Abstract— Inductive displacement sensors are commonly used in active magnetic bearing (AMB) applications. In most research, conventional models used to analyze inductive sensors in terms of determining sensitivity and obtaining a relationship between output voltage and displacement ignore the effects of fringing in air gaps. However, the effects of flux fringing on the performance of these sensors cannot be ignored in industrial applications. In this article, by using the Schwarz-Christoffel transformation, 3-D self- and mutual inductances for the radial and axial poles of a 3-degree-of-freedom inductive sensor are calculated, with the effects of fringing taken into account. The results of these calculations are compared with finite element results. The results show that the model based on the Schwarz-Christoffel method outperforms the ideal model in which flux fringing is ignored, with an inductance calculation error of about 8% for radial poles and 6.5% for axial poles, respectively.

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