Abraded optical fibres have successfully been employed in bending sensors (Godaba et al., 2020). The bending of abraded optical fibres causes attenuation of transmitted light, such that by monitoring the light attenuation transmitted through the fibre to the receiver, one can estimate the fibre curvature.

All optical fibres display some attenuation of transmitted light when bent. However, in a standard, commercial optical fibre, this light loss is minimal and only small attenuation is experienced at very high curvatures. To use an optical fibre in a bending sensor, the sheath is stripped off and the cladding is removed, such as by sanding the fibre surface. This procedure increases the amount of light that scatters out from the fibre core when the fibre is bent, resulting in a significant reduction in the transmitted optical signal intensity. This is shown in Figure 2.

Light attenuation in abraded optical fibres in response to bending can also be used to measure force. Figure 3 shows the cross-sectional view of our proposed design. The optical fibre integrated into the silicone dome has been abraded in two specific areas as shown. The mechanism works as follows: when a force is applied to the top of the dome, it undergoes deformation and moves downwards; this increases the curvature of the two abraded regions, resulting in a decrease in light intensity transmitted through the fibre. In contrast to designs using abraded region at the centre of the dome, our two abraded sections near the sides of the dome allow for changes in light intensity across a large compression range, thereby increasing the force sensing range.

The design and the internal components of the sensor are shown in the cross-sectional view of Figure 3.

First, a two piece mould for the hollow silicone dome (40 mm diameter and 2.5 mm wall thickness thickness) was designed and 3D printed using PLA (Polylactic Acid) filaments on a commercial 3D printer (Ultimaker S3). Then the optical fibre (Mitsubishi Eska) with an outer diameter of 1 mm and core diameter of 0.5 mm, was stripped and abraded in two 10 mm sections. The abraded optical fibre was held in place in the mould by passing it through pre-printed holes, before closing it up with four M5 screws. Parts A and B of curable silicone EcoFlex 00-50 (Smooth-On, Inc.) were mixed in equal parts and degassed to remove any entrapped air bubbles. EcoFlex was then injected into the mould, degassed for a second time, and then cured at room temperature. The dome was designed with a thicker flat region between the abraded sections. This modification concentrates the deformation in the abraded areas of the fibres, leading to an increase in curvature.

Once cured, the silicone dome with the integrated abraded optical fibre was taken out of the mould. A base for the silicone dome was then 3D printed, also using PLA. This base had two holes through which to connect each end of the abraded optical fibre with the opto-electronic circuitry. A pneumatic inlet was designed to vary the pressure within the silicone dome, which was affixed to the base using silicone glue (Silpoxy by Smooth-On, Inc.) and tested to ensure there was no air leakage.

The experimental setup consisted of two systems - one pneumatic and one optical. The air pressure was generated by using a lead screw-based injection pump. The lead screw was coupled with a stepper motor controlled by an Arduino. The air pressure inside the sensor was manually controlled, using an RS Component digital pressure indicator as feedback. An opto-electronic system (Keyence sensor, FS-N11MN) was used to measure the light intensity from the abraded optical fibre. A Keyence opto-electronic system emits and receives light through the optical fibre and measures the change in the light intensity. These sensors emit light of a certain wavelength (630 nm) and have the added advantage of optical isolation which means that the ambient light doesn’t affect the sensor reading. The Keyence opto-electronic converts the change in light intensity to a voltage (0-5 V) and this voltage is recorded using an Analogue to Digital Converter (ADC) of an Arduino Uno micro-controller. The complete experimental setup is shown in the Figure 4.

To calibrate the sensor for force, we used a universal testing machine, the Instron 5900, equipped with a 100 N load cell. For the experiments, a flat circular indenter with a 60 mm diameter was 3D printed using PLA (Polylactic Acid) and mounted on the moving head of the universal testing machine. The indentation depth was set at 6 mm for all experiments, as deeper indentation affects the vertical sections of the fiber. Rather than merely deflecting the middle section, higher indentations could increase the risk of fiber fracture. The displacement and force data from the Instron 5900 was recorded using analogue outputs. These were also connected to the Arduino. A Python code was written to enable communication with the laptop and Arduino, and data was recorded in. csv files. The data acquisition rate was calculated to be 60 Hz (60 data samples per second). Figure 5 shows the flowchart illustrating the connections of various components during experimentation.

Force sensing response and the dynamic force range for different dome pressures, are evaluated through a series of experiments. The sensor is cyclically loaded to 6 mm compression using the 3D printed indenter at two different displacement rates of 5 mm/min and 20 mm/min, these two rates chosen in order to observe the rate-dependent hysteresis in the sensor. To understand the influence of internal dome pressure on the dynamic force range of the sensor, these cyclic load/unload tests at each displacement rate, were conducted for internal dome pressures of 0 psi (0 kPa), 0.5 psi (3.45 kPa) and 1 psi (6.9 kPa). Five samples of each set-up were recorded.

The sensor was also subjected to repeatability tests, involving ten cycles of 6 mm indentations at the higher indenter displacement rate of 100 mm/min for each of the three set pressures (0 psi, 0.5 psi and 1 psi).

As discussed in the previous section, each experiment was repeated five times. At each internal pressure, the loading and unloading data of these five experiments was fitted with third order polynomial. This polynomial fitting is plotted with 95% confidence interval and is shown in Figures 6, 7.

Both the Figures 6, 7 show that with increased pressure the force range of the sensor also increases while its sensitivity decreases. Although third order fit has been used, each light intensity change corresponds to only a single value of force. By comparing the two Figures 6, 7, it is obvious that the 95% confidence interval band widens when the indentation rate is higher. The goodness of the fit and the variability of the data was analyzed through regression analysis. Adjusted R², Root Mean Square Error (RMSE) in Newtons are calculated for the performance evaluation of third order polynomial fitting at 5 mm/min and 20 mm/min. These evaluations are shown in Tables 1, 2, respectively.

Another interesting observation in Figures 6, 7 relates to the saturation of the sensor data. At lower internal pressure values, the sensor response does not show any saturation against measured force. However, when higher pressure is applied, sensitivity starts decreasing as the force range increases. This phenomenon is evident when 1 psi is applied and the sensor response starts saturating.

This can be explained by considering the change in stiffness of the sensor. At lower pressure the compliance of the silicone dome and the optical fibres mitigates the saturation phase of the sensor response. However, at elevated pressures, the stiffness of the silicone dome increases, resulting in sensor response saturation.

Comparison of Figures 6, 7 suggests that hysteresis increases for higher indentation rates (Mukashev et al., 2022). By comparing the maximum force measured during saturation for 6 mm indentations, we observe that the force achieved at a rate of 20 mm/min is higher than when using the lower 5 mm/min rate. This is because at a higher strain rate, greater force is required to create the same amount of deformation (Tatiraju and Han., 2010; Kenry et al., 2015).

The maximum percentage errors calculated for the hysteresis at two indentation rates of 5 mm/min and 20 mm/min are shown in Table 3. Similarly, Table 4 shows the maximum force being measured at each pressure and indentation rates.

To investigate the effect of repeated loading and unloading cycles on sensor response, a repeatability test was conducted at an internal pressure of 0 PSI. During this test, the sensor was indented to a depth of 6 mm at a feed rate of 100 mm/min. The indentation was maintained for two seconds, with no time delay between cycles. A total of 105 samples were tested, with the first five samples excluded from the analysis. Figure 8 presents the first and last five samples from the remaining 100 cycles.

During the repeatability experiment, a drift in the sensor response was observed. This phenomenon can be attributed to the viscoelastic relaxation behaviour of silicone materials. To reduce this effect, sufficient relaxation time between each cycle is typically required. However, the objective of this experiment was to push the sensor to its limits by applying maximum indentation at a high rate, with no relaxation time between cycles. The observed drift in the sensor’s zero state and indented state was calculated to be 5.53% and 4.28%, respectively.

The stiffness of the sensor can be calculated by using Hooke’s law that states, F = k x (1) where, F is the applied force, k is the stiffness of the spring and x is the displacement. Stiffness was therefore calculated using the force measured by the Instron load cell and the displacement of the indenter. Values for sensor stiffness under different pressures are shown in Table 5. These values were calculated using five samples of the data for a slow indentation rate, i.e. 5 mm/min.

The sensitivity of a sensor is defined as, S e n s i t i v i t y = Δ O u t p u t Δ I n p u t (2) where Δ Output is the change in output - Analogue-Digital-Units in our case - and Δ Input is the change in force. Values for sensitivity under different pressures are shown in Table 6. These values were also calculated using five samples of the data for slow indentation rate, i.e. 5 mm/min.

Notably, the values for stiffness and sensitivity were calculated under the assumption of the sensor’s linear behaviour. Non-linear response would result in values that vary along the force-displacement and ADU-force curves of the sensor.

The results presented in Tables 5, 6 have also been plotted and shown in the Figure 9.

The accuracy of force estimation was assessed by comparing the repeatability test data with the third order polynomial equations. Root Mean Square Error (RMSE) and R² values were calculated at each internal pressure.

Figure 10 shows the sensor response for ten loading/unloading cycles at three different applied pressures using an indentation rate of 100 mm/min. Curve fitting equations were used to estimate the force from the sensor data. Measured force and estimated force are shown in subplots for each applied pressure. We can see that at higher inflation pressure, when the indenter reaches maximum compression, the actual force reduces with time while the estimated force value is nearly constant. This is because the optical fibre sensor reading is based on the deformation of the fibre, which remains constant during this period in which the indenter is not moving. However, silicone rubber is a viscoelastic material and undergoes stress relaxation. Due to this property of the material, the actual force reduces with time. The first subplot shows the indentation profile. These performance metrics have been presented in Table 7.

It is to be noted here that the cyclic loading/unloading tests were performed at an indentation rate of 100 mm/min. Results show that force estimation at 0 psi is precise, with minimal drift. At higher pressures, however, the error increases due to hysteresis.

The experiments presented in this section aim to assess the effectiveness of the proposed sensor in estimating the stiffness of various materials. The section is divided into two parts: the first addresses the development of the material phantoms, while the second focuses on estimating their Modulus of Elasticity.