# Analysis of Different Guide Elements' Designs in Hydraulic Cylinders
## 5 Discussion
### Guidance with Hydrostatic Bearing  
For all pressures and radial loads (Figures 16-18), all diagrams show that the frictional force decreases rapidly with increasing velocity up to 0.2 m/s and then increases slightly with increasing velocity. The highest friction force values are observed at the highest radial loads, which indicates a greater influence of the radial load on the bearing. The friction force values are not significantly affected by the pressure, but the friction force increases faster at higher pressures (240 bar) after reaching the minimum value than at 20 bar and 120 bar (the curves have a steeper slope).  
Other researchers [14] have also found that the curves (Figures 10-18) have a similar shape to [PERSON]'s [45] curve. The curve illustrates three different types of friction: boundary, mixed, and hydrodynamic friction. At the beginning, the surfaces are in direct contact, which leads to the highest friction (boundary friction). In the area of mixed friction, the surfaces are partially separated by the lubricant, which reduces the friction to a minimum value. When this minimum is reached, hydrodynamic friction begins, in which the surfaces are completely separated by a thin layer of lubricant and the friction is mainly caused by the viscose friction induced by shear stresses within lubricating film [32; 59]. According to the classic Stribeck curve and the hydrodynamic lubrication regime, such a scenario is to be expected, but only if the following conditions are met: At the lowest speeds (and with a radial load of 50 kg), there is direct contact between the contact surfaces. In this case, the system is subject to friction at the'solid-solid' level, which is very high, as the lubricating film cannot separate the two contact surfaces. As the speed increases, a thicker and thicker lubricating film forms, which reduces the friction contribution at the solid level and thus also the overall friction. When the film is full, the viscous component of the friction begins to dominate and increases with speed, as a higher speed also means a higher shear stress in the lubricant, as shown in Equation (\(\tau=\eta\cdot\left(\frac{\mathrm{p}}{\mathrm{h}}\right)\)). According to the equation, as the sliding speed increases, the shear also increases (although this makes the lubricating film thicker (h), but the increase in speed (v) is greater than the increase in thickness, h).  
Figures 20 and 21 show a comparison of the individual guide elements used: guide ring, labyrinth seal, and hydrostatic bearing. Figure 20 shows the minimum values of the frictional force, while Figure 21 shows the maximum values of the frictional force at different pressures and radial loads. The minimum frictional forces were achieved at velocities of around 0.2 m/s, with the maximum being reached at the minimal velocity.  
The highest friction force at start-up (1800 N) was measured with the guide rings at 240 bar and a radial load of 50 kg, while the lowest (238 N) was measured with the labyrinth seal at 120 bar and no radial load. The highest average frictional force (988 N) during movement was measured with the guide rings at 240 bar with no radial load, while the lowest (17 N) was measured with the labyrinth seal at 120 bar and a radial load of 10 kg.  
Figure 20: Minimal friction force values of each guide element used: guide ring, labyrinth seal, and hydrostatic bearing at different pressures and radial loads.