# 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 algorithm provides the values of the computed variables \(Q\), \(H\), \(P_{m}\) and \(\eta_{P}\) of the pump's operating point. Moreover, the following values are found as output data: \(Q(\eta_{P_{P_{P_{P}P}}})\), \(H(\eta_{P_{P_{P}P}})\) and \(P(\eta_{P_{P_{P}P}})\), and the 10 coefficients of the polynomial functions that approximate the input data for the pump: three coefficients (\(h_{2}\), \(h_{1}\) and \(h_{0}\)) for the \(H(Q)\) curve, four coefficients (\(p_{3}\), \(p_{2}\), \(p_{1}\) and \(p_{0}\)) for the \(P_{m}(Q)\) curve, three coefficients (\(e_{2}\), \(e_{1}\) and \(e_{0}\)) for the \(\eta_{P}(Q)\) curve, and, finally, those three \(R^{2}\) coefficients that allow for accurate estimation of the read data. In the end, the user is also provided with the regime and the color of the regime where the pump's operating point is found. Additionally, the relative percentage error of the \(Q\) flow rate is presented, computed in relation to the measured flow rate value \(Q_{ms}\) if this variable has been included in the input data set. If the value of \(Q_{ms}\) was not mentioned in the input data set, then the relative percentage error of the flow rate will be missing. We have used experimental data obtained for centrifugal pump PCN 65/200 at speed of \(n=2900\) rpm to validate the results supplied by the software. Preliminary validation of the software was performed at a speed of \(n=2500\) rpm. The data measured on the test rig available at the Hydraulic Machinery Laboratory of the \"Politehnica\" University Timisoara, presented in Figure 4, have been obtained using the IEC60193 methodology [33]. A 22 kW asynchronous electrical motor is installed on the test rig to actuate the PCN 65/200 centrifugal pump. An ACS 850 45 kW Direct Torque Control (DTC) [34] inverter is used to vary the speed of the electrical motor from 500 rpm up to 3000 rpm [35]. A software platform completely controls the test rig. Firstly, an acquisition system was implemented to acquire sensor data for overall pressure, temperature, discharge, torque, speed and electrical power. The acquisition system with 32 input channels (voltage/current differential inputs) and a maximum 100 kb/s acquisition frequency was developed. The data is transferred to a computer using an RS232 interface. A remote control system was implemented, increasing  
Figure 4: The test rig available at the Hydraulic Machinery Laboratory of the “Politehnica” University Timisoara. Schematic view of the test rig with actual dimensions in mm and photo. the operability of the test rig [36]. Next, a SCADA platform was implemented to acquire the needed variables (suction and discharge pressures, temperature, discharge, speed and torque) and store them in a log file. The total uncertainty (\(f_{t}\)) is obtained by combining the uncertainties due to systematic (\(f_{s}\)) and random (\(f_{r}\)) errors. The systematic and random errors are evaluated taking into account the measuring system and the operating conditions of the pump (18). \[f_{t}=\sqrt{(f_{s})^{2}+(f_{r})^{2}} \tag{18}\]  
The first step in the estimation of the pump efficiency uncertainty is to identify each component that can influence its value. As a result, the total uncertainty of the pump efficiency (\(f_{t_{\eta_{p}}}\)) of the discharge (\(f_{t_{Q}}\)), suction pressure (\(f_{t_{p_{s}}}\)), discharge pressure (\(f_{t_{p_{d}}}\)), speed (\(f_{t_{n}}\)) and torque (\(f_{tT}\)) (19). \[f_{t_{\eta_{p}}}=\sqrt{(f_{t_{Q}})^{2}+(f_{t_{p_{s}}})^{2}+(f_{t_{p_{d}}})^{2}+ (f_{t_{n}})^{2}+(f_{tT})^{2}} \tag{19}\]  
The systematic errors are provided by the measuring devices. An electromagnetic flowmeter is used to measure discharge values up to \(45\times 10^{-3}\) m\({}^{3}\)/s with \(\pm 0.4\%\) accuracy. This device is installed on the rig's top pipe. The suction pressure sensor range is \(-1\div+2.5\) bars with an accuracy of \(\pm 0.25\%\).