Page 385 - Shigley's Mechanical Engineering Design

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360 Mechanical Engineering Design
7–1 Introduction

A shaft is a rotating member, usually of circular cross section, used to transmit power
or motion. It provides the axis of rotation, or oscillation, of elements such as gears,
pulleys, flywheels, cranks, sprockets, and the like and controls the geometry of their
motion. An axle is a nonrotating member that carries no torque and is used to support
rotating wheels, pulleys, and the like. The automotive axle is not a true axle; the term
is a carryover from the horse-and-buggy era, when the wheels rotated on nonrotating
members. A nonrotating axle can readily be designed and analyzed as a static beam, and
will not warrant the special attention given in this chapter to the rotating shafts which are
subject to fatigue loading.
There is really nothing unique about a shaft that requires any special treatment
beyond the basic methods already developed in previous chapters. However, because of
the ubiquity of the shaft in so many machine design applications, there is some advantage
in giving the shaft and its design a closer inspection. A complete shaft design has much
interdependence on the design of the components. The design of the machine itself will
dictate that certain gears, pulleys, bearings, and other elements will have at least been
partially analyzed and their size and spacing tentatively determined. Chapter 18 provides
a complete case study of a power transmission, focusing on the overall design process. In
this chapter, details of the shaft itself will be examined, including the following:

• Material selection
• Geometric layout
• Stress and strength
Static strength
Fatigue strength
• Deflection and rigidity
Bending deflection
Torsional deflection
Slope at bearings and shaft-supported elements
Shear deflection due to transverse loading of short shafts
• Vibration due to natural frequency

In deciding on an approach to shaft sizing, it is necessary to realize that a stress analy-
sis at a specific point on a shaft can be made using only the shaft geometry in the vicinity
of that point. Thus the geometry of the entire shaft is not needed. In design it is usually
possible to locate the critical areas, size these to meet the strength requirements, and then
size the rest of the shaft to meet the requirements of the shaft-supported elements.
The deflection and slope analyses cannot be made until the geometry of the entire
shaft has been defined. Thus deflection is a function of the geometry everywhere,
whereas the stress at a section of interest is a function of local geometry. For this rea-
son, shaft design allows a consideration of stress first. Then, after tentative values for
the shaft dimensions have been established, the determination of the deflections and
slopes can be made.

7–2 Shaft Materials

Deflection is not affected by strength, but rather by stiffness as represented by the mod-
ulus of elasticity, which is essentially constant for all steels. For that reason, rigidity
cannot be controlled by material decisions, but only by geometric decisions.