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B C l E N C C D I R E C T . @ Journal of Bionic Engineering 3 (2006) 087-091

Effect of Microscale Contact State of Polyurethane Surface on Adhesion and Friction

Yu Min , Ji Ai-hong , Dai Zhen-dong

Institute of Bio-inspired Structure and Sulface Engineering,

Nanjing University of Aeronautics and Astronautics, Nanjing 210016, k? R. China

Abstract The effect of microscale contact of rough surfaces on the adhesion and friction under negative normal forces was experi-

mentally investigated. The adhesive force of single point contact - sapphire ball to flat polyurethane did not vary with the normal force. With rough surface contact, which was assumed to be a great number of point contacts, the adhesive force increased logarithmically with the normal force. Under negative normal force adhesive state, the tangential force (more than hundred mN) were much larger than the negative normal force (several mN) and increased with the linear decrease of negative normal force. The results reveal why the gecko’s toe must slide slightly on the target surface when it makes contact on a surface and suggest how a biomimetic gecko foot might be designed. Keywords: polyurethane, rough surface, adhesion, friction

Copyright 0 2006, Jilin University. Published by Science Press and Elsevier Limited. All rights reserved.

1 Introduction

A wall-climbing robot could be useful in industry and society, but the stability and reliability of the robot lags far behind the requirements of various circum- stances because of the difficulty of designing a foot whose attachment is based on suction or magnetic at- traction On the other hand, nature has designed wonderful creatures, gecko, bee, fly etc. that can move freely on various surfaces, rough or smooth, wall or ceiling.. The geometry and mechanisms of these feet, and how the adhesion and tangential forces are generated, have been studied by many Jiao et U Z . [ ~ ] measured the adhesive forces between a locust’s foot and a glass surface, and found that adhesion is not enough to allow a locust to move across an up-side-down surface.

Geckos can walk freely on a smooth wall and even crawl quickly while adhering to the ceiling. By using Scanning Electron Microscopy (SEM), it was revealed

that there are hundreds and thousands of setae on the gecko’s foot. Each seta is 30 pm to 120 pm in length and several pm in diameter as shown in Fig. 1. Autumn et U Z . ‘ ~ . ’ ~ ] believed that the adhesive force is generated by the van der Waals’ force between the molecules of gecko’s seta and the surface, but research revealed that geckos require a tiny relative movement during contact, in which tribology plays a very important role. To de- velop biomimetic gecko’s feet, we have to select mate- rials with appropriate properties and to understand the

Corresponding author: Dai Zhen-dong E-mail: zddai@nuaa.edu.cn Fig. 1 SEMs of rows of setae from a toe of a Gecko.

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effect of microscale contact of surfaces on the develop- ment of adhesion and friction.

According to Hertz theory, there is no adhesion between two surfaces in contact. But research'"] sug- gested possible adhesion between surfaces. Greenwood et a1."2'131 and Johnson et a1.[l4' produced several models. In microscale to nanoscale contact, the surface force becomes the decisive factor in determining adhesion and deformation between two solid surfaces[15'. However, the models adopted by the above studies assume ideal conditions such as smooth surface contact. Dai, Hui and Gorb'I6] studied the effect of roughness on the adhesive properties of polyurethane (PU) without refemng to the frictional properties of the materials.

In this paper we study the effect of contact pa- rameters on the adhesion and friction between rough and smooth surfaces, which will set up basic map for the design of biomimetic gecko's feet. Our experiments and analysis use approximately ideal point contact of a sin- gle convex with a plane (sapphire ball versus PU plane) and the surface contact between a large amount of spheres and a plane (glass plane versus PU plane).

2 Materials and methods 2.1 Single point contact: sapphire ball to PU plane

The adhesion between a sapphire ball and flat polyurethane were measured with a Biotester Basalt-01 (Tetra GmbH, Ilmenau Germany, Fig. 2). The machine consists of a sensor (G) made from crystal glass, mi- cro-deflection sensor (FOS) and mirror (M), an upper sample sapphire ball (diameter 1.5 mm, Goodfellow,

Fig. 2 Illustration of Biotester Basalt-01.

Cambridge, England), sample plate (P), and lower sam- ples of polyurethane (S, supplied by Dow Chemical, Germany) with diameter of 60 mm and thickness of 4 mm and was cut according to the required dimensions. The sensor G was driven by a motor to move down and up to load and unload. The deflection of the sensor (proportional to force) was recorded and processed by the computer.

The elastic modulus of target material samples S 1, S2, S3 and S4 of polyurethane were measured to be 1206f80, 55f1.2, 93f1.0 and 104M13.6 kPa ( n = 4 ) respectively.

'

2.2 Multipoint contact: rough PU plane to flat glass The experiments were carried out on a test machine

of adhesion and friction as shown in Fig. 3. The upper sample (glass, 10 mm in diameter) was glued to a can- tilever, which included two dimensional sensors and was driven by a step motor. The normal force was detected and as feedback was sent to the motor to control it. The lower sample of polyurethane 10 mm x 10 mm x 4 mm (lengthxwidthx thickness), was fixed to a sample plate. Two series of experiments were performed on this tester: (1) relationship between adhesive force and normal force; (2) relationship between negative normal force (adhesive state) and tangential force.

(Glass)

Lower sample (Polyurethane)

Sample plate

Fig. 3 Illustration of tester for adhesion and friction.

3 Results and discussions

3.1 Adhesion for single point contact The adhesion of four polyurethane samples, S 1, S2,

S3 and S4, with a sapphire ball was measured. Fig. 4 is

Yu Min et al.: Effect of Microscale Contact State of Polyurethane Surface on Adhesion and Friction 89

the plot of adhesion against normal load, and linear re- gression gives:

Fad=O.OlFn+ 0.1415 (R2= 0.0562) for S1, F a d = 0.0045Fn + 0.3 (R2 = 0.1938) for s2 , F a d = O.O2F, + 0.1487 (R2 = 0.235) for S3, F a d = 0.O065Fn + 0.1676 (R2 = 0.0648) for s4,

respectively. All the correlation coefficient R2 are smaller than the critical reliability coefficient R ~ 0 , o . o ~ = 0.273, which suggests that the normal load F, does not affect the adhesive force Fad. Comparison of the results using the t-test shows that adhesive force with S2 (mean 0.328 mN) is the greatest, that of material S3 (mean 0.28 mN) is higher than S1 (mean 0.261 mN) and no differ- ence between S 1 and S4 (mean 0.228 mN).

I A A I

0.0 1 I , I I I I I 0 2 4 6 8 10 12 14

Normal load (mN)

Fig. 4 Adhesion of polyurethane with sapphire ball under various normal loads.

Considering the microscale elastic contact between the hard sphere and the soft elastic flat polyurethane, the contact situation is the same as that of Derjaguin's model "'I. In accordance with the JKR theory, the adhe- sive force F a d iS given by F a d = 1.5nRw, which is equivalent to the first power of the ball radius R and to the surface energy w, but is independent of contact area and elastic modulus'' ' I . The differences of adhesion among the four samples probably result from the varia- tion in surface energy because, generally speaking, the softer the polyurethane, the higher the surface energy.

3.2 Adhesion for multipoint contact Fig. 5 shows the normal force versus time when a

flat glass contact with polyurethane sample S2. The upper sample was moved down to A and contacted the sample S2 until the normal load reached B, then moved up and the adhesion between two surfaces broken. C is

the adhesive force corresponding to the normal load B. The normal loads in the experiment were random in the range from 45 mN to 230 mN and the number of tests was 100. The experimental results are shown in Fig. 6a. The regression of the data gives Fad = 1 13.7 1 x Ln(Fn) - 371.46 with correlation coefficient of R2 = 0.9814. The equation suggests that the adhesive force increases with the normal load in a logarithmic rule.

200 - B

-200 - I 0 20

Time (s)

Fig. 5 The relationship of adhesive force and normal load versus time.

250 -

-

so I 50 I00 150 200 250

Normal load (mN)

(a) Experimental results

250 r

0 Y 0 50 I00 IS0 200 250

Normal load (mN)

(b) Numerical results

Fig. 6 The relationship between adhesive force and normal load.

In accordance with the JKR theory, the sticking force F, between the glass plane and a polyurethane sphere of radius R, is given by

90 Journal of Bionic Engineering (2006) Vo1.3 No.2

(1 )

where a is the radius of the contact area; w = 2 6 is

the work of adhesion, 71 = 21.4 mJ.m-2 and y2 = 160 mJ.m-* are the surface energy of glass and polyurethane;

2 K = - - 3 [ - v' + - iy ) is effective elastic constant,

4 E, where El and E2 are the Young's modulus of glass and polyurethane, U I and u2 are their Poisson ratio. El = 55 GPa, uI = 0.25 for glass and E2 = 1041 kPa, u2 = 0.45 for Polyurethane Sample S2.

When the two spheres are pulled off, the sticking force has its maximum value, that is, the adhesive force

In the model of Greenwood and Williams "*I, mi- croscale contact between two rough surfaces is equiva- lent to the contact between a plane and a large number of spheres. When the polyurethane surface and the glass plane are pressed together by the applied normal load, the total contact number is

Fad.

lim f" NA @*(s) ds E+O

at any height d of the glass plane, where N is the number of spheres per unit square millimeter, A is the contact area, @*(s) is the probability density of the height of the peaks of the rough surface, which is in accord with Gauss distribution with a mean square deviation 6. Us- ing R = 0. I7 pm, 6 = 0.3 pm, N = 6x lo8, A = 78 mm2(the area of the upper glass sample) and considering the force produced by all the contact points, the overall sticking force between the rough polyurethane surface and the glass plane can be calculated by Eq.( I ) . Loading at an interval of 0.006 pm from 0 to 30, we got the adhesive forces between polyurethane surface and glass plane at different normal loads. The relationship of the adhesive force versus the normal load was obtained using MATLAB shown in Fig. 6b. The adhesion change trend is accordant with that in Fig. 6a from experiments.

According to the result in section 3.1, adhesive forces of a single sphere to a plan are not affected by normal loads and the increasing contact area. Therefore, taking into account the contact of a large amount of spheres to a plan, the adhesive forces increased with the

normal loads in respect that the contact number rises steady. However, when the normal forces were much greater, the adhesive forces increased quite slowly. There are some reasons as follows. On one hand, the contact number increased no longer though the contact area still increased; on the other hand, the lower adhe- sive points were separated by the compression of the higher contact points while unloading the normal force. So the effective contact number remained steady, as well as the adhesive force. Furthermore, when the normal load is relatively large and reaches the yield stress of material, plastic deformation was generated and the contact number increased whereas stress did not rise. Thereby, the adhesive force tends to remain steady.

3.3 The tangential force under adhesion condition In this experiment the upper sample was moved

down and loaded to 150 mN, then moved up until the negative normal force reached a predetermined value, then the sample was moved horizontally (two surfaces still adhering) at speed of 1 m m K i . The negative force was less than 10 mN. Fig. 7 is the relation between the tangential force and the negative normal force, which follows linear relation Y = 9 . 9 7 8 ~ + 178.8 with correla- tion coefficient of R2 = 0.654 (number of data 100). Fig. 7 tells us that the tangential force (more than hundred mN) is much greater than the negative load (several mN) and increase with the linear decrease of negative normal force. These results hint why geckos require a tiny rela- tive movement during contact procedure and why the gecko can climb a smooth wall easily.

so I , I I

-10 -5 0 5 i n

Negativc noniial force (mN)

Fig. 7 The relationship of tangential force versus negative normal force.

Yu Min et al.: Effect of Microscale Contact State of Polyurethane Surface on Adhesion and Friction 91

4 Conclusion

(1) When a sapphire ball and a flat polyurethane surface is in single point contact, the adhesion is ir- relevant to the normal force, but is probably related to the surface energy of the polyurethane.

(2) The contact between flat glass and flat polyure- thane can be modeled as a large sphere contacting a plane. This makes the adhesion increase with the num- ber of real contact points.

(3) Under the negative force between two surfaces, tangential force (more than 100 mN) is much greater than the negative load (several mN). The results hint why geckos require a tiny relative movement during contact and how a gecko can climb a smooth wall.

(4) Both adhesion and friction play important roles for geckos moving on walls and ceilings. The biomi- metic gecko’s foot should be designed to increase the number of contact points to generate sufficient adhesion and friction. In order to increase the number of contact points, the properties of material, great attention should be paid to the geometric design of the terminal part and the structure of the artificial setae.

References

Nishi A. Development of wall-climbing robots. Computers

& Electrical Engineering, 1996.22. 123- 149. Bahr B, Li Y, Najafi M. Design and suction cup analysis of a wall climbing robot. Computers & Electrical Engineering, 1996,22, 193-209. Zhang Y, Nishi A. Low-pressure air motor for wall-climbing robot actuation. Mechatronics, 2003, 13, 377-392. Dickinson M H, Farley C T, Full R J, Koehl M A, Kram R, Lehman S. How animals move: An integrative view. Science, 2000,288, 100-106. Persson B N J. On the mechanism of adhesion in biological systems. Journal of Chemical Physics, 2003, 118, 761 4-762 1.

Gorb S. Walking on the ceiling: Structures, functional prin-

ciples, and ecological implications. Arthropod Structure &

Development, 2004, 33, 1-2. Spolenak R, Gorb S, Arzt E. Adhesion design maps for bio-inspired attachment systems. Acta Biomaterialia, 2005, 1, 5-13. Jiao Y K, Gorb N S, Scherge M. Adhesion measured on the attachment pads of Tettigonia viridissima (Orthoptera In- sects). Journal of Experimental Biology, 2000, 203, 1887-1 895. Autumn K, Liang Y, Hsieh T, Kenny T, Liang L, Zesch W, Full R J. Adhesive force of a single gecko foot hair. Nature, 2000,405,68 1-684. Autumn K, Setti M, Liang Y, Peattie A, Hansen W, Spon- berg S, Kenny T, Fearing R, Israelachvili J, Full R J. Evi- dence for van Der Waals adhesion in gecko setae. Proceedings of the National Academy of Sciences, 2002.99, 12252-12256. Johnson K L, Kendall K, Roberts AD. Surface energy and the contact of elastic solids. Proceeding of the Royal Society of London, A , 1971,324,301-313. Greenwood J A. Adhesion of elastic spheres. Proceeding of the Royal Society of London A, 1997,453, 1277-1297. Greenwood J A, Johnson K L. An alternative to the maugis model of adhesion between elastic spheres. Journal of

Physics D: Applied Phvsics, 1998,31, 3279-3290. Johnson K L, Greenwood J A. An adhesion map for the contact of elastic spheres. Journal of Colloid and Interface Sciences, 1997, 192, 326-333. Landman U. Atomistic mechanisms and dynamics of adhe- sion, nanoindentation, and fracture. Science, 1990, 248, 454-46 I . Dai Z D, Hui C, Gorb S. Effect of roughness on the adhesive properties of polyurethane. Tribologv, 2003, 23, 245-249, (in Chinese). Derjaguin B V, Muller V M, Toporov Y P. Effect of contact deformations on adhesion. Journal of Colloid and Interface

Science, 1975.53, 314-326. Greenwood J A, Williamson J B P. Contact of nominally flat surfaces. Proceeding of the Roval Society of London A,

1966,295,300-3 19.