gate machine design book

8/10/2019 GATE Machine Design Book

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Machine Design

For

Mechanical Engineering

By

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Syllabus Machine Design

THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30 th Cross, 10 th Main, Jayanagar 4 th Block, Bangalore-11080 65700750 i f @ h d h d b h d

Syllabus for Machine Design

Design for static and dynamic loading; failure theories; fatigue strength and the S-Ndiagram; principles of the design of machine elements such as bolted, riveted andwelded joints, shafts, spur gears, rolling and sliding contact bearings, brakes andclutches.

Analysis of GATE Papers(Machine Design)

Year Percentage of marks Overall Percentage

2013 6.00

6.48

2012 8.00

2011 3.00

2010 6.00

2009 6.00

2008 9.33

2007 11.33

2006 5.33

2005 3.33


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Content Machine Design

THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30 th Cross, 10 th Main, Jayanagar 4 th Block, Bangalore-11080 65700750 i f @ h d C i h d W b h d P i

C O N T E N T S

Chapters Page No.

1. Design for static Loading 1 - 18 Introduction 1 Theories of Failure 1 - 7 Solved Examples 8 - 13

Assigment 1 14- 15 Assigment 2 15 - 16 Answer Keys 17 Explanations 17 - 18

2. Design for Dynamic Loading 19 - 43 Introduction 19 Stress Concentration 19 20

Fatigue and Endurance Limit 21 31 Solved Examples 32 36 Assignment 1 37 38 Assignment 2 38 39 Answer Keys 40 Explanations 40 43

#3. Design of Joints 44-69 Introduction 44 Riveted Joints 44 51 Bolted/Screw Joints 51 57 Solved Examples 58 63 Assignment 1 64 65 Assignment 2 65 66 Answer Keys 67 Explanations 67 69


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THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30 th Cross, 10 th Main, Jayanagar 4 th Block, Bangalore-11080 65700750 i f @ h d C i h d W b h d P ii

4. Design of Shaft and Shaft Components 70-89 Introduction 70 Shaft design for stress 70 72 Shaft components 72 78 Solved Example 79 83 Assignment 1 84 Assignment 2 85 86 Answer Keys 87 Explanations 87 89

5. Design of Bearing 90-112 Introduction 90 Rolling contact Bearings 90 96 Bearing Life 96 99 Sliding contact/Journal Bearing 99 103 Solved Example 104 106 Assignment 1 107 108 Assignment 2 108 109

Answer Keys 110 Explanations 110 112

6. Design of Brakes and Clutches 113-135 Introduction 113 Brake Design 113 118 Clutch Design 119 124 Solved Example 125 127 Assignment 1 128 129 Assignment 2 129 131 Answer Keys 132 Explanations 132 135

7. Design of Spur Gears 136-150 Introduction 136 Gear Nomenclature 136 138 Spur Gear: Theory of Machines 138


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THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30 th Cross, 10 th Main, Jayanagar 4 th Block, Bangalore-11080 65700750 i f @ h d C i h d W b h d P iii

Lewis Equation Beam strength of gear teeth 138 139 Permissible working stress 139 141

Solved Example 142 145 Assignment 1 146 Assignment 2 147 Answer Keys 148 Explanations 148 150

Module Test 151-161

Test Questions 151 156

Answer Keys 157

Explanations 157 161

Reference Books 162


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Chapter 1 Machine Design

THE GATE ACADEMY PVT.LTD. H.O.: #74, Keshava Krupa (third Floor), 30 th Cross, 10 th Main, Jayanagar 4 th Block, Bangalore-11080 65700750 i f @ h d C i h d W b h d P 1

CHAPTER 1

Design for Static Loading

Introduction

A static load is a stationary force or couple applied to a member. To be stationary, the force orcouple must be unchanging in magnitude, point or points of application and direction. A staticload can produce axial tension or compression, a shear load, a bending load, a torsional load, orany combination of these. To be considered static, the load cannot change in any manner. In mosttesting of those properties of materials that relate to the stress-strain diagram, the load isapplied gradually, to give sufficient time for the strain to fully develop. Furthermore, thespecimen is tested to destruction, and so the stresses are applied only once. Testing of this kindis applicable, to what are known as static conditions; such conditions closely approximate theactual conditions to which many structural and machine members are subjected. Another

important term in design is failure.The definition of failure varies depending upon thecomponent and its application. Failure can mean a part has separated into two or more pieces;has become permanently distorted, thus ruining its geometry; has had its reliabilitydowngraded; or has had its function compromised, whatever the reason.

Theories of Failure

Events such as distortion, permanent set, cracking and rupturing are among the ways that amachine element fails. In uni-axial tension test the failure mechanisms is simple as elongationsare largest in the axial direction, so strains can bThe failure conclusion becomes challeng-axial or tri-axial.Unfortunately, there is no universal theory of failure for the general case of material propertiesand stress state. Instead, over the years several hypotheses have been formulated and tested,

leading to todays accepted practices. These used to analyse the failure of materials.

Structural metal behaviour is typically classified as being ductile or brittle, although underspecial situations, a material normally considered ductile can fail in a brittle manner Ductile

materials are normally classified such that f

0.05 and have an identifis often the same in compression as in tension (S yt = S yc = S y ). Brittle materials, f < 0.05, do notexhibit identifiable yield strength, and are typically classified by ultimate tensile andcompressive strengths, S ut and S uc , respectively (where S uc is given as a positive quantity).

The generally accepted theories are:

Ductile Materials (yield criteria)

Maximum shear stress (MSS) Distortion energy (DE) Octahedral shear stress theory

Brittle Materials (fracture criteria)


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Maximum normal stress (MNS)

Maximum-Shear-Stress Theory for Ductile Materials

The maximum-shear-stress theory predicts that yielding begins whenever the maximum shearstress in any element equals or exceeds the maximum shear stress in a tension test specimen ofthe same material when that specimen begins to yield. The MSS theory is also referred to as theTresca or Guest theory. Many theories are postulated on the basis of the consequences seen fromtensile tests. As a strip of a ductile material is subjected to tension, slip lines (called Lder lines)form at approximately 45 with the axis of the strip. These slip lines are the beginning of yield,and when loaded to fracture, fracture lines are also seen at angles approximately 45 with theaxis of tension. Since the shear stress is maximum at 45 from the axis of tension, it can beconsidered as the mechanism of failure.MSS theory is an acceptable but conservative predictorof failure; and can be applied to many cases where over design is not a problem.

Recall that for simple tensile stress, = P/A.And the maximum shear stress occurs on a surface45 from the tensile surface with a magnitude of = /2. So the maximum shear stress atyield is = /2. For a general state of stress, three principal stresses can be determined andordered such that . The maximum shear stress is then = )/2 Thus, fora general state of stress, the maximum-shear-stress theory predicts yielding when

= Note that this implies that the yield strength in shear is given by

=0.5 Which as we will see later is about 15 percent low (conservative)

For design purposes, equation can be modified to incorporate a factor of safety, n. Thus

= nor =n Distortion-Energy Theory for Ductile Materials The von Mises or von Mises Hencky theory)

The distortion-energy theory predicts that yielding occurs when the distortion strain energy perunit volume reaches or exceeds the distortion strain energy per unit volume for yield in simpletension or compression of the same material. The distortion-energy (DE) theory originated fromthe observation that ductile materials stressed hydrostatically exhibited yield strengths greatlyin excess of the values given by the simple tension test. Therefore it was postulated that yieldingwas not a simple tensile or compressive phenomenon at all but, rather that it was relatedsomehow to the angular distortion of the stressed element.To develop the theory, note in Fig. a, the unit volume subjected to any three-dimensional stress

state designated by the stresses 1, 2, and 3. The stress state shown in Fig. b is one ofhydrostatic tension due to the stresses av acting in each of the same principal directions as inFig. a. The formula for av is simply = (a)


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Thus the element in Fig. b undergoes pure volume change, that is no angular distortion. If we

regard av

as a component of 1

, 2

and 3, then this component can be subtracted from them,

resulting in the stress state shown in Fig. c. This element is subjected to pure angular distortionthat is, no volume change.

(a) Element with triaxial stresses; this element undergoes both volume change and angulardistortion.

(b) Element under hydrostatic tension undergoes only volume change(c) Element has angular distortion without volume change.

The strain energy per unit volume for simple tension is u = . For the elements of figure (a)the strain energy per unit volume is u = [ ]. Substituting equation for theprincipal strain gives

=[ )] ) The strain energy for producing only volume change u can be obtained by substituting for, , and in equation (b). The result isu= E ) . ) If we now substitute the square of equation (a) in equation (c) and simplify the expression weget

= [ ] ) Then the distortion energy is obtained by subtracting equation (d) from equation (b). This gives

u=u u= E ) ) ) )

=

) ) )


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Maximum-Normal-Stress Theory for Brittle Materials

The maximum-normal-stress (MNS) theory states that failure occurs whenever one of the threeprincipal stresses equals or exceeds the strength. Again we arrange the principal stresses for ageneral stress state in the ordered form . This theory then predicts that failureoccurs whenever

or (p)where S ut and S uc are the ultimate tensile and compressive strengths respectively, given aspositive quantities.

For plane stress, with the principal stresses with ,Eq. (p) can be written as

or (q)which is plotted in Fig. a. As before, the failure criteria equations can be converted to designequations. We can consider two sets of equations for load lines where as

Note that the distortion energy is zero if ==.For the simple tensile test, at yield = and ==0 and the Eq. (e) the distortion energyis

u= vE f) So for the general of stress given by Eq. (e) yield is predicated if Eq. (e) equals or exceeds Eq. (f)this gives

)

0

)


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) ) )/

g) If we had a simple case of tension , then yie. Thus, the left of Eq. (g)can be thought of as a single, equivalent or effective stress for the entire general state of stressgiven by , , and . This effective stress is usually called the von Mises stress, named afterDr. R. von Mises, who contributed to the theory. Thus Eq. (g) for yield, can be written as

) where the von Mises stress is

= ) ) )/ )

For plane stress, let and be the two nonzero principal stresses. Then from Eq. (i) we get= ) . ) Octahedral- Shear Stress Theory

Octahedral-shear-stress theory is an extension of Distortion-Energy theory and it is based on theassumption that critical quantity is the shearing stress on the octahedral plane.

Consider an isolated element in which the normal stresses on each surface are equal to thehydrostatic stress . There are eight surfaces symmetric to the principal directions thatcontain this stress. This forms an octahedron as shown in Fig. The shear stresses on thesesurfaces are equal and are called the octahedral shear stresses (Fig. has only one of theoctahedral surfaces labeled). Through coordinate transformations the octahedral shear stress isgiven by

=[ ) ) )] m)

Octahedral surfaces


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