Friction coefficient definition

Castagnetti, D., Dragoni, E., 2012. Predicting the macroscopic shear strengfli of adhesively-bonded friction interfaces by microscale finite element simulations. Computational Materials Science. 64, 146-150. Croccolo, D., Cuppini, R., Vincenzi, N., 2008. Friction coefficient definition in compression-fit couplings applying the DOE method. Strain. 44, 170-179. 

In order to complete the demonstration of the equivalence between the two approaches of sections (A) and (C), we need a proof of the equivalence between the definitions (179) and (242) of the friction coefficient... 

Here, M is the torque of the rolling object, hr is the coefficient of rolling friction, FL is the normal force (load), Ff is the friction force and R is the radius of the rolling object (see Fig. 11.4). In this case the friction coefficient is not dimensionless but has the unit of length. Other definitions use... 

All the preceding particulate handling steps are affected by the unique properties of all particulates, including polymeric particulates while they may behave in a fluidlike fashion when they are dry, fluidized and above 100 pm, they also exhibit solidlike behavior, because of the solid-solid interparticle and particle-vessel friction coefficients. The simplest and most common example of the hermaphroditic solid/ fluidlike nature of particulates is the pouring of particulates out of a container (fluidlike behavior) onto a flat surface, whereupon they assume a stable-mount, solidlike behavior, shown in Fig. 4.2. This particulate mount supports shear stresses without flowing and, thus by definition, it is a solid. The angle of repose, shown below, reflects the static equilibrium between unconfined loose particulates. 

Subslituting into its definition gives the local friction coefficient. 

By applying the F definition of Benyahia et al [12], the closure can be expressed as a function of the friction coefficient j3 instead of the dimensionless drag coefficient F [92] ... 

The softening dispersions of entangled low-molecular-weight polymers are often modeled by the Rouse modes modified for undiluted polymers. From their very definition only involving the coordinates of a single chain, the Rouse modes are not intermolecularly coupled, and their relaxation times, t/ /, are proportional to the monomeric friction coefficient, fo that is. 

FIG. 12-5. Sketch to illustrate definition of monomeric friction coefficient fo . a group of n monomer units moving together with translational velocity v encounter a frictional force of nfou. Reproduced, by permission, from Science and Technology of Rubber, edited by F. R. Elrich, Academic Press, 1978. 

The result indicates that the ratio Cr/< r should be independent of the choice of the sequence. This is true if the friction coefficient Cr is proportional to the number of monomer units in the sequence. Strictly speaking, the latter property constitutes a basic requirement for the validity of the Rouse-model The friction coefficient of a sequence has to be proportional to the number of monomer units. In fact, this is not trivial and clear from the very beginning. It seems to be correct in a melt because, as we shall see, here the Rouse-model works quite satisfactorily, if compared with experimental results. On the other hand, the assumption is definitely wrong for isolated polymer chains in a solvent where hydrodynamic interactions strongly affect the motion we shall be concerned with this point in a subsequent section. 

According to the definition, i h is the radius of a spherical particle which possesses the same friction coefficient as the given colloid. 

L. C. Towle (Naval Research Laboratory) As I understand your comments today and your preprint you state that the friction force observed with polymers is not given by the expression F = pN. My understanding of the definition of the coefficient of friction is that it has an operational definition, i.e. to measure the friction between solids A and B one forces A to slide against B under measured load N and simultaneously measures the tangential force F. The friction coefficient is then defined to be the ratio p = F/N. If this is the case, then it would seem that one always has F = pN being valid. If this is not the case, then I wonder how does one define the friction coefficient ... 

L. C. Towle Since we have fundamental disagreement on when one can apply a definition of friction coefficient, there is no hope to resolve other differences. In regard to the thickness dependence, it is not possible to do this kind of experiment because once you load the sample and extrude down, the thickness is determined by mechanical properties of the polymer. 

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