# Additive Manufacturing for Sensors: Piezoresistive Strain Gauge with Temperature Compensation
## 3 Results
### F1: Force Profile of 5 Cycles (Range: 90 g, 0.6 mm)  
Fifty-one labels are identified through segmentation for test F1, where a force profile with 20 g steps was defined in a 90 g range by performing a feedback control loop with a proportional constant of 0.0078 mm/g. The temperature range during the test has been about 3.7 \({}^{\circ}\)C. Table 1 shows that \(R_{a}\) has the highest correlation with \(R_{d}\). Regarding the re  
Figure 4: Preliminary on-off tests PF1 and PF2. From top to bottom: the digital temperature sensor (\(T_{2}\)), the resistance of the dummy sensor (\(R_{d}\)), the resistance of the sensor under test before (\(R_{d}\)) and after (\(R_{c}\)) compensation, and measured (\(F_{m}\)) and fitted (\(\bar{F}\)) force. Each label’s beginning and end are a red and a blue vertical line, respectively. The 0–10 g test PF1 (**a–e**) has 5 labels, whereas the 0–50 g test PF2 (**f–j**) has 11 labels.  
maining references, a better correlation is shown with the digital temperature sensors with respect to the thermocouple. This is probably due to different thermal inertia phenomena: the digital sensors are covered with a case, resulting in more similar to the FFF sensors (it somehow acts as the TPU structure of the FFF sensors, with a slower response to temperature changes), whereas the thermocouple is more directly exposed to fast temperature variations. Therefore, using the dummy sensor is well motivated and reduces any behavior differences that may occur when employing commercial temperature sensors.  
The presence of hysteresis introduces errors during the compensation procedure. Hence, to reduce this effect, three calibrations are performed for both force and displacement by considering (i) only the increasing trait of each cycle, then (ii) only the decreasing trait, and finally (iii) the whole cycle.  
The results obtained by applying temperature compensation are given in Table 2 for the calibration of force and Table 3 for the calibration of displacement, showing similar performance. Worst case, RMSE and \(r\) are 13.5% and 9.1% of the considered range, respectively. The performance metrics slightly improved when considering only the decreasing trait of the cycles.  
By comparing different cycles, it has been observed that the robot elongation increases for increasing cycle index, which is more evident for higher forces. This is probably due to viscoelasticity and relaxation phenomena: the TPU structure slightly relaxes when the force step is applied repeatedly, thus becoming more flexible and opposing less mechanical resistance to the applied stress; hence, the force measured by the load cell decreases, and the robot moves furtherly to apply the desired force. Since this is common to all tests, the relationship between displacement and force change will be shown only in the discussion of test D2 for brevity.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Test** & \(R_{d}\) & **T1** & **T2** & **TC** \\ \hline F1 & 0.8407 & 0.5456 & 0.7221 & 0.3695 \\ D1 & 0.9192 & 0.8934 & 0.9135 & 0.6045 \\ D2 & 0.9938 & 0.9753 & 0.9717 & 0.7585 \\ \hline \end{tabular}
\end{table}
Table 1: Pearson correlation coefficients with respect to \(R_{a}\).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Trait** & **Metric** & **Test F1** & **Test D1** & \multicolumn{3}{c}{**Test D2**} \\ \hline  & & & & **1 st Series** & **2 nd Series** & **All Cycles** \\ \hline Increasing & RMSE & 11.6 & 8.4 & 4.5 & 9.8 & 11.4 \\  & \(r\) & 8.4 & 4.8 & 3.9 & 6.9 & 10.4 \\ Decreasing & RMSE & 9.5 & 3.3 & 4.9 & 7.5 & 13.2 \\  & \(r\) & 8.3 & 2.2 & 4.6 & 6.4 & 11.7 \\ Whole & RMSE & 12.1 & 9.2 & 6.9 & 10.2 & 13.2 \\ cycle & \(r\) & 9.1 & 3.7 & 4.5 & 7.6 & 10.8 \\ \hline \end{tabular}
\end{table}
Table 2: Comparison of results obtained for the three tests by applying the proposed temperature compensation approach based on dummy sensor resistance \(R_{d}\). Calibration is with respect to force. Values are expressed as a percentage of the range.