Page 122 - Tribology in Machine Design

108 Tribology in machine design

Efficiency

Writing tan </> 2 =fr m/r, the efficiency becomes

where/= tan </>! is the true coefficient of friction for all contact surfaces. This
result is of a similar form to eqn (4.22), and can be deduced directly in the
same manner.
In the case of the rotating nut, C —fWr m is the friction couple for the
bearing surface of the nut and, if the pressure is assumed uniformly
distributed:

where r^ and r 2 are the external and internal radii respectively of the contact
surface.
Comparing eqn (4.19) with eqn (4.23), it will be noticed that, in the
former, P is the horizontal component of the reaction at the contact surfaces
of the nut and screw, whereas in the latter, P is the horizontal effort on the
nut at radius r, i.e. in the latter case

which is another form of eqn (4.26).

Numerical example
Find the efficiency and the mechanical advantage of a screw jack when
raising a load, using the following data. The screw has a single-start square
thread, the outer diameter of which is five times the pitch of the thread, and
is rotated by a lever, the length of which, measured to the axis of the screw, is
ten times the outer diameter of the screw; the coefficient of friction is 0.12.
The load is free to rotate.

Solution
Assuming that the screw rotates in a fixed nut, then, since the load is free to
rotate, friction at the swivel head does not arise, so that C=0. Further, it