Sensing Mechanism and Error Analysis of a Capacitive Long-Range Displacement Nanometer Sensor Based on Time Grating

In this paper, the sensing mechanism of a novel capacitive nanometer sensor based on the time grating approach is investigated. A mathematical model of the sensor is established using electric field coupling theory and the area integral method, which indicates that the measured displacement of the object is proportional to the phase shift of the output signal. High frequency time pulses serve as the measurement standard to realize the phase detection, and the displacement is measured by counting the time pulses. To evaluate the performance of the proposed sensor, periodic measurement errors are analyzed in detail. The primary periodic errors are quantified through the derivation of a mathematical error model. Experiments performed with a prototype sensor allow the causes of periodic first, second, and fourth harmonic errors to be traced back to cross interference, installation misalignment, and the effects of the electric field, respectively. After adopting a multilayer structure, adjusting the installation, and increasing the gap width to 0.3 mm, the primary periodic errors are sequentially eliminated. Therefore, the reasonability of the mathematical model and error analysis is validated by the designed experiments. Finally, the experimental results demonstrate that the measurement accuracy attains a value of ±200 nm over a 200 mm measurement range. This paper provides the theoretical guidance for the optimal design of high-performance time grating capacitive sensors.