Page 290 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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If a shaft is subjected to normal stress only, the safety factor is calculated by
−1
S = ≥ [S] (10.8)

K +
a m
And if a shaft is subjected to shear stress only, the safety factor is
−1
S = ≥ [S] (10.9)

K +
a m
The allowable safety factor [S] is selected between 1.3 and 2.5, depending on the prop-
erties of material and application. The variables in Eqs. (10.8) and (10.9) have been
introduced in Chapter 2.
10.3.1.4 Static Strength Analysis
When ashaft is subjectedtoanoverloadimpact, theloadpeakvalue is used to calculate
static strength to avoid excessive plastic deformation by [7]
S S
S S
S ≥ [S ] (10.10)
Sca = √ S
S 2 + S 2
S S
where
S Sca –calculated static safety factor.
[S ] –allowable static safety factor. The allowable static safety factor is selected
S
between 1.2 and 2.2 corresponding to the variation of / from 0.45 to 0.9.
s b
S S –static safety factor when a shaft is subjected to bending and axial stresses only.
s
S S = (10.11)
max
S S –static safety factor when a shaft is subjected to torsional stress only.

s
S = (10.12)
s
max
where
, –yield strength in tension and shear, respectively, MPa, usually
s s
= (0.55–0.62) ;
s s
max , max –maximum bending and shear stresses at critical section, MPa;

10.3.2 Rigidity Analysis
Deflection and rigidity analysis usually follows strength analysis after the geometry
of the shaft has been determined. Shaft deflection, both linear and angular, should
be checked at locations where mating elements like gears and bearings are mounted,
especially for slender shafts.

10.3.2.1 Bending Deflections and Slopes
The calculations of deflections and slopes for a stepped shaft are more complicated
since both moment and cross-sectional moment of inertia change along the shaft. A
stepped shaft can be treated as a uniform diameter shaft with an equivalent diam-
eter of d , and then use the formula in Mechanics of Materials [5] to calculate the
v