Page 33 - Analysis and Design of Machine Elements

An Overview of Machine Design
In summary, failure is the response of a machine or machine element to operating 11
loads and service environments. Imperfection in design, materials and manufacturing
may cause failure. Identification of possible failure modes under prescribed operating
condition is an essential step in the early stage of machine element design. It is the
designer’s responsibility to predict, analyse and prevent prospective failure to ensure
a successful design of machine elements or machines throughout a design’s lifetime.

1.3.3 Design Criteria
Safety is always the paramount criterion in machine design [9], as catastrophic failures
result in life losses, property destruction and environmental damage and must be pre-
vented. To provide a safe, reliable and cost-effective machine element, it is essential to
establish design criteria against potential failure modes. The design criteria commonly
used against the previously discussed failure modes include strength, rigidity, life and
wear criteria.

1.3.3.1 Strength Criteria
Strength is the ability to resist loads. It is expressed in terms of ultimate strength, yield
strength and fatigue strength [1]. Almost all kinds of failure modes, including yielding,
fracture, fatigue, pitting, spalling, wear, scoring, scuffing, galling and seizure, are due
to insufficient material strength to withstand loads. Design approaches must satisfy a
strength criterion in the form of a stress-strength relationship, either within an element
or on the element surface, to ensure safe design.
The strength criterion indicates that the actual stresses acting on an element at a
critical location under operating conditions must be less than the allowable stress of
material [ ], expressed as
≤ [ ] (1.1)

The limiting condition to the right of the inequality depends on material properties.
Under a static load, the allowable stress is the material strength divided by the allowable
safety factor. The material strength is the yield strength in tension, compression or shear
for ductile materials; and ultimate strength for brittle materials. Under a fluctuating load,
the material strength is the endurance strength corresponding to the operating condi-
tions. Detailed discussion about endurance strength will be introduced in Chapter 2.
The ability to quantify stress states at a critical location in a machine element is impor-
tant for assessing failure possibility of an element. Stresses are obtained by simplified
calculations according to various loading conditions. For uniaxial loading, the stress
calculation is quite straightforward, using stress formula loaded by basic tension, shear
or bending. For complex loading, a combined stress theory, either the maximum shear
stress theory or the maximum distortion energy theory, is used to calculate multiax-
ial stresses [14, 15]. For contact loading, the contact stress is calculated by the Hertz
formula [16].
Designers must ensure the maximum stresses at critical locations are less than mate-
rial strength by a sufficient margin to guarantee adequate safety for an element. This
lim
margin is the factor of safety, a reasonable measure of relative safety of a load-carrying
element. Thus, an alternate expression for strength criterion by safety factor S is
lim
S = ≥ [S] (1.2)