Page 132 - Tribology in Machine Design

118 Tribology in machine design

brake shoe considered later. Thus, referring to Fig. 4.22
b = the width of the clutch plate surface,
2i// = the angle subtended at the centre by the effective arc of
contact.
Then, length of arc of contact = 2a\j/, length of chord of contact =2a sin ty
Figure 4.22 and the resultant R of the normal pressure intensity, p, on the contact
surfaces is given by

For an element of length a x d0 of the clutch surface
tangential friction force =fpab x d0.
This 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
fpa b x d0. Integrating between the limits +i/f, the frictional resistance is
then equivalent to
(i) a force at 0 in a direction perpendicular to the line of action of/? given
by

(ii) a couple of moment:

The equivalent system of forces and the couple M acting on each curved
plate are shown in Fig. 4.23, where Wis the axial thrust load in the screw.
Taking moments about the hinge and using the notation shown in the
figures, we have
Figure 4.23

l
where z = the distance of the centre of the hinge from 0, and (j>i =tan fis
the angle of friction for the clutch plate surface.
An alternative approach is to assume that the resultant of the forces R
andfR at O is a force RI =R sec </>! at an angle </>j to the line of action of/?.
Writing