# Software for Monitoring the In-Service Efficiency of Hydraulic Pumps
## 4 The Laboratory Validation of the Software Module for the Pump's Full Operating Range
The discharge pressure sensor range is \(0\div 6\) bar with accuracy reported by the manufacturer of \(\pm 0.25\%\). A T22 torque transducer by HBM is installed on the test rig between the electrical motor and the centrifugal pump. The range from 0 to 100 Nm is covered by the torque transducer with an accuracy of \(\pm 0.5\%\). ROP520 incremental encoder is linked to the electrical motor shaft to measure the speed with an accuracy of \(\pm 0.01\%\). A systematic error of \(\pm 0.732\%\) is obtained for the pump efficiency (\(f_{s_{\eta_{p}}}\)). The random error is determined for the quantity acquired by each measuring device installed on the test rig using a set of ten values for ten operating points. As a result, the following maximum random errors are obtained for the measured quantities: the suction pressure of \(\pm 0.616\%\), the discharge pressure of \(\pm 0.658\%\), the discharge of \(\pm 0.18\%\), the speed of \(\pm 0.471\%\) and the torque of \(\pm 0.387\%\). As a result, a random error value of \(\pm 1.103\%\) is determined for the pump efficiency (\(f_{t_{\eta_{p}}}\)). Then, the total uncertainty of the pump efficiency (\(f_{t_{\eta_{p}}}\)) by \(\pm 1.323\%\) is obtained on the test rig. The ACS850 45 kW (DTC) inverter [34] is also used to acquire the electrical power, the mechanical power and the speed on the test rig. In this case, the total uncertainty for the mechanical power is determined using the accuracy of \(\pm 4\%\) with nominal torque in an open loop and the speed control in a closed loop with an accuracy of \(0.01\%\) from the nominal speed. Then, the systematic error (\(f_{s_{\eta_{p}}}\)) of \(\pm 0.4035\%\) is obtained and the total uncertainty of \(\pm 4.183\%\) for the pump efficiency (\(f_{t_{\eta_{p}}}\)). In conclusion, the total uncertainty of the pump efficiency is 3 times smaller if the torque transducer is installed on our test rig. The software module was verified for the operation of the pump across its full operating range, covering all three operating regimes shown in Figure 5.  
The curves \(H=f(Q)\), \(P_{m}=f(Q)\), and \(\eta_{P}=f(Q)\) for the centrifugal pump PCN 65/200 at speed of \(n=2900\) rpm are shown in Figure 6. The experimental data are marked with dots, whilst the polynomial functions approximating them are plotted as continuous lines. These figures show a proper correlation between the experimental data and the approximation curves. The value of the \(R^{2}\) parameter is shown for each curve, quantifying the accuracy of the approximation degree of the experimental data with the polynomial function selected in the software module. Table 1 contains experimental data for centrifugal pump PCN 65/200. Tables 2-4 show the fitting coefficients for Equations (4), (10) and (11). \begin{table}
\begin{tabular}{c c c c c} \hline \(\mathbf{n}\) [**rpm**] & \(\mathbf{p_{0}}\) & \(\mathbf{p_{1}}\) & \(\mathbf{p_{2}}\) & \(\mathbf{p_{3}}\) & \(\mathbf{R^{2}}\) \\ \hline
2900 & 3.554 & 881.109 & \(-13\),978.015 & 40,315.701 & 0.96804 \\ \hline \end{tabular}
\end{table} 
Table 4: The coefficients of the 2 nd-degree approximation polynomial function for the pump efficiency \(\eta_{P}=f(Q)\) at speed of 2900 rpm. \begin{table}
\begin{tabular}{c c c c c} \hline \(\mathbf{OPno.}\) & \(\mathbf{Q_{ms}\times 10^{3}}\) [**m\({}^{3}\)/s]** & \(\mathbf{H_{ms}}\) [**m**] & \(\mathbf{P_{m_{ms}}}\) [**kW**] & \(\mathbf{\eta_{P_{ms}}}\) [**\%**] \\ \hline OP7 & 6.727 & 49.678 & 11.815 & 27.737 \\ \hline OP8 & 12.289 & 48.861 & 13.497 & 43.629 \\ \hline OP9 & 18.640 & 47.295 & 15.816 & 54.662 \\ \hline OP10 & 24.232 & 45.104 & 17.109 & 62.645 \\ \hline OP11 & 29.604 & 42.387 & 18.145 & 67.818 \\ \hline OP12 & 33.668 & 38.439 & 18.827 & 67.411 \\ \hline OP13 & 37.213 & 36.266 & 18.888 & 70.070 \\ \hline OP14 & 40.037 & 33.721 & 19.110 & 69.282 \\ \hline OP15 & 42.560 & 31.468 & 18.939 & 69.348 \\ \hline OP16 & 44.617 & 28.774 & 18.781 & 67.036 \\ \hline \end{tabular}
\end{table} 
Table 1: The experimental data determined for centrifugal pump PCN 65/200 at speed of 2900 rpm.