Page 50 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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Fluctuating or variable loads vary with time during the normal service of an element.
They are typically applied for a long enough time so the element experiences many thou-
sands or millions of stress cycles during its expected life [3]. An example is the load
acting on a pair of meshing gear teeth. Although every machine load is important, it is
estimated that 60–90% of machine elements fail from fluctuating loads due to fatigue
[1].
Shock or impact loads are the loads applied suddenly and rapidly, like the force when
cars crash. When the applied loads vary irregularly in their amplitudes, such as wind
loads acting on wind turbine blades, the loads are called random loads. The latter two
types of loads will not be addressed in this book.

2.1.3 Types of Stresses
Once the external load applied to an element has been determined, stresses generated
within the element called body stresses can be decided. The calculation of tensile or
shear stresses due to tension, shear, toque and bending can be referred to in Mechanics of
Materials [6]. Detailed stress analyses for specific machine elements will be introduced
in the succeeding chapters.
The primary factor considered when specifying stress types is the stress variation.
Fluctuating stresses in a machine often take a sinusoidal form because of the nature of
rotating machinery. Stress variations are characterized by five parameters; maximum
stress , minimum stress , mean (average) stress ,stressamplitude and
max min m a
stress ratio r, as defined in Figure 2.1. If any two of them are known, the others are

readily computed.
The maximum and minimum stresses can be obtained by theoretical stress analysis,
finite element analysis or experimental measurement. The mean stress and stress ampli-
tude are computed by
max + min
= (2.1)
m
2
max − min
= (2.2)
a
2
The behaviour of a material under fluctuating stresses is dependent on the manner of
stress variation, characterized by the stress ratio, as
min
r = (2.3)

max
2.1.3.1 Static Stress
Static stress is generated when an element is subjected to a slowly applied load that is
held at a constant value. Figure 2.1a shows a diagram of stress versus time due to static
loading. Since = , the stress ratio for static stress is r = 1.
max min

(a) (b) (c) (d)
Figure 2.1 Types of stresses.