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The model equations, which can be readily implemented in software, are the result of a systematic approach that starts from the equations for the selfinductance of a wire and the mutual inductance of two parallel and misaligned wires that lie on the same plane. Accuracy is guaranteed by considering all the magnetic interactions among the individual turns in the two coils, while the simplifications involve only the calculations made at the corners of the coils. The model was validated by taking as reference experimental measurements carried out on a rectangular and a square magnetic coupler. A second analytical model, based on equivalent single-turn coils, was also tested for comparison purposes. The validation was extended with Finite Element Analysis (FEA) tools by considering a wide range of coil side lengths, air gaps, number of turns and lateral misalignments. The proposed model can, therefore, be regarded as a reliable tool to aid in the design of rectangular-shaped air-core magnetic couplers with applications in the contactless transfer power that are not necessarily limited to vehicle electrification.

The proposed design utilizes an internal support structure and magnetic coupling to eliminate the need for an external claw-like support structure. A model of the proposed design is developed and used to evaluate the slip/no-slip operational window. Due to the high-dimensional nature of the model, the design space is sampled using randomly generated design instances and the data is used to train a support vector classification machine. Principal component analysis and feature importance detection are used to identify critical parameters that control the slip behavior and the feasible (no-slip) design space. The classification shows an increase in the feasible design space with the addition of, and increase in, the magnetic coupling force. Based on the results of the machine learning algorithm,  EMS FEA design tools and experimental testing are used to design a spherical magnetic coupler array configuration that can realize the desired magnetic coupling force for the ball drive.