The Winding Function Approach has been used since 1965 to describe the inductance behavior of small air-gap electrical machines, and several works have contributed to its formulation in the presence of mechanical faults, such as eccentricity, leading to the Modified Winding Function Approach (MWFA). In order to use the MWFA, an integral over a full rotation period needs to be computed. Nevertheless, this typically requires the performance of numerical integration, and thus it is affected by integration error, requires relatively high computational effort and, at the same time, it does not easily allow for performance of the analysis of the inductance harmonics. In this work, an exact analytical solution to the MWFA equation is provided in a form that allows to highlight the harmonic content of the inductances. After a thorough mathematical derivation of the solution, a numerical investigation is proposed for verification purposes.

Additively manufactured soft-magnetic components are inherently bulky leading to significant eddy current losses when applied to electrical machines. Prior works have addressed this issue by implementing structures based on the Hilbert space-filling curve which include eddy current suppressing gaps, thereby reducing the fill factor of the soft-magnetic component. The present research aims at investigating a number of space-filling curves in addition to sheets in order to find the optimal eddy current suppressing structure from an electromagnetic point of view. By means of both analysis and finite-element simulation, it was shown that sheets are superior at minimizing eddy current losses while space-filling curves excel at maximizing the fill factor.

The impact of the static eccentricity fault on electrical machines has been extensively explored in the literature. Various contributions have provided valuable models, such as the modified winding function approach (MWFA), which effectively characterizes the inductance behavior of an eccentric permanent magnet synchronous machine (PMSM). Recently, a comprehensive solution for the MWFA formula has been published, presenting an analytical expression for the machine's phase inductances and their harmonic components. Building on this achievement, the presented study investigates how static eccentricity influences the measurements obtained from a sensorless technique reliant on zero-sequence voltage, such as direct flux control (DFC). DFC offers highly consistent and precise inductance-dependent measurements, rendering it a viable option for designing fault detection techniques. In this study, a mathematical model is formulated to analytically describe DFC measurements for an eccentric machine in order to investigate its viability for eccentricity detection. Subsequently, experimental results are provided and analyzed.