A Cylindrical Two-Dimensional Capacitive Sensor Based on Splicing Technology

In industrial applications, multiple single-degree-of-freedom sensors are typically used to simultaneously measure linear and angular displacements. However, this approach can introduce significant Abbe errors and multi-axis cumulative errors due to installation deviations. This paper proposes a combined measurement method for linear and angular displacements and presents the development of a cylindrical two-dimensional capacitive displacement sensor to mitigate these effects. The sensor consists of a rotor and a stator, where the cylindrical rotor is formed by a flexible printed circuit board with square excitation electrodes arranged in a staggered pattern on its surface to generate orthogonal excitation electric fields. The stator comprises two independent sensing units, each consisting of three square sensing electrodes arranged in a spatially differential configuration to receive and output signals. To achieve combined measurement of linear and angular displacements, we propose a multi-channel signal decoupling method for the cylindrical two-dimensional capacitive sensor. By pairwise summing the output signals from the sensing electrodes in the non-measurement direction, the coupled signals are canceled out, enabling displacement signal decoupling. To address the issue of significant measurement errors at the junction gaps of the rotor’s excitation electrodes, two independent sensing units are arranged diametrically along the circumference of the stator. By detecting abnormal measurement values at the junction gaps and switching between the sensing units, spliced displacement measurement is achieved. Experimental results show that the prototype sensor exhibited a measurement error of ±71.7 μm over a linear displacement range of 0 ~ 100 mm mm, and a splicing measurement error of ±263.7″ over an angular displacement range of 0 ~ 360°. In the radial eccentricity experiment, the angular displacement measurement error across 0 ~ 360° was reduced from ±589.6″ to ±551.3″ after correction. The sensor provides a novel technical solution for combined linear and angular displacement measurement in industrial applications.