Page 118 - Tribology in Machine Design

104 Tribology in machine design

components constitute a couple of moment Pr. For the inclined plane, Fig.
4.9, Oab is the triangle for forces from which

where </> is the angle of friction governed by the coefficient of friction.
During one revolution of the screw the load will be lifted a distance p, equal
to the pitch of the thread, so that

Figure 4.9

/
Because W/P= VF/[W tan(a + 0)] according to eqn (4.14), one full revol-
ution results in lifting the load a distance p, so that

If the limiting angle of friction (/> for the contacting surfaces is assumed
constant, then it is possible to determine the thread angle a which will give
maximum efficiency; thus, differentiating eqn (4.15) with respect to a and
equating to zero

that is

or

and finally

so that

For lubricated surfaces, assume/=0.1, so that </> = 6° approximately. Hence
for maximum efficiency a = (%n — ^>)=42° and the efficiency is then 81 per
cent.
There are two disadvantages in the use of a large thread angle when the
screw is used as a lifting machine, namely low mechanical advantage and