# A Method of Two-Stage Pressure Control Based on Multistage Orifices
## 3 Engineering Implementation of Two-Stage Pressure-Control Method
### Reliability Analysis of Pilot Pressure Control  
When all electromagnets of the four solenoid valves were powered on, the three orifices formed a series oil circuit (shown in Figure 2a). On the basis of Equations (9)-(11), \(\Delta p_{1}\), \(\Delta p_{2}\), and \(\Delta p_{3}\) can be expressed as:  
\[\Delta p_{1}=\frac{1}{1+2\left(\frac{d_{1}}{d_{2}}\right)^{4}}\Delta p_{3-z}= \frac{1}{1+2\times\left(\frac{3}{1.2}\right)^{4}}\Delta p_{3-z}\approx 0.013 \Delta p_{3-z} \tag{12}\]  
\[\Delta p_{2}=\Delta p_{3}=\frac{1}{2+\left(\frac{d_{2}}{d_{1}}\right)^{4}} \Delta p_{3-z}=\frac{1}{2+\left(\frac{1.2}{3}\right)^{4}}\Delta p_{3-z}\approx 0.49\Delta p_{3-z} \tag{13}\]  
Maximal theoretical pilot control pressure \(P_{\text{ast}}\) could be obtained as shown in Equation (14), and other pressure \(P_{\text{asp}}\) can be expressed as Equation (15).  
\[P_{\text{ast}}=0.98\Delta p_{3-z}=0.98P_{\text{s}} \tag{14}\]  
\[P_{\text{asp}}=0.49\Delta p_{3-z}=0.49P_{\text{s}} \tag{15}\]  
where \(P_{\text{s}}\) represents the inlet pressure of the first orifice in series.  
The pressure drop of the two short orifices in series could be obtained in the same way, as shown in Equations (16) and (17); \(\Delta p_{\text{s}1.2}\) represents the pressure drop of the second orifice with a diameter of 1.2 mm.  
\[\Delta p_{1}=\frac{R_{1}}{R_{1}+R_{2}}\Delta p_{2-\text{z}}=\frac{1}{1+\left( \frac{d_{1}}{d_{2}}\right)^{4}}\Delta p_{2-\text{z}}=\frac{1}{1+\left(\frac{3 }{1.2}\right)^{4}}\Delta p_{2-\text{z}}\approx 0.025\Delta p_{2-\text{z}} \tag{16}\]  
\[\Delta p_{\text{s}1.2}=\frac{R_{2}}{R_{1}+R_{2}}\Delta p_{2-\text{z}}=\frac{1 }{1+\left(\frac{d_{2}}{d_{1}}\right)^{4}}\Delta p_{2-\text{z}}=\frac{1}{1+ \left(\frac{1.2}{3}\right)^{4}}\Delta p_{2-\text{z}}\approx 0.975\Delta p_{2- \text{z}} \tag{17}\]  
In Figure 2b, the electromagnet of solenoid valve V1 or V3 is in the power-off state, and the second orifice is \"short-circuited\". Maximal theoretical pilot control pressure \(P_{\text{ast}}\) and other pressure \(P_{\text{asp}}\) are expressed as shown in Equation (18).  
\[P_{\text{ast}}=P_{\text{asp}}=0.975\Delta p_{\text{z}}=0.975P_{\text{s}} \tag{18}\]  
In Figure 2c, the electromagnet of solenoid valve V2 or V4 is in the power-off state, and the third orifice is \"short-circuited\". Pressure \(P_{\text{ast}}\) and \(P_{\text{asp}}\) are expressed as shown in Equation (19).  
\[P_{\text{ast}}=0.975\Delta p_{\text{z}}=0.975P_{\text{s}},P_{\text{asp}}=0 \tag{19}\]  
Compared with Equations (14), (15), (18), and (19), the different pressure values of \(P_{\text{asp}}\) between the two schemes of maximal pressure control with a different number of orifices in series can be found. If the electromagnet of a certain solenoid valve is not normally powered on, and the valve port is closed, pilot control pressure \(P_{\text{ast}}\) is basically unchanged, but pressure \(P_{\text{asp}}\) is changed obviously, as shown in Table 2. The following conclusions can be drawn:  
1. The abnormal working state of the directional valve can be forewarned according to the pressure value of \(P_{\text{asp}}\) when three orifices are in series. If pressure \(P_{\text{asp}}\) suddenly rises, the electromagnet of the solenoid valve V1 or V3 is in the power-off state, and the second orifice is \"short-circuited\" (as shown in Figure 2b). If pressure \(P_{\text{asp}}\) suddenly drops, the electromagnet of solenoid valve V2 or V4 is in the power-off state, and the third orifice is \"short-circuited\" (as shown in Figure 2c).
2. The scheme that two orifices are connected in series to realize high control pressure has no warning function.