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This paper presents a computationally efficient, three-dimensional electromagnetic model for eddy-current-based speed sensors featuring an injection coil, two or more pick-up coils and a magnetic yoke. The superposition of incident and reflected fields, which was adopted in previous works, is replaced by a direct formulation; and Maxwell's equations are solved for the magnetic flux density vector, rather than involving a higher-order vector potential. The injected current is accounted for in the boundary conditions, and special attention is given to the modeling of the in-plane spreading of the coils by deriving coil-linkage functions. The magnetic field and eddy current distributions in the whole problem space is obtained by algebraically solving a 12-by-12 linear equation system. Results of the model are compared to experimental results from earlier publications for verifying the validity of the models. Even though derived primarily with the eddy-current-based speed sensing application in mind, the analysis presented in this paper can potentially contribute to various other eddy-current-based applications such as non-destructive testing, where probes with a magnetic yoke are utilized.

Three-Dimensional Analytical Modeling of an Eddy-Current-Based Non-Contact Speed Sensor