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This paper presents an inductive linear displacement sensor with complementary resonant coupling units. The sensor is mainly composed of a stator and two identical movers. The two movers are symmetrically arranged on both sides of the stator, forming a complementary coupling with the stator. The stator contains excitation coils and pickup coils, which generate magnetic field and output induction signals respectively; The movers also contain pickup coils, which are in series with resonance capacitors to generate a secondary magnetic field that reacts on the stator after receiving the excitation magnetic field, rather than outputs induction signals. The structure of this sensor makes the pickup coils on the stator directly receive the magnetic field on the movers in a complementary way, and avoids using leading wires on the movers, which is helpful to improve measurement accuracy and ensure the environmental adaptability of the sensor. The comparison experiments of the sensor prototypes show that the newly designed sensor is insensitive to the change of the gaps between the movers and stator. By improving the sensor prototype, the short-period measurement error is $9 ~\mu \text{m}$ , and the long-period measurement error is not more than $14 ~\mu \text{m}$ within 300mm.

This paper proposes a parasitic time-grating angular displacement sensor for detecting the position of the turntable bearing. The sensor is mainly composed of probe, rotor, and supporting signal circuit. The probe consists of two separated measuring units on the left and right, and each measuring unit is composed of four sensing units with iron cores, excitation windings, and induction windings arranged according to specific rules. The rotor is made of sinusoidal isometric grooves based on the bearing end cover of the original turntable bearing. The signal processing circuit is used to filter, amplify, and compare the induction signal; meantime, it can generate the excitation signal. The high-frequency clock pulse signal is used as the measurement benchmark to realize the analysis of the position information of the induction signal. The structure and working principles of the sensor are presented in detail. Through the finite element method simulation, the feasibility of sensor scheme is verified, and the theoretical resolution of the prototype sensor is estimated to be about 1.33e−5. A sensor prototype is designed for testing, and the experimental results show that its accuracy can reach −0.003611° to 0.002583° in the range of [0°, 360°] after compensating the error point-by-point through the look-up table method.

In the fields of robotics, machine tools and spacecraft, measurement of the gear angular position lays the foundation for closed-loop positional feedback. In this article, an angular displacement sensor based on the tunneling magnetoresistance (TMR) effect is proposed for the precise measurement of angular displacement. The developed sensor mainly consists of a TMR element, a signal conditioning circuit, a permanent magnet and some necessary assembly components. The TMR element is composed of eight magnetic tunnel junctions, which are arranged according to the dual-full bridge structure with a spatial electric angle difference of π/2. Signals containing time information and space information are obtained after the sinusoidal and cosine voltages signals are respectively connected in two bridges. The signals are processed by a signal conditioning circuit, and then the angular displacement is measured by counting the clock pulses. The structure, working principles and signal conditioning method of the sensor are presented in detail. Moreover, a sensor prototype and a conditioning circuit are designed for actual experiments, according to the measured gear with a modulus of 1 and tooth number of 240. The prototype sensor has a theoretical resolution of 0.00001°. The experimental results show that the prototype sensor has a working stability of ±0.00023° within 1 h, and its measurement accuracy is −0.0008611° to 0.001361° in the measurement range from 0° to 360°. Therefore, the proposed sensor can be applied to the highly precise measurement of angular displacement.

This paper presents an inductive-based sensor for absolute angular position measurement. Its structure is basically similar to a resolver, but it has two groups of pickup coils that use the same magnetic field to produce two different signals for absolute measurement and online self-calibration. The proposed sensor mainly consists of a ferromagnetic stator, two ferromagnetic rotors, and four groups of coils. Two groups of coils in the stator working as excitation coils are supplied with quadrature alternating current (AC) signals to generate quadrature magnetic fields both in temporal and spatial domains. The other two groups of coils in the rotors working as pickup coils receive magnetic fields to produce two sine signals whose phases are proportional to the displacement of the rotors. However, the phases of the sine signals have different periods of variation in the full measurement range. The sensor uses this different phase variation to determine the absolute angular position and perform the online self-calibration. A sensor model has been built and simulated first to verify the feasibility of the sensor. Then, a sensor prototype was developed based on the sensor model. The experimental results of the sensor prototype show that the sensor has big but regular measurement error using any group of pickup coils before conducting calibration, and finally, the measurement error reduced up to 85% by use of the online self-calibration method presented in this paper.

Precision measurement of two-dimensional displacements is needed in many domains, such as precision fabrication and detection. This paper presents a novel inductive position sensor with the capability of measuring displacements in $x$ - and $y$ -directions simultaneously. The sensor consists of two parts: a ferromagnetic plate with primary windings that are composed of four layers of spiral coils and a ferromagnetic plate with secondary windings that are composed of four layers of spiral coils. Primary windings are supplied with two quadrature 20-kHz alternating current to generate traveling wave magnetic field along $x$ - and $y$ -directions separately. Secondary windings output two signals whose phases are proportional to the linear displacements in $x$ - and $y$ -directions, respectively. The structure and working principles of the sensor are proposed. Meanwhile, a sensor model is simulated to verify the feasibility of the sensor, and a sensor prototype is fabricated for physical experiment. According to the analysis of the experimental results, the measurement range is up to 140 mm $\times140$ mm, and the maximum linearity in one pitch is 1%. In addition, measurement errors show that the performance of sensor may be improved by optimizing the layout of primary and secondary windings and signal processing circuit

This paper presents a new self-calibration method for angular displacement sensor, named coaxial sensors relative rotation (CSRR) method, which is suitable for sensors working in harsh environments. With a few slight modifications to the machine, CSRR method can also self-calibrate sensors on their application axes. This method works with two sensors. One sensor provides a benchmark and the other provides relative rotation against the benchmark, then each sensor can be self-calibrated by measuring the synchronized angular displacements of sensors and calculating the relative rotation angles. Experimental results indicate that this method is insensitive to relative rotation error of the two coaxial sensors, and it is also insensitive to sampling uniformity in particular situation. In that particular situation, the calibration accuracy can be better than ±2” when the system error of sensor is about ±650”. Compared with equal division averaged method, CSRR method mostly requires fewer sensors to get the same calibration accuracy; and compared with time-measurement dynamic reversal method, CSRR method performs better on the axis supported by rolling bearing. What is more, we propose an evaluation indicator $\vert Y_{\boldsymbol {\Omega }}\vert $ to evaluate the effective range of the CSRR method, and the $\vert Y_{\boldsymbol {\Omega }}\vert $ makes it easier for others to determine whether this method is suitable for their applications.

This paper presents a non-contact inductive linear displacement sensor which is based on planar coils realized by the printed circuit board (PCB) technique. The sensor mainly consists of a ferromagnetic stator, a ferromag-netic mover, several excitation coil-PCBs, and a pickup coil-PCB. Excitation coil-PCBs are embedded in the mover and generate quadrature magnetic fields both in temporal- and spatial-domains. The stator and mover confine the magnetic fields to propagate between them. Pickup coil-PCB is located between the stator and mover to receive the magnetic fields and outputs a signal whose phase is proportional to the displacement of the mover. Simulations of a 3-D sensor model and final experiment of a prototype are introduced and both verify the feasibility of this sensor. In order to overcome inexact quadrature in spatial domain of magnetic fields caused by asymmetric mover structure, a simple but effective compensation method realized in temporal domain is employed by the prototype. Experimental results show that the prototype has original measurement error of less than 50 $\mu \text{m}$ in the range of 0 –208 mm, and moreover, the error is still of great regularity so that the sensor may have better performance if there is digital calibration for measurement data or improvement in sensor structure.

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 &minus, 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 &plusmn, 1.25 &mu, m over the full 600 mm range and &plusmn, 0.25 &mu, m over a single 4 mm period.

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.