Analysis and Compensation of the Longitudinal End Effect in Variable Reluctance Linear Resolvers Using Magnetic Equivalent Circuit Model

This article focused on the longitudinal end effect (LEE) in linear variable reluctance (VR) resolvers. The LEE can significantly decrease the accuracy of the linear sensor. Therefore, a novel method based on a magnetic equivalent circuit (MEC) model is proposed for accurate modeling of this phenomenon and used in an optimization routine to suppress that. The LEE is modeled by adding three extra permeances into the conventional MEC model without increasing the complexity and simulation time. Besides, the method of calculating these permeances is described. After that, some techniques are presented to decrease the computational burden of the MEC model. Then, the model is used to compensate the LEE by optimizing the turn number of coils. Comparing the results of the proposed model and the finite-element method (FEM) shows that the deviation of the model in the prediction of different inductances is less than 5%, while the simulation time is about 31 times less than that of FEM. Besides, the comparison between the initial design and the optimal design shows the usefulness of the model in the optimization process, in which the accuracy of the sensor improved by 74.1%. Finally, experimental tests on the prototype sensor verify the success of the analysis.