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Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz Bazoune King Fahd University of Petroleum.

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Presentation on theme: "Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz Bazoune King Fahd University of Petroleum."— Presentation transcript:

1 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz Bazoune King Fahd University of Petroleum & Minerals Mechanical Engineering Department CH-18 LEC 29 Slide 1

2 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I 18-1 Introduction ……….922 18-2Geometric Constraints ……….927 18-3Strength Constraints ……….933 18-4Strength Constraints – Additional Methods ……….940 18-5Shaft Materials ……….944 18-6Hollow Shafts ……….944 18-7Critical Speeds (Omitted) ……….945 18-8Shaft Design ……….950 18-1 Introduction ……….922 18-2Geometric Constraints ……….927 18-3Strength Constraints ……….933 18-4Strength Constraints – Additional Methods ……….940 18-5Shaft Materials ……….944 18-6Hollow Shafts ……….944 18-7Critical Speeds (Omitted) ……….945 18-8Shaft Design ……….950 CH-18 LEC 29 Slide 2

3 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I 18-1 Introduction ……….922 18-2Geometric Constraints ……….927 18-3Strength Constraints ……….933 CH-18 LEC 29 Slide 3

4 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I  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 CH-18 LEC 29 Slide 4

5 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I 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 CH-18 LEC 29 Slide 5

6 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I 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 CH-18 LEC 29 Slide 6

7 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I CH-18 LEC 29 Slide 7 Common Types of Shaft Keys.

8 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I CH-18 LEC 29 Slide 8 Common Types of Shaft Keys.

9 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I CH-18 LEC 29 Slide 9 Common Types of Shaft Pins.

10 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I CH-18 LEC 29 Slide 10 Common Types of Shaft Pins.

11 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I CH-18 LEC 29 Slide 11 Common Types of Retaining or Snap Rings.

12 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I CH-18 LEC 29 Slide 12 Common Types of Splines.

13 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I CH-18 LEC 29 Slide 13

14 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I CH-18 LEC 29 Slide 14

15 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I CH-18 LEC 29 Slide 15 Rigid Shaft Coupling.

16 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I 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. CH-18 LEC 29 Slide 16

17 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I 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 CH-18 LEC 29 Slide 17

18 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I Static or Quasi-Static Loading on Shaft CH-18 LEC 29 Slide 18

19 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I 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 Normal stress Shear stress Non-zero principal stresses CH-18 LEC 29 Slide 19

20 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I Von Mises stress Maximum Shear Stress Theory Static or Quasi-Static Loading on Shaft CH-18 LEC 29 Slide 20

21 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I (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 Mises stress Maximum Shear Stress Theory CH-18 LEC 29 Slide 21

22 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I Von Mises stress 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

23 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I 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

24 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I 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 M m and M a are the midrange and alternating bending moments, T m and T a are the midrange and alternating torques, and 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 terms can be introduced for c, I, and J resulting in

25 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I 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

26 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I 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 CH-18 LEC 29 Slide 26

27 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I CH-18 LEC 29 Slide 27

28 Dr. A. Aziz Bazoune Chapter 18: Axles and Shafts ME 307 Machine Design I ME 307 Machine Design I CH-18 LEC 29 Slide 28


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