Numerical simulation and linear relationship prediction of LVDT electromagnetic field using face-smoothed finite element method

Abstract The Linear Variable Differential Transformer (LVDT) plays a critical role in measuring relative displacement in seismic attenuation systems, where its performance directly impacts the accuracy of vibration measurements. This study introduces an effective non-contact eddy current field model for analyzing the electromagnetic behavior of LVDTs. Utilizing the face-smoothed finite element method (FS-FEM) with a parsimonious linear tetrahedral mesh, the approach applies smoothing operations to the magnetic vector potential, magnetic flux density, and electric scalar potential gradient, ensuring precise solutions. The magnetic flux density is used to evaluate the LVDT’s linearity under specified conditions. Validation against standard finite element method (FEM) solutions using dense meshes demonstrates that FS-FEM achieves higher accuracy and computational efficiency. Further validation compares numerical predictions of the LVDT’s differential voltage with experimental results, showing that FS-FEM reduces prediction errors to 78.1% of those observed with FEM. The results highlight FS-FEM as a reliable and efficient tool for accurately predicting the linear performance of LVDTs under practical conditions.