4 18-1 IntroductionIn 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.
5 Considerations for Shaft Design 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) Reliability
6 Considerations for Shaft Design The geometry of a shaft is that of a stepped cylinder bending.Gears, bearings, and pulleys must always be accurately positionedCommon Torque Transfer ElementsKeysSplinesSetscrewsPinsPress or shrink fitsTapered fits
16 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.
17 18-3 Strength Constraints The design of a shaft involves the study ofStress and strength analyses: Static and FatigueDeflection and rigidityCritical Speed
19 Static or Quasi-Static Loading on Shaft The stress at an element located on the surface of a solid round shaft of diameter d subjected to bending, axial loading, and twisting isNormal stressShear stressNon-zero principal stresses
20 Static or Quasi-Static Loading on Shaft Von Mises stressMaximum Shear Stress Theory
21 Static or Quasi-Static Loading on Shaft 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) becomeVon Mises stress(6-41)Maximum Shear Stress Theory(6-42)
22 Static or Quasi-Static Loading on Shaft Substitution of the allowable stresses from Eqs and 6-40 we find(6-43)Von Mises stress(6-44)(6-45)Maximum Shear Stress Theory(6-46)
23 Fatigue StrengthBending, 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. 7–14, 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
24 Fatigue StrengthThe fluctuating stresses due to bending and torsion are given bywhere Mm and Ma are the midrange and alternating bending moments, Tm and Ta are the midrange and alternating torques, and Kf and Kfs are the fatigue stress concentration factors for bending and torsion, respectively.Assuming a solid shaft with round cross section, appropriate geometry terms can be introduced for c, I, and J resulting in
25 Assuming a solid shaft with round cross section, appropriate geometry terms can be introduced for c, I, and J resulting in
26 Combining these stresses in accordance with the distortion energy failure theory, the von Mises stresses for rotating round, solid shafts, neglecting axial loads, are given by