Page 248 - Tribology in Machine Design

Friction, lubrication and wear in higher kinematic pairs 233

elastic hysteresis during rolling, rolling friction, and the lubrication of
rollers. Next, film thickness under isothermal elastohydrodynamic con-
ditions, inlet viscous heating, regimes of line contact lubrication are
presented. Finally, contact problems in rolling element bearings, gears, and
cam-follower systems are reviewed and equations to evaluate required
minimum film thickness are discussed.

6.2. Loads acting on In this section loads acting on a contact area and the way they are
contact area transmitted from one surface to another shall be considered. The load on
the contact can be resolved into a normal force P acting along the common
normal and a tangential force T opposed by friction. The relationship
between W and T is given by

where / is the coefficient of limiting friction. T can be resolved into
components T x and T y parallel to axes x and y. In a purely sliding contact the
tangential force reaches its limiting value in a direction opposed to the
sliding velocity. The force transmitted at a normal point of contact has the
effect of compressing 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. This is schematically shown in Fig. 6.1. The
components of this moment M x and M y are called rolling moments and
oppose a rolling motion but are small enough to be neglected. The third
component M z, 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.
Free rolling is defined as a rolling motion in which spin is absent and
where the tangential force T at the contact point is zero. This is the
condition of the unpowered and unbraked wheels of a vehicle if the rolling
resistance and the friction in the bearings are neglected. It is in marked
contrast with the driving wheels or the braked wheels which transmit
Figure 6.1 sizeable tangential forces at their points of contact with the road or rail.

6.3. Traction in the The forces and moments discussed above are transmitted across the contact
contact zone interface by surface tractions at the interface. The normal traction
(pressure) is denoted here by w and the tangential traction (due to friction)
by t, shown acting on the lower surface in Fig. 6.1. For overall equilibrium

With contacts formed by the convex surfaces the contact area lies