Linear variable reluctance (LVR) resolvers have substantial benefits that make them suitable for linear motion control drives. The optimal design of LVR resolvers needs an accurate modeling that is usually achieved by a three-dimensional (3-D) time-stepping finite element method (TSFEM). However, the 3-D TSFEM is a very time-consuming method and is unsuitable for courage with optimization algorithms. So, in this paper an accurate analytical model based on an improved winding function method is proposed. The proposed model is used to calculate the inductances, air-gap flux density, induced voltages, and linear position error. The distinguished feature of the proposed model is the direct usage of the turn function in calculating the inductances. The conventional modified winding function (MWF) method uses the Fourier Seri of the turn function. So, the proposed model is much faster and more accurate than the models based on the conventional MWF method. The results of the proposed model are verified with those of the 3-D TSFEM. Then, the proposed model is used for design optimization of the sensor. Also, two methods are proposed for compensating the longitudinal end effect. Finally, the experimental prototype is used to evaluate the developed analytical model and the optimization process.
