基於阿貝原則分析旋轉平台角度定位誤差之方法與補償

Analysis and Compensation of Angular Positioning Error of Rotary Stages Based on Abbe Principle

李羿宗(Yi-Tsung Li)

指導教授 ： 范光照

共同指導教授 ： 陳亮嘉(Liang-Chia Chen)

國立臺灣大學/工學院/機械工程學研究所/博士(2017年)

https://doi.org/10.6342/NTU201700752

摘要

阿貝原則是位移計量的最基本原則，此原則提供了在儀器設計中量測軸與移動軸的重要設計原則。若無法將量測軸與移動軸設計為共線，則要知道兩軸間的偏移量以及移動軸的偏擺誤差，如此才能補償定位誤差。
旋轉定位平台的角度定位回饋裝置通常來自於旋轉編碼器，如同阿貝原則一樣，其旋轉平台在設計上其工作平面應該與量測平面共平面。但旋轉平台通常不會這樣設計，其旋轉編碼器通常會被安裝在離軸承一定距離處，而這之間的距離也可以被視為一種偏移量。
在本研究中，基於阿貝原則，提出一種分析與校正旋轉平台角度定位誤差之方法，根據理論分析發現，旋轉平台的角度定位誤差將會因為旋轉編碼器之碼盤與旋轉平面存在偏移量以及偏擺誤差的存在而產生。而旋轉軸的徑向誤差與編碼器的碼盤半徑尺寸也會影響角度定位誤差。
實驗結果驗證了所提出之誤差模型的正確性。如同阿貝原則是設計線性位移系統的準則，本研究之結果證明了旋轉平台之旋轉平面亦須與量測平面共平面，若無法將量測平面與旋轉平面設計為共平面，則須了解碼盤半徑之大小、以及碼盤距離最近軸承處之距離、旋轉軸軸心的徑向誤差以及偏擺誤差，如此才能補償角度定位誤差。

關鍵字

旋轉台 ； 阿貝誤差 ； 角度定位誤差 ； 徑向誤差 ； 偏擺誤差

並列摘要

Abbe error provides a design guideline for displacement measurement that the measuring axis should be in line with the moving axis. If it not possible, both the offset between two axes and the angular error in linear motion should be known for the consequence of positioning error compensation.
Similar to the Abbe principle, the angular position of a rotary stage is measured by a rotary encoder, which rotating plane should be in plane with the moving table. It is normally not possible with the fact that the encoder is normally mounted at a distance from the bearing. The distance in between can also be regarded as an offset.
In this research, a novel method of analyzing and correcting angular positioning error for rotary tables is proposed. It is found that the angular positioning error will be induced by the tilt error of the spindle if an offset exists. The radial error of the spindle and the size of the encoder will also affect the angular positioning error. This phenomenon has not been investigated in detail. Experimental results verified the correctness of the proposed error model. Analogous to the Abbe principle that applies to displacement measurement of linear stages in general, a new principle is proposed for the design rule of rotary stages.

並列關鍵字

Rotary stage ； Abbe error ； Angular positioning error ； Tilt error ； Radial error

參考文獻

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