Displacement Sensing Using Bimodal Resonance in Over-Coupled Inductors

This paper presents the theory and key experimental findings for investigating the generation of bimodal resonance (frequency-splitting) phenomena in mutually over-coupled inductive sensors and its exploitation to evaluate relative separation and angular displacement between coils. This innovative measurement technique explores the bimodal resonant phenomena observed between two coil designs-solenoid and planar coil geometries. The proposed sensors are evaluated against first-order analytical functions and finite element models, before experimentally validating the predicted phenomenon for the different sensor configurations. The simulated and experimental results show excellent agreement, and first-order best-fit functions are employed to predict displacement variables experimentally. Co-planar separation and angular displacement are shown to be experimentally predictable to within ±1 mm and ±1° using this approach. This study validates the first-order physics-based models employed and demonstrates the first proof of principle for using resonant phenomena in inductive array sensors for evaluating relative displacement between array elements.