CN107378687A - A kind of large caliber reflecting mirror iteration based on abrasion of grinding wheel prediction pre-compensates for method for grinding - Google Patents

Abstract

An iterative pre-compensation grinding method for a large-diameter reflector based on grinding wheel wear prediction, and the invention relates to an iterative pre-compensation grinding method for a large-diameter reflector. The present invention aims to solve the problems in the prior art that the target surface accuracy is achieved through repeated grinding with multiple replacements of the grinding wheel under the condition of a fixed nominal grinding depth, resulting in serious wear of the grinding wheel, poor surface accuracy and low grinding efficiency. The present invention includes: 1. Establishing a prediction model of grinding wheel grinding ratio G on grinding parameters; 2. Establishing a prediction model of radial dimension wear at the grinding point of the grinding wheel during the grinding process; 3. Establishing a prediction model of aspheric surface shape error ; 4: Calculate the error value of the grinding surface shape at each point on the aspheric generatrix through the iterative pre-compensation method until the requirements are met; Step 5: Record the final predicted value of the nominal grinding depth at each contact point during the iterative process, and perform CNC grinding programming and subsequent processing. The invention is used in the technical field of grinding of optical aspheric mirrors.

Description

An Iterative Pre-Compensation Grinding Method for Large-aperture Mirrors Based on Grinding Wheel Wear Prediction

technical field

The invention relates to the technical field of grinding of optical aspheric mirrors, in particular to an iterative pre-compensation grinding method for large-diameter mirrors.

Background technique

With the rapid development of aerospace technology, the far-reaching exploration of the universe and space by humans has become more and more frequent, and there is a demand for higher precision in space optical systems. Optical mirrors are key components of space optical equipment (such as space telescopes, etc.). The requirements for the accuracy, stability and life of the mirror substrate are getting higher and higher, and the requirements for material performance are more stringent. The current space lens materials mainly use silicon, optical glass, SiC ceramics, etc. SiC ceramics have specific strength, With the advantages of high specific stiffness, high corrosion resistance and high dimensional stability, it is more and more widely used in aerospace optical system mirrors, and the caliber of SiC ceramic mirrors is also increasing, and because of their high hardness and brittle characteristics , so that ultra-precision abrasive processing has become the main processing method for these space lens materials. High-precision grinding and forming have a high removal efficiency in the abrasive processing process, which plays a very key role in improving the processing efficiency and processing accuracy of large mirrors.

Due to the material characteristics of high hardness and high brittleness of SiC ceramics, the wear of ordinary ceramic-based diamond grinding wheels is very serious during the processing of large-diameter mirrors. And the grinding wheel needs to be replaced frequently, which makes the aspherical grinding surface shape error large and the grinding efficiency low. Therefore, it is necessary to design and develop a grinding wheel with a long service life and a new process and method for grinding large-diameter SiC ceramic mirrors. In the grinding process of large-diameter SiC ceramics, frequent replacement of grinding wheels can be avoided, and the aspheric surface can be formed by one grinding wheel with high surface accuracy.

Traditional aspheric grinding generally uses vitrified diamond grinding wheels for grinding. Due to the high brittleness of vitrified bonds, the substrate wears quickly during the grinding process, and the size and shape accuracy of the grinding wheels are severely worn. It has the characteristics of strong abrasive grain holding force, high bonding strength, good wear resistance, and can withstand high grinding pressure. It has a long service life and can be used in the grinding process of large-diameter SiC ceramic mirrors. And the metal-bonded diamond grinding wheel can use ELID online electrolytic sharpening technology, which can keep the grinding wheel at a high sharpness during the grinding process, so as to obtain good and stable processing quality.

Grinding wheel wear is unavoidable in the grinding process of large-diameter SiC ceramic mirrors, and the amount of material removal gradually increases when the aspheric grinding wheel moves from the center of the aspheric surface along the direction of the generatrix to the edge, resulting in uneven wear of the grinding wheel and surface shape errors. There is also a big difference. In traditional grinding, the target surface accuracy is achieved by repeated grinding with multiple replacements of the grinding wheel under the condition of a fixed nominal grinding depth. The wear of the grinding wheel is serious, the surface accuracy is poor, and the grinding efficiency is low. Therefore, It is urgent to optimize and improve the large-diameter aspheric grinding method and process.

Contents of the invention

The purpose of the present invention is to solve the problem that in the prior art, the target surface accuracy is achieved by repeatedly replacing the grinding wheel and grinding repeatedly under the condition of a fixed nominal grinding depth, resulting in serious wear of the grinding wheel, poor surface accuracy and low grinding efficiency. In this paper, an iterative pre-compensation grinding method for large-aperture mirrors based on grinding wheel wear prediction is proposed.

An iterative precompensation grinding method for large-aperture mirrors based on grinding wheel wear prediction includes the following steps:

The method of the present invention is implemented on the basis of only considering the aspheric grinding surface shape error caused by the size wear of the grinding wheel. The method of the present invention establishes the wear prediction model of the arc profile size of the grinding wheel through the basic grinding wear experiment of the diamond grinding wheel, and then establishes the parameters of each point on the aspheric generatrix in the grinding process according to the grinding principle and the grinding wheel-workpiece geometric contact model in the grinding process. Surface error prediction model; the predicted surface error is transformed to change the nominal grinding depth at the corresponding point, and the aspherical grinding surface error is re-predicted according to the corrected nominal grinding depth, in this way the corresponding grinding The nominal grinding depth at the point is corrected iteratively until the maximum value of the predicted aspheric grinding surface error is less than the allowable value of the surface error. The method of the invention uses a metal bond diamond grinding wheel with a long service life as a grinding tool, and can propose a grinding wheel grinding track that meets the surface shape error without performing large-diameter aspheric surface grinding, thereby avoiding repeated operations of replacing the grinding wheel and improving the aspheric surface Grinding accuracy and grinding efficiency.

Step 1: Carry out a grinding experiment with a metal-bonded arc-shaped diamond grinding wheel, and use regression analysis to establish a prediction model for grinding wheel grinding ratio G on grinding parameters;

Among them, α _p is the grinding depth, v _s is the linear speed of the grinding wheel, v _w is the feed speed of the grinding wheel, k, a, b, c are constants, and the grinding parameters refer to α _p , v _s and v _w ;

Step 2: According to the expression of the generatrix of the aspheric surface, combined with the relationship between the grinding removal volume of the aspheric surface material and the volumetric wear of the grinding wheel, a prediction model for the radial dimension wear at the grinding point of the grinding wheel during the grinding process is established;

Δr _x ＝f(α _p ,v _s ,v _w ,R,r,V _w )

Where R is the radius of the base circle of the grinding wheel, r is the radius of the arc surface of the grinding wheel, and V _w is the volume removed by aspheric grinding;

Step 3: Utilize the prediction model for the wear amount of the radial dimension of the grinding wheel established in step 2, and establish an aspherical surface shape error prediction model according to the geometric relationship between the upper shape error of the aspheric generatrix and the wear amount of the radial dimension of the grinding wheel;

Step 4: Using the surface shape error prediction model established in step 3, calculate the grinding surface shape error value of each point on the aspheric surface generatrix, establish a Cartesian coordinate system on the aspheric surface, take the center of rotation of the aspheric surface as the z-axis, and move along the The horizontal direction of the bus is the x-axis. If the grinding surface error value of the x-coordinate point (contact point) is greater than the target surface-shape error value, iterative pre-compensation is performed on the nominal grinding depth of the x-coordinate point and the iterative pre-compensation is calculated. After the surface shape error value of this point, until the calculated value of the surface shape error at this point is less than the target surface shape error value, the processing of the x+1 coordinate point is carried out; if the grinding surface shape error value of the x coordinate point is less than or equal to the target surface shape error value, then process the x+1 coordinate point until the grinding surface shape error values of all points on the aspheric generatrix are less than or equal to the target surface shape error value;

Step 5: Record the final predicted value of the nominal grinding depth at each contact point during the iterative process, and perform CNC grinding programming and subsequent processing.

The beneficial effects of the present invention are:

The use of metal-bonded diamond grinding wheels effectively improves the service life of the grinding wheel, and at the same time provides the possibility for online electrolytic dressing of the grinding wheel; through ordinary grinding experiments, the wear model of the contour size of the arc grinding wheel is obtained, which is used for the prediction of the aspheric grinding surface shape error, The method of the present invention can determine the nominal grinding depth and motion track of the real-time grinding point of the grinding wheel according to the theoretical model provided by the present invention before grinding the large-diameter aspheric surface, and use the metal bond diamond grinding wheel to realize the primary grinding and forming of the aspherical surface , avoiding the process of grinding wheel replacement and repeated grinding, improving the grinding surface shape accuracy and grinding efficiency. The present invention proposes to pre-compensate the nominal grinding depths of different grinding wheel-workpiece contact points in an iterative manner for the first time (that is, adopting various points on the aspheric surface generatrix to change the nominal grinding depths), and proposes a method of changing the nominal grinding depths, which avoids the In the past, frequent replacement of grinding wheels and multiple grinding processes have simplified the aspheric grinding process, and the grinding efficiency of large-diameter mirrors can be increased by 3 to 5 times.

Description of drawings

Fig. 1 is the schematic diagram of profile and size wear of the metal bond diamond grinding wheel used in the present invention. Among them, r is the arc radius of the grinding wheel, R is the radius of the base circle of the grinding wheel, Δr is the wear amount of the arc radius of the grinding wheel, and O(x ₀ , z ₀ ) is the center of rotation of the grinding wheel.

Fig. 2 is a flowchart of the present invention.

detailed description

Specific embodiment one: as shown in Figure 2, a kind of iterative pre-compensation grinding method for large-diameter mirrors based on grinding wheel wear prediction includes the following steps:

Firstly, the size and wear prediction model of metal bonded diamond grinding wheel is established, and the metal bonded arc-shaped diamond grinding wheel is selected according to the characteristics of the aspheric mirror body material-SiC ceramic material. The bonding strength of the bond is high, which can effectively improve the service life of the grinding wheel. On this basis, the organizational parameters and shape parameters of the grinding wheel are determined; using the principle of grinding ratio, the metal bonded diamond grinding wheel is used for grinding experiments to determine the relationship model between the size of the grinding wheel, the volume of material removed by grinding, and the grinding process parameters. Predict wheel size wear for different grinding parameters and material removal. Large diameter generally refers to more than 1.5m.

Step 1: Carry out a grinding experiment with a metal-bonded arc-shaped diamond grinding wheel, and use regression analysis to establish a prediction model for grinding wheel grinding ratio G on grinding parameters;

Among them, α _p is the grinding depth, v _s is the linear speed of the grinding wheel, v _w is the feed speed of the grinding wheel, k, a, b, c are constants, which are determined through grinding experiments and regression analysis.

Design the metal bond arc diamond grinding wheel, the structure parameters and contour parameters of the grinding wheel, and the shape of the grinding wheel is shown in Figure 1.

Step 2: According to the expression of the generatrix of the aspheric surface, combined with the relationship between the grinding removal volume of the aspheric surface material and the volumetric wear of the grinding wheel, a prediction model for the radial dimension wear at the grinding point of the grinding wheel during the grinding process is established;

Δr _x ＝f(α _p ,v _s ,v _w ,R,r,V _w )

Where R is the radius of the base circle of the grinding wheel, r is the radius of the arc surface of the grinding wheel, and V _w is the volume removed by aspheric grinding;

Step 3: Utilize the prediction model for the wear amount of the radial dimension of the grinding wheel established in step 2, and establish an aspherical surface shape error prediction model according to the geometric relationship between the upper shape error of the aspheric generatrix and the wear amount of the radial dimension of the grinding wheel;

Step 4: Using the surface shape error prediction model established in step 3, calculate the grinding surface shape error value of each point on the aspheric surface generatrix, establish a Cartesian coordinate system on the aspheric surface, take the center of rotation of the aspheric surface as the z-axis, and move along the The horizontal direction of the bus is the x-axis. If the grinding surface error value of the x-coordinate point (contact point) is greater than the target surface-shape error value, iterative pre-compensation is performed on the nominal grinding depth of the x-coordinate point and the iterative pre-compensation is calculated. After the surface error value of the point, until the calculated value of the point surface error is less than the target surface error value, the processing of the x+1 coordinate point is performed; if the grinding surface error value of the x coordinate point is less than or equal to the target surface error value value, then process the x+1 coordinate point until the grinding surface shape error values of all points on the aspheric generatrix are less than or equal to the target surface shape error value;

Step 5: Record the final predicted value of the nominal grinding depth at each contact point during the iterative process, and perform CNC grinding programming and subsequent processing.

The invention provides a large-diameter superhard material reflector grinding wheel motion track planning and real-time grinding point nominal grinding depth iterative prediction method. The method of the present invention is on the basis of only considering the impact of grinding wheel size wear on the aspheric reflector grinding surface shape error, first establishes the arc diamond grinding wheel shape and size wear amount on the grinding parameters under the same grinding conditions through theoretical and experimental research. Through the theoretical analysis of the relationship between the size wear of the grinding wheel and the surface shape error at different grinding points in the direction of the aspheric generatrix, a real-time prediction model of the surface shape error caused by the grinding wheel size wear at the grinding wheel-workpiece contact point is established. The target surface shape error is the standard, and the predicted surface shape error is superimposed on the nominal grinding depth at the real-time grinding point through a certain conversion model, and finally the aspheric grinding surface shape error at each point that satisfies the aspheric surface is less than The iteration is stopped when the target surface shape error is reached, the nominal grinding depth of different grinding points in the actual grinding process is determined, and the trajectory of the grinding wheel rotation center is planned based on this. The method of the present invention can determine the nominal grinding depth and motion trajectory of the real-time grinding point of the grinding wheel on the basis of not implementing large-diameter aspherical surface grinding, and select the metal bond diamond grinding wheel as the grinding tool to realize the one-time forming of the surface shape, and improve the Improve the grinding surface accuracy and grinding efficiency.

Specific embodiment two: the difference between this embodiment and specific embodiment one is: the surface shape error prediction model of the contact point between the grinding wheel and the workpiece on the aspheric generatrix in the grinding process is established in the step three, specifically:

Where E _x is the aspheric grinding surface shape error at the x coordinate point on the aspheric generatrix from the center of gyration, expressed by the difference between the aspheric surface detection vector height and the aspheric ideal vector height, β _x is the distance rotation on the aspheric surface generatrix Tangent tilt angle at center x point.

On the basis of the diamond grinding wheel size and wear prediction model, the generatrix expression of the rotary aspheric mirror, the initial grinding parameters and process parameters are given, and the grinding is analyzed based on the grinding principle, aspheric surface profile model and the contact geometric relationship model between the grinding wheel and the workpiece. During the grinding process, the relationship between the material removal volume at the grinding wheel-workpiece contact point, the grinding process parameters and the wear amount of the grinding wheel is established, and the surface shape error prediction model of the grinding wheel-workpiece contact point on the aspheric generatrix during the grinding process is established.

Other steps and parameters are the same as those in Embodiment 1.

Specific embodiment three: the difference between this embodiment and specific embodiment one or two is: if the grinding surface shape error value of the x coordinate point is greater than the target surface shape error value in the step 4, then the nominal grinding surface of the x coordinate point The specific process of iterative precompensation processing for cutting depth is as follows:

By increasing the nominal grinding depth of the grinding point to compensate the aspheric surface error caused by the wear of the grinding wheel, the grinding surface error value of the x-coordinate point is converted and superimposed on the nominal grinding depth, and the superposition is Grinding at the new nominal grinding depth, and calculating the surface error value after iterative pre-compensation; after multiple iterations of pre-compensation until the predicted value of the grinding surface error at the x coordinate point is less than the target surface error value, the x coordinate When the superposition of the nominal grinding depth at point x is over, record the nominal grinding depth α _px(n) and the number of iterations n at point x at this time, and perform the superposition calculation of the nominal grinding depth of the x+1 coordinate point;

The nominal grinding depth expression after superposition is as follows:

α _px(n) ＝α _px(n-1) +ε _x(n-1) (n≥2)

Where ε _x(n-1) is the calculated value of the grinding surface shape error obtained after the n-1 iteration of the x coordinate point, α _px(1) = α _p ,

Other steps and parameters are the same as those in Embodiment 1 or Embodiment 2.

Specific Embodiment 4: The difference between this embodiment and one of specific embodiments 1 to 3 is that: in the iterative process of the nominal grinding depth, the predicted aspheric surface shape error after the nth iteration of the x coordinate point is as follows The equation says:

in, is the predicted value of the surface shape error when the nominal grinding depth at the x coordinate point is α _px(n) , that is: Sum of surface shape errors computed for the first n-1 iterations.

The nominal grinding depth α _px(n) and the number of iterations n at different grinding contact points of the aspheric surface obtained by the method of the present invention are all different.

Other steps and parameters are the same as those in Embodiments 1 to 3.

Embodiment 5: This embodiment differs from Embodiment 1 to Embodiment 4 in that: the movement track of the center of rotation of the grinding wheel determined in step 5 during the grinding process is specifically:

Among them, x ₀ is the x-axis coordinate value of the grinding wheel rotation center, and z ₀ is the z-axis coordinate value of the grinding wheel rotation center.

Other steps and parameters are the same as one of the specific embodiments 1 to 4.

The present invention can also have other various embodiments, without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations are all Should belong to the scope of protection of the appended claims of the present invention.

Claims (5)

1. a large-diameter mirror iterative pre-compensation grinding method based on emery wheel wear prediction, is characterized in that: the large-diameter mirror iterative pre-compensation grinding method based on emery wheel wear prediction comprises the following steps: Step 1: Carry out a grinding experiment with a metal-bonded arc-shaped diamond grinding wheel, and use regression analysis to establish a prediction model for grinding wheel grinding ratio G on grinding parameters; <mrow><mi>G</mi><mo>=</mo><mi>k</mi><mo>&amp;CenterDot;</mo><msubsup><mi>&amp;alpha;</mi><mi>p</mi><mi>a</mi></msubsup><mo>&amp;CenterDot;</mo><msubsup><mi>v</mi><mi>s</mi><mi>b</mi></msubsup><mo>&amp;CenterDot;</mo><msubsup><mi>v</mi><mi>w</mi><mi>c</mi></msubsup></mrow> Among them, α _p is the grinding depth, v _s is the linear speed of the grinding wheel, v _w is the feed speed of the grinding wheel, and k, a, b, c are constants; Step 2: According to the expression of the generatrix of the aspheric surface, combined with the relationship between the grinding removal volume of the aspheric surface material and the volumetric wear of the grinding wheel, a prediction model for the radial dimension wear at the grinding point of the grinding wheel during the grinding process is established; Δr _x ＝f(α _p ,v _s ,v _w ,R,r,V _w ) Where R is the radius of the base circle of the grinding wheel, r is the radius of the arc surface of the grinding wheel, and V _w is the volume removed by aspheric grinding; Step 3: Utilize the prediction model for the wear amount of the radial dimension of the grinding wheel established in step 2, and establish an aspherical surface shape error prediction model according to the geometric relationship between the upper shape error of the aspheric generatrix and the wear amount of the radial dimension of the grinding wheel; Step 4: Using the surface shape error prediction model established in step 3, calculate the grinding surface shape error value of each point on the aspheric surface generatrix, establish a Cartesian coordinate system on the aspheric surface, take the center of rotation of the aspheric surface as the z-axis, and move along the The horizontal direction of the bus is the x-axis. If the error value of the ground surface shape of the x-coordinate point is greater than the target surface shape error value, iterative pre-compensation is performed on the nominal grinding depth of the x-coordinate point, and the value of the point after iterative pre-compensation is calculated. Surface error value, until the calculated value of the point surface error is less than the target surface error value, the processing of the x+1 coordinate point is performed; if the grinding surface error value of the x coordinate point is less than or equal to the target surface error value, then proceed The x+1 coordinate point is processed until the grinding surface shape error value of all points on the aspheric generatrix is less than or equal to the target surface shape error value; Step 5: Record the final predicted value of the nominal grinding depth at each contact point during the iterative process, the determined movement track of the grinding wheel rotation center during the grinding process, and perform CNC grinding programming and subsequent processing. 2. A kind of iterative pre-compensation grinding method for large-diameter mirrors based on grinding wheel wear prediction according to claim 1, characterized in that: the contact point between the grinding wheel and the workpiece on the aspheric generatrix of the grinding process is established in the step 3 The surface shape error prediction model is specifically: <mrow><msub><mi>E</mi><mi>x</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>&amp;Delta;r</mi><mi>x</mi></msub></mrow><mrow><msub><mi>cos&amp;beta;</mi><mi>x</mi></msub></mrow></mfrac></mrow> Where E _x is the aspheric grinding surface shape error at the x coordinate point on the aspheric generatrix from the center of gyration, and β _x is the tangent inclination angle on the aspheric generatrix at the point x from the center of gyration. 3. A kind of iterative pre-compensation grinding method for large-diameter mirrors based on grinding wheel wear prediction according to claim 2, characterized in that: in said step 4, if the grinding surface shape error value of the x coordinate point is greater than the target surface The shape error value, the specific process of iterative pre-compensation for the nominal grinding depth of the x-coordinate point is: By increasing the nominal grinding depth of the grinding point to compensate for the aspherical surface error caused by the wear of the grinding wheel, superimpose the grinding surface error value of the x coordinate point on the nominal grinding depth, and use the superimposed new nominal Grinding at the grinding depth, calculate the surface error value after iterative pre-compensation; after iterative pre-compensation until the predicted value of the grinding surface error at the x coordinate point is less than the target surface error value, the nominal grinding depth at the x coordinate point is iterated At the end of the addition, record the nominal grinding depth α _px(n) at point x and the number of iterations n, n≥2, and perform superposition calculation of the nominal grinding depth at x+1 coordinate point; The nominal grinding depth expression after superposition is as follows: α _px(n) = α _px(n-1) +ε _x(n-1) Where ε _x(n-1) is the calculated value of the grinding surface shape error obtained after the n-1 iteration of the x coordinate point. 4. A kind of iterative precompensation grinding method for large-diameter mirrors based on grinding wheel wear prediction according to claim 3, characterized in that: in the iterative process of the nominal grinding depth, after the nth iteration of the x coordinate point The predicted aspheric shape error for is expressed by the equation shown below: <mrow><msub><mi>&amp;epsiv;</mi><mrow><mi>x</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></msub><mo>=</mo><msub><mi>E</mi><mrow><mi>x</mi><mrow><mo>(</mo><msub><mi>&amp;alpha;</mi><mrow><mi>p</mi><mi>x</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></msub><mo>)</mo></mrow></mrow></msub><mo>-</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></munderover><msub><mi>&amp;epsiv;</mi><mrow><mi>x</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></mrow></msub></mrow> in, is the predicted value of the surface shape error when the nominal grinding depth at the x coordinate point is α _px(n) , that is: Sum of surface shape errors computed for the first n-1 iterations. 5. A kind of iterative pre-compensation grinding method for large-diameter mirrors based on grinding wheel wear prediction according to claim 4, characterized in that: the moving track of the grinding wheel center of rotation determined in the step 5 in the grinding process is specific for: <mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><msub><mi>x</mi><mn>0</mn></msub><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msub><mi>&amp;Delta;r</mi><mi>x</mi></msub><mo>,</mo><msub><mi>&amp;beta;</mi><mi>x</mi></msub><mo>,</mo><msub><mi>&amp;alpha;</mi><mrow><mi>p</mi><mi>x</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></msub><mo>,</mo><msub><mi>v</mi><mi>s</mi></msub><mo>,</mo><msub><mi>v</mi><mi>w</mi></msub><mo>,</mo><msub><mi>V</mi><mi>w</mi></msub><mo>)</mo></mrow></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>z</mi><mn>0</mn></msub><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>,</mo><msub><mi>&amp;Delta;r</mi><mi>x</mi></msub><mo>,</mo><msub><mi>&amp;beta;</mi><mi>x</mi></msub><mo>,</mo><msub><mi>&amp;alpha;</mi><mrow><mi>p</mi><mi>x</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></msub><mo>,</mo><msub><mi>v</mi><mi>s</mi></msub><mo>,</mo><msub><mi>v</mi><mi>w</mi></msub><mo>,</mo><msub><mi>V</mi><mi>w</mi></msub><mo>)</mo></mrow></mrow></mtd></mtr></mtable></mfenced> Among them, x ₀ is the x-axis coordinate value of the grinding wheel rotation center, and z ₀ is the z-axis coordinate value of the grinding wheel rotation center.