Page 120 - Tribology in Machine Design

106 Tribology in machine design

so that

where r = the mean radius of the threads. For the thread, eqn (4.14) applies,
namely

thus,

or

Thus, the efficiency is less than tan a/tan(a + 0), since it is reduced by the
friction at the contact surfaces of the swivel head. If the effective mean
radius of action of these surfaces is r m, it may be written

and eqn (4.21) becomes

where fr m/r may be regarded as the virtual coefficient of friction for the
swivel head if the load is assumed to be distributed around a circle of radius r.

Cose (ii) - The nut rotates
In the alternative arrangement, Fig. 4.12, a torque T applied to the bevel
pinion G drives a bevel wheel integral with the nut A, turning on the block
C. Two cases are considered:
(1) When rotation of the screw is prevented by a key D. Neglecting any
friction loss in the bevel gearing, the torque applied to the nut A is kT, where
k denotes the ratio of the number of teeth in A to the number in the pinion
G. Again, if P is the equivalent force on the nut at radius r, then

Let
r m = the effective mean radius of action of the
bearing surface of the nut,
d = the distance of the centre-line of the bearing
Figure 4.12 surface of the key from the axis of the screw,