**1 Motion and forces at point contact **
**1.3 Forces transmitted at a point of contact**

The resultant force transmitted from one surface to another through a point of contact is resolved into a

*normal force* *P* acting along the common normal, which generally must be compressive, and a

*tangental force* *Q *in the tangent plane sustained by friction. The magnitude of

*Q *must be less than or, on the limit, equal to the force of limiting friction, i.e.

where μ is the coefficient of limitting friction.

*Q *is resolved components

* Qx* and

* Qy* parallel to axes

*Ox* and

*Oy*. In a purely sliding contact the tangential force reaches its limiting value in a direction opposed to the sliding velocity, from which:

The forces transmitted at a nominal point of contact has the effect of compressing deformable solids so that they make contact over an area of finite size. As a result it becomes possible for the contact to transmit a resultant moment in addition to a force (Fig. 1.2). The components of this moment

*Mx* and

**My **are defined as

* rolling moments.* They provide the resistance to a rolling motion commonly called 'rolling friction' and in most practical problems are small enough to be ignored.

Fig. 1.2 Forces and moments acting on contact area *S*.

The third component

*Mz*, acting about the common normal, arises from friction within the contact area and is referred to as the

*spin moment*. When spin accompanies rolling the energy dissipated by the spin moment is combined with that dissipated by the rolling moments to make up the overall rolling resistance.

At this point it is appropriate to define

*free rolling *('inertia rolling' in the Russian literature). We shall use this term to describe a rolling motion in which spin is absent and where the

*tangential force **Q* *at the contact point is zero*. This is the condition of the unpowered and unbraked wheels of a vehicle if rolling resistance and bearing wheels which transmit sizable tangential forces at their points of contact with the road or rail.