Many angle or position sensors rank among the inductive encoders, although their sensing principle is different. The sensor design investigated in this paper is based on coupled coils, whereas the information about the position angle is modulated on the induced voltage, measured at the receiving coils. Unfortunately, no closed solution for most of the physical quantities exists, since this principle is based on eddy currents, which are rather complex to calculate for the given geometry. Consequently, the common way is to calculate the sensor quantities by a 3D finite-element (FE) simulation. However, this leads in most cases to a high time and computational effort. To overcome the limitations with respect to computational resources, a novel method is presented to reduce simulation effort and calculate regression models, which can even replace simulations. In the following investigations, D-optimal designs are used-a subdomain in the field of statistical design of experiments-and combined with a numerical implementation of Faraday's law, in order to calculate the induced voltages afterwards from simulated magnetic field data. With this method, the sensor signals can be calculated for multiple angle positions from one simulated position by shifting the integration boundaries. Hence, simulation time is significantly reduced for a full period. The regression models obtained by this method, can predict the Tx-coil inductance, induced Rx-voltage amplitude and angular error in dependency of geometric design parameters.
Keywords: angle encoders; design of experiments; finite-element simulation; inductive sensors; linear regression; mutual coupling; optimal designs; rotary encoders.