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This paper introduces a noncontact, low-cost, and reliable inductive sensor for angular displacement measurement. It is suitable to work in harsh industrial environments. The sensor has simple structure consisting of three key parts: 1) a ferromagnetic stator, which is a pure plane; 2) a ferromagnetic rotor, which has face slots; and 3) four layers of planar copper coils, including primary and secondary coils. Primary coils are supplied with two orthogonal 4000-Hz ac, and secondary coils output a signal whose phase is proportional to angular displacement. Primary coils are designed with sinusoidal shape, so that magnetic field between the stator and rotor has approximately sinusoidal distribution, and finally linearity between the phase variation of output signal and angular displacement is well helped by this design. The structure and working principles of the sensor are explained in detail. Moreover, a sensor model was simulated to verify the feasibility of the sensor working principles and a sensor prototype was designed for actual experiment. At last actual experiment results are given and analyzed, showing that the sensor prototype has achieved accuracy better than ±12 arcsec in the range of 0°-360°, and this kind of sensor may have a better performance by improving the layout of primary coils and front-end signal-process circuit.Index Terms-Non-contact inductive sensor, angular displacement, planar coils, contrate rotor, sinusoidal shape.

In this study, a dynamic model of absolute time grating, a novel kind of displacement sensor, is established in order to apply the absolute time grating sensor, instead of the optical grating sensor, as an angle encoder to the full closed-loop numerical control (NC) rotary table. Time series analysis is employed in the dynamic model, and given the series of past measured angles, therefore, the dynamic model can be used to forecast the next future measured angle. As a result, the original absolute signal sampled in equal time intervals of an absolute time grating sensor can be transformed into continuous incremental pulses for a full closed-loop NC rotary table. When the current angle is deduced, the latest measured angle of the time series is interpolated as standard quantity to compensate for the last forecast error. In this way, the forecast error can be corrected between neighboring sampling periods, and cumulative errors can be eliminated. The forecasting accuracy of incremental pulses for the time grating sensor can reach ±3″ which validates the dynamic model in improving the performance of the time grating displacement sensor in dynamic measurement.

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