Sliding velocity

The often-cited Amontons law [101. 102] describes friction in tenns of a friction coefiBcient, which is, a priori, a material constant, independent of contact area or dynamic parameters, such as sliding velocity, temperature or load. We know today that all of these parameters can have a significant influence on the magnitude of the measured friction force, especially in thin-film and boundary-lubricated systems. 

Sliding velocity. A factor in mechanical-joint couplings only. 

Gear tooth surface deterioration Misalignment, high sliding velocity... 

Exjuation 8.1 is based on a maximum sliding velocity during misalignment of 5 ips and Equation 8.2 is based on 8 ips. Research by the Naval Boiler and Turbine Laboratory [7] developed these values. Experience indicates that the more conservative range of l-3 A ips is most desirable. 

Newton performed experiments with a viseous fluid sandwiched between plates (Figure 4.9-l). The force, / to slide one plate over the other is proportional to the contact areas. A, the spacing between the plates, r, the sliding velocity, v, and the viscosity t) of the fluid are related as /= r A v/t or in terms of the shear pressure r - f/A as equation 9.1-5. A fluid that obeys equation 9.1-5 is called a Newtonian fluid. ... 

At low speeds, when the high spots make contact due to load, the sliding velocities are not sufficient to generate the heat necessary to cause welding. The wear, which can be quite rapid, is caused by the abrasive action of the teeth on each other. 

Stick-slip motion is another issue that has been explored using SFA. It is found that the occurrence of stick-slip depends on the sliding velocity and the stiffness of the system, and the mechanism of the phenomenon can be interpreted in terms of periodic transition between liquid and solid states of the conhned lubricant [40],... 

Fig. 4—Illustration of the transition from hydrodynamic to boundary lubrication (a) a comparison of pressure of thin EHL film with Hertzian distribution (b) a schematic stress-velocity map showing the dependence of shear stress of lubricating films on sliding velocity.

Phenomenal studies were made to observe the frictional behavior of L-B films and SAMs and its dependence on applied load and sliding velocity, which has been summarized in a review article by Zhang [33]. It has been confirmed that in comparison to the bare surface of the substrates, the friction on molecular films is significantly reduced, with friction coefficients in a range of 0.05-0.1. Friction forces are found... 

The dependence of friction on sliding velocity is more complicated. Apparent stick-slip motions between SAM covered mica surfaces were observed at the low velocity region, which would disappear when the sliding velocity excesses a certain threshold [35]. In AFM experiments when the tip scanned over the monolayers at low speeds, friction force was reported to increase with the logarithm of the velocity, which is similar to that observed when the tip scans on smooth substrates. This is interpreted in terms of thermal activation that results in depinning of interfacial atoms in case that the potential barrier becomes small [36]. 

Fig. 21—Comparisons of friction forces from simulations of commensurate and incommensurate SAMs in relative sliding (a) friction exhibits a linear dependence on applied normal load, (b) friction increases logarithmically with the sliding velocity.

The friction coefficient, n, is assigned with different values in different friction conditions. Fj is the relative sliding velocity of two contacting bodies. 

The process of transition from hydrodynamic to boundary lubrication can be described qualitatively by plotting the measured friction coefficients against film thickness, which depends on the operational conditions, such as load, sliding velocity and lubricant viscosity. A typical diagram known as the "Stribeck Curve is schematically shown in Fig. 27, in which the friction coefficients are given as a function of, ... 

It has been recognized that the behavior of atomic friction, such as stick-slip, creep, and velocity dependence, can be understood in terms of the energy structure of multistable states and noise activated motion. Noises like thermal activities may cause the atom to jump even before AUq becomes zero, but the time when the atom is activated depends on sliding velocity in such a way that for a given energy barrier, AI/q the probability of activation increases with decreasing velocity. It has been demonstrated [14] that the mechanism of noise activation leads to "the velocity... 

Fig. 23—A schematic force curve plotted as a function of sliding velocity. A viscous friction forms the background of the force curve upon which the frictions from superharmonic and parametric resonance are superposed.

Fig. 34—Shear stress on boundary films versus sliding velocity (reproduced after Ref. [33]).

The friction coefficient at PVA gel/OTS modified quartz is 0.300 while that at PVA gel/unmodrfied quartz is 0.076. Frictions were measured by using a rheometer (ARES, TA instruments) as a function of sliding velocity in water and these values were calculated from the experimental resultsoflowestsbdingvelodty,7.5 x 10 m/s. 

The discussion begins below with an overview of proposed energy dissipation mechanisms that lead to friction. This is followed by brief discussions of phenomenological friction laws that describe the dependence of friction upon normal load and sliding velocity. The dependence of friction on the symmetry of the surfaces that are in contact is discussed later. 

Figure 2 Illustration of an instability in the Prandtl-Tomlinson model. The sum of the substrate potential and the elastic energy of the spring is shown at various instances in time. The energy difference between the initial and the final point of the thick line will be the dissipated energy when temperature and sliding velocities are very small.

Once temperature comes into play, the jumps of atoms between minima may be invoked prematurely, i.e., before the formation of instabilities, via thermal fluctuations. These thermally activated jumps decrease the force that is required to pull the surface atom, which leads to a decrease in the kinetic friction. The probability that a jump will be thermally activated is exponentially related to the energetic barrier of the associated process, which can be understood in terms of Eyring theory. In general, the energetic barriers are lower when the system is not at its thermal equilibrium position, which is a scenario that is more prominent at higher sliding velocities. Overall, this renders Fk rate or velocity dependent, typically in the following form ... 

An example of the velocity dependence of friction is given in Figure 5 for a boundary lubricant confined between two incommensurate surfaces.25 For the given choice of normal pressure and temperature, one finds four decades in sliding velocity for which Eq. [7] provides a reasonably accurate description. 

Simulations of incommensurate surfaces showed a similar dependence on Vi, with first-order instabilities occurring if Vi < Vj, where Vj is some positive, critical value that depends on the degree of mismatch between the lattice constants of the top and bottom surfaces. This process leads to nonvanishing Fk as l o goes to zero. In the case where Vi < V, the atoms are dragged with the wall that exerts the maximum lateral force. It, in turn, leads to friction that scales linearly with the sliding velocity. As a result, the friction force will go to zero with vq. 

For a specific resin, the shear stress at the interface depends on the temperature of the interface, pressure, and the sliding velocity, it also depends on resin type, additives and additive levels, and the rheological properties of the resin. Stresses at the interface and the coefficients of friction for numerous resins have been published previously from two sources, and the data can be found in the references [15-31]. Additional stress data are provided in Appendix A4 and in several of the case studies in Chapter 12. 

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