A Precision Trimming Method for Arc-shaped Electroplated CBN Grinding Wheels

Abstract

The invention discloses a dressing method for an arc-shaped electroplated CBN grinding wheel. On a numerically controlled optical curve grinding machine, the radius value of the tool grinding wheel and the contour parameters of the tool grinding wheel are detected by the "copying carbon sheet method", and the collected data is imported into and processed using Matlab software to calculate the coordinates of each point on the arc part of the copying carbon sheet and the angle between each point and the X-axis, thus completing the detection, collection and data processing of the key parameters of the tool grinding wheel. According to the detected contour parameters of the diamond grinding wheel, the numerical control dressing program of the arc-shaped electroplated CBN grinding wheel is optimized, so as to avoid affecting the dressing accuracy of the arc-shaped electroplated CBN grinding wheel due to poor contour accuracy of the tool grinding wheel, and finally realize the batch precision dressing and processing of the arc-shaped electroplated CBN grinding wheel.

Description

Technical Field

[0001] The present invention belongs to the technical field of superhard grinding wheel dressing, and particularly relates to a precise dressing method for an arc-shaped electroplated CBN grinding wheel. Background Art

[0002] An electroplated CBN grinding wheel generally refers to a grinding wheel working layer manufactured by electroplating CBN abrasive grains and matrix metal together on a steel substrate. Compared with superhard material grinding wheels such as resin, ceramic, and sintered metal bond grinding wheels, the working layer of the electroplated CBN grinding wheel is a single-layer abrasive, which has advantages such as strong holding force of the bond for the abrasive grains, high exposure of the abrasive grains, and large chip space in the grinding wheel. With the development of numerical control technology, the steel substrate can be made into various complex curved surfaces, that is, the working layer of the electroplated CBN grinding wheel can be made into various complex profiles, so it is widely used in profile grinding. However, with the improvement of the requirements for forming processing accuracy, the problems of poor consistency in the exposed height of the single-layer electroplated grinding wheel abrasive grains and poor initial profile after plating are becoming increasingly prominent. Therefore, precise electroplated grinding wheels used in fields such as automotive engines, aviation blades, and robots must be dressed.

[0003] For arc-shaped CBN grinding wheels, currently effective dressing methods include: diamond grinding wheel dressing by face grinding, cup wheel dressing, electrical discharge dressing, in-line electrolytic dressing, green silicon carbide grinding stone dressing by face grinding, laser dressing, etc. Although the diamond grinding wheel dressing by face grinding method can achieve the dressing of arc-shaped electroplated CBN grinding wheels, the accuracy of the diamond grinding wheel will seriously affect the accuracy of the electroplated CBN grinding wheel after dressing, and it is difficult to achieve batch precise dressing processing of arc-shaped electroplated CBN grinding wheels; the electroplated CBN grinding wheel has only a single-layer abrasive, and the cup wheel dressing method, electrical discharge dressing method, and in-line electrolytic dressing method are prone to excessive dressing, seriously affecting the service life of the grinding wheel; the green silicon carbide grinding stone dressing by face grinding method has a low dressing efficiency and is not suitable for batch dressing of arc-shaped precise electroplated CBN grinding wheels; although the laser dressing method has a high efficiency, it is difficult to stably achieve a micron-level dressing accuracy, and it is difficult to achieve batch precise dressing of arc-shaped electroplated CBN grinding wheels. Summary of the Invention

[0004] The purpose of the present invention is to address the deficiencies of the above-mentioned existing technologies and provide a precise dressing method for an arc-shaped electroplated CBN grinding wheel, optimize the numerical control dressing program of the arc-shaped electroplated CBN grinding wheel, and achieve batch precise dressing processing of the arc-shaped electroplated CBN grinding wheel.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is:

[0006] A precise dressing method for an arc-shaped electroplated CBN grinding wheel includes the following steps:

[0007] (1) The tool grinding wheel cuts in for grinding and copies the carbon sheet

[0008] On an optical curve grinder, a circular arc diamond grinding wheel is used as a tool grinding wheel and the copy carbon sheet is ground;

[0009] (2) Carbon film detection

[0010] Use a profilometer to detect the copied carbon sheet after grinding, select the arc part of the copied carbon sheet, measure the arc radius size R of the tool grinding wheel, and export the detected data from the profilometer;

[0011] (3) Data processing

[0012] The detection data obtained in step (2) is imported into the software, and each point of the carbon sheet contour is recorded as a point set P0 = {x n ,y n}, intercept the straight line part in the point set P0 and perform the straightening operation, and record it as point set P1 = {x m ,y m}, where m and n are both natural numbers;

[0013] Take the lowest point on the contour of the carbon sheet as the origin O to establish a coordinate system, intercept the arc part in the point set P1 for fitting operation, and calculate the coordinates of each point on the arc part and the angle between each point and the X-axis;

[0014] (4) Preparation and revision of the repair program

[0015] According to the radius R0 of the target arc-shaped electroplated CBN grinding wheel, a dressing program of the arc-shaped electroplated CBN grinding wheel is compiled by using a multi-segment arc method, and the numerical control program is corrected according to the central angle and radius corresponding to each point of the arc portion calculated in step (3);

[0016] (5) Verification of trimming procedures

[0017] On an optical curve grinder, the graphite sample is ground using the numerical control program corrected in step (4). After the graphite sample is ground, the graphite sample is removed and the graphite sample is inspected using a profilometer. The numerical control program is corrected again according to step (4) based on the inspection data of the graphite sample, and the modified numerical control program is used to grind and inspect the carbon copy, and this step is repeated multiple times until the arc radius of the graphite sample reaches the designed size;

[0018] (6) Arc-shaped electroplated CBN grinding wheel dressing

[0019] The arc-shaped electroplated CBN grinding wheel to be dressed is clamped by a mandrel, and then the mandrel is clamped on a rotary fixture of a CNC optical curve grinder, and the arc-shaped electroplated CBN grinding wheel to be dressed is dressed using a CNC program that has been corrected multiple times.

[0020] In step (1), the tool grinding wheel is installed on the spindle of the CNC optical curve grinding machine, and the copy carbon sheet is installed on a special fixture; set the rotation speed of the tool grinding wheel and make it rotate, manually control the tool grinding wheel to grind the side edge of the copy carbon sheet flat, and make the tool grinding wheel cut into the copy carbon sheet, and the cutting depth is not less than the arc radius of the tool grinding wheel.

[0021] In step (2), when detecting the copy carbon sheet, clamp the copy carbon sheet at the fixed position of the rotary precision caliper of the special accessory of the profilometer. The starting position and the ending position of the probe are both the ground side edges of the copy carbon sheet. After the detection, export the data as a "copy carbon sheet.txt" file.

[0022] In step (3), the alignment calculation method is as follows:

[0023] Use the plot function in Matlab to plot the image of the point set P0 = {x n , y n}, intercept two straight

[0024] line parts in the image for fitting, and the fitted straight line equation is denoted as y = kx + b.

[0025] Denote the inclination angle of this straight line as α, then α = tan -1 k,

[0026] If α > 0, use the imrotate function to rotate the point set P0 clockwise by α.

[0027] If α < 0, use the imrotate function to rotate the point set P0 counterclockwise by α.

[0028] The rotated point set is denoted as the point set P1 = {x m , y m};

[0029] where m and n are both natural numbers.

[0030] In step (3), the calculation method of the coordinates of each point and the central angle of the arc part on the copy carbon sheet is as follows: After alignment, take the point (x m , y min ) with the minimum y coordinate value in the point set P1 as the coordinate origin O to establish a coordinate system. Take two points (x c1 , R) and (x c2, , R) with the ordinate y = R on both sides of the coordinate origin as the boundary points. Then all the points in the point set P1 within the boundary are the arc part, denoted as

[0031] Pc = {(x ck , y ck ) │ x ck ∈ (x c1 , x c2 ), yck ∈(0, R)};

[0032] Fit the point set Pc to obtain the equation of the fitted circle, which is

[0033] (x ck - a) 2 +(y ck - b) 2 = r 2 ;

[0034] where x c1 ≤ x ck ≤ x c2 , 0 ≤ y ck ≤ R;

[0035] Let the angle between each point on the arc and the Y-axis be θ ck , and the radius of each point on the arc be R ck , then

[0036]

[0037]

[0038] Let the angle between each point on the arc and the X-axis be γ k , then

[0039] γ k = 90° - θ ck ,

[0040] Then the radius R C corresponding to each point in the point set P ck and form an array A1,

[0041] Then A1 = {(R ck , γ k )};

[0042] where k are all natural numbers.

[0043] In step (4), draw the graph of the arc-shaped electroplated CBN grinding wheel to be machined in CAD software. The radius of the arc-shaped electroplated CBN grinding wheel is denoted as R0. Divide the target arc into several segments with equal central angles. The central angle of each arc segment is denoted as β, and the point set composed of the endpoints of each arc segment is denoted as D N = {D1, D2, D3... D N}), then the central angle of arc D1D2 is β, the central angle of arc D1D3 is 2β,..., and the central angle of arc D1D N is (N - 1)β. Let the array composed of the central angles of each arc segment be A2,

[0044] Then A2 = {β, 2β, 3β,..., (N - 1)β}

[0045] The endpoints of the tool paths corresponding to the endpoints of each arc segment are denoted as the point set T N ={x N , y N}, extract the elements in array A1 that are equal to those in array A2 for γ k , and the corresponding radius R for each point ck , and edit the numerical control program according to R ck and the radius R of the arc to be trimmed for the electroplated CBN grinding wheel N ;

[0046] where N is a natural number.

[0047] The beneficial effects of the present invention are as follows:

[0048] (1) A method for trimming an arc-shaped electroplated CBN grinding wheel disclosed by the present invention optimizes the numerical control trimming program of the arc-shaped electroplated CBN grinding wheel according to the detected contour parameters of the diamond grinding wheel, thereby avoiding the influence of the poor contour accuracy of the tool grinding wheel on the trimming accuracy of the arc-shaped electroplated CBN grinding wheel, and finally realizing the batch precision trimming and processing of the arc-shaped electroplated CBN grinding wheel.

[0049] (2) On a numerical control optical curve grinding machine, the radius value of the tool grinding wheel and the contour parameters of the tool grinding wheel are detected by the "copying carbon sheet method", and the collected data is imported into and processed using Matlab software to calculate the coordinates of each point on the arc part of the copying carbon sheet and the angle between each point and the X-axis, completing the detection, acquisition and data processing of the key parameters of the tool grinding wheel.

[0050] (3) Draw the graph of the arc-shaped electroplated CBN grinding wheel to be processed in CAD software, evenly divide the target arc into several segments with equal central angles, and according to the mapping relationship between the central angle and the detected contour parameters of the tool grinding wheel, edit and correct the numerical control program by means of multi-segment arc fitting. Before trimming the target arc-shaped electroplated CBN grinding wheel, first grind a graphite sample piece, and correct the numerical control program multiple times according to the size of the graphite sample piece until the arc radius of the graphite sample piece reaches the target value. Finally, trim the target arc-shaped electroplated CBN grinding wheel to ensure that the target grinding wheel reaches micron-level accuracy, and batch precision trimming of the arc-shaped electroplated CBN grinding wheel can be realized. Description of the Drawings

[0051] Figure 1 is a schematic structural diagram of a tool grinding wheel;

[0052] Figure 2 is a schematic structural diagram of an arc-shaped electroplated CBN grinding wheel;

[0053] Figure 3 is a schematic diagram for compiling the trimming program of the present invention. Detailed Embodiments

[0054] The following specific embodiments illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification.

[0055] The present invention provides a precise dressing method for an arc-shaped electroplated CBN grinding wheel, as Figures 1 to 3 shown.

[0056] A dressing method for an arc-shaped electroplated CBN grinding wheel is completed on a numerically controlled optical profile grinder. The tool grinding wheel is installed on the machine spindle and rotates with the spindle. The arc-shaped electroplated CBN grinding wheel to be dressed is clamped on a special rotary device on the machine table in a two-center method. The specific dressing process steps are as follows:

[0057] Taking the dressing of an arc-shaped electroplated CBN grinding wheel as an example, the CBN abrasive grain size is 120 / 140, the arc radius R0 = 4 ± 0.005 mm, and the central angle corresponding to the arc is 180°, as Figure 2 shown.

[0058] The tool grinding wheel is preferably a 3A1 type ceramic diamond grinding wheel, and the abrasive grain size is preferably 100 / 120, but is not limited to this grain size. The thickness of the working layer of the grinding wheel is 2 mm, the outer diameter is 150 mm, and the arc radius is 1 mm, but is not limited to this size, as Figure 1 shown.

[0059] The precise dressing of the arc-shaped electroplated CBN grinding wheel is completed on a numerically controlled optical profile grinder. The tool grinding wheel is installed on the machine spindle and rotates with the spindle. The rotation speed is preferably 8000 r / min, but is not limited to this rotation speed; the arc-shaped electroplated CBN grinding wheel to be dressed is installed on a mandrel and clamped on a special rotary device in a two-center method. The rotation speed is preferably 120 r / min, but is not limited to this rotation speed. The specific dressing steps are as follows:

[0060] S1: The tool grinding wheel cuts into the grinding and copies the carbon sheet. On the optical profile grinder, install the copying carbon sheet on a special fixture, manually control the tool grinding wheel to grind the side of the copying carbon sheet flat, and make the tool grinding wheel cut into the copying carbon sheet, which should not be less than the arc radius of the arc-shaped diamond grinding wheel, that is, the arc radius of the tool grinding wheel.

[0061] S2: Detection of the copying carbon sheet. Use a profilometer to detect the ground copying carbon sheet. Clamp the copying carbon sheet at a fixed position on the rotating precision caliper of the special accessory of the profilometer. The starting position and the ending position of the probe are both the ground side of the copying carbon sheet. Select the arc part of the copying carbon sheet, and measure the arc radius size R = 1.0253 mm of the tool grinding wheel. After the detection is completed, export the detection data as a "copying carbon sheet.txt" file.

[0062] S3: Data processing. The detection data obtained in step S2 is imported into Matlab, and each point of the carbon sheet contour is recorded as a point set P0 = {x n ,y n} (n is a natural number), intercept the straight line part in the point set P0 and perform the straightening operation, and record it as point set P1 = {x m ,y m}(m is a natural number), take the lowest point on the outline of the copied carbon sheet as the coordinate origin O to establish a coordinate system, intercept the arc part in the point set P1 for fitting operation, and calculate the coordinates of each point on the arc part and the angle between each point and the X-axis.

[0063] S31: Correct the calculation method. Use the plot function in Matlab to draw the point set P0 = {x n ,y n} (n is a natural number), two straight line parts in the image are intercepted for fitting, and the equation of the fitted line is recorded as y = 0.05284x-45.6754, and the inclination angle of the line is 3.0245°, then α = 3.0245°> 0, and the imrotate function is used to rotate the point set P0 clockwise by 3.0245°. The rotated point set is recorded as point set P1 = {x m ,y m}(m is a natural number).

[0064] S32: Copy the coordinates of each point on the arc part of the carbon sheet, and the calculation method of the angle between each point and the X axis. After alignment, take the point with the smallest y coordinate value (18.4789, -32.4674) in the point set P1 as the coordinate origin O to establish a coordinate system, and take the two points (-1.0232, 1.0253) and (1.0267, 1.0253) on both sides of the coordinate origin with ordinate y = 1.0253 as boundary points, where R is the arc radius of the tool grinding wheel measured in step S2, then all points in the point set P1 within the boundary are arc parts, recorded as

[0065] Pc={(x ck ,y ck )│x ck ∈-1.0232≤x ck ≤1.0267,y ck ∈0≤y ck ≤1.0253}, (k is a natural number)

[0066] Fit the point set Pc and get the equation of the fitting circle, which is

[0067] (x ck -0.02941) 2 +(y ck -1.04875) 2 =1.02532 , (k is a natural number)

[0068] The angle between each point on the arc and the Y-axis is θ ck , and the radius of each point on the arc is R ck , then

[0069] (k is a natural number)

[0070] (k is a natural number)

[0071] Then the angle γ between each point on the arc and the X-axis k :

[0072] γ k = 90° - θ ck , (k is a natural number)

[0073] Then the point set P C The radius R corresponding to each point in ck and form an array A1,

[0074] Then A1 = {(R ck , γ k )}(k is a natural number)

[0075] S4: Programming and correction of the dressing program. According to the nominal radius value R0 = 4mm of the target arc-shaped electroplated CBN grinding wheel, use the CAXA software to draw a semi-circle with a radius of 4mm, and use the "break command" to evenly divide the semi-circle into 36 segments. The central angle β of each segment of the arc is 5°, and the point set composed of the endpoints of each segment of the arc is denoted as D N = {D1, D2, D3... D 37} Then the central angle of the arc D1D2 is 5°, the central angle of the arc D1D3 is 10°, ……, the central angle of the arc D1D 37 is 180°. Let the array composed of the central angles of each segment of the arc be A2,

[0076] Then A2 = {5°, 10°, 15°, …, 180°}

[0077] The endpoints of the tool path corresponding to the endpoints of each segment of the arc are denoted as the point set T N = {x N , y N}(N is a natural number) Extract the elements in array A1 where γ k is equal to those in array A2, and the corresponding radius R of each point ck , and edit the numerical control program according to R ck and the arc radius R0 = 4 of the electroplated CBN grinding wheel to be dressed.

[0078] S5: Trimming Program Verification. On a CNC optical curve grinding machine, use the corrected program to grind a graphite sample piece. After the graphite sample piece is ground, remove it and detect it with a profilometer. After detection, the radius of the graphite sample piece is 4.0021 mm, and the arc radius of the graphite sample piece reaches the designed dimension R0 = 4 ± 0.005 mm.

[0079] S6: Trimming of the Arc-shaped Electroplated CBN Grinding Wheel. Clamp the arc-shaped electroplated CBN grinding wheel with a mandrel, then clamp the mandrel on the special rotary device of the CNC optical curve grinding machine in a double-center-point manner. Use the corrected CNC program to trim the arc-shaped electroplated CBN grinding wheel. Use the trimmed arc-shaped electroplated CBN grinding wheel to grind a carbon piece and detect the carbon piece on a profilometer. The radius of the carbon piece is 4.0037 mm, so the radius of the working layer of the grinding wheel is 4.0037 mm, meeting the tolerance requirements.

[0080] A method for trimming an arc-shaped electroplated CBN grinding wheel disclosed in the present invention. On a CNC optical curve grinding machine, detect the radius value of the tool grinding wheel and the contour parameters of the tool grinding wheel through the "carbon piece copying method", and import the collected data into Matlab software to calculate the coordinates of each point on the arc part of the copied carbon piece and the angle between each point and the X-axis, completing the detection, collection, and data processing of the key parameters of the tool grinding wheel; draw the graph of the arc-shaped electroplated CBN grinding wheel to be processed in CAD software, evenly divide the target arc into several segments with equal central angles, and according to the mapping relationship between the central angle and the collected contour parameters of the tool grinding wheel, edit and correct the CNC program by means of multi-segment arc fitting. Before trimming the target arc-shaped electroplated CBN grinding wheel, first grind a graphite sample piece, and correct the CNC program multiple times according to the size of the graphite sample piece until the arc radius of the graphite sample piece reaches the target value. Finally, trim the target arc-shaped electroplated CBN grinding wheel to ensure that the target grinding wheel reaches micron-level accuracy, and batch precision trimming of the arc-shaped electroplated CBN grinding wheel can be achieved.

[0081] If terms such as "first" and "second" are used in this patent to limit components, those skilled in the art should be aware that the use of "first" and "second" is only for the convenience of describing the present invention and simplifying the description, and these terms have no special meaning.

[0082] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art of this industry should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

[0083] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by terms such as "front", "rear", "left", "right", "center", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus cannot be construed as a limitation on the protected content of the present invention.

Claims

1. A precise dressing method for an arc-shaped electroplated CBN grinding wheel, characterized in that, The following steps are involved: (1) Tool grinding wheel cuts into the carbon sheet for grinding On an optical curve grinder, a circular arc diamond grinding wheel is used as a tool grinding wheel and the copy carbon sheet is ground; (2) Carbon film detection Use a profilometer to detect the copied carbon sheet after grinding, select the arc part of the copied carbon sheet, measure the arc radius size R of the tool grinding wheel, and export the detected data from the profilometer; (3) Data processing The detection data obtained in step (2) is imported into the software, and each point of the carbon sheet contour is recorded as a point set P0 = {x n ,y n }, intercept the straight line part in the point set P0 and perform the straightening operation, and record it as point set P1 = {x m ,y m }, where m and n are both natural numbers; Take the lowest point on the contour of the carbon sheet as the origin O to establish a coordinate system, intercept the arc part in the point set P1 for fitting operation, and calculate the coordinates of each point on the arc part and the angle between each point and the X-axis; (4) Preparation and revision of the repair program According to the radius R0 of the target arc-shaped electroplated CBN grinding wheel, a dressing program of the arc-shaped electroplated CBN grinding wheel is compiled by using a multi-segment arc method, and the numerical control program is corrected according to the central angle and radius corresponding to each point of the arc portion calculated in step (3); (5) Verification of trimming procedures On an optical curve grinder, the graphite sample is ground using the numerical control program corrected in step (4). After the graphite sample is ground, the graphite sample is removed and the graphite sample is inspected using a profilometer. The numerical control program is corrected again according to step (4) based on the inspection data of the graphite sample, and the modified numerical control program is used to grind and inspect the carbon copy, and this step is repeated multiple times until the arc radius of the graphite sample reaches the designed size; (6) Arc-shaped electroplated CBN grinding wheel dressing The arc-shaped electroplated CBN grinding wheel to be dressed is clamped by a mandrel, and then the mandrel is clamped on a rotary fixture of a CNC optical curve grinder, and the arc-shaped electroplated CBN grinding wheel to be dressed is dressed using a CNC program that has been corrected multiple times.

2. A precision dressing method for an arc-shaped electroplated CBN grinding wheel according to claim 1, characterized in that: In step (1), a tool grinding wheel is mounted on the spindle of a CNC optical curve grinder, and a carbon copy sheet is mounted on a special fixture; the tool grinding wheel speed is set and rotated, the tool grinding wheel is manually controlled to grind the side of the carbon copy sheet, and the tool grinding wheel is cut into the carbon copy sheet, and the cutting depth is not less than the arc radius of the tool grinding wheel.

3. A precision dressing method for an arc-shaped electroplated CBN grinding wheel according to claim 1, characterized in that: In step (2), when testing the carbon copy sheet, the carbon copy sheet is clamped in a fixed position on the rotating precision caliper, a special accessory of the profiler. The starting and ending positions of the probe are both the polished sides of the carbon copy sheet. After the test is completed, the data is exported as a "carbon copy sheet.txt" file.

4. A precision dressing method for an arc-shaped electroplated CBN grinding wheel according to claim 1, characterized in that: In step (3), the straightening calculation method is as follows: Use the plot function in Matlab to plot the image of the point set P0 = {x n , y n}. Intercept two straight-line parts in the image for fitting, and the equation of the fitted straight line is denoted as y = kx + b. Let the inclination angle of this straight line be α, then α = tan -1 k, If α>0, use the imrotate function to rotate the point set P0 clockwise by α. If α<0, use the imrotate function to rotate the point set P0 counterclockwise by α. The rotated point set is denoted as point set P1 = {x m , y m}; Among them, m and n are both natural numbers.

5. A precision dressing method for an arc-shaped electroplated CBN grinding wheel according to claim 1, characterized in that: In step (3), the calculation method of the coordinates and the center angle of each point of the arc portion on the copied carbon sheet is as follows: After alignment, take the point with the smallest y - coordinate value in the point set P1 (x m , y min ) as the coordinate origin O to establish a coordinate system. Take two points (x c1 , R) and (x c2 , R) with the ordinate y = R on both sides of the coordinate origin as boundary points. Then all points in the point set P1 within the boundary are the arc part, denoted as P C = {(x ck , y ck ) | x ck ∈(x c1 , x c2 ), y ck ∈(0, R)}; Fit the point set P C to obtain the equation of the fitted circle, which is (x ck -a) 2 +(y ck -b) 2 =r 2 ; where x c1 ≤ x ck ≤ x c2 , 0 ≤ y ck ≤ R; Let the angle between each point on the circular arc and the Y-axis be θ ck , and the radius of each point on the circular arc be R ck , then Let the angle between each point on the circular arc and the x-axis be γ k , then γ k = 90° - θ ck , Then the point set P C The radius R corresponding to each point in ck And form an array A1, Then A1 = {(R ck , γ k )}; Among them, k is a natural number.

6. A precision dressing method for an arc-shaped electroplated CBN grinding wheel according to claim 1, characterized in that: In step (4), draw the graph of the arc-shaped electroplated CBN grinding wheel to be machined in CAD software. The radius of the arc-shaped electroplated CBN grinding wheel is denoted as R0. Divide the target arc into several segments with equal central angles on average. The central angle of each arc segment is denoted as β, and the point set composed of the endpoints of each arc segment is denoted as D N ={D1, D2, D3... D N}, then the central angle of arc D1D2 is β, and the central angle of arc D i D3 is 2β,....... The central angle of arc D1D N is (N - 1)β. Let the array composed of the central angles of each arc segment be A2 Then A2={β, 2β, 3β,..., (N-1)β} The endpoints of the tool paths corresponding to the endpoints of each arc segment are denoted as the point set T N ={x N , y N}, extract each element in array A1 that is equal to γ k in array A2, as well as the corresponding radius R ck of each point, and edit the numerical control program according to R ck and the radius R N of the arc to be trimmed on the electroplated CBN grinding wheel; Wherein, N is a natural number.

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