Page 66 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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When a component is subjected to combined fluctuating stresses, or fluctuating
multiaxial stress, the safety factors of tensile and shear stress are first calculated by
S = −1 and S = −1 , separately, and then use Eq. (2.50) to calculate the

k a + m k a + m
safety factor under the combined stresses.
2.3.7 Measures to Improve Fatigue Strength
From Eqs. (2.20) and (2.21), it is understood that the endurance limit of a machine ele-
ment is influenced by the endurance limit of material and combined influence factor K ,

or to be more precise, the fatigue stress concentration factor k ,sizefactor ,surface

condition factor and intensify factor . The measures to improve fatigue strength
q
can therefore be proposed accordingly.
1. Reduce stress concentration
As discussed previously, the discontinuity in elements along with cyclic stresses may
promote the initiation and propagation of fatigue cracks. One of the important dis-
continuities is geometrical discontinuity. Sudden changes in geometry, like shoul-
ders, keyways, holes, sharp grooves and notches and so on, are geometrical disconti-
nuities where stress concentration occurs. Stress concentration is a highly localized
effect and most likely leads to fatigue failure. Care must be taken in the design and
manufacture of cyclically loaded elements to reduce stress concentration.
2. Select a material with high endurance limits
Materials are processed by forging, casting, welding, rolling, extrusion, drawing, heat

treatments and so on. During material processing, microscopic surface and subsur-
face defects may arise, possibly due to the inclusion of foreign materials, voids or
crystal discontinuities [5], which may reduce the endurance limits of the material.
It is therefore important to select proper composition and process to reduce these
defects.
3. Improve manufacturing quality to reduce initial microcracks
Surface scratches, tool marks and burrs, as well as poor joint design, improper assem-
bly and other fabrication faults, are the regions where microcracks are likely to initi-
ate. Therefore, precise surface geometry and superior surface finish are highly bene-
ficial for fatigue strength.
4. Increase surface strength by surface treatments
Surface treatments, like case hardening, cold rolling, shot peening and so on, intro-
duce compressive residual stresses at critical stress areas. These compressive residual
stresses are beneficial for the improvement of fatigue strength.

2.3.8 Examples of Strength Analyses

Example Problem 2.1
An alloy shaft carrying a maximum stress of max = 480 MPa at critical section must
6
operate at least 10 cycles at a stress ratio of r = 0.25. The material has properties
of −1 = 480 MPa, = 800 MPa and = 0.2. Select the critical number of cycles
s

7
as N = 10 and material constant as m = 9. Assume the combined influence factor is
0
K = 1.5. If the allowable safety factor is 1.5, determine whether the element will meet

the strength requirement.