Ziran Chen

A New Capacitive Displacement Sensor With Nanometer Accuracy and Long Range

A highly stable motion with orthogonally alternating electric field is established to build the relationship between spatial displacement and time standards. Displacement is measured by counting the time pulses that serve as measurement standards. Thus, a displacement method is called time grating. An orthogonally alternating electric field is generated using two rows of differential capacitive sensing electrodes excited by four sinusoidal voltages. Sine-shaped grating planes rather than hyperfine grating lines are used to pick up the displacement signals. Electrode lead wires are designed below the middle of the electrodes and fabricated using multilayer thin-film technology to suppress the cross-sensitivity effect. A time-grating sensor has been fabricated to evaluate the proposed method. The range of measurement is 200 mm, the width of the electrode is 0.2 mm, the interval between two adjacent electrodes is 20

Dynamic model of NC rotary table in angle measurements with time series

\mu \text{m}

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

, and the gap for capacitive sensing is 0.3 mm. Experimental results indicate that the measurement accuracy reaches ±200 nm with 1-nm resolution. Nanometer accuracy and resolution are achieved using sensing units with sub-millimeter periods. So, the cost for manufacturing the time-grating sensor can be decreased effectively in comparison to traditional nanometrology displacement sensors, and it may be a suitable low-cost alternative to long-range nanometrology.

A Time-Grating Sensor for Displacement Measurement With Long Range and Nanometer Accuracy

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.

Features of Capacitive Displacement Sensing That Provide High-Accuracy Measurements with Reduced Manufacturing Precision

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.

Signal interpolation system for linear time grating displacement sensors

It is difficult to achieve long measurement range with high precision in displacement measurement, a new nanometer displacement sensor, named time grating, is proposed to tackle this problem. The proposed displacement sensor uses orthogonally alternating electric fields as the carrier to build the relationship between the object movement in space domain and the signal phase shift in time domain, and the moving displacement of the object is proportional to the phase shift of the composited traveling wave signal that can be measured by time difference. The electric-field distribution of the sensor is simulated to analyze the influences of various factors, such as electrode intervals and electrode width. The results are further validated with experiments. The error characteristics are extracted using error identification technology and traced back to the sensor model, thus the relationships between the error characteristics and the model parameters are obtained. The experiment results prove that the measuring precision reaches ±200 nm and the resolution reaches 1 nm within 200 mm. Submillimeter period sensing unit realizing nanometer precision and resolution has shown significant promise in fabricating large range nanometer displacement sensors with low cost.

Error analysis and modeling for the time grating length measurement system

The capacitive displacement sensing method based on time grating employs a set of movable induction electrodes suspended with some gap width above a set of fixed excitation electrodes, and signals are obtained through electric field coupling. In this paper, we consider three features of time-grating capacitive displacement sensors that reduce the required manufacturing precision while maintaining high-accuracy measurements. First, the effect of edge roughness of the induction electrodes is suppressed by the filtering effect of the overlapping area integral method. Second, the effect of edge roughness of the excitation electrodes can be suppressed by the smoothing effect of the electric field. Third, the averaging effect of multiple induction electrodes is adopted to reduce the effect of geometric errors in the excitation electrodes. Printed circuit board manufacturing technology with a manufacturing accuracy on the order of 10 μm is selected to fabricate a prototype time-grating capacitive sensor, and a linearity of 0.005% is obtained for a single-period range of 0.8 mm. The measurement accuracy is largely independent of the manufacturing precision owing to the three aforementioned smoothing effects, which is promising for transforming the presently challenging technology of long-range displacement measurements with nanometer-scale accuracy into a conventional technology.

Error analysis and method of calibration for linear time grating displacement sensor

As regards the problems of using absolute linear time grating sensors as the position detector for full closed-loop CNC system, it is necessary transform temporal information to spatial information with time-space transformation algorithm for absolute linear time grating sensors. Time grating sensor’ signal interpolation model is established with time series. The purpose is to extract the relation mapping between future measurement value and past measurement value. In this way, original absolute displacement signal sampled in equal time interval can be converted to continuous incremental pulses required by full closed-loop CNC system. Furthermore, the predicted error model is proposed to improve the interpolation accuracy. The experiment results prove that the interpolation accuracy can reach 0.65 μm, the resolution can reach 0.1 μm.

Research on full closed loop NC system of linear cutting machine for high accuracy internal gear machining

Through analyzing errors of the length measurement system in which a linear time grating was the principal measuring component, we found that the study on the error law was very important to reduce system errors and optimize the system structure. Mainly error sources in the length measuring system, including the time grating sensor, slide way, and cantilever, were studied; and therefore total errors were obtained. Meanwhile we erected the mathematic model of errors of the length measurement system. Using the error model, we calibrated system errors being in the length measurement system. Also, we developed a set of experimental devices in which a laser interferometer was used to calibrate the length measurement system errors. After error calibrating, the accuracy of the measurement system was improved from original 36um/m to 14um/m. The fact that experiment results are consistent with the simulation results shows that the error mathematic model is suitable for the length measuring system.

Research on a novel method of real-time detection and dynamic calibration for angular displacement sensor

A combination method for calibrating the errors of linear time grating displacement sensor is presented. Based on further analysis of time grating, periodic errors, Abbe errors and thermal expansion errors are integrated to obtain error curve for setting up error model, which is adopted to compensate errors using Fourier harmonic analysis and the principle of liner expansion, respectively. Results prove that this method solves the difficult issues about error separation in the linear measurement, and significantly improves the accuracy of linear time grating. Furthermore, this method also solves the issues about continuous automatic sampling with computer, so that the calibration efficiency has been greatly enhanced.