# Numerical Investigation of Erosion Wear in the Hydraulic Amplifier of the Deflector Jet Servo Valve
## Formulation of Erosion in Pilot Hydraulic Amplifier
### Erosion Wear in Hydraulic Amplifier  
As illustrated in Figure 1, the jet plate and the deflector are confronted with high-speed fluid and varied degrees of impacts between the fluid and the solid walls. Intuitively, significant erosion wear can happen at the places where either high flow velocity or intense impact occurs. Therefore, it can be speculated that the jet orifice of the jet plate, the side walls inside the deflector, the shunt wedge, and the guide curve outside the receiver are most possible to be susceptible to erosion wear, as shown in Figure 3. In respect of the mechanism of erosion wear, since the molecular force of hydraulic oil exerted on the metal surface is much less than the force brought by solid particles in oil,  
Figure 1: Hydraulic amplifier.  
Figure 2: Function of hydraulic amplifier in whole valve.  
it is assumed that the erosion wear is only caused by continuous particle impacts. That is, because of surface material's ductility, particle impacts will result in formation of tiny craters and abscission of metal scraps. While the effect of particle impact primarily depends on the material performances of particles and target surfaces, the impact direction, the quantity of impact particles and the distribution of particle sizes [5]. For the specific scenario of servo valves, the size and quantity of particles in oil can be characterized as the contamination level, as listed in Table 1.  
The contamination level of hydraulic oil used in the aerospace industry is 13/11 of an enterprise standard QJ2724.1-2724.7-95 [19], which is approximately equivalent to Level 5 of the NAS standard. In addition, for an actual servo valve, a built-in filter with a precision of 10 um is placed before the hydraulic amplifier. As a consequence of that, the actual number of the particles entering the hydraulic amplifier should be below 1% of the original number, which is described as follows [20].  
\[\beta_{10}=N_{u}/N_{d} \tag{1}\]  
where \(N_{u}\) and \(N_{d}\) are the numbers per unit volume of particles exceeding 10 um before and after filtering, respectively; \(\beta_{10}\geq 100\) is the reduction ratio. The material of the deflector and the jet plate is 3J1, with its performance listed in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**Number of Particles in 100 mL Oil**} \\ \hline \multirow{2}{*}{**Contamination Level**} & \multicolumn{6}{c}{**Particle Size Range**} \\ \cline{2-6}  & **5 \(\thicksim\) 15** & **15 \(\thicksim\) 25** & **25 \(\thicksim\) 50** & **50 \(\thicksim\) 100** & **100** \\ \hline
00 & 125 & 22 & 4 & 1 & 0 \\
0 & 250 & 44 & 8 & 2 & 0 \\
1 & 500 & 89 & 16 & 3 & 1 \\
2 & 1000 & 178 & 32 & 6 & 1 \\
3 & 2000 & 356 & 63 & 11 & 2 \\
4 & 4000 & 712 & 126 & 22 & 4 \\
5 & 8000 & 1425 & 253 & 45 & 8 \\
6 & 16,000 & 2850 & 506 & 90 & 16 \\
7 & 32,000 & 5700 & 1012 & 180 & 32 \\
8 & 64,000 & 11,400 & 2025 & 360 & 64 \\
9 & 128,000 & 22,800 & 4050 & 720 & 128 \\
10 & 256,000 & 45,600 & 8100 & 1440 & 256 \\
11 & 512,000 & 91,200 & 16,200 & 2880 & 512 \\
12 & 102,400 & 182,400 & 32,400 & 5760 & 1024 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Optimized results of the circular arch for different slenderness and opening angles [18].  
Figure 3: Erosion areas speculated.