Coulomb’s law of friction

It would appear that no account of friction is complete without first stating Leonardo da Vinci s (or Amonton s) laws and Coulomb s law of friction and pointing out that, in general, polymers do not obey them. The laws are ... 

According to Coulomb s law of friction, the relationship among shear stress, normal stress, coefficient of friction and pore-pressure at the moment of shear slip (critical condition) due to increasing of pore-pressure are described as follow. 

Relation [18.1] is usually referred to as Coulomb s law of frictioa The value of the ratio [18.1] between the tangential stress and the normal stress is the one required to initiate the movement. The associated friction angle is described as static. If the applied traction force is smaller, the solid remains stationary and resists its movement with a resistance force which is equal and opposite to the traction force applied to it. As soon as the solid starts moving, the ratio of the friction stress to the normal stress is modified and becomes less than its value in the static case. When the solid moves, the ratio /is termed the coefficient of kinetic frictioa While Coulomb s law is conceptually simple, its mathematical implementation in a practical problem is delicate, as the tangential force opposing the displacement depends on the amount of force applied and its direction is opposite to the side toward which the solid is being pushed. 

The validity of Coulomb s law has been verified also on the nanoscale Zworner et al. [484] showed that, for different carbon compound surfaces, friction does not depend on sliding velocity in the range between 0.1 /xm/s and up to 24 /xm/s. At low speeds, a weak (logarithmic) dependence of friction on speed was observed by Gnecco et al. [485] on a NaCl(lOO) surface and by Bennewitz et al. [486] on a Cu (111) surface. This can be modeled when taking into account thermal activation of the irreversible jumps in atomic stick-slip [487],... 

The kinetic friction force is independent of sliding velocity (Coulomb s law). 

Coulomb invented a torsion balance, which could measure electrostatic forces in relationship to their distance. We start with Coulomb s law that describes the relationship between force, charge, and distance. He is most famous for his discovery in electrostatics. His other fields of interest were friction phenomena. 

Polymer friction of the bulk polymers and that of the textile polymers follow roughly the same laws, namely that Coulomb s third law of friction (i.e.. that kinetic friction is independent of the speed of sliding) and Amonton s first law (that the frictional force is independent of the area of contact) just do not apply, especially with the thermoplastics. Instead we are faced with the discovery that with a steady increase in the speed of sliding the frictional force can increase until it reaches a point where it can drop dramatically if the friction coelTicient and the linear speed are high enough. But this will of course depend very much on the particular liber type. One illustration of this was found by D. G. Lyne... 

The force and pressure distribution between tool and workpiece in the contact area determine the resulting surface integrity (Borbe 2001). The thrust force on the cutting edge Fj is the vectorial sum of the feed and passive force Ff and Fp. Assuming a friction factor p (Coulomb s law), the normal and tangential forces on the flank Fn and Fja can be estimated at ... 

Velocity-Dependent Friction Research and development work on the numerical specification of contact and friction conditions may include mathematical formulation and implementation of friction models as well as adaptation of the numerical solution methods (Heisel et al. 2009 Neugebauer et al. 2011). Standard implementations may be illustrated using Coulomb s Law and the Friction Factor Law. These two basic models were modified using a stick-slip model. Using these models enables consideration of the relative sliding velocity between the tool and the workpiece. 

The results on crossed polymer fibers obtained by Briscoe and Kremnitzer shown in Fig. 9.16 gave good agreement with Equation (9.16). The friction force increased more rapidly than Coulomb s law predicted at low loads but approached Coulomb s law at high loads. The value of the work of adhesion W from these friction experiments was near 0.1 Jm , close to the value determined in direct adhesion experiments on the same fibers. 

Die compaction of agglomerates has been simulated in a computer sphere model by Thornton et When the particles are in a liquid paste, the liquid is usually expelled through pores in the mold, and the partieles form a filter cake. The mechanism by which this occurs has been modeled by Woodcock et The application of forces to powder beds, sometimes immersed in liquids, is the subject of soil mechanics. " This considers particles to interact via Coulomb s law, Equation (11.16), but also takes into account the hydrodynamic forces acting on the individual particles. Unfortunately, as we have seen. Coulomb s law is not correct for particles which experience molecular adhesion, so the friction coefficients found in soil mechanics theories seem to vary. Friction seems to increase as the particles get smaller because smaller particles adhere more strongly. Soil mechanics is therefore a difficult science. 

Friction force is proportional to the normal load as stated by Amontons-Coulomb s law. For microloads less than 1 mN, which are often found in mechanisms such as microelectromechanical systems (MEMS), Amontons-Coulomb s law is not valid due to the effect of the adhesion force between the contacting surfaces [1]. Studies show that, at such microloads, either the attraction force (adhesion force) caused by the surface tension of water condensed on the surface or the van der Waals force dominates the friction force, and that the friction force is proportional to the sum of the adhesion force (pull-off force) and the normal load [2, 3],... 

Let us now consider that the contacts between the rollers, and between the rollers and the side wall, involve friction forces. If we focus on one roller in contact with the side wall, it can be found that the weight of the rollers located above pushes the respective roller against the wall, on which it applies a pressure force. The contact of the roller against the wall is liable to generate at the wall a vertical friction force onto the roller, oriented upwards, which contributes to preventing its downward displacement. Its magnitude is unknown Coulomb s law provides the maximum... 

In this section we consider contact problems, where contact may occur or disappear. In each contact point we assume friction due to Coulomb s law as discussed in the last section. Due to these phenomena the number of degrees of freedom varies with time. First, we discuss the equations of motion for these problems and then consider the question how to decide which of the contacts is active and if in the point of contact stiction or sliding is present. 

For an active constraint we have to add condition (6.5.1) and the corresponding constraint force. If in this point stiction occurs we have to add condition (6.5.3) and the corresponding constraint force, if sliding occurs we have to add the corresponding friction force Fcou due to Coulomb s law. Assuming riN ax tive contacts, where the nx first points show stiction we end up with the following system of equations... 

Cohesion c and angle of internal friction p are combined as failure criterion in Coulomb s law, which describes the maximum shear stress t at a given normal stress (T (Eq. 7.13) ... 

Under partial slip conditions, the estimate of the stress conditions at the edge of the contacts is complicated due to the unknown frictional behaviour within the partial slip annulus. If Coulomb s friction law is assumed to apply locally within this area, some contact mechanics calculation can, however, be... 

For elastic materials, the contact problem is usually solved as a unilateral contact problem obeying Coulomb s friction law. The algorithms used here are based on those pioneered by Kalker [66]. The contact area, the stick and slip regions, the pressure and traction distributions are numerically determined first and then the stress and displacement distributions within the elastic bodies can be established at the various stages of the tangential cyclic loading. On the basis of these calculations, the occurrence of crack initiation processes can subsequently be analysed in the meridian plane of the contact, y = 0 (Fig. 12), where the cracks first initiate. As a first approach, parameters based on the amplitude of the shear stress, rm, along a particular direction and the amplitude of the tensile stress, [Pg.174]

It is widely accepted that most earthquakes are due to frictional processes on pre-existing faults. The friction is therefore an important empirical ingredient of a fault model [43]. Numerous laboratory experiments have been carried out to characterize frictional behavior of different materials (see e.g. [14]). An important finding is that the friction defined as the ratio of shear stress Tghear and normal stress Tnormal, P-f = Tshear jr-aormal at the initiation of slip, is approximately constant for many materials the value oi Pf lies between 0.6 and 0.85. This observation, known as Byerlee s law, is related to the Coulomb failure criterion ]11] for the Coulomb stress CS,... 

Such a dependence is characteristic of the dry friction, i.e. it agrees with Coulomb s friction law, Ffr = /frFN. Consequently, the model of plastic behavior of a material or disperse system may be represented by two surfaces (two plates) with a mutual friction coefficient, fx, pressed against each other with normal force, FN, causing the tangential force, Ffr, to be equal to the critical shear stress of material (Fig. IX-7). 

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