High Precision Measurement for String Resonator used in FBG Strain Sensors

광섬유 브래그 격자 변형률 센서용 현공진기의 고정밀 측정

This paper describes a string resonator that is used for the interrogation system of a Fiber Bragg Grating(FBG) strain sensor. The strain on the fiber piece is calculated from the measured frequency based on that the natural frequency of a string is a function of the applied absolute strain. Existing research considered a fiber as a string, but a fiber is not a string in the strict sense due to its bending stiffness, thus the fiber should be modeled as a beam accompanied with an axial force. In the vibration modeling, the relationship between the strain and the natural frequency is derived, and then the resonance condition is described in terms of both the phase and the mode shape for sustaining resonant motion. Several experiments verify the effectiveness of the proposed model of the fiber. The performance of the string resonator is analyzed by measuring the frequency change according to the applied strains in the dynamic range of 1100$\mu\varepsilon$ referred to the displacement from capacitance sensor. From the experimental results, the implemented string resonator provides the accuracy of $\pm$3$\mu\varepsilon$, the quasi-static resolution of ~0.1$\mu\varepsilon$(rms) which amount to be $\pm$0.17$\mu\textrm{m}$ and ~6nm respectively, in case of fiber length of 56mm. For a dynamic strain, it can provide the accuracy of ~3$\mu\varepsilon$ until the frequency comes to 8Hz. As a consequence, the string resonator proposed for FBG sensor provides the high accuracy and the high resolution in strain measurement, and also it is expecting to be used, for the application, to not only strain but also displacement measuring device.