Page 153 - Tribology in Machine Design

Friction, lubrication and wear in lower kinematic pairs 139

Hence, for an element of length a d0 of the arc of contact

normal force = pab d0,
tangential friction force =fpab d0.
The latter elementary force can be replaced by a parallel force of the same
magnitude acting at the centre 0 together with a couple of moment
2
dM=fpa b-dQ.
Proceeding as for the rim clutch and resolving the forces at 0 in directions
parallel and perpendicular to the line of action of /?, we have
for the normal force:

for the tangential force:

If p is given in terms of 0, the vanishing integral determines the angle /?.
Further, the resultant force at 0 is

and is inclined at an angle 0=tan ^fto the direction of R. Again, the
couple M together with force R i at 0 can be replaced by a parallel force R!
acting at a perpendicular distance h from 0 given by

The circle with centre 0 and radius h is the friction circle for the contact
surfaces, and the resultant force on the wheel rim is tangential to this circle.
In the case of symmetrical pressure distribution, f$ = ty, and the line of
action of R bisects the angle subtended by the arc of contact at the centre 0.
The angle 0 is then more conveniently measured from the line of action of
R, and the above equations become