# Flexible Shear and Normal Force Sensor Using only One Layer of Polyvinylidene Fluoride Film
## 4 Result and Discussion  
First, to observe the morphology of the film under a shear or normal force, we analyzed the total displacement distributions of the PVDF film by using the FEM procedure in the COMSOL Multiphysics software. The geometry was modeled to be the same as the actual size of the sensor, with the upper PDMS modulus set to 3590 kPa and the lower PDMS modulus set to 980 kPa [37]. In the simulation, shear and normal forces were applied to the sensor modules. The displacement distributions when a shear force and a normal force of 10 N were applied are shown in Figure 4a,b, respectively. At this time, the pressure applied to the sensor was about 85 kPa. Therein, we could observe the morphology of the film consisting of one domain when a force was applied to the sensor. In both cases, the upper bases of the trapezoid had the largest displacement and the displacement distribution was symmetrical with respect to the line MN shown in Figure 1e. Therefore, we were able to predict that the signal pair would be symmetric with respect to the line MN. This result shows that the connection of the two trapezoids affects the symmetric displacement. The connection exists because the sensor is fabricated by using one layer of PVDF film. Moreover, the displacement difference by connection is due to the sensitivity difference between the P1 and P3 sensors. Figure 4: Result of the finite element method simulation for the displacement distribution of the PVDF film. (**a**) Schematic of the sensor (left) and displacement distribution (right) when a shear force was applied. (**b**) Schematic of the sensor (left) and displacement distribution (right) when a normal force was applied. Figure 3: Schematic of the sensing system (**a**) for single unit measurement and (**b**) for sensor array measurement in real time. Figure 5 shows the output voltages of the sensor when shear and normal forces were applied and released. Therein, the voltage offsets of the obtained data were removed, and the voltage outputs were filtered by a low-pass filter of 60 Hz to eliminate power source noise. The inset images show the position of the sensor reading the voltage, and the red arrows show the movement direction of the 3D-printed bar for the shear and normal force tests. Figure 5a shows the measurement results when a 75.67 kPa shear force was applied in the \(+x\) direction. The phases of the signal of the P1 and P2 sensors appeared in opposition to the that of the P3 sensor. The signals when a normal force in the \(-z\) direction were applied are shown in Figure 5b. Therein, the signals had the same phase when a force was applied or released. Therefore, it was possible to distinguish whether the force applied to the sensor was shear or normal by comparing the phase difference of the signals. However, we remark that this PVDF sensor produced a voltage proportional to the change of the strain when the load resistor was under the internal impedance of the sensor [38]. That is, since the peak value of the output voltage depended on the speed at which the force was applied, the magnitude of the force applied to the sensor could not be obtained from the peak value of the output voltage. To obtain the magnitude of the force applied to the sensor, we integrated the output voltages over time according to the following equation:  
\[I_{n}=I_{n-1}+V_{n}\times\Delta t, \tag{1}\]  
where \(I_{n}\) is the processed value, \(V_{n}\) is the output voltage without an offset, and \(\Delta t\) is the sensing time interval measured by the microcontroller. We noted that the processed value was the integration value of the output voltage of the sensor over time. Here, the output voltage was proportional to the change of the strain [2], so the processed value after the integration was proportional to the displacement, which was proportional to the applied force.