# Degradation of Hydraulic System due to Wear Particles or Medium Test Dust
## 2 Materials and Methods
### Hydraulic External Gear Pump--Specimen 1  
The volumetric efficiency of the gear pump was measured with an additional pressure relief valve by switching the manually operated 3/2 ball valve (pos. 17.1, Figure 2), which returned the oil to the tank through the pressure relief valve (pos. 20, Figure 2). Measurements were made at four different pressures: 0 bar, 100 bar, 150 bar, and 200 bar. Then, flow rates were measured with a stopwatch and a weight scale, weighing the oil volume in graduated cylinder. From the density of the oil and the weight of the oil, the volume of the oil and thus the flow rate, according to Equation (1), were indirectly determined:  
\[Q=\frac{V}{t} \tag{1}\]  
where \(Q\) is the flow rate in L/min, \(V\) is the volume of oil m\({}^{3}\), and \(t\) is the time in min. The gear pump model 2 SP A06 D 10-G consisted of the front cover, the side end plate, the main and auxiliary gear shafts, the housing, the second side plate, and the rear cover (Figure 3). Leakage occurred between the gears (path b, Figure 3) and between the gear and the housing (path a, Figure 3). Pressure of the fluid is increasing in steps between the suction and pressurized side (where gear and housing are containing fluid) because of the construction of the pump.  
The actual volumetric pump efficiency (\(\eta_{V,\text{act}}\)), according to equation Equation (2), was in correlation with the pump flow rate.  
\[\eta_{V,\text{act}}=\eta_{V,\text{theor}}\frac{n_{\text{act}}}{n_{\text{theor }}} \tag{2}\]  
where \(\eta_{V,\text{theor}}\) is the theoretical volumetric efficiency calculated as the maximum flow rate (at atmospheric pressure) of the pump divided by the actual flow rate (at actual pressure),  
Figure 3: Schematic representation of leakage paths: (a) between the gear and housing and (b) between the two gears.  
\(n_{\text{act}}\) is the actual rotational speed, and \(n_{\text{theor}}\) is the theoretical rotational speed in rpm. When calculating the flow rate of the pump, it is usually assumed that the rotational speed of the electric motor shaft is constant at all applied pressures, but in reality, it decreases with increasing pressure at the outlet of the pump (torque increases). Also, as the rotational speed increases, the volumetric efficiency increases due to the hydrodynamics inside the pump and then forms a curve with the highest volumetric efficiency at certain speed. If the rotational speed continues to increase, the volumetric efficiency decreases. Table 2 lists the measured rotational speeds at various pressure points. The wearable surfaces on the pump housing are shown in Figure 4. This wear occurred mostly on the suction side of the pump, but was also observed on the pressurized side. The housing was cut open and examined with digital microscope (Hirox HRX-01 and NPS, Hirox Europe, Limonest, France). Examined surfaces are showed on Figure 4d.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Pressure p, Bar** & \
\begin{tabular}{c} **Actual Rotational Speed \(n_{\text{act}}\)**, \\ **rev/min** \\ \end{tabular} &
\begin{tabular}{c} **Theoretical Rotational Speed** \\ **\(n_{\text{theor}}\)**, rev/min** \\ \end{tabular} \\ \hline
0 & 1498 & 1500 \\
50 & 1489 & 1500 \\
100 & 1480 & 1500 \\
150 & 1465 & 1500 \\
200 & 1460 & 1500 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Difference between actual rotational speed and theoretical rotational speed.  
Figure 4: (**a**) Disassembled gear pump, (**b**) wear of pump housing, and (**c,d**) cutting the pump housing and observing the wear on housing with digital microscope.