Page 124 - Tribology in Machine Design

110 Tribology in machine design

Referring to Fig. 4.15, JKL is a portion of a helix on the thread surface at
mean radius, r, and KN is the true normal to the surface at K. The resultant
reaction at K will fall along KM at an angle 0 to KN. Suppose that KN and
KM are projected on to the plane YKZ. This plane is vertical and tangential
to the cylinder containing the helix JKL. The angle M'KN ' = </>' may be
regarded as the virtual angle of friction, i.e. if </>' is used instead of </>, the
thread reaction is virtually reduced to the plane YKZ and the screw may be
treated as having a square thread. Hence

as for a square thread. The relation between 0 and </>' follows from Fig. 4.15

Further, if the thread angle is measured on the section through the axis of
the screw, then, using the notation of Fig. 4.15, we have

Figure 4.15

These three equations taken together give the true efficiency of the
triangular thread. If/'=tan0' is the virtual coefficient of friction then

according to eqn (4.31). Hence, expanding eqn (4.30) and eliminating $',

But from eqn (4.32)

and eliminating \l/ n