# Measuring Torque and Temperature in a Rotating Shaft Using Commercial SAW Sensors
## 2 Materials and Methods
### Setup for Dynamic Measurements  
Figure 5a represents the schematic diagram of the setup for making the measurements under rotation. An alternating current (AC) motor is connected to a steel shaft through a couple of pulleys and a toothed belt. The load cell is attached to this shaft, which, in turn, stands on two bearings. Finally, a brake is connected to the free side of the shaft. Figure 4: (**a**) Simplified schematic representation of the calibration setup; (**b**) detail of the load cell, strain sensors and moveable arm. Considering that the loading of the AC motor by the shaft is negligible, the torque felt by the load cell is equal to the torque produced by the brake. When the brake is pressed by a force \(\overset{\rightarrow}{F}\) parallel to the shaft axis, the generated torque \(M\) is equal to:  
\[M=\frac{2}{3}\cdot\mu\cdot\left|\overset{\rightarrow}{F}\right|\cdot R, \tag{2}\]  
where \(\mu\) is the friction coefficient between the brake disk and the shaft, \(\left|\overset{\rightarrow}{F}\right|\) is the absolute value of the applied force and \(R\) is the radius of the shaft. For the present case, the friction coefficient was \(\mu=0.3\). Figure 5b shows the assembled setup. To control the ambient temperature, the shaft with the attached load cell penetrated a commercial oven perforated for this effect. The shaft was mounted on two mechanical bearings and the stator antenna was fixed to the oven by a metallic L-shaped piece. A motor NORD SK80-LH/2 (Oliveira do Bairro, Portugal), with a nominal rotating speed of 2825 rpm, was connected to the shaft with a toothed belt. The speed of the motor was controlled with a frequency inverter NORDAC AC Vector Drive (Oliveira do Bairro, Portugal) of the SK500E family, with 200-240 V 3-phased power supply. The rotation speed of the shaft was measured with a digital tachometer HS2234. The braking system consisted of a metallic brake pad that was pressed perpendicularly against the shaft to reduce the rotation velocity. A load cell was used to measure the force impressed on the braking system. Whenever necessary, the temperature in the air surrounding the load cell was measured with a J-type thermocouple digital thermometer. Figure 5: (a) Simplified schematic representation of the setup used for measurements under rotation; (b) setup assembled for tests under rotation. This setup was used for three purposes: (i) to measure the temperature response of the strain gages in the absence of applied torque; (ii) to record the response of the temperature sensor at different rotation speeds and (iii) to measure the applied torque under rotation. For task (i), the RF coupler was positioned with a relative orientation of 0\({}^{\circ}\). The resonant frequencies of each gage were measured under static conditions, without any applied external torque, between 0 and 80 \({}^{\circ}\)C with a 10 \({}^{\circ}\)C interval. The resonant frequencies were also measured at the reference temperature 25 \({}^{\circ}\)C. To guarantee the uniform heating of the cell, each heating cycle was followed by a 1 h waiting period. For task (ii), the measurements were performed at three different temperatures (25, 47.5 and 60 \({}^{\circ}\)C), with rotation speeds between 0 and 2300 rpm with increments of \(\approx\)300 rpm in both rotation directions and without applied torque. For each experimental condition, 1000 readings of the resonant frequencies of the temperature and strain sensors were recorded. The average resonating frequencies and corresponding standard deviations were then computed from the experimental data. In order to improve the accuracy of the measurements, the maximum standard deviation allowed to accept an interrogation cycle data frame was 3 kHz and 22 frequency readings were averaged to extract a data point. For task (iii), the tests were performed at room temperature and at a rotation speed of \(\approx\)150 rpm.