Page 247 - Tribology in Machine Design

6 Friction, lubrication and wear in

higher kinematic pairs

6.1. Introduction It is well known in the theory of machines that if the normals to three points
of restraint of any plane figure have a common point of intersection, motion
is reduced to turning about that point. For a simple turning pair in which
the profile is circular, the common point of interaction is fixed relatively to
either element, and continuous turning is possible. A pair of elements in
which the centre of turning changes its position at the completion of an
indefinitely small rotation, i.e. the new position is again the common point
of intersection of the normals at three new points of restraint. For this to be
possible the profiles will, in general, have differing geometric forms, and are
then referred to as a higher pair of elements. Again, since the elements do
not cover each other completely as in lower pairing and are assumed to be
cylindrical surfaces represented by the profiles, contact will occur along a
line or lines instead of over a surface. Relative motion of the elements may
now be a combination of both sliding and rolling.
In higher pairing, friction may be a necessary counterpart of the closing
force as in the case of two friction wheels in contact. Here the force on the
wheels not only holds the cylinders in contact but must be sufficient to
prevent relative sliding between the circular elements if closure is to be
complete. In certain cases it is essential that force closure of higher pairs
shall do more than maintain contact of the functional surfaces. For
example, the ball-bearing functions as a lower pair or as an incomplete
higher pair of elements, it is, however, usually regarded as being a higher
pair.
This chapter is designed to provide familiarization and perspective to
readers planning to pursue in more detail any of the various topics covered
by the collective name of higher kinematic pairs. There are two pervading
objectives:
(i) to develop an understanding of the basic concepts of concentrated
contacts;
(ii) to develop a facility with the analytical techniques for predicting and
assessing the behaviour of concentrated contacts which are typical for
higher kinematic pairs.
The information contained in this chapter can be used to solve a number of
problems common for all higher kinematic pairs. First, problems as-
sociated with contact between two nonconforming surfaces are discussed.
They include the force transmitted at a point of contact, surface tractions,