Page 51 - Analysis and Design of Machine Elements

Figure 2.2 An example of completely reversed Strength of Machine Elements 29
stress.

2.1.3.2 Completely Reversed Stress
When a tensile stress is followed by the same level of compressive stress over thousands
of cycles, the stress is completely reversed stress. Figure 2.1b shows the diagram of stress
versus time for a completely reversed stress. Because =− , the stress ratio for
min max
completely reversed stress is r =−1 and the mean stress is zero.
An example of a completely reversed stress is a rotating circular shaft loaded in bend-
ing, as shown in Figure 2.2. In the position shown, point b at the bottom of the shaft
experiences a tensile stress, while point d at the top of the shaft has the same magnitude
compressive stress. As the shaft rotates, these two points, as well as all the other points,
experience a complete stress cycle during each revolution.

2.1.3.3 Repeated Stress
When a load is applied and removed many times, the stress generated in a machine
element is repeated stress. As shown in Figure 2.1c, the stress varies from zero to a
maximum value within each cycle. The relations among mean stress, stress amplitude
and the maximum stress can be expressed as = = max /2. The minimum stress is
m
a
zero and the stress ratio is r = 0. An example of repeated stress is the stress on the tooth
surfaces of a pair of meshing gears.

2.1.3.4 Fluctuating Stress
A fluctuating stress is an alternating stress with a nonzero mean value, as shown in
Figure 2.1d. The fluctuating stress can be regarded as the superposition of a completely
reversed stress on a static stress. When an axial load is applied to the shaft shown in
Figure 2.2, the shaft experiences a fluctuating stress.

2.2 Static Strength

To ensure safety of a machine element under static or steady loads, stresses need to be
determined analytically or experimentally and compared with an allowable stress of the
material to satisfy strength criteria discussed in Section 1.3.3. Static strength analysis
involves the consideration of several factors, including loads, stress states (uniaxial or
multiaxial) and material types (ductile or brittle).