A super-high-accuracy angular index table

Abstract

This study quantitatively derives a principle for super-high-accuracy angular indexing using an index table formulation, and verifies it in a mathematical simulation. An index table is a rotary table installed on a machine tool. Its main function is to fix the angle position of the rotational shaft. The angle position is measured by a rotary encoder built into the rotary table. The rotary encoder is required to measure the angle with high accuracy. In previous studies, the performance of the rotary encoder has been improved by two methods: direct reduction of the angle error factors, and self-calibration. The angle accuracy in these methods varies from 0.1 to 0.4 arcsecs during one rotation. Instead, the National Institute of Advanced Industrial Science and Technology (NMIJ/AIST) in Japan has developed an angular indexing device with super high accuracy, which measures the static angle position to 0.01 arcsecs. Although the principle of super-accurate angular indexing has been qualitatively discussed, a quantitative understanding is lacking. In the present paper, the principle is derived from a Fourier transform analysis, exploiting the circular closure characteristic of the angle error. The principle is then investigated in mathematical simulation of the quantitative formulation. The simulation has obtained positive results to derive the principle quantitatively.