# Measuring Torque and Temperature in a Rotating Shaft Using Commercial SAW Sensors
## 3 Results
### Measurements under Rotation
#### 3.4.1 Influence of the Rotation in the Temperature Measurements  
Like what was described in Section 2.5, for each rotation velocity and temperature condition, 1000 frequency readings were recorded and the corresponding temperature was determined using Equation (5) and the coefficients determined during the calibration of the sensor. The thermocouple measured the temperature of the air surrounding the load cell in the three tests performed at 25 (ambient temperature), 47.5 and 60 \({}^{\circ}\)C; the temperature measured by the temperature sensor was 25, 42 and 50 \({}^{\circ}\)C, respectively. This large error is related to the difference in the temperature of the air surrounding the load cell and the cell itself. The standard deviation of the arrays of temperature readings is shown in Figure 11a. The deviation shows a clear tendency to increase with rotation velocity at 25 and 42 \({}^{\circ}\)C, reaching a maximum value of \(\approx\)12.4 and 30.4 \({}^{\circ}\)C, respectively. This effect is related with the lack of mechanical stability of the implemented stator coupler. Once the shaft rotates, the coupler rotates at the same speed; however, FR4 is not a rigid material and, as such, it also vibrates in a direction paral to the shaft axis. In addition, the centrifugal force felt by the W.FL coaxial cable is also transmitted to the rotor coupler, which compromises the parallelism of the couplers ever further. Once this happens, the distance between the stator and rotor couplers changes and so does the electromagnetic coupling. For measurements at \(\approx\)1800 rpm clockwise, the deviation shows a sudden increase, more evident at 42 \({}^{\circ}\)C--this may be due to a mechanical resonance condition that further compromises the electromagnetic coupling. For measurements at 50 \({}^{\circ}\)C, however, the deviation shows an erratic behavior, reaching the maximum value of \(\approx\)41.8 \({}^{\circ}\)C. It should be mentioned that the operating temperature range of the epoxy that was used to glue the temperature sensor decreases from 95 \({}^{\circ}\)C in the short term to 65 \({}^{\circ}\)C in long-term operation. At 42 \({}^{\circ}\)C, the behavior of the epoxy should not be a problem; however, if one takes into consideration that the temperature sensor embedded in the aluminum cage weighs 175 times more than a SAW strain gage, it is tempting to conclude that the behavior of the deviation at this temperature reflects the loss of bonding capability of the epoxy. As a general conclusion, it can be said that the error of a single temperature reading in rotation can be as high as 50, 75 or 83% at 25, 42 and 50 \({}^{\circ}\)C, respectively. On the other hand, Figure 11b shows the average temperature value calculated from the average frequency value of the array of readings (red data points). The values are much more stable. Readings at 25 and 42 \({}^{\circ}\)C show the same tendency and maximum absolute/relative errors of 5.2/20 and 4.8 \({}^{\circ}\)C/11%, respectively; the \"deviation\" from the trend line at \(\approx\)1800 rpm reinforces the idea of a mechanical vibration. Again, the average values taken at 50 \({}^{\circ}\)C show a more erratic behavior, even though the maximum absolute error is only 3.57 \({}^{\circ}\)C, with a corresponding relative error of 7%. In an attempt to decrease the influence of the large scattering of the measurements, the mean temperature was calculated again using only frequency readings that fall within the standard deviation--Figure 11b, red data points. The difference is more significant at 50 \({}^{\circ}\)C. This, together with the fact that the average temperature measured by the SAW sensor at 25 and 42 \({}^{\circ}\)C shows an apparent tendency to increase as rotation velocity decreases, suggests that the cell temperature might not have reached its final value when the measurements began. These results fall far from the sub-Kelvin resolution obtained by [PERSON] and his co-workers [23], who used a monopole antenna and not a capacitive coupler.