Predictive modeling of the surface pattern of double-sided polishing process of optical components
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摘要: 针对双面抛光难以建立稳定去除函数进行加工面型预测这一问题，基于双面抛光加工原理，采用坐标变换法推导出元件上下表面相对速度分布方程，然后运用ANSYS软件仿真元件上下表面静态压力分布，采用多项式拟合法将仿真数据导入Matlab软件拟合出元件上下表面压力分布随时间变化公式。根据Preston方程推导修正系数K表达式，通过4组抛光实验数据计算出修正系数K值为2.588×10−15，构建双面抛光加工面型预测模型。最后通过加工实验验证该预测模型，实验结果表明预测PV值误差占元件实际加工后面型PV值的1.07%～7.4%左右，预测模型与实际加工后的面型吻合。Abstract: Addressing the challenge of establishing a stable removal function for double-sided polishing to predict the finished surface profile, this paper builds on the principles of double-sided polishing. We use the coordinate transformation method to derive the relative velocity distribution equations for the upper and lower surfaces of the component. Subsequently, static pressure distributions on both surfaces are simulated using ANSYS software. The simulation data is then imported into Matlab and fitted with a polynomial method to determine the time-varying pressure distribution formulas for the component's surfaces. Based on the Preston equation, an expression for the correction coefficient K is derived. The value of the correction coefficient K is calculated to be 2.588×10−15 from four sets of polishing experimental data, enabling the construction of a predictive model for the surface pattern in double-sided polishing processes. The predictive model is ultimately validated through machining experiments. The experimental results indicate that the error in predicting the PV (Peak-to-Valley) value accounts for approximately 1.07% to 7.4% of the actual PV value after processing, demonstrating good agreement between the predicted model and the actual post-processing surface pattern.
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Key words:
- double-sided polishing /
- surface pattern /
- predictive modeling /
- experimental validation
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图 2 下抛光盘与元件的运动关系简图
Figure 2. Sketch of the relationship between the motion of the down-throwing disc and the element
图 3 上抛光盘与元件的运动关系简图
Figure 3. Sketch of the relationship between the movement of the up-throwing disc and the element
图 4 上盘来回摆动的位置与时间关系示意图
Figure 4. Schematic diagram of the position of the upper disk swinging back and forth versus time
图 5 直径300 mm上抛光盘元件下表面应力分布图
Figure 5. Stress distribution on the lower surface of the upper polishing disk element of 300 mm diameter
图 7 不同时刻下元件表面压强分布
Figure 7. Distribution of pressure on the surface of the element at different moments
图 9 实验加工前后与预测面型对比图
Figure 9. Comparison between experimental machining before and after and predicted surface pattern
图 10 预测与加工面型误差分布图
Figure 10. Distribution of prediction and machining surface pattern errors
表 1 压强分布方程的系数
Table 1. Coefficients of pressure distribution equation
coefficient numerical value p00 0.1528 p10 −0.002813 p01 −0.002813 p20 2.042×10−5 p11 5.041×10−5 p02 2.044×10−5 p30 −6.455×10−8 p21 −1.173×10−7 p12 −1.172×10−7 p03 −6.47×10−8 p40 7.503×10−11 p31 3.041×10−14 p22 2.727×10−10 p13 −1.021×10−13 p04 7.528×10−11 
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表 2 修正实验中的抛光工艺参数
Table 2. Polishing process parameters in the modified experiment
Experimental group
numberelement, upper plate,
lower plate rpm(rpm)oscillation speed
(mm/s)time (s) swing distance
(mm)distance from the center of the element
to the center of the lower plate (mm)1 10.1，10.9，10 5/6 2700 10 0、1260 2 12.1，12.9，10 5/6 1800 3 12.1，12.9，10 1/3 300 4 10.1，10.9，10 1/3 420
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表 3 预测验证实验工艺参数及实验数据与预测数据对比
Table 3. Comparison of predicted validation experimental process parameters and experimental data with predicted data
Experimental
group
numberelement, upper
plate, lower
plate rpm(rpm)oscillation
speed
(mm/s)time
(s)swing
distance
(mm)distance from the center of
the element to the center of
the lower plate (mm)experimental processing
of back type PV
values (μm)Predicting post-processing
type PV
values (μm)1# 12.1，12.9，10 5/6 2700 80 0、1160 2.145 2.122 2# 12.1，12.9，10 2 900 10 0、1160 1.149 1.122 3# 10.1，10.9，8 1/3 600 10 0、1260 0.527 0.566 4# 10.1，10.9，10 1/3 1800 10 0、1260 0.962 0.947 5# 10.1，10.9，10 2 3600 10 110、1160 1.720 1.746
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