Page 117 - Tribology in Machine Design

Friction, lubrication and wear in lower kinematic pairs 103

Equation (4.9) is derived using the law of sines. Also

and so

In the example given; tan a =0.2, therefore a = 11° 18' and since
tana = tan<£ and tan</>=/=0.2, therefore </> = ll° 18'

and thus

4.3. Friction in screws Figure 4.8 shows a square threaded screw B free to turn in a fixed nut A. The
with a square thread screw supports an axial load W, which is free to rotate, and the load is to be
lifted by the application of forces Q which constitute a couple. This is the
ideal case in which no forces exist to produce a tilting action of the screw in
the nut. Assuming the screw to be single threaded, let

p = the pitch of the screw,
r = the mean radius of the threads,
a=the slope of the threads at radius r,
then

Figure 4.8
The reactions on the thread surfaces may be taken as uniformly distributed
at radius r. Summing these distributed reactions, the problem becomes
analogous to the motion of a body of weight J^up an inclined plane of the
same slope as the thread, and under the action of a horizontal force P. For
the determination of P
couple producing motion = Qz = Pr

It will be seen that the forces at the contact surfaces are so distributed as to
give no side thrust on the screw, i.e. the resultant of all the horizontal