shafts and axles chapter 29

Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts

ME 307 Machine Design I

Dr. A. Aziz BazouneKing Fahd University of Petroleum King Fahd University of Petroleum

& Minerals& MineralsMechanical Engineering Mechanical Engineering

DepartmentDepartmentCH-18 LEC 29 Slide 1



18-1 18-1 Introduction ……….Introduction ……….92292218-218-2 Geometric Constraints ……….Geometric Constraints ……….92792718-318-3 Strength Constraints ……….Strength Constraints ……….93393318-418-4 Strength Constraints – Additional Methods Strength Constraints – Additional Methods ……….……….94094018-518-5 Shaft Materials ……….Shaft Materials ……….94494418-618-6 Hollow Shafts ……….Hollow Shafts ……….94494418-718-7 Critical Speeds (Omitted) ……….Critical Speeds (Omitted) ……….945945 18-818-8 Shaft Design ……….Shaft Design ……….950950

CH-18 LEC 29 Slide 2



18-1 18-1 Introduction ……….Introduction ……….92292218-218-2 Geometric Constraints ……….Geometric Constraints ……….92792718-318-3 Strength Constraints ……….Strength Constraints ……….933933




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 Introduction18-1 Introduction



ME 307 Machine Design I Considerations for Shaft Considerations for Shaft

DesignDesign

1.1. Deflection and RigidityDeflection 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

2.2.Stress and StrengthStress and Strength(a) Static Strength

(b) Fatigue Strength

(c) Reliability



ME 307 Machine Design I Considerations for Shaft Considerations for Shaft

DesignDesign The geometry of a shaft is that of a stepped cylinder

bending. Gears, bearings, and pulleys must always be accurately

positioned

Common Torque Transfer ElementsCommon Torque Transfer Elements

Keys Splines Setscrews Pins Press or shrink fits Tapered fits





Common Types of Shaft Keys. Common Types of Shaft Keys.




Common Types of Shaft Pins. Common Types of Shaft Pins.




Common Types of Retaining or Snap Rings. Common Types of Retaining or Snap Rings.




Common Types of Splines. Common Types of Splines.




Rigid Shaft Coupling. 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 Constraints18-3 Strength Constraints



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

ShaftShaft



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

ShaftShaftThe 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 d

3

16xy

T

d

Normal stressNormal stress

Shear stressShear stress

Non-zero principal Non-zero principal stressesstresses

1 22

2,2 2

x y x yA B xy




1/2 1/22 2 2 2

1/22 23

' 3

4' 8 48

A A B B x xy

M Fd Td

1 22 2max

1/22 2max 3

14

2 22

8 64

A Bx xy

M Fd Td

Von Von Mises Mises stressstress

Maximum Maximum Shear Shear Stress Stress TheoryTheory

Static or Quasi-Static Loading on Static or Quasi-Static Loading on ShaftShaft




1/22 23

16' 4 3M T

d

1/22 2max 3

16M T

d

(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 Mises Von Mises stressstress





1/31/22 2

1/22 23

164 3

1 164 3

y

y

nd M T

S

M Tn d S

1/31/22 2

1/22 23

32

1 32

y

y

nd M T

S

M Tn d S

Von Mises Von Mises stressstress


(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 StrengthFatigue 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 StrengthFatigue Strength


The fluctuating stresses due to bending and torsion are given by

where 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




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


shafts and axles chapter 29

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