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Influence of Geometric Properties of Capacitive Sensors on Slope Error and Nonlinearity of Displacement Measurements

Capacitive sensors are widely used in industrial applications, such as CNC machine tools, where reliable positioning in the micrometer range with nanometer accuracy is required. Hence, these sensors are operated in harsh industrial environments. The accuracy of these sensors is mainly limited by slo...

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Autores principales: Daul, Lars, Jin, Tao, Busch, Ingo, Koenders, Ludger
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8271541/
https://www.ncbi.nlm.nih.gov/pubmed/34206437
http://dx.doi.org/10.3390/s21134270
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author Daul, Lars
Jin, Tao
Busch, Ingo
Koenders, Ludger
author_facet Daul, Lars
Jin, Tao
Busch, Ingo
Koenders, Ludger
author_sort Daul, Lars
collection PubMed
description Capacitive sensors are widely used in industrial applications, such as CNC machine tools, where reliable positioning in the micrometer range with nanometer accuracy is required. Hence, these sensors are operated in harsh industrial environments. The accuracy of these sensors is mainly limited by slope errors and nonlinearities. In practice, the required accuracy of these sensors is achieved by a calibration against a metrological high-quality reference such as interferometric displacement measurement systems. This usually involves the use of high-order polynomials as calibration functions based on empirical data. In metrology, this is only the second-best approach and has disadvantages in terms of stability over the measurement range of the instrument. In addition, the validity of these empirical calibrations over time is questionable, and the associated uncertainty can only be roughly estimated. This makes regular recalibration of such sensors at short intervals mandatory to ensure the reliability of the displacement measurement. In this paper, we report on our investigations of the different parameters that affect the accuracy of capacitive sensors. Since the capacitance of these sensors results from the electric fields that build up between the electrodes, these field lines are calculated using FEM simulation models for typical commercial sensors. In the following the influence of various geometric parameters such as edge radius, guard ring size and shape, or thickness of the electrodes are individually analyzed according to their impact on the accuracy of these sensors. Based on these simulations, the deviations of the capacitance as they arise for real detector geometries can then be compared with idealized, de facto unrealizable parallel plate capacitors. This methodology allows overall uncertainty of capacitive sensors to be decomposed into their individual components and sorted in terms of their contribution to the uncertainty budget. The individual FEM-based analysis then enables a systematic analysis of the sources of uncertainty and, thus, reveals possibilities to improve manufacturing processes for capacitive sensors, to put these sensors on a solid metrological basis, and to improve the performance of these displacement measurement systems in the long run, i.e., to provide better sensors for the application.
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spelling pubmed-82715412021-07-11 Influence of Geometric Properties of Capacitive Sensors on Slope Error and Nonlinearity of Displacement Measurements Daul, Lars Jin, Tao Busch, Ingo Koenders, Ludger Sensors (Basel) Article Capacitive sensors are widely used in industrial applications, such as CNC machine tools, where reliable positioning in the micrometer range with nanometer accuracy is required. Hence, these sensors are operated in harsh industrial environments. The accuracy of these sensors is mainly limited by slope errors and nonlinearities. In practice, the required accuracy of these sensors is achieved by a calibration against a metrological high-quality reference such as interferometric displacement measurement systems. This usually involves the use of high-order polynomials as calibration functions based on empirical data. In metrology, this is only the second-best approach and has disadvantages in terms of stability over the measurement range of the instrument. In addition, the validity of these empirical calibrations over time is questionable, and the associated uncertainty can only be roughly estimated. This makes regular recalibration of such sensors at short intervals mandatory to ensure the reliability of the displacement measurement. In this paper, we report on our investigations of the different parameters that affect the accuracy of capacitive sensors. Since the capacitance of these sensors results from the electric fields that build up between the electrodes, these field lines are calculated using FEM simulation models for typical commercial sensors. In the following the influence of various geometric parameters such as edge radius, guard ring size and shape, or thickness of the electrodes are individually analyzed according to their impact on the accuracy of these sensors. Based on these simulations, the deviations of the capacitance as they arise for real detector geometries can then be compared with idealized, de facto unrealizable parallel plate capacitors. This methodology allows overall uncertainty of capacitive sensors to be decomposed into their individual components and sorted in terms of their contribution to the uncertainty budget. The individual FEM-based analysis then enables a systematic analysis of the sources of uncertainty and, thus, reveals possibilities to improve manufacturing processes for capacitive sensors, to put these sensors on a solid metrological basis, and to improve the performance of these displacement measurement systems in the long run, i.e., to provide better sensors for the application. MDPI 2021-06-22 /pmc/articles/PMC8271541/ /pubmed/34206437 http://dx.doi.org/10.3390/s21134270 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Daul, Lars
Jin, Tao
Busch, Ingo
Koenders, Ludger
Influence of Geometric Properties of Capacitive Sensors on Slope Error and Nonlinearity of Displacement Measurements
title Influence of Geometric Properties of Capacitive Sensors on Slope Error and Nonlinearity of Displacement Measurements
title_full Influence of Geometric Properties of Capacitive Sensors on Slope Error and Nonlinearity of Displacement Measurements
title_fullStr Influence of Geometric Properties of Capacitive Sensors on Slope Error and Nonlinearity of Displacement Measurements
title_full_unstemmed Influence of Geometric Properties of Capacitive Sensors on Slope Error and Nonlinearity of Displacement Measurements
title_short Influence of Geometric Properties of Capacitive Sensors on Slope Error and Nonlinearity of Displacement Measurements
title_sort influence of geometric properties of capacitive sensors on slope error and nonlinearity of displacement measurements
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8271541/
https://www.ncbi.nlm.nih.gov/pubmed/34206437
http://dx.doi.org/10.3390/s21134270
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