Planar Two-Dimensional Capacitive Displacement Sensor Based on Time Grating

Abstract

Efforts to meet the demand for planar two-dimensional (2D) displacement measurement systems are limited by the difficulties of manufacturing 2D diffraction gratings with high precision over a large area. The present work addresses this issue by capitalizing on the high-precision of one-dimensional capacitive displacement sensors based on time-grating to develop a planar 2D capacitive displacement sensor technology composed of a large-area array of excitation electrodes positioned on a fixed ruler and a small-area array of induction electrodes assembled on a coplanar moving ruler that travels over the fixed ruler at a fixed separation gap. Firstly, the individual traveling wave signals of the induction electrodes on the moving ruler are analyzed theoretically to develop a method for decoupling information pertaining to the separate displacements in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> directions. Then, the feasibility of the proposed decoupling method is verified by simulations based on a three-dimensional electric field model. Finally, the proposed measurement technology is validated experimentally based on tests conducted using a prototype sensor manufactured using standard printed circuit board technology. The experimental results demonstrate that the prototype sensor achieves measurement errors of ±8.2 μm and ±6.8 μm in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> directions, respectively, over the full 200 mm × 200 mm measurement range of the sensor.