1 Teaching Innovation - Entrepreneurial - Global The Centre for Technology enabled Teaching & Learning, N Y S S, India DTEL DTEL (Department for Technology

1 Teaching Innovation - Entrepreneurial - Global

The Centre for Technology enabled Teaching & Learning , N Y S S, India DTEL(Department for Technology Enhanced Learning)

Department of Mechanical Engineering

V-SEMESTERDesign Of Machine Element

CHAPTER NO.1

Design philosophy and Engineering materials and overview

of design and manufacturing

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Syllabus

UNIT –IDefinition of design, it’s need, types, process, failure criteria and manufacturing considerations in design, basis of good design, machining tolerances, mechanical properties, selection of materials, temperature effects on properties of materials and their applications.

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LECTURE 1:- Design philosophy and Engineering materials

Learning Objective

Basic concept of design in general.

Concept of machine design and their types.

Factors to be considered in machine design

Important mechanical properties of materials

and its application.

Concept of limits and fits.

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Introduction Design is essentially a decision-making process. If we

have a problem, we need to design a solution. In other

words, to design is to formulate a plan to satisfy a particular

need and to create something with a physical reality.

A machine is a combination of several machine elements arranged to work together as a whole to accomplish specific purposes. Machine design involves designing the elements and arranging them optimally to obtain some useful work.

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6YCCE,Nagpur Prof. D.Y.Shahare & Prof.

S.B.Deshpande

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TYPES OF DESIGN1) ADAPTIVE DESIGN : This is based on existing design, for

example, standard products or systems adopted for a new application

2) DEVELOPMENT DESIGN : Here we start with an existing design but finally a modified design is obtained.

3) NEW DESIGN : This type of design is an entirely new one but based on existing scientific principles. No scientific invention is involved but requires creative thinking to solve a problem.

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Based on Methods

1)Rational design : This is based on determining the stresses and strains of components and thereby deciding their dimensions.

2) Empirical design: It depends on empirical formulae based on practical & previous experiences & observations.

3) Industrial design: It is based on industrial considerations & norms viz. market survey, production facilities, use of existing standard products etc.

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RECOGNIZATION/IDENTIFICATION OF NEED

DEFINATION OF PROBLEM

SYNTHESIS

ANALYSIS & OPTIMIZATION

EVALUATION

DOCUMENTATION

RECOGNIZATION / IDENTIFICATION OF NEED

DEFINATION OF PROBLEM

SYNTHESIS

ANALYSIS & OPTIMIZATION

EVALUATION

DOCUMENTATION

THE GENERAL DESIGN

PROCEDURE

ITERATION

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Factors to be considered in Machine Design1)Strength

2)Rigidity

3)Reliability

4)Flexibility

5)Safety

6)Cost and weight

7)Manufacturing processes and workshop facilities

8)LifeDTEL 10


Factors to be considered in Machine Design

9) Noise and vibrations

10)Thermal considerations

11) Frictional resistance, wear and lubrication

12) Maintenance

13) Size and shape

14) Material selection

15) Assembly

16) Conformance to standards, ergonomics, aesthetics.YCCE,NAGPUR Prof. S.B.DESHPANDE & Prof. D.Y.SHAHARE DTEL 11


Factor of SafetyIn the design of a system or its components, there are certain areas of uncertainties. Sometimes it is difficult to determine the exact magnitude of various forces to which a machine component is subjected. In order to ensure the safety of a system against such uncertainties ‘factor of safety ‘ is used in machine design.In case of static loading F.S = Yield Strength/ working stress In case of fatigue loading F.S = Endurance limit/ working stress

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Types of Loadsi) Static load- Does not change in magnitude and direction

and normally increases gradually to a steady value. ii) Dynamic load- a) changes in magnitude- for e.g. traffic of

varying weight passing a bridge. b) changes in direction- for e.g. load on piston rod of a

double acting cylinder. Vibration and shock loading are types of dynamic loading.

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ENGG MATERIALS

METALS NONMETALS

FERROUS NON-FERROUS

e.g. -(i) cast iron (ii) wrought iron (iii) steel.

e.g.- wood, glass, plastics, Timber, leather

e.g.- aluminium and its alloys, magnesium and manganese alloys, nickel, silver, cupper based alloys like brass,Bronze, Duralumin,zinc, lead, ,tin

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Material Properties1)Elasticity- This is the property of a material to regain its original shape after deformation when the external forces are removed.

2)Plasticity- This is associated with the permanent deformation of material when the stress level exceeds the yield point.

3) Hardness- Property of the material that enables it to resist permanent deformation, penetration, indentation etc.

4) Ductility- This is the property of the material that enables it to be drawn out or elongated to an appreciable extent before rupture occurs.

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Material Properties5)Malleability- It is a special case of ductility where it can be rolled into thin sheets.

6) Brittleness- Brittle materials show little deformation before fracture and failure occur suddenly without any warning.

7) Resilience- This is the property of the material that enables it to resist shock and impact by storing energy.

8) Toughness- This is the property which enables a material to be twisted ,bent or stretched under impact load or high stress before rupture.

9) Creep- When a member is subjected to a constant load over a long period of time it undergoes a slow permanent deformation and this is termed as “creep”.

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Heat Treatment of Metals The heat treatment is defined as an operation or a combination of

operations, involving the heating & cooling of a metal or an alloy in the solid state for the purpose of obtaining certain desirable properties without change in chemical composition.

The is to achieve one or more of the followings 1)To increase the hardness of metals or alloys 2) To improve machinability 3) To soften the metal 4) To modify the structure of the material to improve its electrical & magnetic properties. 5) To refine the grain structure 6) To relieve residual stresses set up in the material.

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Various heat treatment processes

1) Normalizing: This process consists of a) heating the metal from 300 to 500 C above its upper critical

temperatureb) holding it at this temperature for about 15 minutesc) cooling slowly in still air

2) Annealing: This process consists of a) heating the metal from 300 to 500 C above its upper critical

temperatureb) holding it at this temperature for some time to enable the

internal changes to take placec) cooling slowly in furnace. The rate of cooling varies from 300 to

2000 C/ hour.

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Various heat treatment processes

3) Hardening: This process consists of a) heating the metal from 300 to 500 C above its upper critical

temperatureb) holding it at this temperature for considerable time depending

upon thicknessc) cooling suddenly in a suitable cooling medium like water, oil or

brine.

4) Tempering: The material hardened by quenching is very hard & brittle with residual stresses . It consists of reheating of metal below lower critical temperature, followed by any desired rate of cooling.

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Limits, Fits and TolerancesA machine element, after design, requires to be manufactured to give it a shape of a product. a designer should have knowledge of basic manufacturing aspects.

First and foremost is assigning proper size to a machine element from manufacturing view point. In case the machine element is a mating part with another one, then dimensions of both the parts become important, because they dictate the nature of assembly.

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Imp terms in Fits and TolerancesTolerance: It is the difference between maximum and minimum dimensions of a component, ie, between upper limit and lower limit. Tolerance is of two types, bilateral and unilateral. When tolerance is present on both sides of nominal size, it is termed as bilateral; unilateral has tolerance only on one side.

FITS: The nature of assembly of two mating parts is defined by three types of fit system, Clearance Fit, Transition Fit and Interference Fit.

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Types of FitsClearance Fit :In this type of fit, the shaft of largest possible diameter can also be fitted easily even in the hole of smallest possible diameter.

Transition Fit : It is the clearance between the minimum dimension of the shaft and the minimum dimension of the hole. Interference Fit :In this case, no matter whatever may be the tolerance level in shaft and the hole, there is always a overlapping of the matting parts. This is known as interference fit. Interference fit is a form of a tight fit.

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SummaryIn this topic the properties and uses of different types of

metals and nonmetals, generally used in machine design,

are discussed. Also we had discuss briefly about some of

the basic manufacturing requirements and processes.

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REFERENCE BOOKS MECHANICAL ENGG. DESIGN – J.E. SHIGLEY MACHINE DESIGN – P.H.BLACK MACHINE DESIGN - B.D.SHIWALKAR MACHINE DESIGN - KHURMI & GUPTA DESIGN OF MACHINE ELEMENTS – V.B.BHANDARI

For more information use following link:-\\172.16.1.4\nptel\NPTEL VIDEOS PHASE1 - PART 2\Mechanical Engineering\Design of Machine Element I

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Machine Design-II

Unit-II Design Cotter and Knuckle joint


YCCE,NAGPUR Prof. S.B.DESHPANDE & Prof. D.Y.SHAHARE

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LECTURE 9:- Design Cotter and Knuckle joint

Syllabus

UNIT -II : Design of cotter and knuckle joint.Riveted joint : Riveted joint for boilers, structural works (uniform strength joint), and eccentric loaded riveted joint.Welded joint : Design of single transverse, double transverse, parallel fillet, combination fillet butt joint, eccentrically loaded welded joints.Bolted joint : Design of bolted fasteners, bolts of uniform strength, bolted joints under eccentric loading.

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Learning Objective

A typical cotter joint, its components and

working principle.

Detailed design procedure of a cotter joint.

A typical knuckle joint, its components and

working principle.

Detailed design procedure of a knuckle joint.

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Introduction (Cotter joint)A cotter is a flat wedge-shaped piece of steel as shown in fig(a). This is used to connect rigidly two rods which transmit motion in the axial direction, without rotation. These joints may be subjected to tensile or compressive forces along the axes of the tensile or compressive forces along the axes of the rods.

(c)

(b)

(a)

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Design of cotter jointIf the allowable stresses in tension, compression and shear for the socket, rod and cotter be σt , σc and τ respectively, assuming that they are all made of the same material, we may write the following failure criteria: Tension failure of rod at diameter d,

Tension failure of rod across slot,


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Tensile failure of socket across slot,

Shear failure of cotter,

Shear failure of rod end,

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Shear failure of socket end,

Crushing failure of rod or cotter,

Crushing failure of socket or rod,

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Crushing failure of collar,

Shear failure of collar,

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Continue…..Bending of cotter

Maximum bending moment =

The bending stress,

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Continue….Some typical proportions are given below:

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Knuckle joint A knuckle joint as shown in fig is used to connect two

rods under tensile load. This joint permits angular misalignment of the rods and may take compressive load if it is guided.

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Design of Knuckle jointSome typical proportions are given below:

Mean diameter of the split pin =

The analyses are shown below assuming the same materials for the rods and pins and the yield stresses in tension, compression and shear are given by σt, σc and τ.

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Failure of rod in tension,

Failure of knuckle pin in double shear,

Failure of knuckle pin in bending

(if the pin is loose in the fork)

Equating the maximum bending

stress to tensile or compressive

yield stress we have,

Bending of a knuckle pin

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Continue… Failure of rod eye in shear:

Failure of rod eye in crushing:

Failure of rod eye in tension:

Failure of forked end in shear:

Failure of forked end in tension:

Failure of forked end in crushing:

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Summary

In this topic cotter and knuckle joints constructional detail have been described. Then the detailed design procedures of both these joints are given with suitable illustrations.

44YCCE,NAGPUR Prof. S.B.DESHPANDE & Prof.

D.Y.SHAHARE

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Machine Design-II

Unit-II Riveted joint


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Syllabus


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Learning Objective

Basic types of riveted joint.

Different important design parameters of a

riveted joint.

Basic failure mechanisms of a riveted joints.

Concepts of design of a riveted joint.

Procedure for designing riveted joint under

eccentric loading.

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Introduction (Riveted joint)Riveting is an operation whereby two plates are joined withthe help of a rivet. Adequate mechanical force is applied to make the joint strong and leak proof. Smooth holes are drilled (or punched and reamed) in two plates to be joined and the rivet is inserted.

Riveting operation

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Types of riveted jointRiveted joints are mainly of two types

Lap joints

Single riveted lap joint


D.Y.SHAHARE

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Types of riveted joint

Double riveted lap joint, chain arrangement

Double riveted lap joint, zig-zag arrangement

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Types of riveted joint Butt joints

Butt joint with single strap

Single riveted butt joint with single and double straps

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Types of riveted joint

Double riveted Butt joint with single and double straps (chain arrangement)

Double riveted Butt joint with single and double straps (zig-zag arrangement)

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Efficiencies of riveted joints in (%)

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Important design parameters of riveted joints

a) Pitch: This is the distance between two centers of the consecutive rivets in a single row. (usual symbol p)

b) Back Pitch: This is the shortest distance between two successive rows in a multiple riveted joint. (usual symbol Pt or Pb)

c) Diagonal pitch: This is the distance between the centers of rivets in adjacent rows of zigzag riveted joint. (usual symbol Pd)

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Important design parameters of riveted joints

d) Margin or marginal pitch: This is the distance between the centre of the rivet hole to the nearest edge of the plate. (usual symbol m) Strength of riveted jointThere are four possible ways a single rivet joint may fail.1) Tearing of the plate: The maximum force allowed in this

case iswhere st = allowable tensile stress of the plate materialp = pitch d = diameter of the rivet hole t= thickness of the plate

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Strength of riveted joints

Failure of plate in tension (tearing)2) Shearing of the rivet: The maximum force withstood by the joint to prevent this failure is

for lap joint, single strap butt joint

for double strap butt joint Where Ss=allowable shear stress of the rivet material


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Strength of riveted joints

Failure of a rivet by shearing

3) Crushing of rivet: If the bearing stress on the rivet is too large the contact surface between the rivet and the plate may get damaged.

With a simple assumption of uniform contact stress the maximum force allowed is

Where Sc=allowable bearing stress between the rivet and plate material

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Eccentrically loaded riveted joints

Consider, now, a bracket, which carries a vertical load F, the force, in addition to inducing direct shear of magnitude F/4 in each rivet, causes the whole assembly to rotate. Hence additional shear forces appear in the rivets.

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Eccentrically loaded riveted joints Taking moment about the centroid

Thus, the additional force is

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Eccentrically loaded riveted joints

The net force in the i-th rivet is obtained by parallelogram law of vector addition as

Where θi=angle between the lines of action of the forcesFor safe designing we must have

Where Ss=allowable shear stress of the rivet.

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Machine Design-II

Unit-IIWelded joint


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Syllabus


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Learning Objective

Different types of welded joints.

Factors that affect strength of welded joint.

Symbols and specifications of welded joint.

Possible failure mechanisms of welded joint.

Procedure for designing welded joint under

eccentric loading.

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Welded jointWelding is a very commonly used permanent joining process. A welded joint has following advantages:

(i) Compared to other type of joints, the welded joint has higher efficiency. An efficiency > 95 % is easily possible.

(ii) Since the added material is minimum, the joint has lighter weight.

(iii) Welded joints have smooth appearances.

(iv) Due to flexibility in the welding procedure, alteration and addition are possible.

(v) It is less expensive.

(vi) Forming a joint in difficult locations is possible through welding.

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Types of welding processesWelding can be broadly classified in two groups

1) Liquid state (fusion) welding where heat is added to the base metals until they melt. Depending upon the method of heat addition this process can be further subdivided, namely

Electrical heating: Arc welding

Resistance welding

Induction welding Chemical welding: Gas welding

Thermit welding Laser welding Electron beam welding.

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Types of welded jointsWelded joints are primarily of two kinds

a) Lap or fillet joint: obtained by overlapping the plates and welding their edges. The fillet joints may be single transverse fillet, double transverse fillet or parallel fillet joints

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Types of welded joints

b) Butt joints: formed by placing the plates edge to edge and welding them. According to the shape of the grooves, the butt joints may be of different types, e.g., Square butt jointSingle V-butt joint, double V-butt joint Single U-butt joint, double U-butt jointSingle J-butt joint, double J-butt jointSingle bevel-butt joint, double bevel butt joint

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Types of welded joints

Different types of butt joints

Other types of welded joints

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Basic weld types & their symbols

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Design of butt joint

The main failure mechanism of welded butt joint is tensile failure. Therefore the strength of a butt joint iswhere =allowable tensile strength of the weld material. t= thickness of the weldl=length of the weld.For a square butt joint t is equal to the thickness of the plates.

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Design of parallel fillet joint

Each weld carries a load P/2.The allowable load carried by each of the joint is where the throat areaThe total allowable load isCombination of transverse and parallel fillet joint

The allowable load is

where At & At’ =throat area along the longitudinal & transverse direction DTEL 71


Design of circular fillet weld subjected to torsion

The shaft is subjected to a torque, shear stress develops in the weld in a similar way as in parallel fillet joint. Assuming that the weld thickness is very small compared to the diameter of the shaft, the maximum shear stress occurs in the throat area.

Thus, for a given torque the maximum shear stress in the weld is

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Design of circular fillet weld subjected to torsion

where T = torque applied.d = outer diameter of the shaft = throat thicknessIp=polar moment of area of the throat section.

When

The throat dimension and hence weld dimension can be selected from the equation

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Eccentrically loaded transverse fillet joint


D.Y.SHAHARE

Consider a cantilever beam fixed to a wall by two transverse fillet joints. The design is based upon the strength of the joint against failure due to shear force along the throat section.

(a)direct shear stress of magnitude F/2bt

where b = length of the weld, t= thickness of the throatand the factor 2 appears in the denominator for double weld.

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Eccentrically loaded parallel fillet joint The joint fails in shear along the throat section. For the given loading, the throat area is subjected to two shear stresses.(a) Direct shear of magnitude F/2ltwhere l = length of the weld t = thickness of the throat.

(b) Indirect shear stress owing to eccentricity of the loading. The shear stress at a point at a distance r from the centroid is given by

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Eccentrically loaded parallel fillet joint where L = distance of the line of action of F from centroid. Thus

Where is the polar moment of the throat section about its centroid.The weld size is designed such that the maximum shear stress does not exceed its allowable limiting value.

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Asymmetric welded sectionAn eccentricity in loading causes extra shear stress in a welded joint, thus it may be useful to reduce the eccentricity in loading. In some applications this is achieved by making the weld section asymmetric.

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Asymmetric welded sectionThe net length of the weld can be calculated from the strength consideration that is

where t = thickness of the throat. Thus the individual lengths of the weld are as following:

and

where b= width of the plate

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Machine Design-II

Unit-II Bolted joint


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Bolted jointInitial tightening load

When a nut is tightened over a screw following stresses are induced:

(i) Tensile stresses due to stretching of the bolt.

(ii) Torsional shear stress due to frictional resistance at the threads.

(iii) Shear stress across threads.

(iv) Compressive or crushing stress on the threads.

(v) Bending stress if the surfaces under the bolt head or nut are not

perfectly normal to the bolt axis.

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Bolted jointb) Tensile stress:

c) Shear stress across the threads

where b is the base width of the thread and n is

the number of threads sharing the load

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Bolted joint

d) Crushing stress on threads:

e) Bending stress:

where x is the difference in height between the extreme corners of the nut or bolt head, L is length of the bolt head shank and E is the young’s modulus.

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Bolted jointStresses due to an external load

where for fine threads dc =0.88d and for coarse threads dc =0.84d, d being the nominal diameter.

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Summary

In this topic stresses developed in screw fastenings due

to initial tightening load and external load have been

discussed . Bolted joints with eccentric loading have been

described.

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Machine Design-II

Unit-III Design of power screw


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Stresses in power screws

A power screw is subjected to an axial load and a turning moment. The following stresses would be developed due to the loading.

Compressive stresses is developed in a power screw due to axial load.

The compressive stress σc is given by

where dc is the core diameter

λ is defined as λ = L/k

where I=Ak2

L is the length of the screw.

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Buckling analysis yields a critical load PC

If both ends are assumed to be hinged critical load is given by

In general the equation may be written as

where n is a constant that depends on end conditions.

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Torsional shear stresses in the screw due to turning moment.

It is given by

where T is the torque applied Bending stresses are developed in the screw thread and is shown in fig(a).

The bending moment

and the bending stress on a single thread is given by

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Here

And F′ is the load on a single thread.

Fig(b) shows a developed thread and fig(c) shows a nut and screw assembly.

This gives the bending stress at the thread root to be

This is clearly the most probable place for failure. Assuming that the load is equally shared by the nut threads

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Fig(a) Loading and bending stresses in screw threads

Fig(b) Dimensions of developed threads

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Fig(c) Screw and nut assembly

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• Bearing stress σbr at the threads is given by

• Again on similar assumption shear stress τ at the root diameter is given by.

Here n’ is the number of threads in the nut. Since the screw is subjected to torsional shear stress in addition to direct or transverse stress combined effect of bending, torsion and tension or compression should be considered in the design criterion.

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Design procedure of screw jackA typical screw jack is shown in fig(d) . It is probably more informative to consider the design of a jack for a given load and lift. We consider a reasonable value of the load to be 100KN and lifting height to be 500mm. The design will be considered in the following steps:

Fig (d) A typical screw jack

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Summary

In this topic firstly the stresses developed in a power

screw are discussed. Design procedure of a screw jack is

then considered and the components such as the screw,

and the nut are designed for strength.

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Machine Design-II

Unit-III Design of Helical springs


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LECTURE 28:- Design of Helical springs

Syllabus

UNIT -II : Design of power screw.Derivation of expression for deflection and shear stress in helical spring, design of helical spring, design of leaf spring.

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Learning Objective

Stresses in a helical springs.

Deflection of a helical springs

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Helical SpringsSpring act as a flexible joint in between two parts or

bodies.• Objectives of spring.

Cushioning , absorbing , or controlling of energy

due to shock and vibration.

Control of motion.

Measuring forces .

Storing of energy .

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Commonly used spring materials Hard-drawn wire : This is cold drawn, cheapest spring steel. Normally used for low stress and static load. Oil-tempered wire : It is a cold drawn, quenched, tempered, and general purpose spring steel. Chrome Vanadium: This alloy spring steel is used for high stress conditions and at high temperature up to 220C. Chrome Silicon: This material can be used for highly stressed springs. Music wire: This spring material is most widely used for small springs. It is the toughest and has highest tensile strength and can withstand repeated loading at high stresses.

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Helical SpringsNomenclature

A Material constant

C Spring index=D/d

d Wire diameter

D Mean coil diameter

f Natural frequency of the spring

F Force/Load

G Shear Modulus (of Rigidity)

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NomenclatureJ Polar Moment of Inertia

k Spring rate or spring stiffness

K Stress correction factor

L Length

N Number of coils

T Torsional Moment

U Strain energy

Helix angle

y Deflection γ Density τ Shear stress in spring

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Design of coil springStresses in helical spring

The flexing of a helical spring creates torsion in the wire and the force applied induces a direct stress.

Replacing the terms,

And re-arranging,

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Stresses in helical spring

Where Ks is the shear-stress correction factor and is defined by the equation:

Curvature Effect

The curvature of the wire increases the stress on the inside of the spring, This effect can be neglected for static loading,

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Stresses in helical spring

The combined effect of direct shear and curvature correction is accounted by Wahl’s correction factor and is given as:

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Deflection and stiffness of the spring

Where N is the number of active coils. The deflection in the spring, using Castigliano’s theorem,

Substituting C=D/d and rearranging

For normal range of C, the term within bracket (contribution of direct shear) is so negligible we can write

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Deflection and stiffness of the spring

The spring stiffness or springs rate,

End Construction

Coil compression springs generally use four different types of

ends. The ends of springs should always be of both squared

and ground, because a better or even transfer of the load is

obtained.

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End Construction


D.Y.SHAHARE

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Spring at various positions

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Machine Design-II

Unit-III Design of Leaf spring


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Learning Objective

Stresses in leaf spring.

Deflection of leaf spring.

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Multi-leaf springs

Multi-leaf springs are widely used for automobile and rail road suspensions. It consists of a series of flat plates, usually of semi- elliptical shape as shown in fig. The longest leaf, called the master leaf. The extra full-length are provided to support the transverse shear force.

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Leaf spring

The leaves are divided into two groups namely master leaf along with graduated-length leaves forming one group and extra full-length leaves forming the other.

Notations :

nf = number of extra full-length leaves

ng =number of graduated-length leaves including master leaf

n= total number of leaves

b= width of each leaf (mm)

t= thickness of each leaf (mm)

L=length of the cantilever or half the length of semi- elliptic spring (mm)

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Leaf Springs

The resultant shape is approximately a triangular plate of thickness t and a maximum width at the support as (ngb).

The bending stress in the plate, which is uniform throughout, is given by

(a)

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Leaf SpringsIt can be proved that the deflection δg at the load point of the triangular plate is given by

(b)

Similarly, the extra full length leaves can be treated as a rectangular plate of thickness t and uniform width (nfb). The bending stress at the support is given by

(c)

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Leaf SpringsThe deflection at the load point is given by

(d)

or (e)

Also (f)

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Leaf SpringFrom equation (e) and (f)

Substituting these valued in Eqs(a) and (c),

(h)

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Leaf Spring

It is seen from the above equations that bending stresses in full-length leaves are 50% more than those in graduated length leaves. The deflection at the end of the spring is determined from Eqs(b) and (h). It is given by

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Summary

In this topic firstly the stresses developed in a leaf

spring are discussed. Procedure to calculate deflection

and stiffness of spring as well nipping of leaf spring is

studied.

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Machine Design-II

Unit-IVDesign of Brakes &Clutches


YCCE,Nagpur

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LECTURE 33:- Design of Brakes &Clutches

Syllabus

Unit –IVDesign of Friction Clutch, single plate, mutiplate, Cone,& Centrifugal Clutch.Design of Brake, shoe Brake, Band Brake, Internal Expanding Brake.

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Learning Objective

Recognize the basic geometries of Clutch and Brakes system.Calculate the frictional forces and torque capabilities in Brake system.Understand the principle of heat generation heat removal from the Brake system.Calculate frictional horsepower and recognize how it use.

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Introduction (Design of Clutch)

A Clutch is a machine member used to connect the driving shaft to a driven shaft, so that the driven shaft may be started or stopped at will, without stopping the driven shaft. A Clutch thus provides the interruptible connection between two rotating shaft. Clutches allow a high inertia load to be started with a small power.

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Single plate clutchBasically, the clutch needs three parts.

These are the engine flywheel,

a friction disc called the clutch plate

and a pressure plate.

Method of analysis:-uniform pressure condition uniform wear condition

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Design of Single plate clutch

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Design of Multiplate clutch

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Cone Clutch

A cone clutch consist of inner and outer conical working surfaces.The outer cone is keyed to the driving shaft, while the inner cone is free to slide axially on the driven shaft due to splines.Leather, cork or asbestos are used for the friction lining on the inner cone.DTEL 126


Design of Cone Clutch

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Centrifugal ClutchWhenever it is required to engage the load after the driving member has attained a particular speed, a centrifugal clutch is used.The centrifugal clutch permits the drive-motor or engine to start, warm up and accelerate to the operating speed without load.

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Design of Centrifugal Clutch

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Design of BrakeBrakes are devices that dissipate kinetic energy of the moving parts of a machine. In mechanical brakes the dissipation is achieved through sliding friction between a stationary object and a rotating part. Depending upon the direction of application of braking force.In a shoe brake the rotating drum is brought in contact with the shoe by suitable force. The contacting surface of the shoe is coated with friction material.

.

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Design of Shoe Brake

Let, F=applied force to the shoe,

Ffr=frictional force,

Pressure distribution,

Coulomb’s law of friction,

Net normal force,

The total frictional torque,

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equivalent force,

Coulomb’s law of

friction

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Design of Band Brake

A flexible band of leather or rope or steel with friction lining is wound round a drum. Frictional torque is generated when tension is applied to the band. It is known tensions in the two ends of the band are unequal because of friction and bear Let,T1=tension in the taut side,

T2=tension in the slack side,

μ =coefficient of kinetic friction and

β =angle of wrap.

Braking torque,

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Simple band brakeIn simple band brake one end of the band is attached to the fulcrum of the lever arm The required force to be applied to the lever is,

for clockwise rotation of the brake drum

for anticlockwise rotation of the brake drum,

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Differential band brake: In this type of band brake, two ends of the band are attached to two points on the lever arm other than fulcrum.

for clockwise rotation of the brake drum and

for anticlockwise rotation of the brake drum,

for clockwise rotation of the brake drum,

for counterclockwise rotation of the brake drum.

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Design of Internal Expanding BrakeThe brake shoes are engaged with the internal surface of the drum.

The forces required are ,

Let Mp & Mf are the moment equilibrium equation

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Machine Design-II

Unit-VThin and Thick Cylindrical Pressure Vessel.


YCCE,Nagpur

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LECTURE 38:- Thin and Thick Cylindrical Pressure Vessel

Syllabus

Unit –VClassification of Thin and Thick cylindrical pressure vessel,Stresses in thin and cylindrical pressure vessels when it is subjected to internal pressure,Expression for circumferential and longitudinal stresses,Design of pressure Vessel, heads and cover plate

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Learning Objective

Stresses developed in thin cylinders.

Formulations for circumferential and longitudinal stresses in thin cylinders.

Basic design principles.

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Introduction(Thin Cylinder)

. If the wall thickness is less than about 7% of the inner diameter then the cylinder may be treated as a thin one. Thin walled cylinders are used as boiler shells, pressure tanks, pipes and in other low pressure processing equipments. Fig shows (a)circumferential or hoop stress,(b)longitudinal stress,(c)Radial stress

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Stresses in thin cylinders In a thin walled cylinder the circumferential stresses may be assumed to be constant over the wall thickness and stress in the radial direction may be neglected for the analysis. Let, σθ =circumferential stress & σz =longitudinal stress ,r =thin cylinder of radius , t =wall thickness , L =length &P=internal pressure ,Consider now an element of included angle dθ at an angle of θ from vertical. For equilibrium we may write,

This gives,

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Considering a section along the longitudinal axis

Let,ri & ro are internal and external radii of the vessel,

ri≈ ro = r

ro – ri = t

σz =

From the equilibrium condition in a cut section we have,

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Design Principles

Pressure vessels are generally manufactured from curved sheets joined by welding. Mostly V– butt welded joints are used. It is probably more instructive to follow the design procedure of a pressure vessel. We consider a mild steel vessel of 1m diameter comprising a 2.5 m long cylindrical section with hemispherical ends to sustain an internal pressure of 2MPa.

The minimum plate thickness should conform to the “Boiler code” as given in table-

Minimum plate thickness:-

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Summary Stresses developed in thin cylinders are first discussed in general and then the circumferential and longitudinal stresses are expressed in terms of internal pressure, radius and the shell thickness. Stresses in a spherical shell are also discussed. Basic design principle of thin cylinders are considered.

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Thick cylinders- Stresses due to internal For thick cylinders such as guns, pipes to hydraulic

presses, high pressure hydraulic pipes the wall thickness is relatively large and the stress variation across the thickness is also significant. In general the stress equations of equilibrium without body forces can be given as,

For axisymmetry about z-axis

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In a plane stress situation if the cylinder ends are free to expand σz = 0 and due to uniform radial deformation and symmetry τrz = τθz = τrθ = 0. The equation of equilibrium reduces to,

This can be written in the following form:

If we consider a general case with body forces such as centrifugal forces in the case of a rotating cylinder or disc then the equations reduce to ,

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It is important to remember that if σθ works out to be positive, it is tensile and if it is negative, it is compressive whereas σr is always compressive irrespective of its sign.

if po = 0 i.e. there is no external pressure the radial and circumferential stress reduce to,

Fig shows the Radial & circumferential

stress

distribution within the cylinder

wall when only internal pressure acts.

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Summary

Stresses and strains in thick cylinders are first discussed and Lame’s equations are derived. Radial and circumferential stress distribution across the wall thickness in thick cylinders have been illustrated.

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Machine Design-II

Unit-VIDesign of Transmission Shaft and keys.

Department of Mechanical Engineering,

YCCE, Nagpur

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LECTURE 41:- Design of Transmission Shaft and keys

Syllabus

Unit –VIDesign of Transmission shafts on the Basis of strength, Rigidity and Critical speed,ASME Code for Shaft Design,Design of Stepped Shaft Axle Splined Shaft,Design of Keys.

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Learning Objective

At the end of this lesson, the students should be able to understand :-Definition of shaft Standard shaft sizes Standard shaft materials Design of shaft based on strength

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Standard sizes of Shafts Typical sizes of solid shaft that are available in the market are,

Up to 25 mm 0.5 mm increments

25 to 50 mm 1.0 mm increments

50 to 100 mm 2.0 mm increments

100 to 200 mm 5.0 mm increments.

Material for Shafts The ferrous, non-ferrous materials and non metals are used as shaft material depending on the application. Some of the common ferrous materials used for shaft are discussed below.

Hot-rolled plain carbon steel

Cold-drawn plain carbon/alloy composition

Alloy steels

Hardening of surface

Case hardening and carburizing

Cyaniding and nitriding.

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Design considerations for shaft Design based on Strength

In this method, design is carried out so that stress at any location of the shaft should not exceed the material yield stress. However, no consideration for shaft deflection and shaft twist is included. Design based on Stiffness

Basic idea of design in such case depends on the allowable deflection and twist of the shaft.

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Design based on Strength The stress at any point on the shaft depends on the nature of load acting on it. The stresses which may be present are as follows.

Basic stress equations : Bending stress,

M : Bending moment at the point of interest

do : Outer diameter of the shaft

k : Ratio of inner to outer diameters of the

shaft ( k = 0 for a solid shaft because inner diameter is zero )

Axial StressF: Axial force (tensile or compressive)

α: Column-action factor(= 1.0 for tensile load)

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Here, α is defined as,n = 1.0 for hinged end n = 2.25 for fixed end n = 1.6 for ends partly restrained, as in bearing K = least radius of gyration, L = shaft length ycσ = yield stress in compression

Stress due to torsion ,

T : Torque on the shaft τ : Shear stress due to torsion

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Combined Bending and Axial stress

Maximum shear stress theory

Substituting the values of σx and τxy in the above equation, the final form is,

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ASME Code for Shaft Design

The shafts are normally acted upon by gradual and sudden loads. Hence, the equation is modified in ASME code by suitable load factors,

Where, Cbm & Ct are the bending and torsion factors.

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ASME code also suggests about the allowable design stress, τ allowable

to be considered for steel shafting,

ASME Code for commercial steel shafting

= 55 MPa for shaft without keyway

= 40 MPa for shaft with keyway ASME Code for steel purchased under definite

specifications

= 30% of the yield strength but not over 18% of the ultimate strength in tension for shafts without keyways. These values are to be reduced by 25% for the presence of keyways.

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Design based on Stiffness Design may be based on stiffness. In the context of shaft, design for stiffness means that the lateral deflection of the shaft and/or angle of twist of the shaft should be within some prescribed limit. Therefore, design for stiffness is based on lateral stiffness and torsional rigidity.

Torsional rigidity :-To design a shaft based on torsional rigidity, the limit of angle of twist should be known.

The angle of twist is given as follows,

Where,

θ = angle of twist

L = length of the shaft

G = shear modulus of elasticity

Ip= Polar moment of inertia

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Based on critical speedCritical speed of a rotating shaft is the speed where it becomes dynamically unstable. It can be shown that the frequency of free vibration of a non-rotating shaft is same as its critical speed.The equation of fundamental or lowest critical speed of a shaft on two supports is,

Where,

W1, W2…. : weights of the rotating bodies

δ1, δ2 …. : deflections of the respective bodies

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Design of KeysThe function of a key is to prevent the relative motion between the transmission shaft and the hub of a rotating element like gear, pulley or sprocket.The key transmits the torque from the shaft to the hub and vice-versa.Types of Keys:-(a) Square key(b)flat key(c)round key(d)kennedy key(e)Woodruff key(f)Gib-headed key(g)Feather Key

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Details of Keys..

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Common type of splined shaft

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Summery:-

In this unit student learn, the design of shaft and their application.Design of Key and their type as well as common type of Splined shaft.

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References :-J.E Shigley and C.R Mischke , Mechanical Engineering Design , McGraw Hill Publication, 5th Edition. 1989. M.F Spotts, Design of Machine Elements, Prentice Hall India Pvt. Limited, 6th Edition, 1991. Khurmi, R.S. and Gupta J.K., Text book on Machine Design, Eurasia Publishing House, New Delhi. Sharma, C.S. and Purohit Kamalesh, Design of Machine Elements, Prentice Hall of India, New Delhi, 2003

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For more information use below link:-

172.16.1.4\nptel\NPTEL VIDEOS PHASE1 - PART 2\Mechanical Engineering\Design of Machine Element I

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