Friction

Friction can be defined as the force between surfaces in contact that resists their relative tangential motion (slipping). Friction is a passive resistance that tends to hinder the relative motion of two bodies in contact. Passive resistance, which produces the loss of dynamic work in contact between bodies in relative motion, can be distinguished in various respects:

• geometric aspect (contact extension): point-like, or extended to a line or surface;
• kinematic aspect (form of relative motion): sliding or rolling; in particular, in extended contact, the relative motion occurs at any time around an axis to which all the contact normals are incident, provided that the collision is excluded and that the bodies are non-deformable;
• nature of bodies: contact between rigid or deformable solids, between solid and fluid, between fluids;
• state of the surfaces: smooth or rough;
• friction form: dry, lubricated.

One of the simpler characteristics of friction is that it is parallel to the contact surface between systems and always in a direction that opposes motion or attempted motion of the systems relative to each other.

Types of friction

In mechanics there are basically three types of friction:

• dry friction: occurs between two bodies in contact on non-lubricated surfaces.
• fluid (viscous) friction: occurs on the surfaces of two bodies in relative motion between which a liquid or gaseous lubricant is interposed, whereby viscous forces of interaction develop between the material body and the molecules of the fluid (liquid or gas) with which it is in relative motion. This viscous friction force is linked to a dimensionless number called Reynolds number.
• internal friction of materials: manifests itself as a non-perfect elasticity of real bodies when they are deformed.

Depending on the presence or absence of relative motion and its type, the following are also distinguished:

• static friction (typical of quiet bodies);
• kinetic or dynamic friction (typical of bodies in relative motion);
• sliding friction;
• rolling friction.

History of friction

The invention of the wheel and its use for the transport of loads and people date back to the fourth millennium BC. It must undoubtedly have been preceded by a long period of experience of protohistoric human communities in the field of transporting large stones and other heavy loads necessary for the buildings (which we now call megalithic) that characterize the latter part of the Neolithic and the beginning of the metal age in the regions of western Europe and those around the eastern Mediterranean.

In these periods, alongside or in place of direct dragging on the ground and towing on sleds, it can be assumed that a technique based on the use, as rollers, of cylindrical sections of tree trunks was used (an idea probably related to practices of successive overturns used to move stones of modest size). The tree trunks used as rollers were perhaps the ancestors of the wheels that came when the problem of connecting the wheels by means of axles to a structure capable of bearing the load was overcome. It is very likely that these inventions go to Mesopotamian proto-history since the first archaeological finds and the first representations of wheeled chariots (dated to the first half of the third millennium BC) come from the city of Ur.

The extraordinary singularity of the rolling of a wheel lies in the role, paradoxical at first sight, of the static friction. In fact, due to static friction, non-cylindrical or non-spherical solid systems (which therefore can only translate) are “kept still” on their support base. In fact, without static friction, a great number of things that “must stay still” could not be: chairs, tables and all other furniture would move with the slightest push in a horizontal direction; screws could not be tightened; one could not lean a ladder against the wall, much less climb on it, and so on.

All this creates, on the level of conceptual representations, a strong correlation between static friction and immobility of things on their supports and makes the effect of static friction on rolling quite paradoxical. But the idea of paradox falls away if the shape of the rolling objects is taken into account. Even a cylinder or a sphere, in fact, are held still with respect to the support by the forces of static friction; but on these two geometric shapes, these forces can act only on a portion of the contact surface which ideally, if the support is perfectly flat, is constituted by the points of a straight line segment (for the cylinder) and even by a single point for the sphere and which in reality is however very limited with respect to the entire surface of the solid.

This implies that, while keeping the support area still, the static friction cannot hinder the rotational movements of the entire solid around this restricted area. This occurs not only for cylinder and sphere but also for any solid with a convex shape, for example an ellipsoid, or a prismatic solid that is overturning around an edge. The peculiarity of cylinder and sphere lies in the fact that, given their particular symmetry, they also enjoy the possibility of being in indifferent equilibrium (if they are homogeneous).

Another feature of rolling that is decisive for the success of wheel (or roller) based transport systems is the extraordinary energy advantage over sliding based systems In rolling, the static frictional forces that hold the contact area on the base stationary, for this reason, do not perform work and therefore have no role in the energy balances. This means that if the wheels and base were perfectly rigid, the only dissipation of mechanical energy for a wagon would be due to the dynamic friction active in the wheel axles (abstracting, of course, from the air resistance).

In reality, perfectly rigid materials do not exist: this entails the need to take into account the possible deformations during rolling and their consequences on motion, both geometric and energetic. In many significant cases, it is possible to ignore the effect of the deformability of the materials on the geometric aspects of the rolling and on the value of the frictional force necessary to avoid sliding. On the other hand, it is never possible to neglect the energetic consequences of the deformability of materials, under penalty of affirming the possibility of creating perpetual motions.

The parameter that, from a phenomenological point of view, interprets the dissipation of mechanical energy due to the deformability of the materials is the rolling friction coefficient. Although it is never zero, it is nevertheless related to energy losses that are much lower than those due to sliding or air resistance.