基于Zernike多项式拟合的自由曲面车削误差补偿技术

Figure Error Compensation of Freeform Surface Turning Based on Zernike Polynomial Fitting

慢刀伺服车削技术是一种特殊的创成加工方法,采用C轴、X轴、Z轴联动的方式在极坐标或圆柱坐标内可车削加工自由曲面光学元件。但是由于各种误差因素的影响,使用慢刀伺服技术仅加工一次获得的光学元件可能不满足精度指标。为此需要研究能够进一步提升慢刀伺服车削加工精度的误差补偿技术。Zernike多项式是面形分析与光学分析之间的理想接口工具,因此本文使用Zernike多项式拟合的方法处理慢刀伺服车削加工的误差,并根据慢刀伺服加工技术的特点,建立慢刀伺服车削加工的误差补偿算法。实验结果表明,基于Zernike多项式拟合的慢刀伺服车削加工误差补偿技术可有效地针对加工中产生的特定误差进行补偿,从而提高自由曲面车削加工精度。

Slow Tool Servo diamond turning is capable of effectively generating freeform optical surfaces or rotationally nonsymmetric surfaces. However, many error sources, such as geometric and thermal errors of machine tool, and the forced vibration, dominate machining accuracy. In order to enhance fabricate accuracy, machining error compensatory approach was studied. Zemike polynomials are powerful in analyzing the relationship between the surface figure and the optical performance. So machining error was analyzed by Zemike polynomial fitting procedure, and the error compensation algorithm based on tool path correction was constructed. Experiments show that the slow tool servo diamond tuming method can generate freeform optical surface, while the compensation method can obviously improve the machining accuracy.