Granular Media Friction Pad for Robot Shoes—Hexagon Patterning Enhances Friction on Wet Surfaces

Abstract

For maximizing friction forces of robotic legs on an unknown/unpredictable substrate, we introduced the granular media friction pad, consisting of a thin elastic membrane encasing loosely filled granular material. On coming into contact with a substrate, the fluid-like granular material flows around the substrate asperities and achieves large contact areas with the substrate. Upon applying load, the granular material undergoes the jamming transition, rigidifies and becomes solid-like. High friction forces are generated by mechanical interlocking on rough substrates, internal friction of the granular media and by the enhanced contact area caused by the deformation of the membrane. This system can adapt to a large variety of dry substrate topologies. To further increase its performance on moist or wet substrates, we adapted the granular media friction pad by structuring the outside of the membrane with a 3D hexagonal pattern. This results in a significant increase in friction under lubricated conditions, thus greatly increasing the universal applicability of the granular media friction pad for a multitude of environments.

1. Introduction

Generating large friction forces on unknown substrate geometries requires high adaptability when approaching the substrate, combined with high energy dissipation when applying transversal load. This is why we recently proposed the granular media friction pad (GMFP) as a potential universal solution for friction enhancement on a wide range of substrates [1].

The GMFP consists of a thin elastic membrane encasing granular material, such as sand, metal powder, plant seeds, etc. When applying load to the GMFP, the granular medium undergoes the jamming transition [2,3]. The result of this is fluid-like behavior [4,5] of the GMFP, when unloaded or approaching the substrate topography (see Figure 1a), and solid-like behavior, when pressed against the substrate (see Figure 1b). Friction forces are generated by the mechanical interlocking of the now solid-like granular material and the substrate asperities, as well as by high internal friction of the granular media [6,7,8,9,10,11]. When taking away the normal load and pushing the GMFP onto the substrate, the granular filling becomes fluid-like again, enabling easy removal from the substrate without requiring high pull-off forces. In addition to this, the thin elastic encasing membrane holding the loosely filled granular material can create large contact areas with the substrate, contributing to the total resulting friction force by adhesion-mediated friction [12,13,14] and by elastic deformation of the soft membrane. In contrast to previous systems employing the jamming transition to create friction or holding forces [4,15,16,17,18,19,20], no active control mechanism (such as the application of a vacuum to control the jamming transition) is needed.

While the GMFP can adapt to a large variety of substrate topologies and form around contaminating particles embracing them [21], this type of structure would probably fail on wet substrates due to its extremely smooth membrane [22,23,24] and the resulting hydrodynamic lubrication when sliding over a substrate.

In nature, numerous animals live in moist or wet environments, but are still able to get a stable grip for secure attachment and locomotion [25]. For a large variety of these animals, a convergent solution appeared in the course of biological evolution to achieve this: microstructuring their attachment pad surface [26,27] with mostly hexagonal arrays of channels, as seen, e.g., in a large diversity of frogs [25,26,28], in bush crickets [27,29], stick and leaf insects [30], and salamanders [31,32]. The microstructure not only helps in spreading secretory fluid over the whole attachment pad for adhesion enhancement, but also to remove surplus fluids and enable intimate contact with the substrate [25,33,34] when gripping but also while sliding. This principle has been adapted in several biomimetic studies both for similar dimensions [22,26,27,32,35] as well as for much larger structures, such as those in the tire industry [27,36,37,38].

While microstructuring of a surface is highly effective for draining fluids and to enable high friction forces on smooth substrates, a second principle can be observed in nature in conforming to wet (or rough) substrates to enhance contact area for friction [39]: The microstructured attachment pads feature a complex superstructure inside, which results in extremely soft attachment pads. This can be done actively [40,41,42] or passively by design [25,29,33,39,43,44].

In this study, we combine the structuring of the membrane with extreme softness and adaptability by enhancing the membrane surface with a hexagon pattern. An increase in friction on wet substrates is expected, while maintaining fluid-like behavior when approaching a rough or contaminated substrate to maximize the contact area. We investigate the friction performance of smooth and hexagonally patterned GMFP on a flat substrate when dry, and also when completely immersed in mineral oil.

2. Materials and Methods

The granular media friction pad (GMFP) was composed of loose granular material that was encased by a thin, elastic membrane. The membrane was put flat on a lightweight, 3D-printed sample holder and clamped down using an adjusting washer (40 mm × 50 mm × 1 mm). Then, the granular material (1.7 ground coffee, Gold 100% Arabica, Markus Kaffee GmbH & Co., KG, Weyhe, Germany, see [1] for more details) was pushed behind the membrane through the lockable hole of the sample holder.

Two different types of GMFP were investigated: one with a smooth membrane (see Figure 2a), and one with a hexagon-patterned membrane (see Figure 2b). The membranes, consisting of Dragon Skin^TM 30 (Smooth-On, Inc., Macungie, PA 18062, USA) with a Young’s Modulus of 0.53 ± 0.02 MPa, were cast by pouring the uncured resin between two plastic foils, which were fixated on glass plates and separated by 1 mm spacers. This resulted in a 1 mm thick silicone membrane. For the hexagon membrane, a hexagon grid with 2.19 mm circumcircle, 0.4 mm groove width and 0.6 mm groove depth was 3D-printed from PLA using an Original Prusa i3 Mk3 (Prusa Research s.r.o., Prague, Czech Republic). The grid was glued onto one of the plastic foils, before molding the membrane in the same way as the smooth membrane, so that the tops of the resulting hexagonal pillars had the same surface properties as the smooth membrane. There are three reasons for the selection of the hexagonal pattern: (1) As mentioned above, many biological systems use this evolutionarily optimized pattern for the purpose of grip enhancement on wet substrates [22,25,26,36,37,38,39]. (2) This pattern has been previously shown to enhance friction on substrates wetted by water [23,27,36,37,38]. (3) This pattern is relatively easy to design and adapt to curved substrates.

The GMFP fixed to the sample holder could slide freely on four vertical linear rods using low-friction linear bearings (see Figure 2c). The substrate, the flat side of wire mesh plywood (100 mm × 100 mm), was pulled horizontally below the GMFP at 1 mm/s for 50 mm using a linear testing machine (Xforce HP 500 N, ZwickiLine, Zwick Roell, Ulm, Germany) that measured the pulling force. To obtain the sliding friction force, the pulling force was averaged for 10 s, 35 s after sliding started (see grey area in Figure 1c). To increase the normal load, F_n, additional weights could be placed on top of the GMFP. The coefficient of friction, µ, was obtained as µ = F_fr/F_n.

To examine the effect of membrane structuring on the friction performance of the GMFP under dry and lubricated conditions, both the smooth and the hexagon-patterned GMFP were produced 12 times and tested subsequently on a dry substrate and on an oily substrate. For the latter, mineral oil (Mineral oil 330779, Sigma-Aldrich Chemie GmbH, Taufkirchen, Germany) was poured onto the substrate with a depth of at least 3 mm to fully submerge the contact area between the GMFP and substrate. For each sample and substrate combination, friction measurements were conducted at four different normal loads ranging from the sample weight itself (1 N) up to a maximum normal load of 19.36 N.

3. Results

The friction performance of the GMFP with smooth and hexagon-structured membranes on a dry substrate and submerged in mineral oil is illustrated in boxplots showing the average pulling force (see Figure 3a) and the resulting friction coefficient, µ (see Figure 3b). The average friction coefficients of all sample and substrate combinations for the four applied normal loads are shown in

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.

Fn [N]	Smooth		Hexagon
	Dry	Oil	Dry	Oil
1.00	7.9 ± 1.5	0.2 ± 0.1	2.7 ± 0.4	1.4 ± 0.3
4.92	4.8 ± 0.4	0.1 ± 0.1	1.7 ± 0.1	0.9 ± 0.2
10.81	3.3 ± 0.2	0.1 ± 0.1	1.5 ± 0.1	0.8 ± 0.2
19.36	2.5 ± 0.1	0.1 ± 0.1	1.4 ± 0.1	0.7 ± 0.2

. For all normal loads, the different GMFP membranes, as well as the contamination of the substrate, led to a significant difference in the friction coefficients (Kruskal–Wallis rank sum test, Holm FWER method).

3.1. Dry Substrate

On the dry substrate, the GMFP with a smooth membrane performs much better than the hexagon-patterned sample. The smooth GMFP achieves extremely high friction forces at a low normal load, with the highest friction coefficient being µ = 7.9 ± 1.5 at the lowest normal load of 1 N. At the highest normal load of 19.36 N, the sample (4 cm diameter) achieves friction forces up to 52 N.

Hexagonal structuring leads to a significant reduction in friction forces on the dry substrate. The friction coefficient is still between µ = 1.4 and µ = 2.7 for all loading conditions examined, but generated friction forces are only about half of those of the smooth membrane.

3.2. Oiled Substrate

While the smooth GMFP performs better on the dry substrate than the hexagon GMFP, the opposite is the case once it is submerged in mineral oil. Here, the smooth GMFP is only able to create a maximum of 3 N friction force under any loading condition, with the friction coefficient, µ, ranging from 0.1 to 0.2. In contrast, the hexagonal-patterned GMFP still achieves high friction forces with a friction coefficient (µ) of 0.7–1.4.

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 µ = 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 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]. This effect could be especially beneficial for an adapted hexagonal GMFP, when the sliding direction is predictable, or when friction anisotropy is desired.