Finite-Element Simulation of Effect of Surface Roughness of Coaxial Cylindrical Electrodes on Small Mass and Force Measurements Using Voltage Balance Apparatus

A voltage balance apparatus that uses the electrostatic force between coaxial electrodes was developed at the National Metrology Institute of Japan for the accurate and traceable measurement of small masses and forces with respect to the new definition of the kilogram. To achieve accurate measurements using the voltage balance, the coaxial electrodes of the apparatus were mechanically aligned by measuring their capacitances. In this study, we investigated the effect of the surface roughness of coaxial electrodes on the capacitance gradient and mass measurements in voltage balance measurements using the finite-element method for 2-D electrostatic problems. The results suggest that when the surface roughness of the electrodes was less than a few tens of micrometers in the average value of the absolute values of roughness height, they did not significantly increase the errors in the capacitance measurements due to mechanical deformation.