In machinery, the general term shaft refers to a member, usually of circular cross-section, which supports gears, sprockets, wheels, rotors, etc., and which is subjected to torsion and to transverse or axial loads acting singly or in combination.An axle is a non-rotating member that supports wheels, pulleys, and carries no torque.A spindle is a short shaft. Terms such as lineshaft, headshaft, stub shaft, transmission shaft, countershaft, and flexible shaft are names associated with special usage.CH-18 LEC 29 Slide *

Deflection and Rigidity(a) Bending deflection(b) Torsional deflection(c) Slope at bearings and shaft supported elements(d) Shear deflection due to transverse loading of shorter shaftsStress and Strength(a) Static Strength(b) Fatigue Strength(c) ReliabilityCH-18 LEC 29 Slide *

The geometry of a shaft is that of a stepped cylinder bending.Gears, bearings, and pulleys must always be accurately positioned

Common Torque Transfer Elements

KeysSplinesSetscrewsPinsPress or shrink fitsTapered fits

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CH-18 LEC 29 Slide *Common Types of Shaft Keys.

CH-18 LEC 29 Slide *Common Types of Shaft Keys.

CH-18 LEC 29 Slide *Common Types of Shaft Pins.

CH-18 LEC 29 Slide *Common Types of Shaft Pins.

CH-18 LEC 29 Slide *Common Types of Retaining or Snap Rings.

CH-18 LEC 29 Slide *Common Types of Splines.

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CH-18 LEC 29 Slide *Rigid Shaft Coupling.

Figure 18-2Choose a shaft configuration to support and locate the two gears and two bearings. (b) Solution uses an integral pinion, three shaft shoulders, key and keyway, and sleeve. The housing locates the bearings on their outer rings and receives the thrust loads.(c) Choose fanshaft configuration. (d) Solution uses sleeve bearings, a straight-through shaft, locating collars, and setscrews for collars, fan pulley, and fan itself. The fan housing supports the sleeve bearings.CH-18 LEC 29 Slide *

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The stress at an element located on the surface of a solid round shaft of diameter d subjected to bending, axial loading, and twisting is

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Under many conditions, the axial force F in Eqs. (6-37) and (6-38) is either zero or so small that its effect may be neglected. With F = 0, Eqs. (6-37) and (6-38) become

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Substitution of the allowable stresses from Eqs. 6-39 and 6-40 we find

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CH-18 LEC 29 Slide *Bending, torsion, and axial stresses may be present in both midrange and alternating components.

For analysis, it is simple enough to combine the different types of stresses into alternating and midrange von Mises stresses, as shown in Sec. 714, p. 361.

It is sometimes convenient to customize the equations specifically for shaft applications.

Axial loads are usually comparatively very small at critical locations where bending and torsion dominate, so they will be left out of the following equations.

The fluctuating stresses due to bending and torsion are given by

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