# Measuring Torque and Temperature in a Rotating Shaft Using Commercial SAW Sensors
## 2 Materials and Methods
### SAW Sensors  
Temperature was measured with a TSE F162 sensor chip (SENSeOR, Besancon, France) mounted in a 5 \(\times\) 5 mm\({}^{2}\) SMD (surface-mount device) packaging. This sensor has two resonators with different temperature coefficients. Room temperature (25 \({}^{\circ}\)C) resonant frequencies and temperature coefficients for each resonator (taken from the data sheet) can be seen in Table 1. In the COTS solution, the SMD packaging comes embedded in a 26 \(\times\) 16 \(\times\) 54.7 mm\({}^{3}\) aluminium cage that can be glued or screwed directly on the surface of the material to be probed. The weight of the sensor chip and aluminium package is 7 g. The cage is further embedded inside a PTFE (polytetrafluoroethylene) radome 54.8 mm-high with a cylindrical 35.5 mm-diameter base--Figure 1a. The weight of the aluminium cage embedded in the radome is 35 g. Inside the radome, an omnidirectional antenna is connected to the sensor by means of ultra-small surface mount coaxial W.FL connectors ([[https://www.hirose.com/product/en/products/W.FL/](https://www.hirose.com/product/en/products/W.FL/)]([https://www.hirose.com/product/en/products/W.FL/](https://www.hirose.com/product/en/products/W.FL/))). It is also possible to obtain the sensor module with an additional coaxial cable that can be connected directly to the interrogation unit (Figure 1a). However, this solution is not appropriate for the current application; on one side, the large volume and height of the radome make it inappropriate to be assembled on a rotating shaft; on the other side, the omnidirectional radiation pattern of the antenna does not guarantee a stable communication link between the sensor and the interrogation unit. As such, the radome and antenna were detached from the sensor chip and corresponding aluminium cage and a W.FL cable was soldered to the male 50 \(\Omega\) SMA connector that is connected to the sensor--Figure 1b. After this step, the sensor (embedded in the aluminium cage) was fixed on the load cell with M-Bond 200 Glue and M-Bond 200 catalyst; thermally conductive paste guaranteed the thermal contact between the sensor chip and the surface of the load cell. The W.FL cable attached to the sensor was then connected (i) directly to the RF coupler or (ii) to the interrogation unit or to a dipole antenna (for calibration purposes) with an SMA (SubMiniature version A) coaxial cable. After being mounted on the load cell surface, the temperature sensors were calibrated using a FITOTERM 22E thermal chamber (Aralab, Lisbon, Portugal) with the sensors and interrogation unit \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sensor Reference** & \(f_{R_{a}}\) **(MHz)** & \(C_{1}\) (\(\times\)**10\({}^{-6}\)/\({}^{o}\)C)** & \(C_{2}\) (\(\times\)**10\({}^{-9}\)/\({}^{o}\)C\({}^{2}\))** \\ \hline TSE F162 & 435.90 \(\pm\) 0.15 & 4.8 & \(-\)24.6 \\ TSE F162 & 436.80 \(\pm\) 0.15 & \(-\)1.4 & \(-\)33.1 \\ SSE E015 & 433.97 \(\pm\) 0.15 & 0.9 & \(-\)24.8 \\ SSE E017 & 433.32 \(\pm\) 0.15 & 0.9 & \(-\)24.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Resonant frequencies at 25 \({}^{\circ}\)C, first and second order temperature coefficients of each resonator of TSE F162 temperature sensor and of SSE E015 and SSE E017 strain gases. Values taken from the sensors’ datasheets. Figure 1: (a) COTS commercial off-the-shelf temperature sensor module, composed of sensor chip embedded in an aluminum cage and attached to a radome with the antenna; (b) ultra-small surface mount coaxial W.FL cable soldered directly on the SMA (SubMiniature version A) connector connected to the sensor chip embedded in aluminum cage; (c) SAW strain gage with W.FL connector clearly visible; (d) SAW (surface acoustic wave) strain gages mounted on load cell using half-bridge configuration. connected directly to dipole antennas.