# Algorithms Utilized for Creep Analysis in Torque Transducers for Wind Turbines
## 2 Creep Study
### Experimental Conditions  
The torque standard machine (TSM) at the Central Office of Measures (GUM) in Poland is a reference machine which uses a DC motor to apply torque and a calibrated reference torque transducer to measure torque (see Figure 1). This TSM is able to generate clockwise and anti-clockwise torque in a range from 10 N\(\cdot\)m up to 5 kN\(\cdot\)m with an expanded relative uncertainty 0.04% (\(k=2\)). As a reference transducer, the HBK transducer (Hottinger Bruel and Kjear) working in the range from 200 N\(\cdot\)m to 5000 N\(\cdot\)m (type TB2/3000 N m; #181030110) was used in GUM's TSM. The amplifier used was a MGCplus/ML38B/DMP41 (with a 0.5 Hz Bessel filter), characterized by the best accuracy class and a resolution of 1 ppm in the measuring interval \(\pm\)2.5 mV/V. The creep tests were conducted at ambient temperatures for the 2 kN\(\cdot\)m torque transducer in clockwise and anti-clockwise directions following the ISO 376:2011 standard. This HBK 2 kN\(\cdot\)m multicomponent torque transducer (type MPZ1512005b, serial no. #210940007), intended to measure torque in both clockwise and anti-clockwise directions, is presented in Figure 2. What is important about this torque transducer is not only its mechanical resemblance to the 5 MN\(\cdot\)m torque transducer but also its additional bridges to measure axial force \(F_{x}\) and bending moments \(M_{\mathrm{x}}\) and \(M_{\mathrm{y}}\). The creep study was conducted for eight measurement points ranging from 200 N\(\cdot\)m to 2000 N\(\cdot\)m. A measured signal was observed in each point by 33 s from the 20 th second after loading. Additionally, at each measurement point, the signal behavior was tested without loading in the same time interval, starting at the 70 th second. The torque transducer indication is given in electrical units (mV/V). A total of 16 readings represent the creep at each measurement point (Figure 3 and Table 1). The dependence of the measured points of the electrical signal \(y_{i}\) at intervals \(t_{i}\) both for the statically determined torque of force and its lack-zero forcing of the torque, in general, is not reproducible and depends on many reasons related to the torque standard machine and environmental conditions. It is seen as a stochastic process. From the point of view of determining the characteristics of the  
Figure 1: (**a**) Two torque transducers installation: the reference torque standard machine (**f**) up to 5 kN\(\cdot\)m at GUM with an expanded relative uncertainty 0.04%; (**b**) special (2 kN\(\cdot\)m) torque transducer (**II**) installed in TSM between two adapters, reference torque transducer (**III**). transducer, the most important are the average values in the time-determined signal (the value of the measurand) and the average value of signal uncertainty (the minimum width of the coverage interval in which the true value of the signal is included). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**High Level of Torque**} & \multicolumn{2}{c}{**Low Level of Torque**} \\ \hline
**Time \(t\) (s)** & **Signal \(y\) (mV/V)** & **Time \(t\) (s)** & **Signal \(y\) (mV/V)** \\ \hline
20 & 1.045500 & 70 & 0.000445 \\
25 & 1.046769 & 75 & 0.000409 \\
27 & 1.046910 & 77 & 0.000393 \\
29 & 1.046901 & 79 & 0.000333 \\
31 & 1.046923 & 81 & 0.000208 \\
33 & 1.046842 & 83 & 0.000230 \\
35 & 1.046813 & 85 & 0.000202 \\
37 & 1.046813 & 87 & 0.000184 \\
39 & 1.046604 & 89 & 0.000176 \\
41 & 1.046791 & 91 & 0.000190 \\
43 & 1.046897 & 93 & 0.000186 \\
45 & 1.046798 & 95 & 0.000172 \\
47 & 1.046705 & 97 & 0.000158 \\
49 & 1.046722 & 99 & 0.000161 \\
51 & 1.046618 & 101 & 0.000158 \\
53 & 1.046679 & 103 & 0.000139 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Measured signal values from the transmitter for two measurement levels. Figure 2: The HBK special torque transducer with a lifting capacity 2 kN\(\cdot\)m and a sensitivity 1.0 mV/V, designed to measure clockwise and anti-clockwise torque.