125 lines
8.4 KiB
Org Mode
125 lines
8.4 KiB
Org Mode
In dry sliding between a given pair of materials under steady conditions, the
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coefficient of friction may be almost constant. This is the basis for two
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EMPIRICAL Laws of Sliding Friction, which are often known as Amontons’ Laws
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and date from 1699. They are in fact not original but a re-discovery of work by
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Leonardo Da Vinci dating from some 200 years earlier.
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Amontons’ Laws of Friction can be stated as follows:
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1. Friction is proportional to normal load.
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2. The friction is independent of the apparent area of contact.
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A third Law of Friction was added by Coulomb (1785):
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3. The friction is independent of sliding velocity.
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These three Laws are collectively known as the Amontons-Coulomb Laws. They
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are based on EMPIRICAL OBSERVATIONS only and there is NO PHYSICAL BASIS
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for these Laws. If a tribological contact does not appear to behave in agreement
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with these Laws, it does not mean that there is something suspect about this
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behaviour. These Laws are not FUNDAMENTAL in the same way that Newton’s
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Laws are fundamental.
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Most metals and many other materials in dry sliding conditions behave in a way
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that broadly agrees with the First Law. Contacts between metals and ceramics
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and metals and polymers rarely agree with the First Law.
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Most materials agree with the Second Law, with the exception of polymers.
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Most materials agree with the Third Law, but only over a moderate range of
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sliding velocities. The transition from rest to sliding at low velocities does not
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agree with the Third Law and at high sliding velocities, in particular in metals,
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the dynamic friction coefficient falls with increasing velocity.
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Further Laws have subsequently been added, until we end with:
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1. Friction is proportional to normal load.
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2. Friction is independent of the apparent area of contact.
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3. Friction is independent of sliding velocity.
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4. Friction is independent of temperature.
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5. Friction is independent of surface roughness.
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These are, in sum, the classical laws of friction. Ceramics and polymers usually
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do not conform to these laws.
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Modern understanding of friction stems from the work of Philip Bowden and
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David Tabor (mostly at Cambridge) between the 1930s and the 1970s and is
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based on careful analysis of contact mechanics. Their model for sliding friction
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assumes firstly that all frictional effects take place at the level of micro (or
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asperity) contacts and that the total friction force has two components: an
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adhesion force and a deformation or ploughing force. The former is associated
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with the real area of contact at an asperity level, the latter with the force
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needed for the asperities of the harder surface to plough through the softer
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surface. These assumptions are sufficient to explain why many material
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contacts do not behave in accordance with the classical Laws of Friction.
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In a metal-metal contact, the deformation at an asperity level is mostly plastic.
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This means that the real area of contact is proportional to load. Increasing load
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leads to an increase in the number of asperity contacts rather than an increase
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in the average asperity contact surface area; more asperities are brought into
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action to support the increased load. Because of this, there is minimal increase
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in penetration depth of the asperities. As the ploughing component of friction
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depends on penetration depth, it is thus not highly dependent on load. The
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adhesion component however is proportional to the real area of contact, hence
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the load. Hence, the total friction in this type of contact is effectively
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proportional to load. It is of course important to note that even this agreement
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with the Classical Laws breaks down once oxide and other surface films are
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present or once work hardening at an asperity level takes place.
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By comparison with the metal-metal contact, metal-ceramic and metal-polymer
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contacts tend to give rise to elastic deformation at an asperity level. In
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ceramics, this is because of very high hardness. In polymers this is because the
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ratio between Young’s modulus and hardness is low. This means that, except in
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the case of contact between a polymer and a very rough surface, the contact is
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almost completely elastic.
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A further consideration in respect of contacts involving polymers is the strong
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time dependence of their mechanical properties; most polymers are visco-
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elastic.
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In those contacts where the deformation at asperities level is elastic (as
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opposed to plastic) the real area of contact for a single asperity will be
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proportional to the load raised to the power 2/3. The real area of contact thus
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increases by less than proportional to load. Because of this, the friction force
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tends to decrease with increasing load, but this is only true with a relatively
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smooth metal counter face, where adhesion friction predominates.
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Whereas surface roughness does not have much impact on the friction in a
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metal-metal contact other than during running-in processes, this is not the case
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with the metal-polymer contact. Minimum friction is achieved with a metal
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surface roughness of around 0.2 Ra. With higher surface roughness, the
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ploughing contribution to friction increases sharply with increased penetration of
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the polymer surface, whereas with very smooth surfaces the adhesion
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component of friction increases dramatically. Of course, these frictional
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responses will be modified by the presence of either transfer films or entrained
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debris.
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Before leaving the issue of surface roughness, it is worth noting that in addition
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to the bulk effect of surface roughness, asperity orientation and shape also
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have an effect on friction. With a metal surface ground in one direction, the
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frictional response of a polymer sliding across the surface may depend on the
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orientation of the surface topography relative to the direction of sliding. This
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can prove a particular problem in running a polymer pin on the surface of a
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metallic disc in a pin on disc configuration.
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Now, whereas in the metal-metal contact, over a limited speed range, we can
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ignore the effects of sliding velocity, we cannot do the same for the metal-
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polymer contact. This is because of the visco-elastic properties of the polymer:
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the higher the deformation velocity, the higher the effective Young’s modulus of
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the polymer. This results in lower surface penetration at higher speeds and
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hence lower ploughing friction and a lower real area of contact and hence lower
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adhesive friction.
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In our final consideration of the classical Laws of Friction, we should perhaps
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consider temperature. In the metal-metal contact, modest temperatures do not
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give rise to major changes in the mechanical characteristics of the materials, so
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it is perhaps safe (over a modest temperature range) to consider that friction is
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independent of temperature. This is of course no longer the case at elevated
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temperatures or under conditions at which asperity tip temperatures result in
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the softening or melting of the material.
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In the case of polymers, the Young’s modulus falls sharply with rising
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temperature leading to an increase in contact area and an increase in adhesive
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friction. The product of friction and sliding velocity is frictional energy input,
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giving rise to an increasing contact temperature. This is accompanied by a
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further softening of the material and increase in friction, which reaches a
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maximum at the point where the real area of contact approaches the nominal
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area of contact. Further increase in temperature will cause the polymer to melt
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or collapse. This is the PV limit of the material.
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From the above analysis, it should be clear that for many contacts the classical
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Laws of Friction do not apply. A different set of Laws of Friction should perhaps
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be postulated as follows:
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1. Friction is NOT proportional to normal load.
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2. Friction is NOT independent of the apparent area of contact.
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3. Friction is NOT independent of sliding velocity.
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4. Friction is NOT independent of temperature.
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5. Friction is NOT independent of surface roughness.
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Because ceramics and polymers do not obey the classical Laws of Friction,
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because the friction coefficient varies so greatly with load, sliding speed,
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surface roughness and temperature, a list of friction coefficients for such
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materials is of no value. This represents a serious challenge for the
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manufacturers of these materials when attempting to produce data of use in
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engineering design applications.
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And finally, a brief glance at the Stribeck curve should be sufficient to convince
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anyone that the classical laws of dry sliding friction obviously do not apply to
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lubricated contacts!
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