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摘要:
在非球面及自由曲面加工中，应用最为成熟的是计算机控制光学表面成型(CCOS)技术。现有CCOS技术普遍采用恒压力研抛方法，加工过程中研抛压力保持恒压，通过控制驻留时间实现所需的去除量。本文研究了基于变压力的CCOS研抛方法，增加了调控维度，通过同时控制研抛压力和驻留时间实现所需的去除量。首先，对该方法建立了加工控制的数学模型。然后，测量分析了磨头输出力的稳定性和响应速度，去除函数的稳定性。最终，在K9材料平面镜上开展了正弦压力抛光的材料去除实验。结果表明，实测与理想正弦研抛压力周期一致，力误差标准差约为0.35 N，对去除面形PV和RMS的影响均不到9%；实际与仿真加工的面形轮廓周期一致，加工区域的面形误差在17%以内。本文实现了变压力研抛，验证了基于变压力的CCOS研抛方法在光学加工中的有效性。
Abstract:In grinding and polishing of the aspherical and freeform surface, the CCOS technology is widely used. It commonly uses constant pressure during polishing, and thus the desired amount of material to be remove depends on the dwell time. This paper focuses on the variable pressure CCOS polishing technology. It adds one more degree of freedom to the polishing process, in which the desired amount of material to be removed is controlled by both the polishing pressure and the dwell time. Firstly, a mathematical model was established for the variable pressure polishing process. Then, the stability and response speed of the output force of the polishing tool, and the stability of removal function was measured and analyzed. Finally, a material removal experiment that applied sinusoidal force was carried out on a K9 material mirror. Results show that frequency of the measured force is the same as that of the ideal sinusoidal polishing force, with a standard deviation of the force error being about 0.35 N. Its effect on PV and RMS of the finish surface is less than 9%. The spatial period of the measured surface profile is the same as that of surface profile obtained by simulation of the sinusoidal polishing process. The surface profile error is within 17%. In this paper, variable pressure polishing was achieved, and its effectiveness for optical processing was verified.
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Key words:
- optical processing /
- CCOS /
- variable pressure /
- grinding and polishing
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Overview: The aspherical and freeform surface mirror, as one of the key elements in optical system, is needed more and more. Both higher figure accuracy and higher fabricating efficiency are demended with the development of the optical systems. In grinding and polishing of the aspherical and freeform surface, the CCOS technology is widely used. It is a process during which errors can be corrected quantificationally by a small tool that can follow the local curves of the aspherical and freeform surface. The CCOS technology commonly uses constant pressure during polishing, and thus the desired amount of material to be removed depends on the dwell time. This paper focuses on the variable pressure CCOS polishing technology. It adds one more degree of freedom to the polishing process, in which the desired amount of material to be removed is controlled by both the polishing pressure and the dwell time. Firstly, a mathematical model was established for the variable pressure polishing process. Then, the stability and response speed of the output force of the polishing tool, and the stability of removal function was measured and analyzed. Finally, a material removal experiment that applied sinusoidal force was carried out on a K9 material mirror. Results show that: 1) The mathematical model for the variable pressure polishing process is correct; 2) Frequency of the measured force is the same as that of the ideal sinusoidal polishing force, with a standard deviation of the force error being about 0.35 N. Its effect on PV and RMS of the finish surface is less than 9%; 3) The spatial period of the measured surface profile is the same as that of surface profile obtained by simulation of the sinusoidal polishing process. The surface profile error is within 17%. In this paper, variable pressure polishing was achieved, and its effectiveness for optical processing was verified. Compared with the constant pressure CCOS polishing technology, the variable pressure CCOS polishing technology adds one more degree of freedom to the polishing process, so it need to control both the polishing pressure and the dwell time. In theory, it can improve processing efficiency and convergence rate. At the same time, it need have higher requirements for the force active control system, such as the output force range, response speed and precision. These performance parameters can affect the processing results. Therefore，the key to developing the variable pressure CCOS polishing technology is to research the polishing tool, which must have high performance force active control system.
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图 2 实验设备。(a)研抛机器人和磨头；(b)高精度力测试平台
Figure 2. Experimental setup. (a) Grinding robot and tool; (b) High precision force measurement platform
图 4 正弦压力抛光的材料去除实验加工过程
Figure 4. Machining process of sinusoidal pressure polishing experiment
图 5 磨头输出力实测结果。(a)磨头输出力保持不变；(b)磨头输出力变化(2 N-30 N-2 N)
Figure 5. The measured output force of the polishing tool. (a) Constant force; (b) Changing force (2 N-30 N-2 N)
图 7 正弦压力抛光实验仿真加工面形
Figure 7. Simulated machined surface of the sinusoidal pressure polishing experiment
图 9 加入仿真力误差的仿真面形
Figure 9. Simulated machined surface when the simu-lated sinusoidal force is applied
图 10 正弦压力抛光实验。(a)实测力值曲线；(b)力误差曲线
Figure 10. Sinusoidal pressure polishing experiment. (a) Measured and desired output force; (b) Force error
图 11 加入实测力误差的仿真面形
Figure 11. Simulated machined surface when the measured sinusoidal force is applied
图 12 正弦压力抛光实验。(a)实际加工面形；(b)实际与仿真去除面形轮廓及误差
Figure 12. Sinusoidal pressure polishing experiment. (a) Measured machined surface; (b) Measured and simulated machined surface profile and profile error
表 1 研抛实验工艺参数
Table 1. Grinding and polishing experimental process parameters
移动机构 磨头 工件材料 抛光液材料 抛光液浓度/% 磨盘材料 磨盘直径/mm 公转速度
/(r/min)自转速度
/(r/min)偏心距
/mm研抛压力
/N驻留时间
/s工业机器人
Staubli TX200气缸式主动力控制磨头 K9平面镜 氧化铈 20 聚氨酯 15 -150 180 4 5~30 > 0.05 
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表 2 去除函数实验结果
Table 2. Removal function test results
压力(压强) 时间/s 实测去除量 去除函数(归一化1N1min) PV/nm V/μm3 PV/nm PV偏差/% V/μm3 V偏差/% 保持恒定 15 N(849 g/cm2) 30 417.8 73832079 55.71 -7.82 9844277 0.47 15 N(849 g/cm2) 45 632.0 111129247 56.18 -7.04 9878155 0.81 15 N(849 g/cm2) 60 920.7 150357930 61.38 1.56 10023862 2.30 15 N(849 g/cm2) 90 1400.5 225229297 62.24 2.98 10010191 2.16 线性变化 5 N(283 g/cm2) 240 1175.2 185795136 58.76 -2.77 9289757 -5.19 10 N(566 g/cm2) 120 1276.8 191565012 63.84 5.63 9578251 -2.25 15 N(849 g/cm2) 90 1381.1 248036904 61.38 1.56 9878155 0.81 20 N(1132 g/cm2) 60 1280.0 197706222 64.00 5.90 9885311 0.89
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