Inductance calculation of planar eddy-current sensor coils in grating-type displacement measurement system

Eddy-current sensor used in grating-type displacement measurement system usually works under axial asymmetric measurement conditions. In the measurement system, the coil is placed parallel to the detected target with both an axial displacement and a radial displacement. For it is difficult to perform derivation directly from the Maxwell´s equations, a new calculation method of eddy-current sensor coil inductance is proposed. With the method combining both analytical derivation and finite element analysis, formulas to calculate the inductance of the sensor coil under axial asymmetric measurement conditions are derived. The formulas describe the inductance of a sensor coil as a function of target´s axial position and radius position relative to the coil as well as other factors such as geometrical and electromagnetic parameters of the coil and target and so on. Simulations and practical measurements are carried out based on a typical device and the results validate the proposed formulas. The proposed calculation method provides a new and useful tool for eddy-current sensor design and optimization.