Geometry-based lateral displacement measurement using overlap-area difference of dual non-contact probes

초록

Conventional non-contact displacement sensors predominantly estimate displacement from variations in axial lift-off, inherently coupling the measurable range to the available axial clearance and limiting applicability in compact or space-constrained systems. This paper proposes a geometry-based formulation for lateral displacement measurement that exploits the differential overlap area between a moving conductive target and two laterally spaced probes operated at an approximately constant lift-off. By explicitly isolating the geometric contribution from transducer-specific physics, the geometry-based formulation establishes a scale-independent analytical framework. Closed-form expressions are derived to characterize sensitivity, linearity, and nonlinear behavior as functions of normalized probe spacing and target width. The analysis reveals a geometry-dependent trade-off between sensitivity and linearity, and identifies a practical geometric guideline (lambda d approximate to lambda w) that provides a balanced compromise between usable linear range and sensitivity. Experimental validation using eddy-current probes confirms the analytically predicted geometry-driven trends. Under a unified deviation-from-straight-line evaluation based on the API 670 criterion, the lateral sensor exhibited higher sensitivity and modestly improved linearity under the evaluated configuration, accompanied by increased equivalent noise and repeatability deviations. The results demonstrate that geometric modulation can improve linear measurement characteristics without modifying the sensing hardware, while introducing sensitivity-noise trade-offs. The proposed formulation provides a compact and scalable geometric guideline for displacement sensing in applications with limited axial clearance.

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