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Screws, Fasteners, and the Design of Nonpermanent Joints 417
which, since thread friction has been eliminated, is the torque required only to raise
the load. The efficiency is therefore
T 0 Fl
e = = (8–4)
T R 2πT R
The preceding equations have been developed for square threads where the nor-
mal thread loads are parallel to the axis of the screw. In the case of Acme or other
threads, the normal thread load is inclined to the axis because of the thread angle 2α
and the lead angle λ. Since lead angles are small, this inclination can be neglected
and only the effect of the thread angle (Fig. 8–7a) considered. The effect of the angle
α is to increase the frictional force by the wedging action of the threads. Therefore
the frictional terms in Eq. (8–1) must be divided by cos α. For raising the load, or for
tightening a screw or bolt, this yields

Fd m l + π fd m sec α
T R = (8–5)
2 πd m − fl sec α
In using Eq. (8–5), remember that it is an approximation because the effect of the
lead angle has been neglected.
For power screws, the Acme thread is not as efficient as the square thread, because
of the additional friction due to the wedging action, but it is often preferred because
it is easier to machine and permits the use of a split nut, which can be adjusted to
take up for wear.
Usually a third component of torque must be applied in power-screw applications.
When the screw is loaded axially, a thrust or collar bearing must be employed between
the rotating and stationary members in order to carry the axial component. Figure 8–7b
shows a typical thrust collar in which the load is assumed to be concentrated at the
mean collar diameter d c . If f c is the coefficient of collar friction, the torque required is

Ff c d c
T c = (8–6)
2
For large collars, the torque should probably be computed in a manner similar to that
employed for disk clutches.
Nominal body stresses in power screws can be related to thread parameters as follows.
The maximum nominal shear stress τ in torsion of the screw body can be expressed as
16T
τ = 3 (8–7)
πd
r
Figure 8–7 d c
(a) Normal thread force is
increased because of angle α;
(b) thrust collar has frictional F F⁄ 2 F⁄ 2
diameter d c. F cos
Collar
Nut

Thread
2 =
angle

F⁄ 2 F⁄ 2

(a) (b)