基于蒙特卡洛法的圆光栅测角误差分析与补偿

Measuring angle′s error analysis and compensation of circular grating sensor based on Monte Carlo method

在一类以圆光栅传感器作为测角元件的舵机减速器力能传递实验中,圆光栅传感器的同轴度、读数头读数和仪器示值,这些传感器自身的误差会影响减速器转角的测量精度。本文以圆光栅传感器作为研究对象,分析了多种转角测量误差的导致因素,并将其归类为系统误差和随机误差;通过物理分析和数值计算获得了转角误差的分布特性,提出通过基于蒙特卡洛法(MCM)的不确定度计算获得实际转角的误差补偿量从而提升转角数据处理能力并提高转角测量精度的新方法。直方图仿真曲线给出了转角误差的概率分布规律,并以此计算了理论上的角度测量误差的补偿量。实验以某舵机减速器为测试设备依本文方法进行转角数据处理,结果将测角精度提高到角秒数量级(10″),证明了方法的有效性。

In a series of steering gear reducer′s force transmitting experiment with circular grating sensor as rotating angle measuring device,when the concentricity of circular grating sens or,the read head′s readings and the instruments indicate errors,the combined effect of these facto rs will make the final measured angle distorted,and these errors will affect the sensor reducer angle′ s measurement precision.In this paper,with a circular grating sensor as the research object,th e factors leading to a variety of angle measurement errors are analyzed,which will be classified as systematic errors and random errors.The distribution characteristics of rotating angular error are obtained by means of physical analysis and numerical calculation,and the new method is proposed to achieve actual rotati ng angle error compensation amount,thereby enhancing rotating angle data processing capabilities and improv ing rotating angle measurement precision based on the Monte Carlo method （MCM）. Experimental results indicate that the precision of the measured angle is improv ed to arc-seconds magnitude （10＂）,and demonstrate the effectiveness of this me thod.