lecture 4

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 carry-over from the horse-and-buggy era, when the wheels rotated on nonrotating members. A non-rotating 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 designapplications, 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 analysis at a specific point on a shaft can be made usingonly 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 requirementsof 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 reason, 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