Transcript Shafts and Axles - KFUPM Open Courseware
ME 307 Machine Design I Dr. A. Aziz Bazoune
Dr. A. Aziz Bazoune
King Fahd University of Petroleum & Minerals Mechanical Engineering Department Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 1
ME 307 Machine Design I 18-1 Introduction ……….
922 18-2 Geometric Constraints ……….
927 18-3 Strength Constraints ……….
933 18-4 Strength Constraints – Additional Methods ……….
940 18-5 Shaft Materials ……….
944 18-6 Hollow Shafts ……….
944 18-7 Critical Speeds (Omitted) ……….
945 18-8 Shaft Design ……….
950 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 2
ME 307 Machine Design I 18-1 Introduction ……….
922 18-2 Geometric Constraints ……….
927 18-3 Strength Constraints ……….
933 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 3
ME 307 Machine Design I
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.
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 4
ME 307 Machine Design I
Considerations for Shaft Design
1. 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
2. Stress and Strength
(a) Static Strength (b) Fatigue Strength (c) Reliability
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 5
ME 307 Machine Design I
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 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 6
ME 307 Machine Design I
Common Types of Shaft Keys.
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 7
ME 307 Machine Design I
Common Types of Shaft Keys.
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 8
ME 307 Machine Design I
Common Types of Shaft Pins.
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 9
ME 307 Machine Design I
Common Types of Shaft Pins.
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 10
ME 307 Machine Design I
Common Types of Retaining or Snap Rings.
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 11
ME 307 Machine Design I
Common Types of Splines.
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 12
ME 307 Machine Design I Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 13
ME 307 Machine Design I Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 14
ME 307 Machine Design I
Rigid Shaft Coupling.
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 15
ME 307 Machine Design I Figure 18-2
(a) 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.
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 16
ME 307 Machine Design I
18-3 Strength Constraints
The design of a shaft involves the study of 1. Stress and strength analyses: Static and Fatigue 2. Deflection and rigidity 3. Critical Speed Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 17
ME 307 Machine Design I
Static or Quasi-Static Loading on Shaft
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 18
ME 307 Machine Design I
Static or Quasi-Static Loading on Shaft
The stress at an element located on the surface of a solid round shaft of diameter twisting is
d
subjected to bending, axial loading, and Normal stress Shear stress
x
32
M
d
3 4
F d
2
xy
16
T
d
3
Non-zero principal stresses
A B
x
y
2
x
y
2 2 2
xy
1 2
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 19
ME 307 Machine Design I
Static or Quasi-Static Loading on Shaft Von Mises stress
Maximum Shear Stress Theory
' '
A
2
A B
B
2 1/2 4
d
3 8
M
Fd
2
x
2 3
xy
2 1/2 48
T
2 1/2 max
A
B
2 max 2
d
3 8
M
1 2
x
2 4 2
xy
1 2
Fd
2 64
T
2 1/2
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 20
ME 307 Machine Design I
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
' 16
d
3 4
M
2 3
T
2 1/2 (6-41)
Maximum Shear Stress Theory
max 16
d
3
M
2
T
2 1/2 (6-42)
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 21
ME 307 Machine Design I
Static or Quasi-Static Loading on Shaft
Substitution of the allowable stresses from Eqs. 6-39 and 6-40 we find Von Mises stress
d
1
n
16
n
S y
4
M
2 3
T
2 1/2 1/3 16 3
d S y
4
M
2 3
T
2 1/2 (6-43) (6-44)
Maximum Shear Stress Theory
d
1
n
32
n
S y
M
2
T
2 1/2 1/3 32 3
d S y
M
2
T
2 1/2 (6-45) (6-46)
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 22
ME 307 Machine Design I
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. 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 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 23
ME 307 Machine Design I
Fatigue Strength
The fluctuating stresses due to bending and torsion are given by where
M m
and
M a
are the midrange and alternating bending moments,
T m
and
T a
are the midrange and alternating torques, and terms can be introduced for c, I, and J resulting in
K f
and
K fs
are the fatigue stress concentration factors for bending and torsion, respectively.
Assuming a solid shaft with round cross section, appropriate geometry Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 24
ME 307 Machine Design I Assuming a solid shaft with round cross section, appropriate geometry terms can be introduced for
c, I,
and
J
resulting in Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 25
ME 307 Machine Design I 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 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 26
ME 307 Machine Design I Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 27
ME 307 Machine Design I Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts CH-18 LEC 29 Slide 28