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DYNAMICS OF MACHINE

UNIT: 1Prepared by:

Jasvinder Singh

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CONTENTS INTRODUCTION ABOUT TURNING MOMENT DIAGRAM

TURNING MOMENT DIAGRAM FOR A SINGLE CYLINDER DOUBLE

ACTING STEAM ENGINE TURNING MOMENT DIAGRAM FOR A FOUR STROKE CYCLE INTERNAL

COMBUSTION ENGINE

TURNING MOMENT DIAGRAM FOR A MULTI-CYLINDER ENGINE

DETERMINATION OF MAXIMUM FLUCTUATION OF ENERGY

COEFFICIENT OF FLUCTUATION OF ENERGY

FLYWHEEL

DIFFERENCE BETWEEN GOVERNOR & FLYWHEEL

COEFFICIENT OF FLUCTUATION OF SPEED

ENERGY STORED IN A FLYWHEEL

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CONTENTS

STATIC FORCE ANALYSIS

STATIC EQUILIBRIUM

FREE BODY DIAGRAM

ANALYSIS OF STATIC FORCES IN MECHANISM

DYNAMICS FORCES IN MECHANISMS

DALEMBERTS PRINCIPLE

EQUIVALENTS OFFSET INERTIA FORCE

DYNAMICS OF RECIPROCATING PARTS

(a) PISTON EFFORT

(b) CRANK EFFORT

EQUIVALENT DYNAMICAL SYSTEM INERTIA FORCE IN RECIPROCATING ENGINES BY GRAPHICAL METHOD

ANALYTICAL METHOD FOR INERTIA TORQUE

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INTRODUCTION ABOUT TURNING

MOMENT DIAGRAM

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TURNING MOMENT DIAGRAM FOR A SINGLE

CYLINDER DOUBLE ACTING STEAM ENGINE

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TURNING MOMENT DIAGRAM FOR A SINGLE

CYLINDER DOUBLE ACTING STEAM ENGINE

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TURNING MOMENT DIAGRAM FOR A SINGLE

CYLINDER DOUBLE ACTING STEAM ENGINE

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TURNING MOMENT DIAGRAM FOR A FOUR STROKE

CYCLE INTERNAL COMBUSTION ENGINE

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TURNING MOMENT DIAGRAM FOR A FOUR STROKE

CYCLE INTERNAL COMBUSTION ENGINE

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TURNING MOMENT DIAGRAM FOR A

MULTI-CYLINDER ENGINE

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DETERMINATION OF MAXIMUM

FLUCTUATION OF ENERGY

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DETERMINATION OF MAXIMUM

FLUCTUATION OF ENERGY

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DETERMINATION OF MAXIMUM

FLUCTUATION OF ENERGY

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COEFFICIENT OF FLUCTUATION OF ENERGY

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COEFFICIENT OF FLUCTUATION OF ENERGY

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FLYWHEEL

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DIFFERENCE BETWEEN GOVERNOR &

FLYWHEEL

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COEFFICIENT OF FLUCTUATION OF SPEED

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COEFFICIENT OF FLUCTUATION OF SPEED

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ENERGY STORED IN A FLYWHEEL

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ENERGY STORED IN A FLYWHEEL

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ENERGY STORED IN A FLYWHEEL

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ENERGY STORED IN A FLYWHEEL

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INTRODUCTION:

In the design of machine mechanisms, it is imperative to know the

magnitudes as well as the directions of forces transmitted from the input tothe output.

The analysis helps in selecting proper sizes of the machine components to

withstand the stresses developed in them.

If proper sizes are not selected, the components may fail during the

machine operation. If components of a machine accelerate, inertia forces are produced due to

their masses.

However, if the magnitude of these forces are small compared to the

externally applied loads, they can be neglected while analyzing the

mechanism. Such an analysis is known as STATIC FORCES ANALYSIS. For Example:- In lifting cranes, the bucket load & the static weight loads

may be quiet high relative to any dynamic loads due to accelerating masses,

& thus static forces analysis is justified.

When the inertia effect due to the mass of the components is also

considered, it is called Dynamic Force Analysis.

STATIC FORCE ANALYSIS

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A body is in static equilibrium, if it remains in its static of rest or motion.

If the body is at rest, it tends to remain at rest & if it is in motion, it tends to keep

the motion.

IN STATIC EQUILIBRIUM:-

(I) The vector sum of all the forces acting on the body is zero.

(II) The vector sum of all the moments about any arbitrary point is zero.

Mathematically,

F = 0 (i)

T = 0 .(ii)

In a Planer system,

Forces can be described by two-dimensional vectors, and therefore,

Fx = 0 (iii)

Fy = 0 .(iv)

Tz = 0 ..(v)

STATIC EQUILIBRIUM

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FREE BODY DIAGRAM

The term body as used here may consist of an entire machine, several connected

parts of a machine, a single part, or portion of a machine part.

A free-body diagram is a sketch or drawing of the body, isolated from the rest of themachine & its surrounding, upon which the forces & moment are shown in action.

It is usually desirable to include on the diagram the known magnitudes & directions

as well as other pertinent information.

Advantages of using free body diagrams:

They make it easier for one to translate words, thoughts & ideas into physicalmodels.

They assist in seeing & understanding all facets of a problem.

They help in planning the approach to the problem.

They make mathematically relations easier to see or find.

They are useful for storing the methods of solutions for future reference. They assist our memory & make it easier to present & explain our work to others.

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ANALYSIS OF STATIC FORCES IN MECHANISM

In analyzing the forces in machines we shall almost always need to separate the

machine into its individual components or subsystems & construct free body

diagram showing the forces that act upon each.

Figure (a) shows a four link mechanism. The free body diagrams of its member 2, 3

& 4 are shown in figure b, c, d respectively. Each member is in equilibrium

individually.

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ANALYSIS OF STATIC FORCES IN MECHANISM

Member 4 is acting upon by three forces F, F34 & F14.

Member 3 is acting upon by two forces F23 & F43.

Member 2 is acting upon by two forces F32 & F12 & a Torque T.

(I) Assume:- forces F on member 4 is known completely. To know the other two

forces acting on this members completely, the direction of one more forces must be

known.

(II) For link 3 is a two-forces member & for its equilibrium F23 & F43 must act along

BC. Thus F34, being equal & opposite to F43, also acts along BC.

(III)For member 4 to be in equilibrium, F14 passes through the intersection of F & F34.

(IV)By drawing a force triangle (F is completely known), magnitude of F14 & F34 can

be known. (figure e).

Now F34 = F43 = F23 = F32

Member 2 will be in equilibrium if F12 is equal, parallel & opposite to F32

And, T = F12 h = F32 h

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INTRODUCTION:

Dynamic forces are associated with accelerating masses. As all machines

have some accelerating parts, dynamics forces are always present when the

machines operates.

For Example:- in case of rotors which rotates at speeds more than 80,000

r.p.m., even slightest eccentricity of the centre of mass from the axis ofrotation produces very high dynamic forces. This may lead to vibrations,

wear, noise or even machine failure.

DYNAMICS FORCES IN MECHANISMS

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DALEMBERTS PRINCIPLE

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EQUIVALENTS OFFSET INERTIA FORCE

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DYNAMICS OF RECIPROCATING PARTS

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DYNAMICS OF RECIPROCATING PARTS

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DYNAMICS OF RECIPROCATING PARTS

DYNAMICS OF RECIPROCATING PARTS

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DYNAMICS OF RECIPROCATING PARTS

CRANK EFFORT

DYNAMICS OF RECIPROCATING PARTS

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DYNAMICS OF RECIPROCATING PARTS

CRANK EFFORT

EQUIVALENT DYNAMICAL SYSTEM

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EQUIVALENT DYNAMICAL SYSTEM

EQUIVALENT DYNAMICAL SYSTEM

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EQUIVALENT DYNAMICAL SYSTEM

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INERTIA FORCE IN RECIPROCATING

ENGINES BY GRAPHICAL METHOD

INERTIA FORCE IN RECIPROCATING

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INERTIA FORCE IN RECIPROCATING

ENGINES BY GRAPHICAL METHOD

INERTIA FORCE IN RECIPROCATING

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INERTIA FORCE IN RECIPROCATING

ENGINES BY GRAPHICAL METHOD

INERTIA FORCE IN RECIPROCATING

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INERTIA FORCE IN RECIPROCATING

ENGINES BY GRAPHICAL METHOD

INERTIA FORCE IN RECIPROCATING

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INERTIA FORCE IN RECIPROCATING

ENGINES BY GRAPHICAL METHOD

INERTIA FORCE IN RECIPROCATING

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INERTIA FORCE IN RECIPROCATING

ENGINES BY GRAPHICAL METHOD

ANALYTICAL METHOD FOR INERTIA

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ANALYTICAL METHOD FOR INERTIA

TORQUE

ANALYTICAL METHOD FOR INERTIA

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ANALYTICAL METHOD FOR INERTIA

TORQUE

ANALYTICAL METHOD FOR INERTIA

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ANALYTICAL METHOD FOR INERTIA

TORQUE

ANALYTICAL METHOD FOR INERTIA

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ANALYTICAL METHOD FOR INERTIA

TORQUE

ANALYTICAL METHOD FOR INERTIA

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ANALYTICAL METHOD FOR INERTIA

TORQUE

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THANK YOU