# A Hydraulic Semi-Active Suspension Based on Road Statistical Properties and Its Road Identification
## 3 Road Identification Method
### Acquisition Method of the Current Damping Ratio \(\zeta^{\prime}\)  
According to Equation (8), it can be seen that, to accurately identify the current road conditions, the relationship \(\zeta^{\prime}=\zeta^{\prime}(\theta^{\prime})\) between the current damping ratio \(\zeta^{\prime}\) and the feedback signal \(\theta^{\prime}\) must be established. According to the structure of the controllable hydraulic damper shown in Figure 2, the throttling hole area \(A^{\prime}\) can be expressed as [35]  
\[A^{\prime}(\theta^{\prime})=2\bigg{[}\tan\frac{\theta^{\prime}}{2}\sqrt{(R^{2 }-r^{2})\left(r^{2}\sec^{2}\frac{\theta^{\prime}}{2}-R^{2}\tan^{2}\frac{ \theta^{\prime}}{2}\right)}-r^{2}\text{arc}\cos\left(\frac{\sqrt{R^{2}-r^{2} }}{r}\tan\frac{\theta^{\prime}}{2}\right)\bigg{]}\frac{R\sin\left(\text{arc} \sin\frac{r}{R}-\frac{\theta^{\prime}}{2}\right)}{r-\sqrt{R^{2}-r^{2}}\tan \frac{\theta^{\prime}}{2}} \tag{9}\]  
where \(r\) is the radius of the orifice hole and \(R\) is the outer radius of the rotary shaft. The oil path of the damper recovery valve is shown in Figure 4. When the oil flows through the throttle orifice, the piston hole, the piston gap, and the controllable throttle hole, the damping force is produced. In Figure 4, the piston hole and the throttle orifice are in series; moreover, the whole of them is in parallel with the piston gap and the controllable throttle hole. Thus, the throttle pressure \(p_{0}\) of the throttle orifice can be expressed as [35]  
\[p_{0}=\frac{1}{4}\bigg{(}\sqrt{E^{2}+4p_{\text{H}}}-E\bigg{)}^{2} \tag{10}\]  
where \(E=\frac{128\mu_{\text{H}}L_{\text{be}}A_{0}\mu_{0}}{\pi n_{\text{h}}d_{\text{h} }^{2}}\sqrt{\frac{2}{\rho}}\), \(A_{0}\) is the throttle orifice area, \(\epsilon_{0}\) is the flow coefficient of the throttle orifice, \(\rho\) is the oil density, \(n_{\text{h}}\) is the number of piston holes, \(d_{\text{h}}\) is the piston hole diameter, \(L_{\text{he}}\) is the equivalent length of the piston hole. According to the oil continuity theorem, it can be obtained [35]  
\[\frac{\pi D_{\text{H}}\delta_{\text{H}}{}^{3}(1+1.5e^{2})p_{\text{H}}}{12\mu_ {\text{L}}{}_{\text{H}}}+A^{\prime}\epsilon\sqrt{\frac{2p_{\text{H}}}{\rho} }+A_{0}\epsilon_{0}\sqrt{\frac{2p_{0}}{\rho}}=VS_{\text{h}} \tag{11}\]  
Figure 4: The oil path of the damper recovery valve. where \(\varepsilon\) is the flow coefficient of the controllable throttle hole, \(D_{\rm H}\) is the inner diameter of the damper cylinder, \(L_{\rm H}\) is the length of the piston gap, \(\delta_{\rm H}\) is the mean value of the piston gap, \(e\) is the piston eccentricity, \(\mu_{\rm t}\) is the oil kinetic viscosity, \(p_{\rm H}\) is the throttle pressure of the piston gap, and \(V\) is the working velocity of the damper. Substituting Equation (10) into Equation (11) obtains the following:  
\[J_{3}p_{\rm H}+J_{2}\sqrt{p_{\rm H}}+J_{1}\sqrt{E^{2}+4p_{\rm H}}+J_{0}=0 \tag{12}\]  
where \(J_{3}=\pi D_{\rm h}\delta_{\rm H}^{3}(1+1.5e^{2})\), \(J_{2}=12\mu_{\rm t}L_{\rm H}A^{\prime}\varepsilon\sqrt{2/\rho}\), \(J_{1}=6\mu_{\rm t}L_{\rm H}A_{0}\varepsilon_{0}\sqrt{2/\rho}\), and \(J_{0}=-12\mu_{\rm t}L_{\rm H}VS_{\rm h}-EJ_{1}\). Solving Equation (12), \(p_{\rm H}\) can be obtained. According to the calculated \(p_{\rm H}\), the current damping coefficient \(C\) can be obtained as  
\[C=S_{\rm r}p_{\rm H}/V \tag{13}\]  
where \(S_{\rm r}\) is the annular area between the piston cylinder and the piston rod. According to the damping coefficient \(C\), the damper installation lever ratio \(i\), the installation angle \(\alpha\), the sprung mass \(m_{2}\), and the suspension stiffness \(K_{\rm s}\), the current damping ratio of the semi-active suspension system can be obtained as  
\[\xi^{\prime}=\frac{Ci^{2}\cos^{2}\alpha}{\sqrt{Km_{2}}} \tag{14}\]  
From the derivation process of Equation (14), it can be seen that \(\xi^{\prime}\) is related to \(A^{\prime}\), thus \(\xi^{\prime}=\xi^{\prime}(A^{\prime})\). According to Equation (9), \(A^{\prime}=A^{\prime}(\theta^{\prime})\).