saw blade with an abrasive particle parameterized arrangement according to claim 6, wherein the distribution function comprises Weibull distribution function, skewed distribution function, Rayleigh distribution At least one of a function, an exponential distribution function, a polynomial distribution function, and a normal distribution function.

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