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Department p of Material and Engineering g g Design, g , Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

BDA 3083 Notes – Mechanical Engineering Design I

Week 6

Chapter 5

Sh ft Design Shaft D i Prepared by: Mohd Azwir Bin Azlan

BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

Learning Outcomes At the end of this topic topic, the students would be able to apply and appreciate the knowledge to: •

select suitable material for f shaft f design

•

perform load, stress, and power calculations analytically as applied to a shaft components components.

•

design a shaft with some consideration on static and fatigue failure.

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

What you will be learn here?

• 5.1 - Introduction • • • •

5.2 5 2 5.3 54 5.4 5.5

- Shaft Materials - Shaft Layout - Shaft Design for Stress - Limits and Fits

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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CHAPTER 5 – Shaft Design

BDA 3083 – Mechanical Engineering Design I

5 1 – Introduction 5.1 What is shaft?! ~a rotating member, usually of circular cross section ti What it is used for?! ~to transmit power or motion ~It provides the axis of rotation, or oscillation, of elements such as gears, pulleys flywheels, pulleys, flywheels cranks and the like, and controls the geometry of their motion. Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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CHAPTER 5 – Shaft Design

BDA 3083 – Mechanical Engineering Design I

5 1 – Introduction – cont… 5.1 cont What is axle?! An axle is a nonrotating member that carries no torque and

What it is used for?! is used to support rotating wheels, pulleys and etc. Train wheels are affixed to a straight axle, such that both wheels rotate in unison. Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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CHAPTER 5 – Shaft Design

BDA 3083 – Mechanical Engineering Design I

5 1 – Introduction – cont… 5.1 cont

What is spindle?! 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.

Tapered roller bearings used in a mowing-machine spindle. This design represents good practice for situations where one or more torque-transfer elements e e e ts must ust be mounted ou ted outboa outboard. d Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 2 – Shaft Materials 5.2 • Many shafts are made from low carbon, cold-drawn or hot-rolled steel, such as ANSI 1020-1050 steels. • A good practice is to start with an inexpensive, low or medium carbon steel for the first time through the design calculations calculations. • If strength considerations turn out to dominate over deflection, then a higher strength material should be tried, allowing the shaft sizes to be reduced until excess deflection b becomes an iissue. • Shafts usually don’t need to be surface hardened unless they serve as the actual journal of a bearing surface. Typical material choices for surface hardening include carburizing grades of ANSI 1020, 4320, 4820, and 8620. • Cold drawn steel is usually used for diameters under about 3 inches. The nominal diameter of the bar can be left unmachined in areas that do not require fitting of components. • Hot rolled steel should be machined all over.

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 2 – Shaft Materials – cont… 5.2 cont • For large shafts requiring much material removal, the residual stresses may tend to cause warping (bend out of shape - distortion and twisting). • If concentricity is important, it may be necessary to rough machine, then heat treat to remove residual stresses and increase the strength strength, then finish machine to the final dimensions. • In approaching material selection, the amount to be produced is a salient factor. • For low production - turning is the suitable process. • For High production - conservative shaping method (hot or cold forming, casting), and minimum material in the shaft can become a design goal goal. Cast iron may be specified if the production quantity is high, and the gears are to be integrally cast with the shaft. • Stainless steel may be appropriate for some environments – e.g. Involved in food processing. i

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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CHAPTER 5 – Shaft Design

BDA 3083 – Mechanical Engineering Design I

5 3 – Shaft Layout 5.3 Various method to attach element on shaft. snap ring

clamp collar key y hub bearing

taper pin

hub shaft

step

bearing

step

press fit

step

step press fit

axial clearance

sheave frame

frame sprocket

gear

Assembly/Disassembly A bl /Di bl → progressively i l smaller ll di diameter toward d the h ends d Axial clearance → to allow machinery vibration Keys/pins/rings y p g → to secure rotating g elements ( g gear, p pulley, y etc)) Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 3 – Shaft Layout – cont… 5.3 cont • Significant detail is required to completely specify the geometry needed to fabricate a shaft. • The geometry of a shaft is generally that of a stepped cylinder. • The use of shaft shoulders is an excellent means of axially locating the shaft elements and d to t carry any th thrustt loads.

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 3 – Shaft Layout – cont… 5.3 cont Common shaft l di mechanism: loading h i

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 3 – Shaft Layout – cont… 5.3 cont Common torque transfer elements:

• • • • • •

Keys Splines Setscrews Pins Press or shrink fits Tapered fits

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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CHAPTER 5 – Shaft Design

BDA 3083 – Mechanical Engineering Design I

5 3 – Shaft Layout – cont… 5.3 cont Pins:

Round pins

Taper pins

Split tubular spring i pins i

- Pins are used for axial positioning and for the transfer of torque or thrust or both. - Some pins should not be used to transmit very much torque - Weakness – will generate stress concentration to the shaft Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 3 – Shaft Layout – cont… 5.3 cont Keys and keyseats:

Keys are used to transmit torque from a component to the shaft. shaft Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 3 – Shaft Layout – cont… 5.3 cont Spline shaft and Hub:

- Used when large amounts of torque are to be transferred - Stress St concentration t ti is i generally ll quite it moderate d t Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 3 – Shaft Layout – cont… 5.3 cont Locational device:

• • • • • • • •

Nut and washer Sleeve Shaft shoulder Ring and groove Setscrew Split hub or tapered two-pieces hub Collar and screw Pins

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 3 – Shaft Layout – cont… 5.3 cont Nut and Washer:

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 3 – Shaft Layout – cont… 5.3 cont Sleeve:

is a tube or enclosure used to couple two mechanical components together, or t retain to t i two t components t together; t th this thi permits it two t equally-sized ll i d appendages d to be connected together via insertion and fixing within the construction.

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 3 – Shaft Layout – cont… 5.3 cont Shaft shoulder :

The use of shaft shoulders is an excellent means of axially locating the shaft elements and to carry any thrust loads.

Example:

(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. Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 3 – Shaft Layout – cont… 5.3 cont Spring loaded Retaining Ring :

• • •

Most p popular p used because g give an economical solution to some problem. “Bowed” retaining rings provide restoring forces to the components p being g held. Flat retaining rings allow small amounts of axial motion of the held component.

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 3 – Shaft Layout – cont… 5.3 cont Set Screw :

is a type of screw generally used to secure an object within another object. bj Th The set screw passes through a threaded hole in the outer object and is tightened against i t th the iinner object bj t tto preventt it from moving relative to the outer object.

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 3 – Shaft Layout – cont… 5.3 cont Split Hub :

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 3 – Shaft Layout – cont… 5.3 cont Collar and Screw :

• is a simple, short ring fastened over a rod or shaft • found in many power transmission applications most notably motors and gearboxes. • used as mechanical stops, locating components, and bearing faces. The simple design lends itself to easy installation - no shaft damage. • Since the screws compress the collar, a uniform distribution of force is imposed on the shaft, leading to a holding power that is nearly twice that of set screw collars.

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 4 – Shaft Design for Stress 5.4 Critical Location :

• It is not necessary to evaluate the stresses in a shaft at every point; a few potentially critical locations will be adequate adequate. • Critical locations will usually be on the outer surface, at axial locations where the bending moment is large, where the torque is present, and where stress concentrations exist. • Most shafts will transmit torque through a portion of the shaft. Typically the torque comes into the shaft at one gear and leaves the shaft at another gear. The torque is often relatively constant at steady state operation. • The bending moments on a shaft can be determined by shear and bending moment diagrams. diagrams Since most shaft problems incorporate gears or pulleys that introduce forces in two planes, the shear and bending moment diagrams will generally be needed in two planes. Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 4 – Shaft Design for Stress – cont… 5.4 cont Critical Location :

• Resultant moments are obtained by summing moments as vectors at points of interest along the shaft shaft. In situations where a bearing is located at the end of the shaft, stresses near the bearing are often not critical since the bending moment is small. • Axial stresses on shafts due to the axial components transmitted through helical gears or tapered roller bearings will almost always be negligibly small compared to the bending moment stress. They are often also constant, so they contribute littl tto ffatigue. little ti • Consequently, it is usually acceptable to neglect the axial stresses induced by the gears and bearings g g when bending g is p present in a shaft. If an axial load is applied pp to the shaft in some other way, it is not safe to assume it is negligible without checking magnitudes.

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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CHAPTER 5 – Shaft Design

BDA 3083 – Mechanical Engineering Design I

5 4 – Shaft Design for Stress – cont… 5.4 cont Shaft Stresses :

• The fluctuating stresses due to bending and torsion are given by: -

σa = K f

M ac I

; σm = K f

M mc I

τ a = K fs

Tm c Ta c K τ = ; m fs J J

Under many conditions, the axial components F is either zero or so small that it can be neglected.

• A Assuming i a solid lid shaft h ft with ith round d cross section, ti appropriate i t geometry t terms t can be introduced for c, I, and J resulting in

σa = K f

32 M a 32 M m = K σ ; m f πd 3 πd 3

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

τ a = K fs

16Ta 16Tm τ = K ; m fs πd 3 πd 3 26

CHAPTER 5 – Shaft Design

BDA 3083 – Mechanical Engineering Design I

5 4 – Shaft Design for Stress – cont… 5.4 cont Shaft Stresses :

• Combining bending and shear stresses accordance to the von Misses stress at two stress element are given by: 2

σ 'a = (σ + 3τ )

⎡⎛ 32 K f M a ⎞ ⎛ 16 K fsf Ta ⎞ = ⎢⎜⎜ + 3⎜⎜ 3 3 ⎟ ⎟ d π d π ⎢⎣⎝ ⎝ ⎠ ⎠

2 1/ 2

σ 'm = (σ + 3τ )

⎡⎛ 32 K f M m ⎞ ⎛ 16 K fsTm ⎞ = ⎢⎜⎜ + 3⎜⎜ 3 3 π d π d ⎢⎣⎝ ⎠ ⎠ ⎝

2 1/ 2

2 a

2 1/ 2 a

2

2 m

2 1/ 2 m

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

⎤ ⎥ ⎦⎥

⎤ ⎥ ⎥⎦

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 4 – Shaft Design for Stress – cont… 5.4 cont Shaft Stresses :

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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CHAPTER 5 – Shaft Design

BDA 3083 – Mechanical Engineering Design I

5 4 – Shaft Design for Stress – cont… 5.4 cont DE-Goodman DE Goodman : Fatigue failure curve on the modified Goodman diagram

1 16 = 3 n πd

⎧1 2 2 ⎨ 4( K f M a ) + 3( K fsTa ) ⎩ Se

[

]

1/ 2

[

1 + 4( K f M m ) 2 + 3( K fsTm ) 2 Sut

]

1/ 2

⎫ ⎬ ⎭

Equation for the minimum diameter

⎛ 16n ⎧ 1 2 2 ⎜ d =⎜ 4 ( K M ) 3 ( K T ) + ⎨ f a fs a S π ⎩ e ⎝

[

]

1/ 2

[

1 4( K f M m ) 2 + 3( K fsTm ) 2 + Sut

]

1/ 2

⎫⎞ ⎬ ⎟⎟ ⎭⎠

1/ 3

This criteria does not guard against yielding, so required separate check for possibility of static failure (yield occur) in the first load cycle. cycle Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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CHAPTER 5 – Shaft Design

BDA 3083 – Mechanical Engineering Design I

5 4 – Shaft Design for Stress – cont… 5.4 cont DE-Gerber DE Gerber : Fatigue failure curve on the Gerber diagram

where

2 1/ 2 ⎫ ⎧ ⎡ ⎛ 2 BS e ⎞ ⎤ ⎪ 1 8A ⎪ ⎟⎟ ⎥ ⎬ = 3 ⎨1 + ⎢1 + ⎜⎜ n πd S e ⎪ ⎢ ⎝ ASut ⎠ ⎥ ⎪ ⎦ ⎭ ⎩ ⎣

A = 4( K f M a ) 2 + 3( K fsTa ) 2 B = 4( K f M m ) 2 + 3( K fsTm ) 2

Equation for the minimum diameter

⎛ ⎧ ⎜ 8nA ⎪ ⎡ ⎛ 2 BS e ⎞ d =⎜ ⎨1 + ⎢1 + ⎜⎜ ⎟ π S AS ⎢ ut ⎠ ⎜ e ⎪ ⎣ ⎝ ⎩ ⎝

2 1/ 2

⎤ ⎥ ⎥⎦

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

1/ 3

⎫⎞ ⎪ ⎬ ⎪⎭ ⎟ ⎠

This criteria does not guard against yielding so required separate check for yielding, possibility of static failure (yield occur) in the first load cycle.

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5 4 – Shaft Design for Stress – cont… 5.4 cont DE-ASME DE ASME Elliptic : Fatigue failure curve on the ASME Elliptic diagram

2 2 2 2 ⎡ ⎛ K f Mm ⎞ ⎛ K fsTm ⎞ ⎤ ⎛ K fsTa ⎞ 1 16 ⎢ ⎛ K f M a ⎞ ⎟ ⎥ ⎟ + 3⎜ ⎟⎟ + 4⎜ ⎟⎟ + 3⎜⎜ = 3 4⎜⎜ ⎜ S ⎟ ⎜ S ⎟ ⎥ Se ⎠ n πd ⎢ ⎝ S e ⎠ y ⎝ ⎝ ⎠ ⎝ y ⎠ ⎦ ⎣

1/ 2

Equation for the minimum diameter

⎧ 2 2 ⎡ ⎛ K f Mm ⎞ ⎛ K fsTm ⎞ K M K T ⎛ fs a ⎞ ⎪16n ⎢ ⎛ f a ⎞ ⎟ ⎟ + 3⎜ ⎟⎟ + 4⎜ ⎟⎟ + 3⎜⎜ 4⎜⎜ d =⎨ ⎟ ⎜ ⎟ ⎜ π S S S S ⎢ e e y y ⎝ ⎠ ⎝ ⎠ ⎪ ⎝ ⎠ ⎝ ⎠ ⎣ ⎩ 2

2 1/ 2

⎤ ⎥ ⎥ ⎦

1/ 3

⎫ ⎪ ⎬ ⎪ ⎭

This criteria takes yielding into account, but is not entirely conservative, so also required separate check for possibility of static failure (yield occur) in the first load cycle. cycle Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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5 4 – Shaft Design for Stress – cont… 5.4 cont DE-Soderberg DE Soderberg : Fatigue failure curve on the Soderberg diagram

1 16 = 3 n πd

⎧⎪ 1 2 2 ⎨ 4( K f M a ) + 3( K fsTa ) ⎪⎩ S e

[

]

1/ 2

[

1 + 4( K f M m ) 2 + 3( K fsTm ) 2 S yt

]

1/ 2

⎫⎪ ⎬ ⎪⎭

Equation for the minimum diameter

⎛ 16n ⎧⎪ 1 2 2 ⎜ d= 4 ( K M ) 3 ( K T ) + f a fs a ⎜ π ⎪⎨ S e ⎩ ⎝

[

]

1/ 2

[

1 4( K f M m ) 2 + 3( K fsTm ) 2 + S yt

]

1/ 2

⎫⎪ ⎞ ⎬ ⎟⎟ ⎭⎪ ⎠

1/ 3

This criteria inherently guards against yielding, so it is not required to check for possibility of static failure (yield occur) in the first load cycle. cycle Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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CHAPTER 5 – Shaft Design

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5 4 – Shaft Design for Stress – cont… 5.4 cont Check for yielding :

ny =

Factor of safety

where

σ 'max = (σ ' +σ ' 2 a

Sy

σ 'max

)

2 1/ 2 m

⎡⎛ 32 K f ( M a + M m ) ⎞ ⎛ 16 K fs (Ta + Tm ) ⎞ = ⎢⎜⎜ + 3⎜⎜ 3 3 π d π d ⎠ ⎠ ⎝ ⎣⎢⎝ 2

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

2 1/ 2

⎤ ⎥ ⎥⎦

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 4 – Shaft Design for Stress – cont… 5.4 cont For a rotating shaft with constant bending and torsion, the bending stress is completely reversed and the torsion is steady. Therefore

σm = 0

τa = 0

These will simply drops out some of previously terms.

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 4 – Shaft Design for Stress – cont… 5.4 cont Example 5 5-11 :

At a machined shaft shoulder the small diameter d is 28 mm mm, the large diameter D is 42 mm, and the fillet radius is 2.8 mm. The bending moment is 142.4 Nm and the steady torsion moment is 124.3 Nm. The heat-treated steel shaft has an ultimate strength of Sut = 735 MPa and a yield strength of Sy = 574 MPa. The reliability goal is 0.99. ((a)) Determine the fatigue g factor of safety y of the design g using g each of the fatigue failure criteria described in this section. (b) Determine the yielding factor of safety.

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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CHAPTER 5 – Shaft Design

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5 4 – Shaft Design for Stress – cont… 5.4 cont Solution 5 5-11 :

M a = 142.4 Nm

Ta = 0 Nm

M m = 0 Nm

Tm = 124.3 Nm

a) Determine the fatigue factor of safety of the design:

D 42 = = 1.50 d 28 r 2. 8 = = 0.10 d 28

Kt = 1.68 (figure A-15-9) Kts = 1.42 (figure A-15-8)

r = 2.8

q = 0.85 0 85 (figure 4 4-1) 1)

Sut = 0.735 GPa

qs = 0.92 (figure 4-2)

K f = 1 + 0.85(1.68 − 1) = 1.58

K fs = 1 + 0.92(1.42 − 1) = 1.39 Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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5 4 – Shaft Design for Stress – cont… 5.4 cont S e ' = 0.5(735) = 367.5 MPa

k a = 4.51(735) −0.265 = 0.787

S e = (0.787)(0.87)(0.8814)(367.5) = 205 05 MPa

⎛ 28 ⎞ kb = ⎜ ⎝ 7.62 ⎠

⎧1 2 ⎨ 4( K f M a ) ⎩ Se

[

[

]

1/ 2

+

[

1 3( K fsTm ) 2 Sut

⎧ 4(1.58(142.4)) 2 16 ⎪ = ⎨ π (0.028)3 ⎪ 205 x106 ⎩

]

1/ 2

= 0.87

kc = k d = k f = 1.0

Applying Eq. DE-Goodman criteria gives

1 16 = 3 n πd

−0.107

]

1/ 2

⎫ ⎬ ⎭

ke = 0.814

[3(1.39(124.3)) ] + 2

735 x106

1/ 2

⎫ ⎪ ⎬ ⎪⎭

= 232004(2.195 x10 −6 + 0.407 x10 −6 ) = 0.604

∴ n = 1.65 Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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5 4 – Shaft Design for Stress – cont… 5.4 cont Similarly, apply same technique for other failure criteria,

∴ n = 1.87

DE-Gerber

∴n = 1.88

DE ASME Elliptic DE-ASME

∴n = 1.56

DE-Soderberg

b) Determine the Yield factor of safety : 2

2

⎛ 32(1.58)(142.4) ⎞ ⎛ 16(1.40)(124.3) ⎞ ⎟⎟ + ⎜⎜ ⎟⎟ = 125.4 3 3 ⎠ ⎝ π (0.028) ⎠ ⎝ π (0.028)

σ 'max = ⎜⎜

∴ ny =

Sy

σ 'max

574 = = 4.58 125.4

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

5 5 – Limits and Fits 5.5 3 types of fitting

Cl Clearance Fit Fits. No interference occur.

Interference Fits. An interference fit is the condition that exist when, due to the limits of the dimensions, mating parts must be pressed together.

Transition Fits. The fit can have either clearance or interference.

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 5 – Limits and Fits – cont… 5.5 cont Capital p letters always y refer to the hole; lowercase letters are used for the shaft.

Definitions applied to a cylindrical fit.

D = basic size of hole d = basic size of shaft δu = upper deviation δl = lower deviation δF = fundamental deviation D = tolerance grade for hole d = tolerance grade for shaft Note that these quantities are all deterministic deterministic. Thus, for the hole, Dmax = D + ∆D Dmin = D For shafts with clearance fits c, c d d, ff, g g, and h h, dmax = d + δF dmin = d + δF − ∆d For shafts with interference fits k, n, p, s, and u, dmin = d + δF dmax = d + δF + ∆d Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 5 – Limits and Fits – cont… 5.5 cont Table 5–1 Descriptions of Preferred Fits Using the Basic Hole System Source: Preferred Metric Limits and Fits, ANSI B4.2-1978. See also BS 4500.

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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CHAPTER 5 – Shaft Design

5 5 – Limits and Fits – cont… 5.5 cont Table A–11 A Selection of International Tolerance Grades—Metric Series (Size Ranges Are for Over the Lower Limit and Including the Upper Limit. All Values Are in Millimeters) Source: Preferred Metric Limits and Fits Fits, ANSI B4 B4.2-1978. 2 1978 See also BSI 4500. 4500

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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BDA 3083 – Mechanical Engineering Design I

CHAPTER 5 – Shaft Design

5 5 – Limits and Fits – cont… 5.5 cont Table A–12 Fundamental Deviations for Shafts—Metric Series ((Size Ranges g Are for Over the Lower Limit and Including the Upper Limit. All Values Are in Millimeters) Source: Preferred Metric Limits and Fits , ANSI B4.2-1978. See also BSI 4500.

Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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5 5 – Limits and Fits – cont… 5.5 cont Example 5-2 : Find the shaft and hole dimensions for a loose running fit with a 34-mm basic size. Solution 5 5-2 2: From Table 5–1, the ISO symbol is 34H11/c11. From Table A–11, we find that tolerance grade IT11 is 0 0.160 160 mm. mm The symbol 34H11/c11 therefore says that ∆D = ∆d = 0 0.160 160 mm mm. Using Eq. (Dmax = D + ∆D) for the hole, we get Dmax = 34 + 0 0.160 160 = 34 34.160 160 mm

Dmin = D = 34.000 34 000 mm

The shaft is designated as a 34c11 shaft. From Table A–12, the fundamental deviation is δF = −0.120 0 120 mm. U Using i E Eq. “for “f shaft h ft with ith clearance l fit fits”, ” we gett the th shaft h ft dimensions di i dmax = d + δF = 34 + (−0.120) = 33.880 mm dmin = d + δF − ∆d = 34 + (−0.120) (−0 120) − 0.160 0 160 = 33.720 33 720 mm Department of Material and Engineering Design, Faculty of Mechanical and Manufacturing Engineering, University of Tun Hussein Onn Malaysia (UTHM) Johor.

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