# Additive Manufacturing for Sensors: Piezoresistive Strain Gauge with Temperature Compensation
## 2 Materials and Methods
### Calibration Tests  
Several tests have been performed to obtain relations between sensor resistance, applied force and displacement. During the experiments, all those quantities have been continuously monitored while the robot is controlled to follow any one of the force or displacement profiles described in detail below and shown in Figure 3.  
Before each calibration test, the robot is automatically placed in a contact position with the following procedure: a zeroing of the load cell is performed; then, the robot moves down towards \(S_{a}\); when a force significantly higher than the standard deviation of load cell noise is measured, the robot moves up until the force is no longer detected. Two preliminary tests, here named for reference as PF1 (Preliminary Force profile 1) and PF2, have been performed to observe the response of \(S_{a}\), to quantify its sensitivity (ohm per gram), tune the proportional force control, and evaluate the effect of temperature. For that purpose, 0 g-10 g (test PF1) and 0 g-50 g (test PF2) cyclic on-off load profiles have been defined, with a corresponding displacement range of 0.1 mm and 0.4 mm, respectively. These two preliminary tests have led to identifying a step of 20 g as the minimum force step suitable for the following calibration tests (as explained in Section 3). Hence, three force/displacement profiles have been defined to calibrate \(S_{a}\):  
1. F1 (Force profile 1): it is composed of 5 cycles with a force range of 90 g, corresponding to a displacement range of about 0.6 mm. Each cycle is composed of the following steps: 0 g (relaxation step), then increasing force from 10 g (chosen as threshold value)  
Figure 2: Experimental set-up. to 90 g with a step of 20 g (as obtained by the preliminary tests), then decreasing force down to 10 g, and finally 0 g. Each step has a duration of 3 min. Each relaxation step has a duration of 10 min. Since the actuation of the robot is in terms of position, proportional force control is performed by choosing a feedback control constant \(k_{f}=0.0078\) mm/g. 2. D1 (Displacement profile 1): in this case, the vertical position of the robot (instead of impressed force) is directly given as a function of time; hence the test is defined despite any change in the force-displacement relation and is unaffected by force control errors. The profile comprises 6 cycles with a displacement range of 0.7 mm, corresponding to about 114 g. The range and number of cycles have been slightly increased with respect to the previous profile to ensure to cover the whole previous force range despite possible changes in material behavior due to viscoelasticity and the Mullins effect [17]. Each cycle is composed of the following steps: from 0 mm (no load) to 0.7 mm (maximum load), then back to 0 mm, with steps of 0.1 mm (corresponding to about 20 g). Each step lasts 3 min (49 min per cycle). The no-load step between two consecutive cycles has a duration of 10 min. During this test, the set-up was changed: a cardboard barrier was placed around the test area to make it less sensitive to temperature variations. 3. D2 (Displacement profile 2): in order to validate the obtained results, we decided to calibrate the sensor by defining a longer calibration test, composed of 12 cycles (force range of about 114 g, displacement range of 0.7 mm), to verify if the number of performed test cycles affects the results due to material softening. As in Test D1, each cycle is composed of the following steps: from 0 mm (no load) to 0.7 mm (maximum load), then back to 0 mm, with a step of 0.1 mm. Each step has a longer duration of 5 min (75 min per cycle) to allow the mechanical settling of \(S_{a}\) and the force to stabilize. The no-load step between two consecutive cycles has a duration of 10 min. The 12 cycles are divided into two subsets of 6 cycles, separated with a no-load step of 60 min, to evaluate for possible material recovery from stress.