Investigation of the influence of the main error sources on the capacitive displacement measurements with cylindrical artefacts

Capacitive displacement sensors are usually used with flat-targets in dimensional metrology applications, which require measurements with nanometer-level uncertainties. The use of capacitive sensors has recently expanded to cover the measurement of cylindrical artefacts (roundness, straightness and cylindricity). The error produced by the curved shape leads to the increase of the nonlinearity, since the sensing range between the targets and the sensitive part shrinks. This phenomenon cannot be ignored for applications requiring a nanometer-level uncertainties.In the context of LNE's (French National Metrology Institute NMI) on-going development of a machine for form measurement with an uncertainty of a few nanometres (<5 nm) using capacitive sensors, an experiment has been developed to characterize the behaviour of two commercial capacitive sensors. The experiment enabled the evaluation of the major error sources (axial and radial error motions as well as the deviation/tilt of the capacitive sensors) which influence capacitive displacement measurements. The research was completed with a flat-target and cylindrical artefacts whose diameter values varied between 50 and 200 mm. For radial error motion, both experimental and theoretical results were compared and were found to agree within 2 nm, especially when the radial error motions were small (<50 μm). Finally, the polynomial fitting methods using terms up to 4 and 6 resulted in a deviation between measured displacements and fit of 0.005%FS (FS: Full Scale corresponds to the working range of 90 μm).

► We characterize the behaviour of two capacitive sensors (linear residual, inclination, radial offset, and radial error).
► We model the effect of the radial error
► We compare both the theoretical and experimental results.
► We investigate the nonlinear residual only of the big capacitive sensor.
► Increasing the order of the polynomial fitting terms reduce the nonlinear residuals to few nanometres.