Page 117 - Analysis and Design of Machine Elements

(a) b Hub Detachable Fastenings for Shaft and Hub 95
Shear plane
Reaction of
h 2 hub on key
a F
h
F a
Force of
shaft on key
d T Shaft
O

(b) Area in shear
Area in crushing
l

Distributed force F
on bearing area
h
h/2
b
Figure 4.5 Forces acting on a key.

where
l – working length of key, mm. For Type A key, l = L − b;Type B, l = L;Type C,
l = L − b/2.
If either shear or crushing strength is insufficient, double keys oriented at 180 ∘
intervals from one another along the shaft circumference may be used to carry the
load. Considering the nonuniform load distribution, the strength calculation should
introduce a factor of 1.5 instead of 2.
Keys are often made from cold-drawn low-carbon steel, high-carbon steel or heat-
treated alloy steels for higher strength requirements. The allowable bearing stresses
[ ] for key, hub and shaft made from steels or cast iron are between 60–150 and
p
30–80 MPa, respectively. Larger values are selected for static loads, while smaller values
are for impact loads [5]. The allowable shear stress can be roughly estimated as half of
the allowable bearing stress by the maximum-shear-stress theory, expressed as
= 0.5 (4.3)
p
Example Problem 4.1
A steel shaft is to transmit a stable torque of 1000 N m to the steel spur gear through a
key. The diameter of the shaft connecting the gear is d = 80 mm and the width of hub is
w = 120 mm, as shown in Figure E4.1. Select a proper key to transmit the torque. If the
transmitted torque is doubled, modify the design.