Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I Dr. A. Aziz Bazoune King Fahd University of Petroleum & Minerals King Fahd University of Petroleum & Minerals King Fahd University of Petroleum & Minerals King Fahd University of Petroleum & Minerals Mechanical Engineering Department Mechanical Engineering Department Mechanical Engineering Department Mechanical Engineering Department CH-18 LEC 29 Slide 1
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Dr. A. Aziz Bazounelibvolume6.xyz/.../designofshaftspresentation2.pdfDr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I Considerations for Shaft Design 1. Deflection
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Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts
ME 307 Machine Design I
Dr. A. Aziz Bazoune
King Fahd University of Petroleum & MineralsKing Fahd University of Petroleum & MineralsKing Fahd University of Petroleum & MineralsKing Fahd University of Petroleum & Minerals
Mechanical Engineering DepartmentMechanical Engineering DepartmentMechanical Engineering DepartmentMechanical Engineering Department
1. Stress and strength analyses: Static and Fatigue
2. Deflection and rigidity
3. Critical Speed
18-3 Strength Constraints
CH-18 LEC 29 Slide 17
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts
ME 307 Machine Design I Static or Quasi-Static Loading on Shaft
CH-18 LEC 29 Slide 18
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts
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 d subjected to bending, axial loading, and twisting is
3 2
32 4x
M F
d dσ
π π= +
3
16xy
T
dτ
π=
Normal stress
Shear stress
Non-zero principal stresses
1 22
2,
2 2
x y x y
A B xy
σ σ σ σσ σ τ
+ − = ± +
CH-18 LEC 29 Slide 19
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts
ME 307 Machine Design I
( )
1/2 1/22 2 2 2
1/22 2
3
' 3
4' 8 48
A A B B x xy
M Fd Td
σ σ σ σ σ σ τ
σπ
= − + = +
= + +
( )
( )
1 22 2
max
1/22 2
max 3
14
2 2
28 64
A Bx xy
M Fd Td
σ στ σ τ
τπ
−= = +
= + +
Von Mises
stress
Maximum Shear Stress Theory
Static or Quasi-Static Loading on Shaft
CH-18 LEC 29 Slide 20
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts
ME 307 Machine Design I
1/22 2
3
16' 4 3M T
dσ
π = +
1/22 2
max 3
16M T
dτ
π = +
(6-41)
(6-42)
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
Static or Quasi-Static Loading on Shaft
Von Misesstress
Maximum Shear Stress Theory
CH-18 LEC 29 Slide 21
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts
ME 307 Machine Design I
( )
( )
1/3
1/22 2
1/22 2
3
164 3
1 164 3
y
y
nd M T
S
M Tn d S
π
π
= +
= +
( )
( )
1/3
1/22 2
1/22 2
3
32
1 32
y
y
nd M T
S
M Tn d S
π
π
= +
= +
Von Misesstress
Maximum Shear Stress Theory
(6-43)
(6-44)
Substitution of the allowable stresses from Eqs. 6-39 and 6-40 we find
(6-45)
(6-46)
Static or Quasi-Static Loading on Shaft
CH-18 LEC 29 Slide 22
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts
ME 307 Machine Design I Fatigue Strength
CH-18 LEC 29 Slide 23
� 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
ME 307 Machine Design I Fatigue Strength
CH-18 LEC 29 Slide 24
� The fluctuating stresses due to bending and torsion are given by
where Mm and Ma are the midrange and alternating bending moments, Tmand 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
Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts
ME 307 Machine Design I
CH-18 LEC 29 Slide 25
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
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