Dr. A. Aziz Bazounelibvolume6.xyz/.../designofshaftspresentation2.pdfDr. A. Aziz Bazoune Chapter 18:...

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

CH-18 LEC 29 Slide 1



18-1 Introduction ……….92218-2 Geometric Constraints ……….92718-3 Strength Constraints ……….93318-4 Strength Constraints – Additional Methods ……….94018-5 Shaft Materials ……….94418-6 Hollow Shafts ……….94418-7 Critical Speeds (Omitted) ……….94518-8 Shaft Design ……….950




18-1 Introduction ……….92218-2 Geometric Constraints ……….92718-3 Strength Constraints ……….933




� 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.

18-1 Introduction



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



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





Common Types of Shaft Keys.




Common Types of Shaft Pins.




Common Types of Retaining or Snap Rings.




Common Types of Splines.




Rigid Shaft Coupling.



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.




The design of a shaft involves the study of

1. Stress and strength analyses: Static and Fatigue

2. Deflection and rigidity

3. Critical Speed

18-3 Strength Constraints



ME 307 Machine Design I Static or Quasi-Static Loading on Shaft



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

+ − = ± +




( )

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




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


Von Misesstress





( )

( )

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


(6-43)

(6-44)

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

(6-45)

(6-46)




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


ME 307 Machine Design I Fatigue Strength


� 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




Assuming a solid shaft with round cross section, appropriate geometry terms

can be introduced for c, I, and J resulting in



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


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