# Granular Media Friction Pad for Robot Shoes--Hexagon Patterning Enhances Friction on Wet Surfaces
## 4 Discussion  
On the dry substrate, the better friction performance of the smooth GMFP results from the larger contact area [12; 13; 45] in contrast to the grooved pattern of the hexagon membrane. It is known that soft, smooth rubber on a smooth glass surface can reach a frictional coefficient of \(\mu\) = 2.8 [46]. The observed experimental result, where the coefficient of friction decreases with an increasing normal load (Figure 3b), can be explained by the relatively stronger contribution of adhesion at lower loads. This is not surprising for relatively smooth and soft contact pairs and was previously observed in [47]. In addition, the deformation of the hexagon pillars during sliding could reduce the occurring friction forces by decreasing contact area even further [22; 47; 48; 49]. However, for structured and microstructured surfaces, a reduction in uncontrolled stick-slip friction is expected due to a distribution of the crack propagation to the individual hexagonal pillars, which could result in higher peeling forces [27]. Submerged in oil, the picture is inverted: The lubrication never breaks down for the smooth membrane, resulting in extremely low friction coefficients. For the hexagon GMFP, however, breakdowns of the lubrication film and high friction forces occur. The drainage channels between the hexagonal pillars have to be large enough for draining the lubricant, depending on the viscosity of the lubricating fluid [25; 27], the cross-section of the channels [25; 27], and the sliding velocity [32; 41], while still maintaining a pillar size sufficient for large contact areas. In the case of the GMFP, the deformation of the thin elastic membrane under normal load and also from stretching during sliding results in different channel geometries (depending on substrate, loading condition and occurring friction forces). The bending of the hexagonal pillars [22; 48; 49], which reduces the contact area during sliding, has to be considered as well. The effect of the friction enhancement of micropatterned surfaces in oil is potentially even stronger in water [27], because oil \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Fn [N]**} & \multicolumn{2}{c}{**Smooth**} & \multicolumn{2}{c}{**Hexagon**} \\ \cline{2-5}  & **Dry** & **Oil** & **Dry** & **Oil** \\ \hline
1.00 & 7.9 \(\pm\) 1.5 & 0.2 \(\pm\) 0.1 & 2.7 \(\pm\) 0.4 & 1.4 \(\pm\) 0.3 \\ \hline
4.92 & 4.8 \(\pm\) 0.4 & 0.1 \(\pm\) 0.1 & 1.7 \(\pm\) 0.1 & 0.9 \(\pm\) 0.2 \\ \hline
10.81 & 3.3 \(\pm\) 0.2 & 0.1 \(\pm\) 0.1 & 1.5 \(\pm\) 0.1 & 0.8 \(\pm\) 0.2 \\ \hline
19.36 & 2.5 \(\pm\) 0.1 & 0.1 \(\pm\) 0.1 & 1.4 \(\pm\) 0.1 & 0.7 \(\pm\) 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average friction coefficients with standard deviation of the smooth and hexagon GMFP on dry substrate and when completely submerged under mineral oil for all normal loads. has much higher wetting properties on all the surfaces and has much higher viscosity than water. In this study, the number of sliding cycles was relatively low. After running in, the coefficient of friction might change due to the changes of the surface structure through abrasive wear. Our experimental design was selected to avoid the influence of wear on the results of our tests. In the future, tests with a high number of cycles would be desirable to study frictional behavior of both types of surface structure after running in (in the presence of wear). For a further optimization of friction forces, the sliding direction of the hexagon GMFP could be considered. In our experiment, all hexagonal GMFPs were tested in the same orientation, i.e., with the side of the hexagons facing the sliding direction. In [26], an increase of up to 20% in friction force was observed when sliding with the hexagon tips forward. Even higher geometry-dependent anisotropies were observed for elongated pillar shapes due to drainage flow and a change in tangential contact stiffness [27; 35].