Page 133 - Tribology in Machine Design

Friction, lubrication and wear in lower kinematic pairs 119

it follows that the couple M and the force R : at 0 may be replaced by a force
K! acting through the point C on the line of action of R as shown in Fig.
4.23. This force is the resultant reaction on the clutch plate and, taking
moments as before

which agrees with eqn (4.50).

4.7.2. Auxiliary mechanisms
If
r = the mean radius of the operating screw threads,
a = the slope of the threads at radius r,
P = the equivalent force on the screw at radius r,

then, since both ends of the screw are in action simultaneously

where </> is the angle of friction for the screw thread surfaces.
The equivalent force at the end of each lever of length L, is then

and if k is the velocity ratio of the axial movement of the collar to the
circumferential movement of Q, in the position 2 when the clutch plates are
initially engaged, then

In passing from the position 2 to position 3, this axial force will be
momentarily exceeded by an amount depending partly upon the elasticity
of the friction lining, together with conditions of wear and clearance in the
joints of the operating mechanism. Theoretically, the force Q will pass
through an instantaneous value approaching infinity, and for this reason,
the movement of 2 to 3 should be as small as is possible consistent with the
object of sustaining the load when the axial force is removed.