Critical discussion of the most important literature results

experi-mental data taken from the literature. The evaluation of Mofidi et al.’s test results, however, is complicated by the fact that the nominal contact area varies as a function of the applied nor-mal load and no information on wear and deformation of rubber due to the friction force is available in the study of Mofidi et al. [44]. For the sake of completeness, in this section, the effect of hysteresis, adhesion, rubber roughness, wear, ambient temperature, lubricant, fric-tional heating and rubber elasticity on rubber friction will be discussed in depth.

It is very interesting to compare Persson’s [3] (micro hysteresis) theory with that of Smith [8]. Persson considers micro hysteresis friction to be adhesion and applied normal pres-sure dependent phenomenon but, in his predictions, the effect of adhesion is not taken into account. According to his opinion if the roughness is large enough (this is not the case for apparently smooth surfaces) the increase in the hysteresis contribution to the friction from the adhesion induced increase in the contact area may be very small [50]. The larger the rough-ness is the smaller the adhesion-induced increase is in the micro hysteresis friction contribu-tion. Smith’s theory contrasts strongly with this because he assumes an adhesion dependent micro hysteresis friction contribution which is apparently independent of the applied normal pressure (see the largely nominal contact pressure independent results of Denny in Fig.

4.28a). In his theory, the penetration of the rigid asperities into the rubber surface is controlled by the adhesional interaction between the surfaces and the increasing applied normal pressure does not measurably increase the hysteresis friction contribution due to the small micro asper-ity depth of the harder, apparently smooth surface. Smith concluded that higher the adhesion larger the micro hysteresis friction contribution.

In [44], Mofidi et al. studied the effect of micro hysteresis friction in the presence of lubricant but the conditions for adhesion-eliminating lubricant film formation were unfavora-ble. The very high apparent coefficients of friction reported prove that there was no continu-ous adhesion-eliminating boundary lubricant layer between contacting surfaces. As it is known a discontinuous boundary lubricant layer, however, cannot eliminate adhesion entirely but can reduce its effect. It must also be mentioned that as the cylinder was smooth a

relative-ly large real area of contact was formed in the tests of Mofidi et al. [44]. Adhesive component of rubber friction depends not only on the real area of contact but also on the sliding velocity, contact pressure and temperature dependent shear strength of adhesive contact. For the first sight it seems that the sliding velocity dependency of friction does not play role in [44] be-cause the amplitude and frequency of the reciprocating motion were kept constant during fric-tion tests. The real sliding velocity, however, may differ from the theoretical one (especially at higher temperatures) as it will be pointed out at the end of this section. As it is well known adhesion component of friction originates from interaction of contacting surfaces, acts at the interface of the contacting bodies and is directly correlated to the real area of contact. As re-ported by Smith [8], in case of apparently smooth surfaces, adhesive friction may be very high because the smoothness of the paired, harder surface promotes adhesion. Contrary to the very unfavorable lubrication conditions Mofidi et al. made no mention of the possible development of adhesive friction and did not provide measurement results for dry surfaces. Without dry results, however, the real contribution of micro hysteresis component to rubber friction cannot be estimated reliably.

Importance of rubber roughness is emphasized, among others, by Salant et al. [41], Rana et al. [56] and Arnold et al. [57]. Studies cited by Rana et al. [56] shows clearly that the roughness of metal surfaces does not affect the friction much if its roughness is significantly lower than the seal roughness. It was found experimentally that when oil-lubricated smooth metal surface is reciprocated with a rough elastomeric seal at a velocity lower than 100 mm/s mixed friction or boundary lubrication dominates the friction. Arnold et al. [57] emphasize also the importance of rubber roughness and point out that roughening a rubber surface de-creases its adhesion-friction-force-development potential when sliding on smooth materials.

In the friction tests of Mofidi et al. [44], the RMS roughness of rubber surface prior to tests was about 0.4 m. Although experimental results show clearly that rubber roughness and surface energies of the contacting bodies have considerable effect on the friction force the common practice in friction prediction is not in accordance with this. Effect of rubber rough-ness and surface energies is, almost without exception, neglected in friction force predictions.

Albeit rubber wear (deposited rubber layer on the metal surface, damage of rubber sur-face, etc.) has considerable effect on friction neither microscopic images on worn surfaces nor surface roughness measurements are presented by Mofidi et al. [44]. The real area of contact reduction and the smoothing effect of wear debris may also be mentioned among the effects of rubber wear. Effect of lubricant on the rubber friction can be appear in different forms such as frictional resistance due to the lubricant viscosity, change in the frictional resistance due to the change in lubricant viscosity, real area of contact and surface roughness reduction due to lubricant pool formation in the roughness valleys of harder, rough surface, formation of adhe-sion eliminating boundary layer, development of capillary forces, decreasing friction and in-creasing separation of contacting surfaces due to the inin-creasing hydrodynamic effect, etc. An important consequence of the latter is the decreasing adhesive and micro hysteresis friction.

At the same time while both the hydrodynamic effect and the closed fluid pools decrease the real (solid-solid) area of contact while the squeezing effect increases it.

Very little information is available in the literature on the effect of ambient tempera-ture on apparently smooth steel surface generated micro-hysteresis. Studies of Mofidi et al.

[44, 53] are exceptions of this. Their results show that the friction force for apparently smooth steel surface sliding on lubricated nitrile rubber decreases with increasing ambient tempera-ture. Although the cylinder on flat sample test configuration was used in both cases, condi-tions were not exactly the same. As in [44] disc shaped NBR 75 Shore A specimens were used in [53] but the thickness was 6 mm instead of 4 mm. Additionally lubricating oil (polyol ester in [53] and polyalphaolefin in [44]), test duration (30 min in [53] and 15 min in [44]), mean sliding velocity (200 mm/s in [53] and 100 mm/s in [44]), stroke (2.5 mm in [53] and 1

mm in [44]), and applied normal load (200 N in [53] and 20, 50, 100, 150, 300 N in [44]) were also different. Mean sliding velocity of 200 mm/s implies that friction processes are complicated with frictional heat generation yielding real contact temperature higher than the ambient one. At the same time the higher velocity increases the frequency with which the rubber surface is excited. While the latter increases the former (higher contact temperature) decreases the micro-hysteresis, nevertheless, at room temperature, the apparent coefficients of friction reported by Mofidi et al. in [44] and [53] are consistent (they are close to 0.6). How-ever, the decrease in apparent coefficient of friction due to an increase in the ambient temper-ature from 25°C to 80°C is much smaller in [53] than in [44] (see Figs. 4.31, 4.32 and 4.33).

The small change in the apparent coefficient of friction (see Fig. 4.31) does not reflect the strongly temperature dependent properties of rubber. In other words, the temperature depend-ent micro-hysteresis, contrary to [44], has little contribution to rubber friction in [53]. It is worth to mention that while the apparent coefficients of friction measured at room tempera-ture are similar, the ones observed at elevated temperatempera-ture are drastically different in [53] and [44]. At room temperature the apparent coefficients of friction reported are in accordance with each other and indicate boundary lubrication. Unfortunately, in [44], no measurement results are available on the temperature dependency of apparent coefficient of friction for polyol es-ter. However friction test results of [44] show clearly that the apparent coefficient of friction is 0.66 for polyol ester and about 0.5 for polyalphaolefin at T=40°C. Contrary to this signifi-cant difference in apparent coefficient of friction Mofidi et al. concluded that the lubrisignifi-cant has negligible influence on the friction in their tests. As it is demonstrated in Smith’s book [8], the adhesion friction force is also lower at higher temperatures because both the hysteresis and adhesion component of rubber friction are directly related to viscoelastic properties of rubber.

According to Grosch [1], the expected sliding velocity and temperature dependence of rubber friction under constant normal load and on a given surface can be described by a friction force-sliding velocity master curve and the Williams-Landel-Ferry (WLF) equation (see Ap-pendix A.4). Consequently, the increasing ambient temperature decreases both the hysteresis and adhesion component of friction.

In [44], it is assumed that the friction measured is due to the internal friction (hystere-sis) of the rubber and the drop in the apparent coefficient of friction for large loads (applied normal load  100 N) is most likely due to the increasing frictional heat generation caused by the internal friction in the rubber. The frictional heat fluxes (heat energy production per unit area and unit time) defined as pv, where , p and v denote apparent coefficient of tion, mean contact pressure, and sliding velocity, however, do not support the increasing fric-tional heating because they are nearly equal for loads larger than or equal to 100 N. The cause of this is that the increasing mean contact pressure is accompanied by decreasing apparent coefficient of friction.

As the rubber has very low elastic modulus the friction force may be able to deform the rubber sample. This may cause that in certain part of the stroke the displacement of the rubber surface measured in sliding direction equals to that travelled by the cylinder (sticking phase). At high temperatures where the rubber has low modulus the effect of sticking on rub-ber friction may be particularly important. In order to prove this a simple, three-dimensional, linear elastic finite element model has been developed (see Fig. 4.34a). The bottom of the rubber sample was fixed while the displacement of the nodes being in the symmetry plane was restrained perpendicularly to the symmetry plane (symmetry condition). Like in friction tests of Mofidi et al. [44] the steel cylinder was pressed against the rubber sample with a giv-en normal load (due to the half model only half of the applied normal load must be used in the FE model) and reciprocated with cyclic frequency of 50 Hz and amplitude of 0.5 mm. Normal load, apparent coefficient of friction and elastic modulus concerning excitation frequency of 50 Hz were specified based on [44]. Fig. 4.34b shows the x-position of the center point of the

rubber sample being in contact with the cylinder as a function of the x-position of the cylinder in the first cycle.

(a)

(b)

Fig. 4.34. (a) FE model of Mofidi et al.’s test configuration. Restraints are not visualized and due to the symmetry only half of the rubber disc is modeled. The figure is taken from [131].

(b) Position of the center point of rubber sample being in contact with the cylinder as a func-tion of posifunc-tion of the cylinder. Applied normal load referring to the complete rubber sample

is FN= 100 N. The figure is taken from [131].

The FE results prove that the effect of sticking may be considerable, especially at higher temperatures where the modulus is very low. Based on these results not only the real sliding distance and real mean sliding velocity but the real frictional heat flux can also be de-termined. Finally, it is worth to mention that the sticking phase indicated by the simulation was the longest in the center point of the contact area.

As a last point, it must be mentioned that the effect of stresses and frictional heat gen-eration on the mechanical properties of the rubber should also be considered when studying rubber friction. In [133], Mokhtari and Schipper pointed out that a tribo-modified surface lay-er with degraded elastic modulus exists on the top of a rubblay-er surface being in contact with a rigid counter surface. Furthermore it was found that the thermal and stress-induced degrada-tion of a thin rubber layer becomes more intensive as the contact pressure and sliding velocity increases. However, as demonstrated by Mokhtari et al. [134], excessive wear can prevent the formation of such layer. Additionally, it was also concluded that the degradation of rubber matrix at the surface does not affect the real area of contact but change the frictional shear stress required to shear a thin surface layer (adhesion component of rubber friction) and mi-cro-hysteresis substantially.