Page 294 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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absorption properties and low cost. If shafts operate in a corrosive environment or at an
elevated temperature, stainless steel or titanium alloy are required in spite of high costs
or great difficulty with fabrication [6].
If strength is a critical issue in shaft design, a higher strength material like heat-treated
alloy steel may be a proper selection; on the contrary, if deflection is of principle con-
cern, the size of cross section rather than material strength should be increased to
improve rigidity, as stiffness is represented by elastic modulus, which is essentially
constant for all steels [2]. Table 10.1 lists commonly used shaft materials and their
mechanical properties. Because of variations in composition, heat treatments or for-
mation, data listed in the table are the averages for specimens with diameter less than
100 mm. Designers should consult suppliers or arrange tests for material properties for
critical element design.

10.4.3 Design Criteria

As introduced before, the main failure modes in a shaft are fatigue fracture, excessive
deflection and critical speed resonance. A good design indicates that a shaft should have
enough strength to prevent fracture failure, sufficient rigidity to avoid excessive deflec-
tion and acceptable critical speed to prevent resonance.
Generally, most shafts require strength analysis by satisfying strength criteria selected
from Eqs. (10.6)–(10.10), depending on stress states. Slender shafts need to check rigid-
ity by satisfying rigidity criteria listed in Eqs. (10.17), (10.18) and (10.21), depending on
mounted elements. High speed shafts require critical speed analysis by Eqs. (10.23) or
(10.24) to ensure the fundamental natural frequency is significantly above the operating
frequency to avoid violent vibration.

10.4.4 Design Procedure and Guidelines
In shaft design practice, the two tasks of shaft design, that is, load carrying capacity
analysis and structural design, alternate with each other. A general design procedure is
suggested next:
1. Select materials and heat treatments, determine mechanical properties, that is, the
ultimate strength, yield strength, endurance limits and so on.
2. Determine the initial minimum diameter of the shaft
3. Design preliminary structure
– Based on the functional requirement, specify the location of each element to be
mounted on the shaft, including bearings;
– Start from the minimum shaft diameter, determine the diameter and axial length
of each segment of stepped shaft according to the width of the hub of mounted ele-
ments and the space between them. The diameters of each shaft segment should
be integers. The size and tolerance of shaft diameters should be compatible with
mounted elements. The overall length of shaft should be kept small to reduce bend-
ing moments and deflections;
– Propose an initial structure of shaft, considering factors about manufacturing
and assembly; Specify design details such as fillet radii, shoulder heights, keyseat
dimensions and tolerances.