CN101670541B - Fast polishing traversing processing method of heavy-calibre planar optical elements - Google Patents

Abstract

The invention discloses a fast polishing and traverse processing method for a large-diameter flat optical element, relating to a large-diameter flat optical element. Provided is a fast polishing and traverse processing method for large-caliber planar optical elements. CNC polishing machine is adopted, equipped with polishing disc, polishing pad, vacuum film, workpiece rotating shaft, dressing wheel, dressing wheel shaft and working traverse shaft. Select the processing method, set the processing parameters, and use the spatial coordinate transformation and Fourier series to calculate the relative velocity of the workpiece to the polishing disc; use the pressure distribution surface model to calculate the pressure distribution during the workpiece traverse process, and perform linear processing on a traverse process cycle of the workpiece Cutting, combined with the Princeton formula to obtain the material removal rate of the points on the different radii of the workpiece; calculate the probability of the points on the workpiece on different radii exposing the polishing disc and falling into different pressure areas, and use the ratio to weight the obtained material removal rate to predict after processing The change trend of the workpiece surface shape, and the steps in which the inspection results after processing are in line with the predictions.

Description

Rapid Polishing and Traversing Processing Method of Large Aperture Plane Optical Components

technical field

The invention relates to a large-diameter flat optical element, in particular to a fast polishing and traverse processing method for the large-diameter flat optical element.

Background technique

At present, the processing of large-size and high-precision optical components is valued at home and abroad. How to realize high-efficiency batch processing of high-precision large-diameter optical components, especially large-diameter flat and aspheric components, is an important issue in the field of optical manufacturing. It is also a serious challenge to the current field of optical manufacturing. (Refer to literature: 1. Zhu Haibo, "Research on CNC polishing technology for large-diameter planar components," [D]. Dissertation for Master of Engineering, Sichuan University, 2005; 2. J.Luo and D.A.Domfeld, "Material removal mechanism in chemical mechanical polishing: theory and modeling," [J]. IEEE Transactions on Semiconductor Manufacturing, Vol.14, No, 2, 112-123, 2001).

After rough grinding, fine grinding or precision grinding, large-aperture planar optical components are required to be polished to improve the surface accuracy of the workpiece and reduce surface roughness and subsurface defects. Traditional primary polishing and circular polishing are mechanochemical polishing (CMP) processes, which can meet the processing requirements of workpieces, but require experienced engineers to obtain the required surface shape of workpieces, which consumes a lot of time and reduces production efficiency. The two processes of initial polishing and circular polishing are both processes that connect the preceding and the following, and the processed results have a great influence on the processing effect and efficiency of the subsequent processes. Therefore, it is necessary to improve the processing technology of initial polishing and ring polishing, improve processing efficiency and processing accuracy, predict and control the change trend of surface shape, and process a surface morphology that is beneficial to CNC polishing.

The rapid polishing traverse processing method can greatly improve the processing efficiency, and the material removal rate (Material Removal Rate, MRR) can reach 5-10um/h, which is 8-10 times that of initial polishing. Compared with ring polishing, it can More accurately predict and control the change trend of workpiece surface shape. The rapid polishing traverse processing method utilizes the inhomogeneity of the pressure distribution in the contact area between the workpiece and the polishing disc during the traverse process to realize the uneven removal of the workpiece material as a whole, so as to obtain the required surface accuracy of the workpiece.

Contents of the invention

The object of the present invention is to provide a fast polishing and lateral movement processing method for large-diameter planar optical elements in order to address the shortcomings of low efficiency and difficulty in predicting and controlling the variation trend of workpiece surface shape in the polishing process of large-diameter planar optical elements.

The present invention adopts a fast polishing system for large-caliber planar optical elements (that is, a numerically controlled polishing machine tool). The numerically controlled polishing machine tool is provided with a polishing disc, a polishing pad, a vacuum film, a workpiece rotating shaft, a dressing wheel, a dressing wheel shaft and a working traverse shaft. The polishing disc is provided with a rotating shaft of the polishing disc, and the polishing disc rotates independently under the drive of the rotating shaft of the polishing disc. With a certain surface roughness and flatness, the dressing wheel can dress the surface of the polishing pad as required under the drive of the dressing wheel shaft. Inject polishing fluid on the polishing pad.

The polishing pad can be a polyurethane polishing pad.

The polishing disc can be a marble polishing disc.

The polishing liquid may be composed of cerium oxide mixed with deionized water.

The present invention comprises the following steps:

1) a step of selecting a processing method, setting processing parameters, and calculating the velocity of the workpiece relative to the polishing disc by using spatial coordinate transformation and Fourier series;

2) One uses the pressure distribution surface model (skin model) to calculate the pressure distribution during the workpiece traversing process, performs linear cutting on the workpiece for one traversing processing cycle, and combines the Princeton (Preston) formula to obtain the material removal rate of the points on the different radii of the workpiece (Material Removal Rate, MRR) steps;

3) One calculates the probability of exposing the polishing disc and falling into different pressure areas on different radii on the workpiece, and uses the ratio to weight the obtained material removal rate MRR according to the probability to predict the surface shape change trend of the workpiece after processing. The step in which the detection results match the prediction.

In step 1), the processing method is preferably a traversing processing method, and the processing parameters are external pressure, polishing disc rotation speed, workpiece rotation speed, Princeton (Preston) coefficient, polishing disc radius, workpiece radius, eccentricity , traversing speed and the maximum exposed edge distance of the workpiece. The steps of selecting the processing method, setting the processing parameters, and calculating the speed of the workpiece relative to the polishing disc by using spatial coordinate transformation and Fourier series can establish two coordinate systems of relative movement and relative stillness at the center of the workpiece, and establish relative motion at the center of the polishing disc. Moving and relatively static two coordinate systems, using space coordinate transformation and Fourier series to calculate the relative velocity of the workpiece during the traverse process.

In step 2), the "Use the pressure distribution surface model (skin model) to calculate the pressure distribution during the workpiece traverse process, perform linear cutting on the workpiece during one traverse process cycle, and combine the Princeton (Preston) formula to obtain the different radii of the workpiece. The material removal rate (Material Removal Rate, MRR) of the point, can use the pressure distribution surface model to calculate the pressure distribution during the workpiece traverse process, perform linear cutting on a traverse processing cycle of the workpiece, establish the cutting point, and use the pressure distribution surface model Calculate the pressure distribution of each cutting point during the traverse of the workpiece; combined with the Princeton (Preston) formula, calculate the material removal rate MRR of the points on different radii of the workpiece at the cutting point for one revolution, and finally, according to the moving distance of the workpiece and each The material removal rate of one rotation of cutting point can be integrated to the material removal rate of the whole lateral movement process, and calculates the total material removal rate of points on different radii on the workpiece; said Princeton (Preston) formula is MRR=k·p· v, where k is the Princeton Preston coefficient, p is the pressure on a certain point on the workpiece, and v is the speed of a certain point on the workpiece relative to the polishing disc.

In step 3), the probability of exposing the polishing disk and falling into different pressure regions on different radii on the workpiece is calculated, and the obtained material removal rate MRR is weighted according to the probability, and the surface shape of the workpiece after processing is predicted. Trend, the step in which the detection results after processing are consistent with the prediction is to calculate the probability of the points on the workpiece with different radii exposed to the polishing disc and falling into different pressure areas, and the total material of the points on the workpiece with different radii obtained by integrating the ratio according to the probability The removal rate MRR is weighted to predict the change trend of the workpiece surface shape after processing, and the detection results after processing are consistent with the prediction.

The principle of rapid polishing is to use polymer material-polyurethane as a polishing pad, and according to the applied pressure, combine with relatively fast relative speed and traverse processing method to quickly polish large-diameter flat optical elements. Compared with other polishing methods, the polyurethane polishing pad used in the present invention can avoid the hydration precipitation layer produced by the asphalt polishing pad to polish workpieces, reduce subsurface defects, and reduce heat generated during polishing. The relatively fast relative speed and the traverse processing method can significantly improve the polishing efficiency, predict and control the change trend of the workpiece surface shape.

The invention adopts a fast polishing system for large-diameter flat optical elements (ie, a numerically controlled polishing machine tool), which includes a 3-axis linkage machine tool, a polyurethane polishing pad, a diamond dressing wheel and a polishing liquid supply system. The surface processing of large-diameter flat optical elements is completed by rapid polishing using the traverse processing method, and the surface shape change trend of the workpiece after processing is predicted. The detection results after processing are consistent with the prediction, so it can be used to control the surface shape change trend of the workpiece during processing.

Description of drawings

FIG. 1 is a schematic structural diagram of a fast polishing system for a large-aperture planar optical element (ie, a numerically controlled polishing machine tool) adopted in an embodiment of the present invention.

FIG. 2 is a schematic top view of the structure of FIG. 1 .

Fig. 3 is a flow chart of predicting and controlling the change trend of workpiece surface shape adopted by the embodiment of the present invention.

Fig. 4 is a schematic diagram of calculating the relative velocity of a certain point N on the workpiece used in the embodiment of the present invention.

Fig. 5 is a schematic diagram of a pressure distribution surface model (skin model) used in an embodiment of the present invention.

Fig. 6 is a diagram showing the relationship between the material removal rate of the N point on the workpiece with a radius of 100 mm and the distance traveled by the center of the workpiece used in the embodiment of the present invention. In Fig. 6, the abscissa is the travel distance (m) of the center of the workpiece, and the ordinate is the average removal rate of the material thickness (m/s).

为160mm。Fig. 7 is a diagram showing the relationship between the material removal rate at N points on different radii on the workpiece and the distance traveled by the center of the workpiece during the traverse processing adopted in the embodiment of the present invention. In Fig. 7, the abscissa is the travel distance (m) of the center of the workpiece, and the ordinate is the average removal rate of the material thickness (m/s). ■ is 0mm, ● is 20mm, ▲ is 40mm, 60mm, ☆ is 80mm, ◇ is 100mm, □ is 120mm, ○ is 140mm,

is 160mm.

Fig. 8 is a schematic diagram of the total material removal rate of N points on different radii in one traversing cycle obtained by integrating the curves in Fig. 7 in the traversing machining process adopted in the embodiment of the present invention. In Fig. 8, the abscissa is the workpiece radius (m), and the ordinate is the average removal rate of material thickness (m/s).

Fig. 9 is a schematic diagram of the total material removal rate of N points on different radii predicted in one traverse cycle during the weighted traverse machining process adopted in the embodiment of the present invention. In Fig. 9, the abscissa is the workpiece radius (m), and the ordinate is the average removal rate of material thickness (m/s).

Fig. 10 and Fig. 11 are the surface measurement diagrams of the x and y directions of the workpiece after data processing adopted in the embodiment of the present invention. In FIGS. 10 and 11, the abscissa is the workpiece radius (m), and the ordinate is the measured height difference (nm).

Detailed ways

The following embodiments will further illustrate the present invention in conjunction with the accompanying drawings.

Referring to Figures 1 and 2, the rapid polishing system for large-diameter flat optical elements (ie, a numerically controlled polishing machine tool) used in the present invention includes a 3-axis linkage machine tool, a polyurethane polishing pad, a diamond dressing wheel and a polishing liquid supply system. The surface processing of large-diameter flat optical elements is completed by rapid polishing using the traverse processing method, and the surface shape change trend of the workpiece after processing is predicted. The detection results after processing are consistent with the prediction, so it can be used to control the surface shape change trend of the workpiece during processing.

In Figures 1 and 2, the workpiece 21 is adsorbed by the vacuum film 22, and the workpiece rotation axis Z1 can be raised and lowered to apply different pressures to the workpiece 21. The workpiece 21 is driven by the workpiece rotation axis Z1 to rotate independently, and the working traverse axis Z3 can be Drive the workpiece 21 to move laterally. The polyurethane polishing pad 23 is pasted on the marble polishing disk 24 by superglue, and the polishing disk 24 rotates independently under the drive of the polishing disk rotation axis Z4. In order to keep the polishing pad 23 with a certain surface roughness and smoothness, the diamond dressing wheel 25 can dress the surface of the polishing pad 23 as required under the driving of the dressing wheel shaft Z2. The polishing liquid P (the polishing liquid is composed of cerium oxide and deionized water mixed, and the ratio of cerium oxide and deionized water is preferably 10:1 in terms of mass ratio) is supplied to the system and sprayed on the surface of the polishing pad 23 during processing. The three axes of axis Z1, axis Z3 and axis Z4 are linked to remove material from the workpiece 21. In FIG. 2, the dressing wheel 25 has a radius R and the workpiece 21 has a radius R1.

The CNC polishing machine used in the embodiment of the present invention is an ultra-precision fast polishing machine, which is a PPS100 fast polishing machine from Beijing NorthTiger Machine Tool Co., Ltd.

Fig. 3 is a flow chart of the present invention for predicting and controlling the change trend of workpiece surface shape. The process is the beginning—choose the processing method and set the processing parameters—calculate the relative velocity—calculate the pressure distribution using the surface model—calculate the MRR (material removal rate) during the cutting traverse process—weight the MRR——test results and Predictions are met—closed.

Main implementation steps of the present invention are:

1) Select the processing method, set the processing parameters, and use the spatial coordinate transformation and Fourier series to calculate the speed of the workpiece relative to the polishing disc:

The processing method is the traverse processing method, the processing parameters are selected as the external pressure 105.84N, the rotation speed of the polishing disc is w1, the rotation speed of the workpiece is w2, w1=w2=36rad/s, and the coefficient k of Princeton (Preston) is 0.7×10 ^-12 m ² /N ² , polishing disc radius R=550mm, workpiece radius R1=160mm, eccentricity e=160mm, traverse speed Vx=1000mm/min, workpiece maximum exposed edge distance d=80mm.

Fig. 4 provides the schematic diagram of calculating the relative velocity of a certain point N on the workpiece for the present invention. In Fig. 4, four Cartesian coordinate systems are respectively established: 1. The coordinate system x ₂ o ₂ y ₂ moving with the workpiece, the origin is Workpiece motion center o ₂ ; 2. The relative stationary coordinate system X ₂ O ₂ Y ₂ of the workpiece, the origin is the workpiece static center O ₂ ; 3. The coordinate system x ₁ y ₁ o ₁ moving with the polishing disc, the origin is the polishing disc movement Center o ₁ ; 4. The relative stationary coordinate system X ₁ O ₁ Y ₁ of the polishing disc, the origin being the stationary center O ₁ of the polishing disc. The rotational speed of the polishing disc is w ₁ , the rotational speed of the workpiece is w ₂ , the eccentricity is e, the radius of the workpiece is R1, the radius of the polishing disc is R, and the lateral moving speed of the workpiece is Vx. Take any point N on the workpiece, the radius relative to the workpiece motion coordinate system x ₂ o ₂ y ₂ is r, and the angle relative to the x ₂ axis is a. The speed of a certain point N on the workpiece relative to the polishing disc can be obtained by using the space coordinate change and the Fourier series.

In the coordinate system x ₂ o ₂ y ₂ :

x ₂ =r·cos(a), y ₂ =r·sin(a);

In _{the coordinate} system _X2O2Y2 :

X ₂ ＝x ₂ ·cos(w2·t)-y ₂ ·sin(w2·t)

Y ₂ =x ₂ ·sin(w2·t)+y ₂ ·cos(w2·t);

In the coordinate system X ₁ O ₁ Y ₁ :

X ₁ =X ₂ +e+F(t)

Y ₁ =Y ₂ ;

In the coordinate system x ₁ y ₁ o ₁ : x ₁ ＝X1·cos(w1·t)+Y1·sin(w1·t)y ₁ ＝-X ₁ ·sin(w1·t)+Y ₁ ·cos( w1·t).

in

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}}{\frac{\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; Vx</span>}}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; Vx</span>}<span\; class="notranslate">\; \&CenterDot;</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; Vx</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; t</span>}}{\frac{\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; Vx</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; t</span>}}{\frac{\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; Vx</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; 5</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; t</span>}}{\frac{\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; Vx</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ]</span>$

上式中，S为工件左右运动摆幅。N point on the workpiece relative to the speed of the polishing disc

In the above formula, S is the left and right movement swing of the workpiece.

2) Use the pressure distribution surface model (skin model) to calculate the pressure distribution during the workpiece movement, perform linear cutting on the workpiece for one traversing processing cycle, and combine the Preston formula (MRR=k·p·v) to obtain the points on the workpiece with different radii The material removal rate step:

Fig. 5 is the schematic diagram of the pressure distribution surface model (skin model) that the present invention provides, and the workpiece and the polishing disc contact zone pressure distribution are divided into two parts, A zone and B zone, wherein B zone is an annular zone, and width is S. Suppose the pressure in area A is p, the pressure in area B is p+p0, the radius of the polishing disc is R, the radius of the workpiece is R1, the distance between the exposed edge of the workpiece is d, and the distance between the center of the workpiece and the edge of the polishing disc is d1. Point M1 is the intersection point of the workpiece circle and the ring s circle in FIG. 5 , and point M2 is the intersection point of the workpiece circle and the polishing disc circle in FIG. 5 . The formula of the relationship between the width of the ring belt s and the relationship between the exposed edge distance and d can be expressed as the following equation:

$\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; \&le;</span>\frac{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="R"\; filenames="DEST\_PATH\_HSB00000455233200011.png,H2009101125484E00021.png"\; state="\{\{state\}\}">R</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d\; R"\; filenames="DEST\_PATH\_HSB00000455233200011.png,H2009101125484E00021.png"\; state="\{\{state\}\}">d</figure-callout></span><figure-callout\; id="1"\; label="d\; R"\; filenames="DEST\_PATH\_HSB00000455233200011.png,H2009101125484E00021.png"\; state="\{\{state\}\}">\; </figure-callout>}& \frac{\mathrm{<span\; class="notranslate">\; </span>}}{}\frac{\mathrm{<span\; class="notranslate">R</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="R"\; filenames="DEST\_PATH\_HSB00000455233200011.png,H2009101125484E00021.png"\; state="\{\{state\}\}">R</figure-callout></span>}\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.$

According to the balance formula of force and moment in Newton's law, the equations can be obtained:

$\underset{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}<span\; class="notranslate">\; \&Integral;</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dxdy</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}$

$\underset{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}<span\; class="notranslate">\; \&Integral;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dxdy</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

According to the above equations, p can be obtained by using the double integral, which can be expressed as:

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; B</span>}}{<span\; class="notranslate">\; \&Integral;</span><span\; class="notranslate">\; \&Integral;</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; dxdy</span>}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; A</span>}}{<span\; class="notranslate">\; \&Integral;</span><span\; class="notranslate">\; \&Integral;</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; dxdy</span>}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; B</span>}}{<span\; class="notranslate">\; \&Integral;</span><span\; class="notranslate">\; \&Integral;</span>}\mathrm{<span\; class="notranslate">\; dxdy</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; B</span>}}{<span\; class="notranslate">\; \&Integral;</span><span\; class="notranslate">\; \&Integral;</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; dxdy</span>}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; A</span>}}{<span\; class="notranslate">\; \&Integral;</span><span\; class="notranslate">\; \&Integral;</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; dxdy</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; B</span>}}{<span\; class="notranslate">\; \&Integral;</span><span\; class="notranslate">\; \&Integral;</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; dxdy</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; B</span>}}{<span\; class="notranslate">\; \&Integral;</span><span\; class="notranslate">\; \&Integral;</span>}\mathrm{<span\; class="notranslate">\; dxdy</span>}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; A</span>}}{<span\; class="notranslate">\; \&Integral;</span><span\; class="notranslate">\; \&Integral;</span>}\mathrm{<span\; class="notranslate">\; dxdy</span>}<span\; class="notranslate">\; )</span>}$

The workpiece lateral movement processing method is a relatively complicated process, which includes both the rotation of the workpiece and the polishing disc, and the lateral movement of the workpiece. At the same time, during the lateral movement, the workpiece will still be exposed to the polishing disc for part of the time without material removal. Therefore, to simplify this machining process, a linear cut can be made to the workpiece traversing machining cycle. Without loss of generality, a point N on an arbitrary radius r of the workpiece is selected for analysis. The linear cutting of this lateral movement process is divided into the following two parts:

工件在这个区域旋转一圈材料厚度平均去除率为H0。The first part: the polishing disc is not exposed on the edge of the workpiece. During this part of the movement, the point N is always located in the polishing disc, and the pressure

The average removal rate of material thickness is H0 when the workpiece rotates one circle in this area.

The second part: the process of exposing the polishing disc from the edge of the workpiece to the maximum distance. Assuming that there are some cutting points, every 8mm is 1 point, and the maximum exposed distance is 10 points. When the center of the workpiece moves to each cutting point, assuming that it stops and rotates at each cutting point for 1 revolution, the average removal rate of material thickness obtained by N points at these 10 cutting points is H1, H2, H3...H10 , and then according to the moving distance of the workpiece and the material removal rate of each cutting point for one revolution, the material removal rate of the entire lateral movement process can be integrated to calculate the total material removal rate of N points. At each cutting point, due to the difference in relative eccentricity e, p and p0 calculated using the pressure distribution surface model (skin model) are also different. According to the relative velocity obtained in step 1) and the p and p0 calculated by the pressure distribution surface model, the material removal rate of a certain point N on the workpiece radius at each cutting point can be calculated according to the Princeton Preston formula (MRR=k p v) .

Figure 6 is a graph showing the relationship between the material removal rate at the 100mmN point on the workpiece radius and the distance traveled by the workpiece circle center. The abscissa indicates the travel distance of the center of the workpiece, in m, and the ordinate indicates the average removal rate of the material thickness, in m/s. It can be seen from Figure 6 that the first turning point of the curve change occurs at the first cutting point. The reason is that the workpiece begins to expose the polishing disc, and the pressure distribution begins to change from uniform to surface model; the second turning point of the curve change The turning point appears at the 8th cutting point. From the 1st cutting point to the 7th cutting point, the material removal rate has been on the rise. At the 8th cutting point, the material removal rate begins to decline. The reason is that From the 8th cutting point, point N began to fall into the outer area of the polishing disc for part of the time, without material removal, resulting in a significant drop in material removal rate.

Fig. 7 is the material removal rate curve of point N on different radii of the workpiece in the process of traversing machining.

Fig. 8 shows the total material removal rate of points N on different radii in one traversing cycle obtained by integrating the curves in Fig. 7 during traversing processing.

3) Calculate the probability of exposing the polishing disc and falling into different pressure regions on different radii on the workpiece, and use the ratio to weight the obtained material removal rate according to the probability:

According to the assumption of linear cutting to calculate the average thickness removal rate of the material thickness for one revolution, the N point on the larger radius has a higher probability of exposing the polishing disc, and its removal rate should be smaller, and the N point on the smaller radius does not expose the polishing disc. CD, then its removal rate should be higher. However, due to the discontinuity of motion and the incompleteness of rotation, there are certain limitations in linear cutting. The workpiece will not stop at a certain cutting point and rotate for a circle, then continue to rotate and move laterally to the next cutting point to stop and stop again. One revolution; and it may not be one revolution, it may be a fraction of a revolution. In the actual processing process, it is possible that the N point with a smaller radius falls into the area of pressure p when the cutting point rotates, while the N point with a larger radius falls into the p+p0 area which is much larger than the pressure p when the cutting point rotates , in order to balance the probability of exposing the polishing disc and the influence of point N falling into different pressure regions on the average removal rate of material thickness, this effect can be expressed by a ratio, and the center coordinate of the trajectory of point N on the radius of 0mm is from the edge of the polishing disc The distance between this distance and the distance between the center coordinates of N points on different radii and the edge of the polishing disc is used as a measurement parameter to indicate the probability of exposing the polishing disc during processing and the possibility of falling into a high pressure area. According to the influence of property, the material removal rate in Fig. 7 is weighted according to different ratios. Table 1 shows the material removal rate after the weighted assignment of the removal rate according to the ratio of the distance between the coordinates of the center of the circle and the edge of the polishing disc.

Table 1

Fig. 9 shows the total material removal rate of points N on different radii predicted in one traversing cycle during traversing machining after weighted assignment.

Fig. 10 and Fig. 11 are the upper surface measurement diagrams of the workpiece in x and y directions after data processing.

As mentioned above, it can be seen from Figures 9 to 11 that as the radius of the workpiece increases, the predicted material removal rate is higher and higher, so the edge of the workpiece is lower and lower; the closer to the center of the workpiece, the higher the height, and the closer to the workpiece The lower the edge, the lower the height, the change trend of the workpiece surface shape after actual processing is consistent with the prediction. Therefore, the workpiece can be polished efficiently by adopting different motion modes according to the rapid polishing traverse method, and the actual processed surface shape of the workpiece can be controlled according to the predicted result.

In addition, the present invention is not limited to the above-mentioned embodiments, and various changes can be made without departing from the gist of the present invention.

Claims (8)

1. The rapid polishing and traverse processing method of large-diameter planar optical elements is characterized in that a numerically controlled polishing machine tool is used, and the numerically controlled polishing machine tool is provided with a polishing disc, a polishing pad, a vacuum film, a workpiece rotating shaft, a dressing wheel, a dressing wheel shaft and The working traverse axis, the polishing disc is equipped with the rotating shaft of the polishing disc, and the polishing disc rotates independently driven by the rotating shaft of the polishing disc, the polishing pad is set on the polishing disc, the workpiece is set on the workpiece rotating shaft of the polishing pad, and the vacuum film is set on the surface of the workpiece. Inject polishing fluid on the polishing pad; Described processing method comprises the following steps: 1) a step of selecting a processing method, setting processing parameters, and calculating the velocity of the workpiece relative to the polishing disc by using spatial coordinate transformation and Fourier series; 2) A step of using the pressure distribution surface model to calculate the pressure distribution during the traversing process of the workpiece, linearly cutting the workpiece for one traversing processing cycle, and combining the Princeton formula to obtain the material removal rate of the points on the different radii of the workpiece; 3) One calculates the probability of exposing the polishing disc and falling into different pressure areas on different radii on the workpiece, and uses the ratio to weight the obtained material removal rate MRR according to the probability to predict the surface shape change trend of the workpiece after processing. The step in which the detection results match the prediction. 2 . The rapid polishing traverse processing method for large-diameter planar optical elements according to claim 1 , wherein the polishing pad is a polyurethane polishing pad. 3 . 3. The rapid polishing and traversing processing method for large-diameter planar optical elements as claimed in claim 1, wherein the polishing disc is a marble polishing disc. 4. The rapid polishing traverse processing method for large-aperture planar optical elements as claimed in claim 1, characterized in that the polishing liquid is composed of cerium oxide and deionized water. 5. The rapid polishing and traversing processing method of large-diameter planar optical elements as claimed in claim 1, characterized in that in step 1), the processing method is a traversing processing method, and the processing parameters are externally applied Pressure, polishing disc rotation speed, workpiece rotation speed, Princeton coefficient, polishing disc radius, workpiece radius, eccentricity, traversing speed and maximum exposed edge distance of the workpiece. 6. The fast polishing and traversing processing method of large-aperture planar optical elements as claimed in claim 1, characterized in that in step 1), the selection of the processing method, the setting of processing parameters, and the use of spatial coordinate transformation and Fourier level The steps for numerically calculating the speed of the workpiece relative to the polishing disc are to establish two coordinate systems of relative motion and relative rest at the center of the workpiece, and establish two coordinate systems of relative motion and relative rest at the center of the polishing disc, using spatial coordinate transformation and Fourier series calculation The velocity of the workpiece relative to the polishing disc during traverse. 7. The fast polishing and traversing processing method of large-diameter planar optical element as claimed in claim 1, is characterized in that in step 2), said utilize pressure distribution surface model to calculate the pressure distribution in the workpiece traversing process, to The workpiece is linearly cut in one traversing processing cycle, and the material removal rate of points on different radii of the workpiece is obtained by combining the Princeton formula. The pressure distribution in the process of workpiece traversing is calculated by using the pressure distribution surface model, and linear cutting is performed on a traversing processing cycle of the workpiece. , to establish the cutting point, and use the pressure distribution surface model to calculate the pressure distribution of each cutting point during the workpiece traversing process; then combine the Princeton formula to calculate the material removal rate of the point on the workpiece with different radii for one revolution at the cutting point; finally, according to the workpiece The moving distance and the material removal rate that each cutting point rotates one week, the material removal rate of the whole lateral movement process is integrated, and the total material removal rate of points on different radii on the workpiece is calculated; the Princeton formula is MRR=k· p·v, where k is the Princeton Preston coefficient, p is the pressure on a certain point on the workpiece, and v is the speed of a certain point on the workpiece relative to the polishing disc. 8. The rapid polishing traverse processing method of large-diameter planar optical elements as claimed in claim 1, characterized in that in step 3), the points on different radii on the calculation workpiece expose the polishing disc and fall into different pressure regions According to the probability, the obtained material removal rate MRR is weighted by using the ratio to predict the change trend of the workpiece surface shape after processing. The step that the detection results after processing are consistent with the prediction is to calculate the points on the workpiece with different radii to expose the polishing disc. And the probability of falling into different pressure areas, according to the probability, use the ratio to weight the total material removal rate of points on different radii on the workpiece obtained by the integration, predict the surface shape change trend of the workpiece after processing, and the detection results after processing are consistent with the prediction .

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