# A Study on Failure Analysis and High Performance of Hydraulic Servo Actuator
## 3 Design of Hydraulic Servo Actuators
### Low Friction Hydrostatic Bearing  
Previously, low fraction elastic seals were used in servo actuators, but friction occurred excessively depending on the characteristics of the seal in direct contact with fast operating frequencies, resulting in a reduced lifetime as well as reduced control precision. Therefore, in this design, four pockets of static pressure bearing were applied for the rod part, as shown in Figure 5, and the labyrinth seal type static pressure bearing for the piston part. Analysis of the flow characteristics of the static pressure bearing of a typical hydraulic servo actuator shows that the flow from the orifice is the same as Equation (2), and the flow through clearance through the piston rod \(q_{2}\) and bearing land \(q_{3}\) part in the bearing pocket is shown in Equation (3). The flow rate of the land from the static-bearing pocket to the pocket is negligible due to little pressure difference in the neighboring pocket. Where Equations (2)-(4) are combined, the pressure and flow of the pockets can be calculated and the power consumed by the use of static pressure bearing can be identified [29; 30]. \[q_{1}=CA\sqrt{\frac{2g}{r}(P_{s}-P)}\times 60 \tag{2}\]  
Figure 4: Comparison of elastic seal type and labyrinth seal type. (**a**) Low friction seal; (**b**) Labyrinth seal. \[q_{2}=\frac{\delta_{0}^{3}P}{12\times\frac{a}{100}\times\frac{r}{g}\times l}\times \frac{\pi}{4}\mathrm{d}\times 2\times 60 \tag{3}\]  
\[q_{3}=0 \tag{4}\]  
here, \(\delta_{0}\) is the radial clearance, \(P\) is the internal pressure (MPa), \(g\) is the gravity acceleration (m/s\({}^{2}\)), \(r\) is the oil specific gravity, \(l\) is the clearance length(m), d is the rod diameter(m), and \(\alpha\) is the oil viscosity. In the piston section, the labyrinth seal type static pressure bearing is arranged repeatedly by multiple lands and grooves, and in the modeling tool, the ring gaps of Figure 6 with different diameters are connected repeatedly. The pressure drop \(P_{AB}\) passing through the ring gap is then the subtraction of outlet port pressure (port \(B_{p}\)) from input port pressure (port \(A_{p}\)) as shown in Equation (5) and the volume flow \(Q\) is the sum of pressure driven flow \(Q_{dp}\) (lamina pipe flow or Poiseuille flow) and the velocity driven flow \(Q_{dv}\) (drag flow or Couette flow) as shown in Equation (6). In addition, the volume flow rate of the lateral flow condition, disregarding the pressure drop, is the same as Equation (7), and Equation (8) when considering the pressure drop. At this time, \(K(Re)\) is determined by the Reynolds number and the gap structure [31]. \[P_{AB}=portA_{p}-portB_{p} \tag{5}\]  
\[Q=Q_{dp}+Q_{dv} \tag{6}\]  
\[Q=\frac{\pi\cdot d_{m}\cdot s^{3}}{12\cdot L\cdot v\cdot\rho}\left(1+\frac{3}{ 2}\frac{e^{2}}{s^{2}}\right)P_{AB} \tag{7}\]  
\[Q=\frac{\pi\cdot d_{m}\cdot s^{3}}{12\cdot L\cdot v\cdot\rho}\left(1+\frac{3}{ 2}\frac{e^{2}}{s^{2}}\right)\left(\frac{1}{1+K(Re)}\right)\cdot P_{AB} \tag{8}\]  
here, \(d_{m}\) is the middle diameter in the gap(m), \(s\) is the mean gap height (m), \(L\) is the length (m), \(v\) is the kinematic viscosity (m\({}^{2}\)/s), \(\rho\) is the density (kg/m\({}^{3}\)), \(Re\) is the Reynolds number, and \(e\) is the factor of eccentricity (m). In this study, the internal diameter of the cylinder tube was 63.05 mm, in which the diameter of the piston with 22 lands was 63 mm, and the diameter of the piston with 21 grooves arranged 1 mm apart from each land was 61 mm, so the piston and tube gap was designed to be 0.025 mm, as shown in Figure 7.  
Figure 5: Flow characteristics of hydrostatic bearing. Using Simulation X 3.7, a dynamic special analysis tool, we modeled the labyrinth seal, as shown in Figure 7, for design optimization and performed the simulated analysis of it with Figure 4:0  
Figure 4:1 Modeling of labyrinth seal for piston. Figure 4:2 Ring gap for modeling the piston labyrinth seal. Figure 4:3 Dimensional arrangement of the five square grooves.