Page 34 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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Safety factors are employed to consider uncertainties and variabilities in loads,
material strength, manufacturing qualities and operation conditions, as well as assump-
tion in stress calculations. The selection of an appropriate value of allowable safety
factor is based primarily on the these considerations, together with design codes and a
designer’s previous experience with similar products and conditions [8]. They should
be carefully chosen to meet the required reliability at a reasonable cost. The allowable
safety factor [S] is generally within the range of 1.25–4 [8–10].
1.3.3.2 Rigidity Criteria
Rigidity is the ability to resist deformation or deflection. It ensures accurate and pre-
cise operation of a machine. All machine elements deform under load, either elastically
or plastically. Excessive deformation or deflection may cause interference between ele-
ments and premature failure due to vibration, wear and fatigue. When deflection is
critical to safety or performance of an element the deflection must be analysed to satisfy
rigidity criterion. Elastic strain, deflection, stiffness and stability are important consid-
erations for the design of some elements.
Criteria for failure due to excessive deflection are often highly dependent on the appli-
cation of machine. For example, machine tool frames must be extremely rigid to main-
tain manufacturing accuracy. Also, in a transmission, the shaft supporting gears must
be rigid enough to avoid excessive deflection that may lead to gear disengagements. The
following criteria are used to assess the rigidity of an element in different forms of deflec-
tion. When an element is subjected to a bending moment M, the deflection y and slope
should satisfy
y ≤ [y] (1.3)

≤ [ ] (1.4)
When an element is subjected to a twisting moment T, the angular deflection should
satisfy
≤ [ ] (1.5)
Detailed calculation of deflection y,slope and angular deflection depends on the
cross-section geometry and loads, which can be referred to in Mechanics of Materials
[14], or by finite element analysis for more complex geometries or loads. The allow-
able values of deflection [y], slope [ ] and angular deflection [ ] are selected by design
requirements.

1.3.3.3 Life Criteria
Normally, it is a requirement that the life L of an element should be longer than the
expected life [L]. Therefore
L ≥ [L] (1.6)

Detailed applications of life criteria can be found in Chapter 11 for the design of rolling
contact bearings.