一种基于单转位特征角的圆度误差分离方法研究

Research on the roundness error separation method based on single transposition characteristic angle

为提高光学标准球形状误差测量准确度,提出了一种基于单转位特征角的圆度误差分离方法。本文方法基于严格的数学原理,利用特征角在形状比较中参照作用,可完全回避开可能产生谐波抑制的所有"盲点";通过一次转位,并分别将转位前后的采样数据进行傅里叶变换,在频域中实现光学标准球圆度误差和主轴径向回转误差的分离,再将分离后的数据变换到时域,可以在使分离后的信号在进入滤波器之前无任何信号损失,使得建模过程无任何原理误差,实现主轴径向回转误差和光学标准器圆度误差的完全分离。实验表明,当每周采样点数为1 024、转位特征角为21.09′时,分离后圆度误差包含所有频次的谐波,无任何谐波抑制,表明光学标准球圆度误差与仪器主轴的回转误差得到严格分离。本文方法不仅可以用于超精密级光学标准球的圆度测量,而且可用于建立精度水平最高的理想的基/标准级圆度测量系统。

In order to improve the measurement accuracy of the optical standard bali＇s shape errors, a roundness error separation method based on single transposition characteristic angle is proposed. The method is based on strict mathematical theory and uses the characteristic angle in the shape of the reference,and it can completely avoid all the blind spots which may produce a harmonic suppression. Through one transposition, the method makes Fouier transformation on the pre-and post-sampling data, and separates the optical standard ball^s roundness errors and radial rotation errors in frequency domain. And then it makes the separated data transformed to time domain,and makes no loss of the separated signal before the filter. The modeling process introduces no principle error. The separation of the radial rotation error and the roundness error of the optical standard ball is achieved completely. Experimental show that when the circle sampling points are 1 024 and the translocation characteristic angle is 21.09 ＇,the roundness error contains all frequency harmonics and no harmonic suppression after separation, indicating a strict separation. The method can be used for ultra-precision optical standard ball roundness measurement and establishing an ideal benchmark / standard circle measurement system.