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...
Main Authors: | , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2021-06-01
|
Series: | Sensors |
Subjects: | |
Online Access: | https://www.mdpi.com/1424-8220/21/13/4270 |
id |
doaj-c37eed07546e4c758578b649de8c6019 |
---|---|
record_format |
Article |
spelling |
doaj-c37eed07546e4c758578b649de8c60192021-07-15T15:44:51ZengMDPI AGSensors1424-82202021-06-01214270427010.3390/s21134270Influence of Geometric Properties of Capacitive Sensors on Slope Error and Nonlinearity of Displacement MeasurementsLars Daul0Tao Jin1Ingo Busch2Ludger Koenders3Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, GermanySchool of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology (USST), Yangpu District, Shanghai 200093, ChinaPhysikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, GermanyPhysikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, GermanyCapacitive 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.https://www.mdpi.com/1424-8220/21/13/4270capacitive sensorsdisplacement measurementsslope errornonlinearityFEM simulation |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Lars Daul Tao Jin Ingo Busch Ludger Koenders |
spellingShingle |
Lars Daul Tao Jin Ingo Busch Ludger Koenders Influence of Geometric Properties of Capacitive Sensors on Slope Error and Nonlinearity of Displacement Measurements Sensors capacitive sensors displacement measurements slope error nonlinearity FEM simulation |
author_facet |
Lars Daul Tao Jin Ingo Busch Ludger Koenders |
author_sort |
Lars Daul |
title |
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_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_sort |
influence of geometric properties of capacitive sensors on slope error and nonlinearity of displacement measurements |
publisher |
MDPI AG |
series |
Sensors |
issn |
1424-8220 |
publishDate |
2021-06-01 |
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. |
topic |
capacitive sensors displacement measurements slope error nonlinearity FEM simulation |
url |
https://www.mdpi.com/1424-8220/21/13/4270 |
work_keys_str_mv |
AT larsdaul influenceofgeometricpropertiesofcapacitivesensorsonslopeerrorandnonlinearityofdisplacementmeasurements AT taojin influenceofgeometricpropertiesofcapacitivesensorsonslopeerrorandnonlinearityofdisplacementmeasurements AT ingobusch influenceofgeometricpropertiesofcapacitivesensorsonslopeerrorandnonlinearityofdisplacementmeasurements AT ludgerkoenders influenceofgeometricpropertiesofcapacitivesensorsonslopeerrorandnonlinearityofdisplacementmeasurements |
_version_ |
1721298562821652480 |