Force-Displacement Analysis in Diaphragm-Embedded Fiber Bragg Grating Sensors.

This paper presented the force and displacement analyses of a diaphragm-embedded fiber Bragg grating (FBG) sensor. In the first step, a numerical analysis (via finite element method) was performed considering linear elastic materials, where there is a linear variation on the strain in the optical fiber for both displacement and force (or pressure). In the second step, the experimental analysis was performed using two approaches: (i) controlling the displacement applied in the diaphragm-embedded FBG (while the force is also measured). (ii) Controlling the force applied in the sensor (also with the measurement of the displacement). Results showed reflected optical power variations and wavelength shift following the application of displacement and force. The sensitivities of both wavelength shift and optical power were different (and non-proportional) when displacement and force were compared. However, a higher correlation, determination coefficient (R) of 0.998, was obtained in the analysis of the wavelength shift as a function of the displacement, which indicated that the strain transmission in the optical fiber is directly related to the strain in the diaphragm, whereas the force has an indirect relation with the strain and depends on the material features. Then, the possibility of simultaneous estimation of force and displacement was investigated, where the linear relation of both parameters (displacement and force) with the wavelength shift and the optical power were obtained in a limited range of displacement and force. In this range, root mean squared errors of 0.37 N and 0.05 mm were obtained for force and displacement, respectively. In addition, the force variation with a step displacement input also shows the possibility of using the proposed FBG device for the characterization of the materials' viscoelastic features such as phase delay, creep, and stress relaxation, which can be employed for in situ characterization of different viscoelastic materials.