基于傅里叶变换的转台分度误差分离与补偿方法

Separation and compensation method for indexing error of rotary table based on Fourier transformation

为了保证和提高转台测角系统的现场测量精度,本文针对基于傅里叶变换的转台分度误差分离与补偿方法开展研究。在原理证明傅里叶变换实现转台分度误差分离的基础上,建立转台分度误差与读数头测量值之间的函数模型;根据傅里叶变换中传递函数性质,重点说明双读数头安装角度间隔与测量误差谐波阶次间关系,优化了双读数头布置;在现场可编程门阵列电路平台上实现多读数头测量值的同步获取,采用坐标旋转数字计算方法完成谐波误差函数实时计算。搭建实验平台进行误差分离与补偿效果验证实验,实验结果证明采用优化布置的双读数头信号进行分度误差分离并补偿后,转台的分度误差峰峰值由57.58″减小到3.36″,补偿后的转台测角系统扩展测量不确定度为0.9″(k=2)。

To ensure and improve the field measurement accuracy of the rotary table angular measurement system,a research on the separation and compensation method of rotary table indexing error based on Fourier transformation is proposed.Based on the proof of principle of Fourier transformation to separate the indexing error of the rotary table,the function model between indexing error of the rotary table and the measurement value of the reading head is formulated.According to the nature of transfer function in Fourier transformation,the relationship between the installation angle interval of the double reading head and the harmonic order of the measurement error is highlighted.The arrangement of the double reading head is optimized.The measurement value of multiple reading heads is realized on the field programmable gate array(FPGA)circuit platform.The simultaneous acquisition of the measured values of multiple reading heads is realized in the FPGA circuit platform,and the harmonic error function is calculated in real time by using the coordinate rotation digital computer.The experimental results show that the indexing error can be separated and compensated by using the optimized double reading head signals,the peak value of indexing error of rotary table is reduced from 57.58″to 3.36″,and the expanded measurement uncertainty of angle measuring system of compensated rotary table is 0.9″(k=2).