Effects of spherical targets on capacitive displacement measurements

Capacitive displacement sensors are widely used in precision manufacturing and metrology because they measure displacements with nanometer resolution. Prior literature usually treats capacitive sensors consisting of electrodes arranged as parallel plates. In this work, the target electrode is spherical, which is common in machine tool metrology, spindle metrology, and the measurement of sphericity. The capacitance due to a gap between flat and spherical electrodes is less than that of two flat electrodes, which causes four effects. As the diameter of the target electrode is reduced, the sensitivity increases, the sensing range decreases, the sensing range shifts toward the target, and the sensor becomes nonlinear. This paper demonstrates and quantifies these effects for a representative capacitive sensor, using finite element analysis and experimental testing. For larger spheres, the effects are correctible with apparent sensitivities, but measurements with the smallest spheres become increasingly nonlinear and inaccurate.