CH18 LEC 29 Slide 1

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Chapter 18
Shafts and Axles
Dr. A. Aziz Bazoune King Fahd University of
Petroleum Minerals Mechanical Engineering
Department
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Chapter Outline
18-1 Introduction .92218-2 Geometric
Constraints .92718-3 Strength Constraints
.93318-4 Strength Constraints Additional
Methods .940 18-5 Shaft Materials
.94418-6 Hollow Shafts .94418-7 Critical
Speeds (Omitted) .945 18-8 Shaft Design
.950
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LECTURE 29
18-1 Introduction .92218-2 Geometric
Constraints .92718-3 Strength Constraints
.933
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18-1 Introduction

• 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.

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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 shafts
• Stress and Strength
• (a) Static Strength
• (b) Fatigue Strength
• (c) Reliability

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Considerations for Shaft Design

• 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
• Keys
• Splines
• Setscrews
• Pins
• Press or shrink fits
• Tapered fits

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Common Types of Shaft Keys.
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Common Types of Shaft Keys.
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Common Types of Shaft Pins.
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Common Types of Shaft Pins.
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Common Types of Retaining or Snap Rings.
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Common Types of Splines.
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Rigid Shaft Coupling.
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• Figure 18-2
• Choose 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.

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18-3 Strength Constraints

• The design of a shaft involves the study of
• Stress and strength analyses Static and Fatigue
• Deflection and rigidity
• Critical Speed

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Static or Quasi-Static Loading on Shaft
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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 is

Normal stress
Shear stress
Non-zero principal stresses
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Static or Quasi-Static Loading on Shaft
Von Mises stress
Maximum Shear Stress Theory
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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) become

Von Mises stress
(6-41)
Maximum Shear Stress Theory
(6-42)
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Static or Quasi-Static Loading on Shaft

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

(6-43)
Von Mises stress
(6-44)
(6-45)
Maximum Shear Stress Theory
(6-46)
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Fatigue Strength

• 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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Fatigue Strength
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