# Development of Proportional Pressure Control Valve for Hydraulic Braking Actuator of Automobile ABS
## 4 Design and Test of Proportional Valve  
### Design of the Proportional Valve Body  
A proportional pressure control valve is composed of the proportional electromagnet set and valve body set, which comprises a magnetic armature, spool valve, housing, and needle valve seat. The design is shown in Figure 18. The outlet and inlet \(P_{\mathit{c}ul}\) are connected, and they both have connection calipers. Although the valve body has four ports, it is three-port and two-position structure.  
Through the shuttle shaft operation, the needle valve port must be closed, and it allows no internal leakage when there is no actuation. With the cone design, the check valve within the shuttle shaft is a safety device. If the needle valve malfunctions, the shuttle shaft cannot be returned to the  
Figure 16: Configuration of the proportional valve solenoid force test: (**a**) test rig; and (**b**) structure.  
Figure 17: Simulation and test results for the proportional valve solenoid force.  
original position, but the caliper pressure can still be relieved through the check valve. If the spring pre-pressuring is ignored, the shuttle shaft force equation is as follows:  
\[F_{m}=F_{em}+F_{cal} \tag{13}\]  
In addition \(F_{m}=P_{m}*A_{sp}\), \(F_{cal}=P_{cal}*(A_{sp}-A_{ol})\).  
Substituting Equation (13),  
\[P_{cal}=(F_{m}-F_{em})/(A_{sp}-A_{ol}) \tag{14}\]  
Where \(F_{m}\) is the master cylinder pressure acting on the shuttle shaft force; \(F_{em}\) is the proportional solenoid force; \(F_{cal}\) is the caliper chamber pressure acting on the shuttle shaft force;\(P_{m}\) is the master cylinder pressure; \(P_{cal}\) is the caliper pressure; \(A_{sp}\) is the spool valve cross-sectional area; and \(A_{ol}\) is the needle valve hole cross-sectional area.  
Assuming that the master cylinder pressure (\(P_{m}\)) is 172 bars, the general ABS specifications must reduce the calipers pressure (\(P_{cal}\)) to 69 bars or less. The spool shaft diameter is 1.8 mm, the proportional solenoid force is about 3.0 kgf, and the needle valve hole and calipers hole are 0.6 mm. The spool valve is fully closed when it moves 0.6 mm. Then, substituting values into Equation (14), the pressure relief value is calculated and the design meets requirements.  
Regarding the rated flow calculation [17], the master cylinder pressure must remain constant. The pressure \(P_{c}\) which is flowing through the spool valve is the supply pressure for the brake calipers with flow rate \(Q_{c}\). The valve orifice area \(A_{c}\) may vary with the displacement changes of shuttle shaft. Pressure \(P_{r}\) flows through the needle valve with flow rate \(Q_{r}\), and the needle valve orifice area is \(A_{r}\). The equation which the spool valve port and the needle valve port flow through is as follows.  
\[P_{cal}=\frac{(\frac{172\pi\pi\pi 0.182}{4}-3.0)}{\frac{\pi}{4}(0.182^{2}-0. 06^{2})}=60.8\;bars\]  
\[Q_{c}=C_{d}A_{c}\sqrt{\frac{2(P_{m}-P_{c})}{\rho}} \tag{15}\]  
\[Q_{r}=C_{d}A_{r}\sqrt{\frac{2(P_{c}-P_{r})}{\rho}} \tag{16}\]  
The opening size of spool valve port and needle valve port are in a relation of mutual growth and decline. The maximum flow rate probably occurs when the two vale ports are in half-open position,  
Figure 18: Proportional valve body construction and fluid force.  
which means the stroke is in the 0.3 mm position. The relationship of pressure is \(P_{m}-P_{c}=P_{c}-P_{r}\) and \(P_{r}\) is close to zero. Thus, \(P_{c}\) is approximately a half of \(P_{m}\). In the steady state, \(Q_{c}=Q_{r}\), the maximum flow rate could be obtained by estimating the flow of spool valve. The half-open cross-sectional area of spool valve is as follows.  
\[A_{c}=\frac{1}{2}(\frac{\pi(0.06)^{2}}{4})=0.001413\;\text{cm}^{2}\]  
Substituting Equation (15),  
\[Q_{c}=0.7*0.001413*100*\sqrt{\frac{2*(172-86)*10^{5}}{1000}}\] \[=13\;\text{cm}^{3}/\;\text{sec}=0.78\;1/\text{min}\]