Friction

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Friction forces between surfaces causes energy loss that has enormous practical importance. It is estimated that, in the U.S. alone, the cost of our imperfect understanding of friction is more than 500 billion dollars. Friction, which is worse in vacuum, has caused irreversible failures in many space instruments. On the other hand, friction is useful in many instances.  Without friction we would not be able to walk, cars will not move, and violins would not work. In other cases one wants to maximize friction, like when stopping a train. 

The first practical application of friction dates from nearly a million years ago, when it was discovered that heat from friction could be used to light a fire.  The use of liquid lubricants to minimize the work needed to transport heavy objects was discovered more than 4,000 years ago.  Leonardo da Vinci made the first experiments on friction using a rectangular block sliding on a dry, flat surface.  His main observations are that:

1) the friction force is independent of the area of the surfaces in contact.

2) the friction force is proportional to the applied load.

These were framed as laws by Amontons in 1699 and researched by Coulomb in 1781, who also noted the distinction between static friction (force needed to start motion) and kinetic friction (force needed to maintain friction).  Aristoteles had already noted that applying a constant force to an object on the floor moves it with a constant velocity.  This everyday observation causes difficulty in grasping Newton's law that, in the absence of friction, a constant force produces a constant acceleration (rather than velocity).

Here we will limit the material to friction between dry surfaces.  The role of lubricants and boundary layer friction has to do with the properties of liquids and will only be mentioned on passing. Hydrodynamic lubrication with viscous fluids was first studied theoretically by Reynolds in 1886.  

The figure illustrates the essence of the friction experiment.  A force F needs to be applied to the block to make it slide on the table (static case) or to keep it moving at a constant speed (kinetic case).  F depends on the value of the load L.  

The Amontons' laws can be cast as a relation between the friction force F and the load L:

F = mL

the constant m is called the coefficient of friction, which depends on the materials.  m is different in a static situation (static friction, m0) than when the bodies are in motion (kinetic friction, mk).   The law is useful but there is no microscope theory that explains friction at the atomic level, in the practical case where surfaces are rough and have adsorbed gases or films. 

The table gives some typical values of the coefficient of static friction.

Materials m
steel/steel 0.8
copper/steel 0.5
Auto brakes (clean) 0.4
Auto brakes (wet) 0.2
aluminum on snow 0.35
ski wax on snow 0.04
ice on ice 0.05-0.15

Microscopic contact

To understand why friction is independent on the surface area we need a microscopic view of the contact.  Practical surfaces are rough, and they only touch through contact "points" or "junctions". The figure shows two rough surfaces sliding past each other.  When the load increases (bottom) the asperities become flattened by elastic deformation.  This increases the effective contact area, and therefore friction.

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The effective contact area A' is only a small fraction of the apparent macroscopic area A. One can derive an average shear yield stress at the contacts,

t = F/A'                                                                         (1)

Microscopic friction models

Bowden and Tabor suggested a simple form for s to explain Amontons' laws. If t increases with local pressure P = L/A', then t = t0 + aP. so F = t0A' + aL, or:

m = a + t0/P                                                                 (2)

which leads to m independent of load L and macroscopic area A if P is constant or much larger than t0. This fails when adhesion is strong (large t0).

A similar justification of Amontons' law can be reached by assuming that each contact junction is at the the largest compressive stress, just before plastic deformation begins. This means a penetration hardness sc, and A' = L/sc. In steel, sc ~ 109 N/m2, so for a load L = 100 N, A' = 0.1 mm2. For A = 1 m2 this means that the contact area is just 10-5 of the macroscopic area.   Experiments show that the area of a juction is of the order of (10 mm)2, which implies about 1000 junctions at the interface between the materials.  In this model, the sliding friction force is that required to shear the "cold-welded" contacts.  If the shear stress is tc, then we obtain Eq. (1) and the friction coefficient, m = F/L is:

m = tc/sc                                                                 (3)

independent of A.  Since tc and sc are of the same order for metals, this explains m of the order of 1, as shown in the table.

When the surfaces are lubricated, the situation changes radically, the much smaller friction force is that require to shear the lubricant fluid.

Dynamic friction

In a simple case of friction, if we apply a force parallel to the surface, there is no motion until we exceed a minimum force, see the figure.

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when motion begins, the force falls to correspond to the friction at the velocity of motion.  A common case, is the stick-slip motion, that is shown in the next figure.

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This can be observed, for instance, when opening a door. When the door is opened slowly, noise due to the stick-slip motion occurs.  If the door is opened fast enough, sliding occurs and no noise is generated.  It is common that the stick-slip motion disappears if the force is large enough or the motion fast enough.

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Frictional Heating

If all the work goes into heat, the power generated is:

q= F v = mLv

Examples of frictional heating is when lighting a match, or when machine tool gets red hot during sharpening at the grinding wheel. 

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Copyright 2002, by Raśl Baragiola, University of Virginia. All rights reserved.