Based on different mechanical structures, existing FBG-based inclinometers can be categorized into cantilever beam structures and pendulum structures. The sensitivity of cantilever beam structure inclinometers is lower than that of pendulum structure inclinometers with the same mass block. This is because the cantilever beam structure cannot fully convert changes in gravity into axial strain changes in the FBG. The cantilever beam also shares part of the force. In addition, precise control of the adhesive thickness used to fix the FBG on the surface of the cantilever beam is difficult. Uneven adhesive thickness can reduce the consistency of the inclinometer’s tilt measurements. To improve the sensitivity and consistency of inclinometers, researchers have proposed inclinometers based on a pendulum structure. This design directly converts the pendulum swing caused by gravity into axial strain on the FBG. This not only significantly improves the strain transfer efficiency and increases the sensitivity of the inclinometer, but also enhances the consistency of the measurement results. However, existing FBG inclinometers based on pendulum structures have drawbacks such as a limited tilt measurement range and a larger size. Additionally, to increase sensitivity, these sensors typically use heavier masses and longer pendulum rods, which can lead to deformation of the pendulum rod in cases of large tilt measurements. To address the issues with the aforementioned FBG-type inclinometer, we design a novel FBG inclinometer based on a simple pendulum structure. The aim is to achieve a reduction in sensor size while enabling a wide range of high-precision, repeatable tilt measurements and overcoming the temperature sensitivity issues of FBG.

We employ a method that combines simulation design and experimental validation to design the proposed FBG inclinometer. To reduce the size of the sensor and minimize the deformation of the pendulum rod during large tilt angle measurements, the pendulum structure is designed with an integrated pendulum rod and pendulum mass (Fig. 1). This successfully enables wide-range, high-precision, and high-sensitivity measurements of tilt angles. At the same time, the sensor, through the configuration of dual FBGs, can measure both the tilt direction and angle simultaneously, and effectively addresses the issue of temperature sensitivity. The main components of the sensor are manufactured using 3D printing technology, which not only reduces the weight and cost of the sensor but also enhances its magnetic resistance. In addition, to ensure uniform and consistent prestress applied to the two FBGs, we have designed a new prestrain application device for optical fibers (Fig. 7). The device allows for the free adjustment of the magnitude and direction of the applied prestress through a combination of weights and pulleys and ensures that the direction of the applied prestress is along the fiber axis.

The designed FBG inclinometer is tested for sensitivity and hysteresis using the demodulation system shown in Fig. 8. Figure 10(a) presents the experimental measurement results of the FBG wavelength difference versus the tilt angle of the designed inclinometer. For easy comparison and analysis, the simulation results are also shown in Fig. 10(a). It can be observed that the designed inclinometer exhibits good linearity within the ±15°, consistent with the simulation results. The theoretical and experimental tilt sensitivities obtained are 106.90 pm/(°) and 103.10 pm/(°), respectively, with a sensitivity difference of less than 6.54%, indicating the rationality of the inclinometer’s structural design and the effectiveness of the fabrication process. Figure 10(b) shows the results of the hysteresis test on the proposed inclinometer. According to formula (12), the hysteresis of the proposed inclinometer is calculated to be 0.65%. This result indicates that the inclinometer has low hysteresis, demonstrating high consistency in measurements between forward and reverse strokes. To verify the temperature compensation characteristics of the sensor, a temperature experiment is conducted. The obtained measurement results are shown in Fig. 11. From the results, it can be observed that the change in the center wavelength difference of the two FBGs during the heating and cooling processes is essentially consistent. In the temperature variation range, the maximum change in the wavelength difference is 21.39 pm, corresponding to an angle of approximately 0.21°. In addition, our research conducts a creep resistance test on the designed inclinometer. First, the inclinometer is fixed on an angular displacement platform, then the platform is rotated to the sensor’s maximum range of 15°, and this inclination is maintained for 24 h. The experimental results are shown in Fig. 12. The fluctuation range of the variation in the center wavelength difference between FBG1 and FBG2 is -3 to 4 pm, corresponding to a fluctuation range of 0.068° in tilt measurement.

In this work, we design a compact FBG inclinometer based on a pendulum structure, which features temperature-insensitive characteristics. The specially designed pendulum rod structure compresses the sensor’s height and length to 45 and 67 mm, respectively. The sensor exhibits a good linear response within a measurement range of -15° to 15°, with a sensitivity of 103.10 pm/(°). It also demonstrates excellent stability and creep resistance, with a fluctuation range of 0.068° for long-term tilt measurements. By adjusting the vertical distance between the FBG and the pendulum rob and the mass block, the sensitivity of the sensor can be further increased. By measuring the variation in the difference between the center wavelengths of the two FBGs, the influence of temperature changes on the inclinometer measurements can be eliminated.