Page 58 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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Table 2.2 Stress concentration factors for a stepped shaft with a shoulder fillet [12].
r

D d
Shaft in tension, k Shaft in bending, k Shaft in torsion, k

r = 4F = 32M = 16T
d d 2 d 3 d 3
D/d
2.0 1.5 1.1 1.05 1.01 3.0 1.5 1.2 1.05 1.01 2.0 1.33 1.2 1.09

0.04 2.8 2.57 1.99 1.82 1.42 2.4 2.21 2.09 1.88 1.61 1.84 1.79 1.66 1.32
0.10 1.99 1.89 1.56 0.46 1.23 1.80 1.68 1.62 1.53 1.36 1.46 1.41 1.33 1.17
0.15 1.77 1.68 1.44 1.36 1.18 1.59 1.52 1.48 1.42 1.26 1.34 1.29 1.23 1.13
0.20 1.63 1.56 1.37 1.31 1.15 1.46 1.42 1.39 1.34 1.20 1.26 1.23 1.17 1.11
0.25 1.54 1.49 1.31 1.27 1.13 1.37 1.34 1.33 1.29 1.17 1.21 1.18 1.14 1.09
0.30 1.47 1.43 1.28 1.24 1.12 1.31 1.29 1.27 1.25 1.14 1.18 1.16 1.12 1.09

where q is the notch sensitivity factor, ranging from 0 to 1.0, depending on the strength

and hardness of material and notch geometry. Since reliable values of notch sensitivity
factor are difficult to obtain, this book will use the safest and most conservative value of
k = k [2, 3].
f t
The values of fatigue stress concentration factor vary with axial tension, bending and
torsional loading conditions, and designated by k and k for tensile and shear fatigue

stress concentration factor, respectively. Abridged geometric stress concentration fac-
tors of a stepped shaft with a shoulder fillet are listed in Table 2.2. Detailed information
of stress concentration factors with different geometric discontinuities can be found in
references [10, 12].

Size Factor, or Small size elements usually have greater fatigue strength than larger

ones with the same surface finish, material and configuration. The larger the element,
the greater the statistical probability of flaws existing within an element and the more
likely the reduction of fatigue strength. The nonuniformity of material properties due to
size is measured by size factor for tension and for shear. Detailed data of size factor

can be found in references [3, 10] and limited data used in this book are presented in
Figure 2.6.

Surface Condition Factor, or Since fatigue failures originate from relative weak areas

on the surface, the surface quality is of particular importance. Poor surface quality,
represented by scratches and irregularities, will reduce fatigue strength. This effect is
measured by surface condition factor, which can be found in Table 2.3. Fatigue strength
of material increases rapidly as surface qualities are progressively improved through
machining, grinding and polishing. When experimental data for torsional shear fatigue