High precision angular displacement measurement based on self-correcting error compensation of three image sensors
Hai Yu, Qiuhua Wan, Xinran Lu, Changhai Zhao, Lihui Liang
Abstract
As the feedback link of a numerical control system, the measurement accuracy of absolute angular displacement measurements directly affects the control performance of a numerical control system. In previous research, angular displacement measurements based on dual image sensors can achieve higher measurement performance. However, the elimination of harmonic error by the dual image sensor is still limited. For this reason, this paper proposes an image-type angular displacement measurement method based on self-correction error compensation of three image sensors. First, the mathematical model of harmonic error is established, and the shortcomings of using dual image sensors to compensate the error are analyzed. Then, a high precision angular displacement measurement method based on three image sensors is proposed. Finally, the self-correction error compensation method of three image sensors is applied to the angular displacement measurement system, and the measurement performance is verified. The experimental results show that a measurement accuracy of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>1.7</mml:mn> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>6</mml:mn> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-variant" mathvariant="normal">′</mml:mi> <mml:mi class="MJX-variant" mathvariant="normal">′</mml:mi> </mml:mrow> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> can be achieved on the circular grating with a diameter of 96 mm. In contrast, the dual image sensor can only achieve a measurement accuracy of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2.8</mml:mn> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>8</mml:mn> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-variant" mathvariant="normal">′</mml:mi> <mml:mi class="MJX-variant" mathvariant="normal">′</mml:mi> </mml:mrow> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . It is concluded that the odd number of image sensors can achieve higher measurement accuracy than the even number. This research lays a foundation for the realization of high precision image angular displacement measurement.