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This paper proposes a new planar inductive sensor with printed circuit boards (PCB) based stator and rotor, which can perform more precision measurement than traditional inductive angular displacement sensors. The sensor uses PCB technique to realize accurately configured planar coils. The stator consists of a ferromagnetic base plate and a PCB with three groups of circular excitation coils and two groups of sine shape pickup coils working as two sense channels. The rotor consists of a ferromagnetic base plate and a PCB with two circles of copper pieces. Copper pieces on the rotor PCB produce eddy current in the time-varying magnetic field and alter the outputs of two sense channels of pickup coils cyclically with the rotor’s rotation. Two sense channels can make incremental angle measurement individually and work together to make absolute angle measurement. A prototype with 63 and 64 period sense channels was designed and developed for experiments, and test results show that it was finally examined with short-period error of $14.7^{\prime \prime }$ and full range error of $20.6^{\prime \prime }$ . The possessed characteristics of inductive principle, absolute measuring and good accuracy make this type of sensor is very suitable for high precision, reliable measurement in harsh environments.

Angular displacement sensor with shared magnetic field has strong environmental adaptability and high measurement accuracy. However, its 3-D structure is multi-pole double-layer structure, using time stepping finite element method (TSFEM) to optimize the structure is time-consuming and uneconomical. Therefore, a magnetic equivalent loop method (MELM) is proposed to simplify the optimal design of sensors. By reasonably setting the node position, the mechanical structure parameters, winding coefficients and input voltage of the sensor are integrated into a mathematical model to calculate of the induced voltage. The calculation results are compared with the simulation results, and a sensor prototype is made to test the optimized effect of the MELM.

Nanometer-scale measurement devices with high accuracy and absolute long-range positioning capability are increasingly demanded in the field of computer numerical control machining. To meet this demand, the present report proposes a capacitive absolute linear displacement sensor with time-grating that employs a vernier-type structure based on a previously proposed single-row capacitive sensing structure. The novel proposed vernier-type absolute time-grating (VATG) sensor employs two capacitor rows, each with an equivalent measurement range. The first capacitor row is designed with n periods to realize fine measurement, while the second capacitor row is designed with n − 1 periods, and the phase difference between the second row and the first row is employed to obtain absolute positioning information. A prototype VATG sensor with a total measurement range of 600 mm and n = 150 is fabricated using printed circuit board manufacturing technology, and its measurement performance is evaluated experimentally. Harmonic analysis demonstrates that the measurement error mainly consists of first-harmonic error, which is mostly caused by signal crosstalk. Accordingly, an optimized prototype VATG sensor is fabricated by adding a shielding layer between the two capacitor rows and designing a differential induction structure. Experimental results demonstrate that the measurement error of the optimized prototype sensor is ±1.25 μm over the full 600 mm range and ±0.25 μm over a single 4 mm period.