CN107378687A - A kind of large caliber reflecting mirror iteration based on abrasion of grinding wheel prediction pre-compensates for method for grinding - Google Patents
A kind of large caliber reflecting mirror iteration based on abrasion of grinding wheel prediction pre-compensates for method for grinding Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 69
- 238000005299 abrasion Methods 0.000 title claims abstract description 25
- 238000012804 iterative process Methods 0.000 claims abstract description 4
- 238000012545 processing Methods 0.000 claims description 23
- 229910003460 diamond Inorganic materials 0.000 claims description 19
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- 238000003754 machining Methods 0.000 abstract description 5
- 238000005516 engineering process Methods 0.000 abstract description 3
- 229910001651 emery Inorganic materials 0.000 abstract 3
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B13/00—Machines or devices designed for grinding or polishing optical surfaces on lenses or surfaces of similar shape on other work; Accessories therefor
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Abstract
A kind of large caliber reflecting mirror iteration based on abrasion of grinding wheel prediction pre-compensates for method for grinding, and the present invention relates to large caliber reflecting mirror iteration to pre-compensate for method for grinding.The present invention in order to solve prior art is ground repeatedly by repeatedly changing emery wheel to reach target surface figure accuracy in the case of the nominal grinding depth of fixation, causes the problem of emery wheel loss is serious, the poor low and grinding efficiency of surface figure accuracy is low.The present invention includes：One：Wheel grinding is established than forecast models of the G on grinding parameter；Two：Establish radial dimension Abrasion prediction model at grinding process medium plain emery wheel grinding points；Three：Establish aspheric surface error prediction model；Four：Method is pre-compensated for by iteration and calculates each point grinding surface shape error amount on aspherical bus, until meeting to require；Step 5：The final predicted value of name grinding depth at each contact point, carries out numerical control grinding machining prgraming and following process in record iterative process.The present invention is used for optical aspherical surface speculum Grinding Technology field.
Description
Technical Field
The invention relates to the technical field of grinding of optical aspheric reflectors, in particular to an iterative precompensation grinding method for a large-aperture reflector.
Background
Along with the rapid development of aerospace technology, the deep and distant exploration of the universe and the outer space by human beings is more and more frequent, the requirement on the high precision of a space optical system is met, an optical reflector is a key part of space optical equipment (such as a space telescope, and the like), the requirements on the precision, the stability, the service life and the like of a reflector substrate are more and more high, the requirement on the material performance is more rigorous, the current space lens material mainly adopts silicon, optical glass, SiC ceramic and the like, the SiC ceramic has the advantages of specific strength, high specific rigidity, high corrosion resistance, high dimensional stability and the like, the application in the space optical system reflector is more and more extensive, the caliber of the SiC ceramic reflector is also more and more large, and due to the higher hard and brittle characteristics of the SiC ceramic, the ultra-precise abrasive processing becomes the main processing means of the current space lens materials, and the high-precision grinding forming has higher removal efficiency in the abrasive processing, the method plays a very key role in improving the processing efficiency and the processing precision of the large mirror.
Because the SiC ceramic has the characteristics of high hardness and high brittleness, the common ceramic-based diamond grinding wheel is very seriously worn in the processing process of the large-caliber reflecting mirror, the radial wear of the diamond grinding wheel reaches dozens of microns in one-time grinding forming process, and the grinding wheel needs to be frequently replaced, so that the aspheric surface grinding surface shape error is large, and the grinding efficiency is low. Therefore, a grinding wheel with a long service life and a new process and a new method for grinding and processing the large-caliber SiC ceramic reflecting mirror need to be designed and developed. The grinding wheel can be prevented from being frequently replaced in the grinding process of the large-caliber SiC ceramic, and the purposes that one grinding wheel can finish aspheric surface forming and has higher surface shape precision can be achieved.
The traditional aspheric surface grinding is generally carried out by adopting a ceramic-based diamond grinding wheel, because the ceramic bond has very high brittleness, the abrasion of a matrix is fast in the grinding process, and the abrasion of the size and shape precision of the grinding wheel is serious, and because the metal bond grinding wheel has the characteristics of strong abrasive grain holding force, high bonding strength, good abrasion resistance, capability of bearing larger grinding pressure and the like, the metal bond grinding wheel has longer service life and can be used for the grinding process of the large-caliber SiC ceramic reflector. And the metal bond diamond grinding wheel can use an ELID on-line electrolytic dressing technology, so that the grinding wheel can keep higher sharpness in the grinding process to obtain good and stable processing quality.
Abrasion of a grinding wheel is inevitable in the grinding process of the large-caliber SiC ceramic reflector, the material removal amount of the aspheric grinding wheel gradually increases when the aspheric grinding wheel moves from the center of the aspheric surface to the edge along the bus direction, so that the abrasion of the grinding wheel is uneven, the surface shape error also has large difference, the traditional grinding method is used for repeatedly grinding the grinding wheel to achieve the target surface shape precision by replacing the grinding wheel for many times under the condition of fixed nominal grinding depth, the abrasion loss of the grinding wheel is serious, the surface shape precision is poor, the grinding efficiency is low, and therefore the large-caliber aspheric surface grinding method and process are urgently needed to be optimized and improved.
Disclosure of Invention
The invention aims to solve the problems of serious grinding wheel loss, poor surface shape precision and low grinding efficiency caused by repeated grinding by replacing a grinding wheel for multiple times under the condition of fixing the nominal grinding depth in the prior art, and provides an iterative precompensation grinding method for a large-caliber reflector based on grinding wheel wear prediction.
An iterative precompensation grinding method for a large-aperture reflector based on grinding wheel wear prediction comprises the following steps:
the method is implemented on the basis of only considering the aspheric surface grinding surface shape error caused by the abrasion of the size of the grinding wheel. The method comprises the steps of establishing a grinding wheel circular arc outline dimension wear prediction model through a diamond grinding wheel basic grinding wear experiment, and further establishing a surface shape error prediction model of each point on an aspheric surface generatrix in a primary grinding process according to a grinding principle and a grinding wheel-workpiece geometric contact model in the grinding process; and changing the nominal grinding depth of the predicted surface shape error at the corresponding point through conversion, and predicting the aspheric surface grinding surface shape error again according to the corrected nominal grinding depth, and carrying out iterative correction on the nominal grinding depth at the corresponding grinding point for multiple times in such a way until the maximum value of the predicted aspheric surface grinding surface shape error is smaller than the surface shape error allowable value. The method of the invention takes the metal bond diamond grinding wheel with long service life as a grinding tool, can provide the grinding track of the grinding wheel meeting the surface shape error requirement without carrying out large-caliber aspheric surface grinding, avoids the repeated grinding wheel replacement operation, and improves the aspheric surface grinding precision and grinding efficiency.
The method comprises the following steps: carrying out a grinding experiment by using a metal bond arc surface diamond grinding wheel, and establishing a prediction model of grinding wheel grinding ratio G on grinding parameters by using a regression analysis method;
α thereinpTo grind depth, vsIs the linear velocity of the grinding wheel, vwThe grinding parameters are α, k, a, b and c are constants for the feed speed of the grinding wheelp、vsAnd vw；
Step two: according to an aspheric surface bus expression, establishing a radial dimension wear loss prediction model at a grinding point of the grinding wheel in the grinding process by combining the relation between the grinding removal volume of the aspheric surface material and the volume wear loss of the grinding wheel;
Δrx＝f(αp,vs,vw,R,r,Vw)
wherein R is the radius of the grinding wheel base circle,r is the radius of the circular arc surface of the grinding wheel, VwRemoving volume for aspheric surface grinding;
step three: establishing an aspheric surface shape error prediction model according to the geometric relation between the aspheric surface bus upper surface shape error and the grinding wheel radial dimension abrasion loss by using the grinding wheel radial dimension abrasion loss prediction model established in the step two;
step four: calculating grinding surface shape error values of all points on an aspheric surface generatrix by using the surface shape error prediction model established in the third step, establishing a Cartesian coordinate system on the aspheric surface, taking the aspheric surface rotation center as a z-axis and taking the x-axis along the horizontal direction of the generatrix, if the grinding surface shape error value of an x coordinate point (a contact point) is greater than a target surface shape error value, performing iterative precompensation processing on the nominal grinding depth of the x coordinate point, calculating the surface shape error value of the point after the iterative precompensation until the calculated value of the surface shape error of the point is less than the target surface shape error value, and performing processing on an x +1 coordinate point; if the grinding surface shape error value of the x coordinate point is less than or equal to the target surface shape error value, processing the x +1 coordinate point until the grinding surface shape error values of all points on the aspheric surface bus are less than or equal to the target surface shape error value;
step five: and recording the final predicted value of the nominal grinding depth of each contact point in the iterative process, and performing numerical control grinding machining programming and subsequent machining.
The invention has the beneficial effects that:
the metal bond diamond grinding wheel is adopted, so that the service life of the grinding wheel is effectively prolonged, and meanwhile, the possibility is provided for the online electrolytic finishing of the grinding wheel; the method can determine the nominal grinding depth and the motion trail of a real-time grinding point of the grinding wheel according to the theoretical model provided by the invention before large-caliber aspheric surface grinding, and realizes one-time grinding forming of the aspheric surface by using the metal bond diamond grinding wheel, thereby avoiding the processes of replacing and repeatedly grinding the grinding wheel and improving the precision of the grinding surface and the grinding processing efficiency. The invention firstly provides the method for pre-compensating the nominal grinding depth of different grinding wheel-workpiece contact points in an iterative mode (namely, each point on an aspheric surface bus is adopted to change the nominal grinding depth), and provides the grinding method with the variable nominal grinding depth, so that the frequent grinding wheel replacement and multiple grinding processes in the prior art are avoided, the aspheric surface grinding process is simplified, and the grinding efficiency of the large-caliber reflector can be improved by 3 to 5 times.
Drawings
FIG. 1 is a schematic view of the profile and dimensional wear of a metal bond diamond wheel used in the present invention. Wherein R is the radius of the grinding wheel arc, R is the radius of the grinding wheel base circle, Delta R is the abrasion loss of the grinding wheel arc radius, O (x)0,z0) Is the rotation center of the grinding wheel.
FIG. 2 is a flow chart of the present invention.
Detailed Description
The first embodiment is as follows: as shown in fig. 2, an iterative precompensation grinding method for a large-aperture reflector based on grinding wheel wear prediction includes the following steps:
firstly, establishing a size wear prediction model of a metal bond diamond grinding wheel, selecting the metal bond arc surface diamond grinding wheel according to the characteristics of an aspheric mirror body material-SiC ceramic material, wherein the bonding strength of the bonding agent is high, the service life of the grinding wheel can be effectively prolonged, and the tissue parameters and the shape parameters of the grinding wheel are determined on the basis; by utilizing a grinding ratio principle, a grinding experiment is carried out by using a metal bond diamond grinding wheel, and a relation model of the size abrasion loss of the grinding wheel, the volume of a grinding removal material and grinding process parameters is determined and is used for predicting the size abrasion loss of the grinding wheel under the conditions of different grinding parameters and material removal amounts. The large caliber is generally more than 1.5 m.
The method comprises the following steps: carrying out a grinding experiment by using a metal bond arc surface diamond grinding wheel, and establishing a prediction model of grinding wheel grinding ratio G on grinding parameters by using a regression analysis method;
α thereinpTo grind depth, vsIs the linear velocity of the grinding wheel, vwK, a, b and c are constants for the feed speed of the grinding wheel, and are determined by grinding experiments and regression analysis.
Designing a metal bond arc diamond grinding wheel, wherein the structure parameters and the profile parameters of the grinding wheel are shown in figure 1.
Step two: according to an aspheric surface bus expression, establishing a radial dimension wear loss prediction model at a grinding point of the grinding wheel in the grinding process by combining the relation between the grinding removal volume of the aspheric surface material and the volume wear loss of the grinding wheel;
Δrx＝f(αp,vs,vw,R,r,Vw)
wherein R is the grinding wheel base radius, R is the grinding wheel arc surface radius, VwRemoving volume for aspheric surface grinding;
step three: establishing an aspheric surface shape error prediction model according to the geometric relation between the aspheric surface bus upper surface shape error and the grinding wheel radial dimension abrasion loss by using the grinding wheel radial dimension abrasion loss prediction model established in the step two;
step four: calculating grinding surface shape error values of all points on an aspheric surface generatrix by using the surface shape error prediction model established in the third step, establishing a Cartesian coordinate system on the aspheric surface, taking the aspheric surface rotation center as a z-axis and taking the x-axis along the horizontal direction of the generatrix, if the grinding surface shape error value of an x coordinate point (a contact point) is greater than a target surface shape error value, performing iterative precompensation processing on the nominal grinding depth of the x coordinate point, calculating the surface shape error value of the point after the iterative precompensation until the calculated value of the surface shape error of the point is less than the target surface shape error value, and performing processing on an x +1 coordinate point; if the grinding surface shape error value of the x coordinate point is less than or equal to the target surface shape error value, processing the x +1 coordinate point until the grinding surface shape error values of all points on the aspheric surface bus are less than or equal to the target surface shape error value;
step five: and recording the final predicted value of the nominal grinding depth of each contact point in the iterative process, and performing numerical control grinding machining programming and subsequent machining.
The invention provides a motion trajectory planning and real-time nominal grinding depth iterative prediction method for a large-caliber superhard material reflector grinding wheel. On the basis of only considering the influence of the size abrasion of the grinding wheel on the grinding surface shape error of the aspheric surface reflector, the method firstly establishes a prediction model of the shape and size abrasion loss of the arc diamond grinding wheel under the same grinding condition on the grinding parameters through theoretical and experimental researches, by theoretically analyzing the relationship between the size abrasion loss and the surface shape error of the grinding wheel at different grinding points in the aspheric surface bus direction, a surface shape error prediction model caused by the size abrasion of the grinding wheel at the grinding contact point of the real-time grinding wheel and a workpiece is established, the target surface shape error is taken as a standard, and superposing the predicted surface shape error to the nominal grinding depth of the real-time grinding point through a certain conversion model, finally stopping iteration when the aspheric surface grinding surface shape errors at all the aspheric surface points are smaller than the target surface shape error, determining the nominal grinding depth of different grinding points in the actual grinding process and planning the motion track of the rotation center of the grinding wheel on the basis of the nominal grinding depth. The method can determine the nominal grinding depth and the motion trail of the real-time grinding point of the grinding wheel on the basis of not implementing large-caliber aspheric surface grinding, and selects the metal bond diamond grinding wheel as a grinding tool to realize one-step forming of the surface shape, thereby improving the grinding surface shape precision and the grinding processing efficiency.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: the step three of establishing a surface shape error prediction model of the contact point of the grinding wheel and the workpiece on the aspheric surface bus in the grinding process specifically comprises the following steps:
wherein ExThe error of the aspheric grinding surface shape at the x coordinate point from the revolution center on the aspheric generatrix is expressed by the difference between the aspheric detection vector height and the aspheric ideal vector height, βxThe inclination angle of a tangent line at a point x away from the rotation center on the aspheric surface bus is shown.
On the basis of a diamond grinding wheel dimension wear prediction model, a rotary aspheric surface reflector generatrix expression is given, grinding parameter process parameters are initialized, the relation between the material grinding removal volume at the grinding wheel-workpiece contact point, the grinding process parameters and the grinding wheel dimension wear amount in the grinding process is analyzed according to a grinding principle, an aspheric surface profile model and a grinding wheel-workpiece contact geometric relation model, and a surface shape error prediction model of the grinding wheel-workpiece contact point on an aspheric surface generatrix in the grinding process is established.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: if the grinding surface shape error value of the x coordinate point is greater than the target surface shape error value in the fourth step, the specific process of performing iterative precompensation processing on the nominal grinding depth of the x coordinate point is as follows:
compensating aspheric surface shape error caused by grinding wheel abrasion by increasing nominal grinding depth of grinding point, converting the grinding surface shape error value of x coordinate point, superposing on the nominal grinding depth, grinding with new superposed nominal grinding depth, calculating surface shape error value after iterative precompensation, iterative precompensation for multiple times until the predicted value of grinding surface shape error of x coordinate point is less than target surface shape error value, finishing superposition of nominal grinding depth of x coordinate point, recording the nominal grinding depth α at the x point at the momentpx(n)And the number of iterations n, nPerforming superposition calculation on nominal grinding depth of a line x +1 coordinate point;
the expression of the nominal grinding depth after superposition is as follows:
αpx(n)＝αpx(n-1)+x(n-1)(n≥2)
whereinx(n-1)The calculated value of the grinding surface shape error obtained after the n-1 iteration of the x coordinate point is αpx(1)＝αp，
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is: in the iteration process of the nominal grinding depth, the predicted aspheric surface shape error of the x coordinate point after the nth iteration is represented by the following equation:
wherein,to a nominal grinding depth of α at the x-coordinate pointpx(n)The predicted value of the time-surface shape error is as follows:the sum of the surface shape errors calculated for the first n-1 iterations.
Nominal grinding depth α at different grinding contact points of aspheric surface obtained by the method of the inventionpx(n)And the number of iterations n are different.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is: the movement track of the grinding wheel rotation center determined in the step five in the grinding process is specifically as follows:
wherein x0Is the x-axis coordinate value of the rotation center of the grinding wheel, z0Is the z-axis coordinate value of the grinding wheel rotation center.
Other steps and parameters are the same as in one of the first to fourth embodiments.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.
Claims (5)
1. An iterative precompensation grinding method for a large-aperture reflector based on grinding wheel wear prediction is characterized by comprising the following steps: the iterative precompensation grinding method for the large-aperture reflector based on the grinding wheel wear prediction comprises the following steps of:
the method comprises the following steps: carrying out a grinding experiment by using a metal bond arc surface diamond grinding wheel, and establishing a prediction model of grinding wheel grinding ratio G on grinding parameters by using a regression analysis method;
<mrow> <mi>G</mi> <mo>=</mo> <mi>k</mi> <mo>&CenterDot;</mo> <msubsup> <mi>&alpha;</mi> <mi>p</mi> <mi>a</mi> </msubsup> <mo>&CenterDot;</mo> <msubsup> <mi>v</mi> <mi>s</mi> <mi>b</mi> </msubsup> <mo>&CenterDot;</mo> <msubsup> <mi>v</mi> <mi>w</mi> <mi>c</mi> </msubsup> </mrow>
α thereinpTo grind depth, vsIs the linear velocity of the grinding wheel, vwK, a, b and c are constants which are the feed speed of the grinding wheel;
step two: according to an aspheric surface bus expression, establishing a radial dimension wear loss prediction model at a grinding point of the grinding wheel in the grinding process by combining the relation between the grinding removal volume of the aspheric surface material and the volume wear loss of the grinding wheel;
Δrx＝f(αp,vs,vw,R,r,Vw)
wherein R is the grinding wheel base radius, R is the grinding wheel arc surface radius, VwRemoving volume for aspheric surface grinding;
step three: establishing an aspheric surface shape error prediction model according to the geometric relation between the aspheric surface bus upper surface shape error and the grinding wheel radial dimension abrasion loss by using the grinding wheel radial dimension abrasion loss prediction model established in the step two;
step four: calculating grinding surface shape error values of all points on an aspheric surface generatrix by using the surface shape error prediction model established in the third step, establishing a Cartesian coordinate system on the aspheric surface, taking the aspheric surface rotation center as a z-axis and taking the x-axis along the horizontal direction of the generatrix, if the grinding surface shape error value of the x-coordinate point is greater than the target surface shape error value, performing iterative pre-compensation processing on the nominal grinding depth of the x-coordinate point, calculating the surface shape error value of the point after the iterative pre-compensation until the calculated surface shape error value of the point is less than the target surface shape error value, and performing x +1 coordinate point processing; if the grinding surface shape error value of the x coordinate point is less than or equal to the target surface shape error value, processing the x +1 coordinate point until the grinding surface shape error values of all points on the aspheric surface bus are less than or equal to the target surface shape error value;
step five: and recording the final predicted value of the nominal grinding depth of each contact point in the iterative process, determining the moving track of the grinding wheel rotation center in the grinding process, and performing numerical control grinding processing programming and subsequent processing.
2. The iterative precompensation grinding method for the large-caliber reflecting mirror based on the grinding wheel wear prediction as claimed in claim 1, characterized in that: the step three of establishing a surface shape error prediction model of the contact point of the grinding wheel and the workpiece on the aspheric surface bus in the grinding process specifically comprises the following steps:
<mrow> <msub> <mi>E</mi> <mi>x</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&Delta;r</mi> <mi>x</mi> </msub> </mrow> <mrow> <msub> <mi>cos&beta;</mi> <mi>x</mi> </msub> </mrow> </mfrac> </mrow>
wherein ExFor aspheric grinding profile error at x coordinate point from the center of rotation on the aspheric generatrix, βxThe inclination angle of a tangent line at a point x away from the rotation center on the aspheric surface bus is shown.
3. The iterative precompensation grinding method for the large-caliber reflecting mirror based on the grinding wheel wear prediction as claimed in claim 2, characterized in that: if the grinding surface shape error value of the x coordinate point is greater than the target surface shape error value in the fourth step, the specific process of performing iterative precompensation processing on the nominal grinding depth of the x coordinate point is as follows:
compensating the aspheric surface shape error caused by the abrasion of the grinding wheel by increasing the nominal grinding depth of the grinding point, superposing the grinding surface shape error value of the x coordinate point on the nominal grinding depth, grinding by the superposed new nominal grinding depth, and calculating the surface shape error value after iterative precompensation; grinding surface from iteration precompensation to x coordinate pointWhen the predicted value of the profile error is smaller than the target profile error value, the superposition of the nominal grinding depths of the x coordinate points is finished, and the nominal grinding depth α of the x point at the moment is recordedpx(n)Iteration times n is more than or equal to 2, and superposition calculation of nominal grinding depth of the x +1 coordinate point is carried out;
the expression of the nominal grinding depth after superposition is as follows:
αpx(n)＝αpx(n-1)+x(n-1)
whereinx(n-1)And calculating the error value of the grinding surface shape obtained after the n-1 iteration of the x coordinate point.
4. The iterative precompensation grinding method for the large-caliber reflecting mirror based on the grinding wheel wear prediction as claimed in claim 3, characterized in that: in the iteration process of the nominal grinding depth, the predicted aspheric surface shape error of the x coordinate point after the nth iteration is represented by the following equation:
<mrow> <msub> <mi>&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>&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>&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>&epsiv;</mi> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </msub> </mrow>
wherein,to a nominal grinding depth of α at the x-coordinate pointpx(n)The predicted value of the time-surface shape error is as follows: the sum of the surface shape errors calculated for the first n-1 iterations.
5. The iterative precompensation grinding method for the large-caliber reflecting mirror based on the grinding wheel wear prediction as claimed in claim 4, characterized in that: the movement track of the grinding wheel rotation center determined in the step five in the grinding process is specifically as follows:
<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>&Delta;r</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>&beta;</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>&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>&Delta;r</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>&beta;</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>&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>
wherein x0Is the x-axis coordinate value of the rotation center of the grinding wheel, z0Is the z-axis coordinate value of the grinding wheel rotation center.
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| CN111638682A (en) * | 2020-05-26 | 2020-09-08 | 四川新迎顺信息技术股份有限公司 | Compensation method for grinding rear cutter face of peripheral tooth spiral blade by using worn grinding wheel |
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| CN118060977A (en) * | 2023-07-31 | 2024-05-24 | 三力五金机械制品(深圳)有限公司 | Aspheric optical lens fine grinding self-adaptive compensation method and device |
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