How is spatial curvature calculated using the strain differences in multi-core gratings?
Spatial curvature is calculated using the strain differences in multi-core gratings by leveraging the principle that mechanical deformation, specifically bending, induces varying levels of strain across the cross-section of the sensor.
Here’s a breakdown of the calculation principle:
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Differential Strain Measurement: An OFSCN® Fiber Bragg Grating Shape Sensor typically incorporates multiple Fiber Bragg Gratings (FBGs) embedded in a multi-core fiber or arranged as a bundle of single-core fibers, positioned at known radial distances and angular separations around a central axis (e.g., three gratings at 120-degree intervals). When the sensor bends, the FBGs on the outer radius of the bend experience tensile strain (elongation), while those on the inner radius experience compressive strain (shortening). FBGs on the neutral axis experience minimal strain.
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Strain-Curvature Relationship: The measured strain (ε) at each FBG is directly related to the local curvature (κ), the radial distance (r) of the FBG from the neutral axis, and its angular position relative to the bending plane. By accurately measuring the wavelength shift of each FBG, the individual strain values can be determined.
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Curvature Calculation: With multiple spatially distributed strain measurements, a set of equations can be formed. These equations correlate the measured strain values with the sensor’s geometry (radial distance and angular position of each FBG) to solve for the two components of local curvature (bending in two orthogonal planes) and the corresponding bending angle. Essentially, the strain differences provide the necessary data to triangulate the bending plane and magnitude.
This method allows for the reconstruction of the sensor’s three-dimensional shape by integrating the local curvature information along its length.
The technology behind this involves highly customized solutions, as offered by OFSCN® Fiber Bragg Grating Shape Sensor, which can be built using OFSCN Multicore Fiber Bragg Gratings.
Here are some visual representations of such sensors:
You can find more detailed information on our product pages:
OFSCN® Fiber Bragg Grating Shape Sensor
OFSCN Multicore Fiber Bragg Gratings / Fiber Bragg Grating Strings (Bare)
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