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Adhesion Rubber Roughness Pre-load Contact Duration

Adhesion between rubber and counter-part is strongly influenced by roughness. The roughness influence on the preload and contact duration dependency has been analysed between two flat samp-les: a smooth glass part and a vulcanized rubber sample with smooth or rough surface depending on the special mould preparation. The measured adhesion shows a strong influence of the surface roughness. With a smooth rubber sur-face no preload and contact duration de-pendency is observable. For rough rub-ber surfaces this dependency is strong. Additionally, model based explanations of the results give a closer understan-ding of the physical effects of adhesion.

Gummiadhäsion auf glatten und rauen Oberflächen Adhäsion Gummi Rauheit Vorlast Kontaktzeit

Die Rauheit beeinflusst die Gummiadhä-sion auf einer Gegenfläche stark. Daher wurde der Rauheitseinfluss auf die Ab-hängigkeit von der Vorlast und der Kon-taktzeit zwischen zwei Flachproben un-tersucht: eine glatte Glasplatte und eine vulkanisierte glatte bzw. raue Gummi-probe, je nach spezieller Präparation der Vulkanisationsform. Die gemessene Ad-häsion ist stark von der Rauheit beein-flusst. Mit glatter Gummiprobe zeigt sich keine Abhängigkeit von der Vorlast oder der Kontaktzeit. Mit rauer Gummi-probe ist diese Abhängigkeit groß. Er-gänzend liefern modellbasierte Erklärun-gen der Ergebnisse einen Einblick in die physikalischen Ursachen der Adhäsion.

Figures and Tables: By a kind approval of the authors.

1. IntroductionRubber contacts have many practical ap-plications. The adhesion in the contact influences the function of many ma-chines. Some practical examples are the tire-road contact and the contact of seals with shafts or rods. Further, rubber con-tacts have relevance for manufacturing processes. Examples are the rubber part to mould contact, which can result in problems while demoulding, or the con-tact between rubber parts in automatic assembling machines, where the contact makes the separation of rubber parts out of accumulations difficult.

In rubber contacts the adhesion main-ly bases on intermolecular forces, e.g. due to van der Waals linkages. Very inter-esting is a rough estimation of the theo-retical possible van der Waals linkages on the nominal contact area combined with the force one linkage could carry. This shows that typical only an extremely small percentage of theoretical possible linkages are active loaded, e.g. 1 of 109, when the maximum adhesion force is observed.

The friction and adhesion behaviour of rubber contacts are important. Adhesion causes also one part of the friction in rub-ber contacts, cp. [1]. In this paper the ad-hesion in normal contacts is investigated.

1.1. State of the artFirst model based investigations of rub-ber adhesion were done by Johnson, Ken-dall und Roberts [2] (JKR model) as well as by Derjaguin, Muller und Toporov [3]. These models base on the Hertzian con-tact theory [4] and describe the adhesive contact properties for static conditions. The adhesion contact properties consid-ering quick relative movements were analysed by Roberts [5] and Barquins [6]. They observed much larger adhesive forces than in static conditions. Barquins [6] gave a very useful and efficient model to consider the dynamic in the adhesive contact. Many scientists analysed the in-fluencing parameters of the adhesion force:

■ First of all, the material properties of the rubber and the contact partner as well as their combination have to be pro-nounced.

■ Further the surface roughness has a large influence. For a long time it was assumed that adhesion can be observed only on smooth surfaces. This is true for static conditions. With high separation velocities adhesion can also be signifi-cant on rough surfaces, cp. [7,8]. Results of these adhesion measurements with rough and smooth cylinders are reprint-ed in Fig. 1. It can be seen that the ad-hesion force Fmin on a rough surface using abrasive paper (c) is smaller than on a smooth surfaces (b) but still sig-nificant. With a wet cylinder surface (a) the adhesion effect is small. This ana-lyse has been done with an adhesion pendulum, like that which is described below. Also other scientists observed this effect, like Andersson [9] who sepa-rates rapidly tired tread blocks from road surfaces.

■ Also very important are the process parameters which describe the dynamic contact: separation velocity, preload and contact duration.

■ The separation velocity was investi-gated e.g. by Roberts [5] using a very in-teresting test rig where a steel ball rolls inside a rotating cylinder on a rubber surface. Also other scientists, like [6,10,11,12], observed this influence.

■ In most investigations the adhesion depends strongly on the preload and contact duration, e.g. [6,8,9,13]. Surpris-ingly this was not the case in the ex-perimental results of Voll [10,11]. He investigated the rapid separation of a flat, circular, very smooth counterpart from an elastomer plate. Variations of the preload between 5 N and 20 N as well as of the contact time between 1 s and about 1000 s show no significant change in the adhesion force. This dis-crepancy was the motivation to investi-gate the adhesion in dynamic contacts here again.

1.2. Analysis of existing resultsIn static contacts the adhesion forces are often of secondary interest because the dominant forces are gravity forces or Hertzian forces. Only for micromechanical applications, where surface forces domi-nate against volume forces, the adhesion force is of great interest. Due to the ex-

Adhesion of Rubber on smooth and rough Surfaces

AuthorsMatthias Kröger, Stefan Nitzsche

Corresponding Author:Matthias Kröger University of Technology Bergakademie Freiberg Institute for Machine Elements Design and ManufacturingAgricolastr. 1, 09599 Freiberg, GermanyE-Mail: kroeger@imkf.tu-freiberg.de Phone: +49 3731 39-2997http://www.imkf.tu-freiberg.de

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treme increase of the adhesion force with the separation velocity, e.g. by a factor of 1000, adhesion forces have large impor-tance also for macroscopic dynamic con-tacts like the tire-road contact.

Focus in this paper is the analysis of preload and contact duration dependen-cies of the adhesion force. There are dif-ferent reasons which explain these de-pendencies:

■ Due to the viscoelastic behaviour of rubber the nominal contact area of many contact applications grows with time in contact. The rubber shows creep and re-laxation processes. A typical example is a steel ball in contact to a flat rubber sam-ple. In the beginning of the contact the contact area is small due to a large com-plex elasticity module. If the applied load is feedback controlled and is held con-stant the contact area grows with time in contact. The maximum contact area is reached when the relaxation process of the rubber is finished after a long time. With increasing contact area the adhe-sion forces grow, too.

■ The viscoelastic material property of rubber influences not only the nominal contact area. If one part has a signifi-cant roughness, which is usually the case in engineering applications, the number of microscopic contact areas and there size depend on time. Due to creep and relaxation the real, micro-scopic contact area grows with time in contact. This causes an increase of the adhesion force, too.

■ The steady state contact area given by the JKR model [2] results from a minimum of elastically stored and sur-face energy. If an increase or decrease of the contact area is reducing the sum of these energies the contact area changes in the direction of this mini-mum. Never the less in a large range around the minimum value of the con-tact area the velocity of the change of

contact area is very small for rubber materials, cp. [6]. Therefore, usually the contact size is not in the steady state and rubber contacts depend on the actual contact force and the contact force history (preload and contact du-ration).

■ Additionally also processes on the molecular scale can influence the macro-scopic contact behaviour, cp. [14,15]. These molecular processes also depend on time. Due to the movement of the chains of the rubber molecular structure van der Waals linkages to the contact partner are permanently built and de-stroyed. These processes are time and temperature dependent which is typical for rubber. Further, on the molecular scale also diffusion processes are of in-terest, which can bring some rubber in-gredients like oil or resin on the rubber surface and into the contact or bring rubber chains into the counterpart for a rubber-rubber contact.

Considering the different reasons for the preload and contact duration dependen-cies it could be expected that these ef-fects are small for:

Fig. 1: Force F versus time t of adhesion pendu-lum impacts of a flat rubber sample against a cylinder: ground wet sur-face a), ground dry surface b) and dry abrasive paper K180 c) [7].

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■ Parallel flat-to-flat contacts because the nominal contact area could not in-crease,

■ Smooth surfaces because the micro-scopic contact area could not increase,

■ Rubber materials with small viscos ef-fects because creep and relaxation is not dominant and influence not very much the contact area.

2. Experimental investigations

2.1. Test rigsAt the Institute for Machine Elements, Design and Manufacturing different test rigs for adhesion measurements has been built and are permanently devel-oped further. One is an adhesion pendu-lum; see Fig. 2, which has the advantage that the contact duration is very small (about 2 ms, see Fig. 1). This is the range of the typical contact time between a tire tread block and the road during rolling. The pendulum has a very small weight, like 10g, to avoid that hysteretic proper-ties due to the deformation dominate the adhesion effects on the surface. De-tailed descriptions of the test rig can be found in [7,8].

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Another test rig is the adhesion tester. In this test rig the movement of one con-tact partner is actuated by an electro-dynamic shaker, see Fig. 3. The actuation gives the possibility to variate the preload, the contact duration and the separation velocity independent of each other. This is not possible in the adhesion pendulum, where only the impact veloc-ity resp. drop height and the pendulum mass can be varied. A detailed descrip-tion of the adhesion tester is given in [12,13].

In the following section some measured results with the adhesion tester are discussed because the preload and the contact duration de-pendencies are the main focus which can be very good investigated with this test rig.

2.2. Experimental resultsFig. 4 reprints some typical measure-ment results of a contact between a ball and a flat rubber sample using the adhe-sion tester. The ball has a small surface roughness. The rubber is a special devel-oped, very adhesive compound. Fig. 4 shows the increase of the adhesion force with preload (left) and with contact du-ration (right), cp. [13]. The left diagram is scaled logarithmical. The measured re-sults build a straight line in the diagram. Therefore, the dependency can be de-scribed very well by a power law. The in-crease of the adhesion force can be ex-plained by an increase of the contact ar-ea especially on the macroscopic scale due to viscoelastic properties and the ball to flat contact.

The interpretation in section 1.2, which is based on the increase of macro-scopic or microscopic contact area, has been proven by tests between two flat surfaces: A flat rubber plate and a flat glass sample. Immediately the whole nominal area is in contact which is checked optically via the glass plate. Both surfaces have a very small rough-ness. Especially in the production of the rubber sample the mould finish has to be optimized and additionally a thin layer is added during vulcanization to reduce the roughness of the rubber surface. The re-sults are shown in Fig. 5, cp. [12]. All eight tested rubber materials show no significant preload dependency of the adhesion force (contact duration 5 s, separation velocity about 0.12 mm/s). Also the contact duration dependency of the adhesion force is quiet small (preload 23 N, separation velocity about 0.25 mm/s). Never the less a small increase of

the adhesion force can be observed for contact durations larger than 2 s. For some rubber materials this increase is very small, for some other it is a little bit larger.

To compare the effect of the rough-ness two rubber samples with different surface roughness are produced. One is again very smooth. The other one has a significant roughness due to sand blast-ing of the mould before vulcanisation. For these tests a new, slightly different compound is used in respect to the re-sults from Fig. 5. The Figure 6 compares the results of the smooth and rough surfaces. For the smooth rubber surface the preload and preload duration de-pendency is vanished again. But a signifi-cant increase of the adhesion force with preload and preload duration can be ob-served for the rough rubber surface (preload duration 5 s resp. preload ap-prox. 23 N, separation velocity between 1 mm/s and 5 mm/s). A variation of the separation velocity is given in Fig. 7. With the separation velocity the adhe-sion force is increasing significantly for the rough as well as for the smooth rub-ber surface. The relative increase is stronger for the rough then for the smooth surface (preload duration 5 s, preload approx. 23 N).

3. ConclusionIn the focus of this work is the influence of preload and contact duration on the adhesion force. In contrast to most re-sults in the literature and own investi-gations, Voll [10,11] showed results where the adhesion force not increase with preload and contact duration. This paper explains the reasons for this dif-

Fig. 3: Sketch of the adhesion tester.

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Spindle frame

Force sensor (DMS)

Triangulations laser

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Fig. 4: Influence of the preload and the preload duration on the adhesion force of a flat, adhesive rubber sample on a ground steel ball [13].

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ferent behaviour. Therefore, physical reasons for the dependencies have been analysed. Main reasons are the viscoe-lastic behaviour of rubber which results for non-flat-contacts or rough surfaces in an increase of the nominal, macro-scopic or real, microscopic contact area. The increase of contact area is the rea-son for the increase of the adhesion force. This assumption has been proven by adhesion tests between a very smooth, flat rubber samples and a glass plate. Eight typical rubber compounds have been investigated. All of them have usual viscoelastic behaviour. The results show that the constant nominal contact area of the flat samples and the small roughness prevent the preload depend. A comparison of the results proves that the preload and contact du-ration dependency is significant on rough rubber surfaces and is vanished on smooth rubber surfaces. Also the contact duration dependency is quiet small for this contact configuration. Therefore, the experiments improve the

physical explanations of the effects in contact. The rough as well as the smooth rubber tests show a strong influence on the separation velocity. This investiga-tion increases strongly the knowledge of the adhesion effects in contacts.

Literature[1] Moldenhauer, P.; Lindner, M.; Kröger, M.;

Popp, K., Modelling of Hysteresis and Adhe-sion Friction of Rubber in Time Domain. Con-stitutive Models for Rubber IV (ECCMR), Stockholm (2005), 515.

[2] Johnson, K. L.; Kendall, K.; Roberts, A. D., Proc. R. Soc. London A., 324 (1971), 301.

[3] Derjaguin, B. V.; Muller, V. M.; Toporov, Yu. P., Journal of Colloid and Interface Science, 53 (1975), 314.

[4] Hertz, H., Journal für die reine und ange-wandte Mathematik, 92 (1881), pp. 156.

[5] Roberts, A. D., J. Nat. Rubber Res., 3(4) (1988), 239.

[6] Barquins, M., Wear, 158 (1992), 87.[7] Kröger, M.; Popp, K., PAMM Proc. Appl. Math.

Mech. 4 (2004), 99.[8] Kröger, M., Adhesion effects in the contact

between rubber and counterpart. ECCMR VIII San Sebastian (2013), 71.

[9] Andersson, P., Modelling interfacial details in tyre/road contact-adhesion forces and non-linear contact stiffness. PhD thesis, Chalmers University of Technology, Gothenborg, Swe-den (2005).

[10] Voll, L. B., Verallgemeinerte Reib- und Adhä-sionsgesetze für den Kontakt mit Elastome-ren: Theorie und Experiment. Dissertation, Technische Universität Berlin (2016).

[11] Voll, L. B.; Popov, V. L., Physical Mesome-chanics, 17(3) (2014), 232.

[12] Nitzsche, S.; Kröger, M., Einfluss der Materi-alparameter auf Adhäsionskräfte. Tribologie Fachtagung GfT, Band 1, Göttingen (2016), pp. 8/1-8/9.

[13] Moldenhauer, P.; Nepp, R.; Kröger, M., Plas-tics, Rubber and Composites, 40 (4) (2011), pp. 169.

[14] Israelachvili, J. N., Intermolecular and Sur-face Forces. Academic Press, Burlington, Third Edition (2011).

[15] Packham, D. E., Surface energy, surface to-pography and adhesion. Int. J. of Adhesion and Adhesives, 23 (6) (2003), pp. 437.

Fig. 5: Influence of the preload and the preload duration on the adhesion force using different very smooth, flat rubber samples with 38 resp. 60 Shore A hardness against a glass plate.

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Fig. 6: Influence of preload and the preload duration on the adhesion force for smooth and rough NBR rubber sample with 60 Shore A hardness against a glass plate.

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Fig. 7: Influence of separation velocity on the adhesion force for smooth and rough NBR rubber sample with 60 Shore A hard-ness against a glass plate.

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