Theory of Machines 2

VISVESVARAYA NATIONAL INSTITUTE OF

TECHNOLOGY

LABORATORY MANUAL

THEORY OF MACHINES - II

(MEP-211)

PREPARED BY

PROF. ANIMESH CHATTERJEE

DR. SATISH D. DHANDOLE

DEPARTMENT OF MECHANICAL ENGINEERING

Name of the Student: ----------------------------------------------------------------------------------------- Date: -----------------------------

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EXPERIMENTAL NO 1: DETERMINATION OF UNKNOWN MOMENT OF INERTIA OF GIVEN COMPONENT USING

TRIFILER PENDULUM

EQUIPMENT/EXPERIMENTAL SETUP NAME: TRIFILAR PENDULUM

The shape of a body is frequently so complex that it is impossible to compute the moment of inertia. Connecting

rod is such examples where due to their complex shapes moment of inertia cannot be computed geometrically.

However it is possible to find the same indirectly through dynamic measurements. Trifiler pendulum is one

such arrangement where moment of inertia of any component can be found out by measuring the time period of

oscillation provided the centre of gravity of the component is known to us.

EQUIPMENT DESCRIPTION:

Trifiler pendulum is a three string torsional pendulum as shown in figure. Three strings of equal l support a

platform and are equally spaced at a distance r from the centre of platform.

Let Mp be the mass of the platform and M be the mass of the component whose moment of inertia I is to be

measured. If T is the time period of torsional oscillation then,

PROCEDURE:

Measured length of the string l and platform radius r. Set the flat form in torsional oscillation and measure the

time period T0. Then put the given component on the platform so that its c.g. lies at the centre of the platform.

Set the platform in oscillation again and measure the time period T1.

Find mass Mp of the platform and calculate its moment of inertia Ip. Then calculate the unknown moment of

inertia of the component using the given formula putting T=T1.

It is not compulsory to measure T0, i.e. time period of oscillation of empty platform. However students are

advised to crosscheck the experimental value of T0 with theoretical value given by

INSTRUCTION:

The sketch is required to be drawn by the students. Report the measured data and show your calculation with

obtained value of moment of inertia. Also calculate the theoretical value of time period of oscillation of the

empty platform T0.

REFERENCE:

1) Theory of machine and mechanism by Shigley, pp 439-440.

2) Theory of machines by S. S. Rattan, pp. 641-642.


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EXPERIMENTAL NO 2: DETERMINATION OF MOMENT OF INERTIA AND LOCATION OF CENTRE OF GRAVITY

OF A CONNECTING ROD

EQUIPMENT/EXPERIMENTAL SETUP NAME: SIMPLE PENDULUM ARRANGEMENT

This experiment is similar to trifiler pendulum, but this is much simpler in the sense that it does not require the

knowledge of C.G. The arrangement has a knife edge suspension over which the connecting rod is suspended

and its time period of oscillation is measured.

PROCEDURE:

First find out the mass M of the connecting rod and measured the end to end distance (a+b) between the big end

and small end bearings as shown in figure below. Suspend the connecting rod from big end bearing side and

note the time period Ta of oscillation. Similarly repeat it for small end bearing end and note time period Tb.

Also (a+b) is known. From these relations find ‘k’ and ‘a’, calculate the moment of inertia using .

The calculated value of ‘a’ gives the location of centre of gravity of connecting rod from big end bearing.

REFERENCE:

1) Theory of machines by S. S. Rattan, pp. 449-450.


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EXPERIMENTAL NO 3: SINGLE PLANE FIELD BALANCING OF ROTOR

EQUIPMENT/EXPERIMENTAL SETUP NAME: DYNAMIC BALANCING MACHINE-I

Single plane field balancing procedure is applicable to industrial rotors in operation when the unbalance amount

and its angular location is not known. This method is useful when a rotor is having static unbalance only or

when couple unbalance is small relative to force unbalance. This method uses vibration measurement data from

support bearings to find out the required balance correction mass.

EQUIPMENT DESCRIPTION:

The rotor to be balanced is supported on a balancing machine and rotated by a motor through belt drive. A

stroboscope is used to measure the phase where amplitude meter indicates the vibration amplitude. A filter

tuning knob is provided to synchronise at 1*rpm so as to indicate vibration at 1 * rpm frequency which is

mainly due to unbalance.

PROCEDURE: First the filter frequency is tuned with rotating frequency. Tuning is confirmed when the

amplitude reaches maximum as well as when stroboscopic indication becomes stationary. Vibration amplitude

and phase indicated by stroboscope is noted. Let it be vector V0. Then a trial mass of Wt gram is put on the rotor

at any angular location in the unbalance plane and the resulting vibration amplitude and phase is noted. Let it be

V1. A vector diagram is constructed on polar graph with vector V0 and V1 as shown next page. represents

the vector difference between V0 and V1 which actually represent the effect of trial weight. The calculation for

correction mass and its angular location is explained in the simple calculation below the vector diagram.

The correction mass is put in required location and vibration reading is taken again. A good correction will

result in considerable reduction of bearing vibration.

INSTRUCTION:

The Schematic diagram of the setup to be drawn on the left page show the vibration readings and correction

mass calculation and below it. Attach polar graph separately. If the residual vibration is not low enough

comment on the factors you think responsible for it.

REFERENCE:

1) Theory of mechanism and machines by Ghosh & Mallick

2) IRD MECHANALYSIS manual.


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EXPERIMENTAL NO 4: DEMONSTARION AND BALANCING OF INERTIA FORCES IN RECIPROCATING

MECHANISM

EQUIPMENT/EXPERIMENTAL SETUP NAME: DYNAMIC BALANCING MACHINE-II

In a reciprocating mechanism unbalance inertia forces are of two types: Primary unbalance and Secondary

unbalance force. If we do an analysis replacing the connecting rod by its dynamic equivalent mass pair system

located at the crank pin end and piston end then we get

Mrec is piston mass plus the equivalent connecting rod mass at piston end and ‘n’ is the connecting rod length to

crank radius ratio.

Both Primary and Secondary inertia forces act along the line of motion of the piston but their magnitude vary as

per the cosine component. Primary unbalance force can be balanced by putting a correction mass equal to Mrec

in opposite direction to the crank. However it introduces a varying force component along perpendicular

direction. Thus the balancing procedure for reciprocating system gives only partial result. In addition to these

inertia forces there would be inertia forces due to rotating unbalance on the crank which is equal to crank

unbalance mass plus the connecting rod equivalent mass at the crank end. This rotating unbalance can be

completely eliminated by putting a correction mass of same amount opposite to crank

PROCEDURE:

Find the connecting rod mass and distribute it at piston end and crank end following the concept of dynamic

equivalent system. Then find total reciprocating mass Mrec and total rotating unbalance mass. Add correction

mass as explain above to balance rotating unbalance completely and for 50% balancing of reciprocating

unbalance. Note the effect after balancing. Then repeat the procedure for 100% balancing of reciprocating

unbalance and note the effect. Compare the two cases for minimum frame motion.

Primary and Secondary

force direction


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EXPERIMENTAL NO 5 DEMONSTRATION AND CHARACTERISATION OF BEARING VIBRATION DUE TO

UNBALANCE IN ROTATING MACHINES

EQUIPMENT/EXPERIMENTAL SETUP NAME: DYNAMIC BALANCING MACHINE-I

Unbalance in a rotating machine can be due to unbalanced inertia force or/and unbalanced inertia couple. when

a rotor construction is very thin with respect to the shaft length as in a fan or single stage pump, unbalanced is

localised around plane only and it can be corrected by providing balance correction mass in the same plane. But

if the rotor construction is distributed such as multistage pump, turbine or electric motor then unbalance can be

distributed in several planes and balance correction masses are required to be put in two different planes which

are called correction planes. Due to unbalanced inertia force and inertia couple bearings are subjected to varying

loads and vibration is set in them. For a linear rotor bearing system vibration vector is linearly related to

unbalance vector as given by

where V is vibration vector, U is unbalance vector and is known as influence coefficient. The basic objective

of any field balancing technique is to find influence coefficients from a set of vibration readings. In this

experiment students are supposed to study the effect of unbalance mass on the bearing vibration; both amplitude

and phase. Determination of influence coefficient can be done analytically or graphically. The second method is

demonstrated in the next experiment.

PROCEDURE: Synchronise the signal measurement filter frequency with the rotating frequency and note down

the vibration amplitude and the stroboscopic phase value. Now put a sample mass anywhere on the rotor and

note the vibration readings again.

Let V0 be the original bearing vibration reading and V1 be the vibration after the sample mass M is put

Influence coefficient = such that ,

A graphical procedure for finding the influence coefficient is demonstrated below.

REFERENCE:

1) Theory of mechanism and machines by Ghosh & Mallick, pp- 252-260

2) Vibration control handbook by Blake & Mitchal

3) IRD Mechanalysis manual.


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EXPERIMENTAL NO 6 TWO PLANE DYNAMIC BALANCING OF MULTIDISC ROTOR


Dynamic balancing is aimed at eliminating both the force unbalance and couple unbalance. Irrespective of

number of unbalance planes number of correction planes is two only for all rigid rotors. Calculation of

correction masses can either be done analytically or by graphical method.

EQUIPMENT DESCRIPTION: A cradle or frame carries the shaft and four discs assembly. Discs are having

provision for attaching the unbalance or correction mass at any angular location at three different radii. When

the rotor is balanced the frame will remain stationary during the running of the rotor, but with unbalance

attached to it the frame starts moving to and fro as well as oscillates due to force and couple unbalance.

PROCEDURE: Start the motor and observe the frame motion if any in initial condition. Put the unbalance

masses as indicated and note the frame motion after this. Then calculate the correction masses graphically and

put them in the correction planes. Frames should now become stationary again.

INSTRUCTION: Draw the sketch of the rotor disc assembly with necessary dimensions. Draw the graphical

analysis in a separate A4 size drawing sheet and attach it.

REFERENCE:

1) Theory of mechanism and machines by Ghosh & Mallick, pp- 252-260


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EXPERIMENTAL NO 7 BALANCING OF TWO CYLINDER RECIPROCATING ENGINE MODEL


In any multi cylinder in-line engine unbalance conditions are of following types

Total primary unbalance force is not zero

Total secondary unbalance force is not zero

Total primary couple not zero

Total secondary couple not zero

Some or all of these unbalance conditions can be eliminated by properly selecting the relative crank positions.

This is known as passive balancing. When these unbalance effects are counteracted by putting balancing mass it

is called active balancing.

PROCEDURE: In the two cylinder reciprocating engine model adjust the relative crank angle at 90 degree and

run the model and see the frame motion. Similarly set the crank angle at 180 degree and observe the frame

motion. Do the theoretical analysis and find out the balance conditions for these crank angles and compare with

practical observations. Try for active balancing in each case now and find out whether the balance condition as

indicated by the frame motion improves or not.

INSTRUCTION: Draw the sketch for the model below. For active balancing select the adjacent planes.


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EXPERIMENTAL NO 8 STUDY OF VIBRATION OF SINGLE D.O.F. AND TWO D.O.F. SPRING MASS SYSTEM

EQUIPMENT/EXPERIMENTAL SETUP NAME: SPRING MASS VIBRATION MODEL

In this experiment the model consists of two parts. In one part we have a mass connected to two springs which

represents a single degree of freedom system. In the second part there are two mass connected to three springs

which represents two degree of freedom system. Vibration is initiated in the models and natural frequency of

oscillation is measured.

PROCEDURE: First the mass in the s.d.o.f. model is displaced and allowed to oscillate. Let the time period be

T0, then

or

Next place a small mass m on the original mass M and note the time period T, Then

Then it can be derived that )/( 2

0

22

0 TTTmM and

Thus, the stiffness of the spring and the mass in the model both can be experimentally found out.

In the two degree of freedom model students are supposed to know the initial conditions for first mode vibration

and second mode vibration and then experimentally apply those conditions and see the first mode and second

mode vibrations. For each mode vibration they will note the time period and compare with theoretical values.

INSTRUCTION: Draw the sketch for the model below. For active balancing select the adjacent planes.


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EXPERIMENTAL NO: DETERMINATION OF NATURAL FREQUENCY OF BENDING VIBRATION OF

CANTILEVER BEAM USING FFT ANALYSER

EQUIPMENT/EXPERIMENTAL SETUP NAME: CANTILVER BEAM VIBRATION MODEL

A beam is said to be a cantilever beam if it’s one end is fixed and other end is free. When such is set into

vibration it vibrates with many frequencies known as natural frequencies. As the beam is a continuous system.

Number of natural frequencies is infinity. The lowest of them is known as fundamental natural frequency. The

locus of maximum amplitude points when the beam vibrates at this frequency is known as first mode shape. In

the figure below a cantilever beam is shown with first mode shape. In this experiment natural frequency will be

found out by free vibration test initiated by impact.

Theory:

A. CANTILEVER BEAM WITH TIP MASS

For this case Rayleigh method gives an approximate solution

[derivation given in structural dynamics by Mario Paz, Pp 126-127]

Where E is the Young's modulus

I is moment of inertia about natural axis = bh3/12 for rectangular section

mb= mass of beam, m= mass at the tip

L is length of the cantilever beam

B CANTILEVER BEAM WITHOUT TIP MASS

a) Rayleigh approximates method can be applied here also by taking m = 0 which gives

b) Euler Bernoulli’s beam theory gives an exact solution

42

51.3

Lm

EIf

Where m is mass per unit length of the beam

DESCRIPTION OF THE SETUP AND INSTRUMENTAION

The instruments required are

a) Piezoelectric vibration transducer or accelerometer

b) Vibration meter

c) Fast Fourier Transform (FFT) analyser

The accelerometer measures the vibration acceleration and gives out charge output which converted into voltage

signal in the vibration meter and then sent to FFT analyser. This signal is in time domain and is transformed

into frequency domain in the analyser by Fast Fourier Techniques developed by Tookey and Cooley around

1966 in MIT, United States. The frequency decomposition is displayed on the oscilloscope of the analyser as a

spectrum fundamental frequency can be noted.

PROCEDURE: First the length and cross sectional details are measured and theoretical values of natural

frequency are calculated by various methods given above. In the experiment free vibration is initiated by hitting

the tip by a hammer and recording the spectrum on FFT analyser. Similarly next a concentrated mass is attached

to the tip of the beam and frequency reading is taken. Then experimental readings are to be compared with

theoretical one.

INSTRUCTION: Draw a schematic diagram of the setup along with instrumentation. Comment on possible

reasons why theoretical values of natural frequency are different from experimental ones. Study further on

working principles of accelerometers, vibration meter and FFT analyser.

REFERENCE:

1) Structural dynamics by Mario Paz

2) Mechanical vibration by Morse Henckle

3) Instruments catalogue


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EXPERIMENTAL NO: DETERMINATION OF NATURAL FREQUENCY OF BENDING VIBRATION OF

CANTILEVER BEAM -- RESONANCE APPROACH

EQUIPMENT/EXPERIMENTAL SETUP NAME: BEAM VIBRATION ON EXCITER SETUP

In this experiment an electromagnetic exciter is used to vibrate the cantilever beams. The exciter is connected

with an oscillator such that the frequency of oscillation can be varied over a range and also the amplitude of

excitation can be changed. This procedure is based on the concept that whenever a vibrating system is excited at

one of its natural frequencies, the response becomes very large and if damping is absent it will become

infinitely large. This is also known as resonance.

PROCEDURE: The setup consists of four beams of different lengths connected with a vibrating fixed with the

exciter. The oscillator magnitude is kept at a level so that vibrations of the beam are just visible but not very

high. The frequency of oscillator is gradually increased till resonance is noticed in a beam. The oscillator

frequency is noted now and this is the natural frequency of the beam which has shown the resonance

phenomenon. Similarly natural frequencies of other beams are also obtained. The experimental values are then

compared with theoretical values from Euler-Bernoulli beam theory.

REFERENCE:

1) Mechanical vibration by Rao and Gupta


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EXPERIMENTAL NO: DETERMINATION OF MATERIAL DAMPING OF STEEL CANTILEVER BEAM BY FREE

VIBRATION TEST

EQUIPMENT/EXPERIMENTAL SETUP NAME: BEAM VIBRATION MODEL

Material damping is inherently present in all the materials to different extent. Steel has a low damping value

whereas that in cast-iron is high. The presence of damping helps to limit the vibration level in the system

particularly near resonance. When damping in a system is only due to material damping, the resulting motion is

under damped, in which successive peaks decay exponentially. In such cases a term logarithm decrement is

defined as

Where Y1 and Y2 are the two successive peak amplitudes.

if the peak amplitude measured are not successive but say first peak and rth peak then

Logarithmic decrement is related to damping factor as given by

PROCEDURE: Connect the instrumentation with the cantilever beam as required in experiment no 9. Initiate free

vibration in the beam and record the vibration signal in time domain on FFT analyser. This will appear as

sinusoidal signal with decaying amplitudes. Measure the amplitudes of any peak and rth peak after. Calculate

logarithmic decrement and there form the damping factor of steel. Also from the display note the cursor values

of successive peaks and draw the trace on graph paper.

REFERENCE:

1) Structural dynamics by Mario Paz

2) Vibration control by A.K. Mallick


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EXPERIMENTAL NO: DETERMINATION OF CRITICAL SPEED OF ROTORS

EQUIPMENT/EXPERIMENTAL SETUP NAME: WHIRLING OF SHAFT SETUP

When a rotor is mounted on a shaft, its centre of mass does not coincide with the centreline of the shaft. These

results into an unbalanced inertia force acting when the rotor is in rotation and the rotor deflects and bends out

of the rotating centreline. The speed at which this deflection reaches its maximum and the shaft rotor system is

found to vibrate violently in transverse direction is called the critical speed. Simply stating critical speed

correspond to the natural frequency of bending vibration of the rotor system.

In industrial applications rotating machines are to be designed carefully such that its operating rpm remains

away from the rotor critical speed. When operating rpm is higher than first critical speed ( in case of flexible

rotors such as turbine) the rotor has to be accelerated carefully through the critical speed such that not much

time is given at the critical speed for vibration build-up.

Theory: The simplest formula for a single disc rotor is

( In this formula mass of the shaft is not considered)

Dunker lay’s method consider mass of the shaft and also is applicable for multidisc rotor. This gives

Where f0 is the natural frequency of shaft alone =

And fi is natural frequency of the ith

disc on the shaft m and L is mass and length of the shaft respectively.

All the relations given above based on the assumption that the bearing conditions are equivalent to simply

supported condition.

PROCEDURE: First measure shaft diameter and length of the shaft between the bearings, mass m of the disc.

Initially the shaft alone is rotated and speed is varied from a low value gradually up till critical speed is

observed through large deflection. RPM is measured with the help of digital infrared tachometer. Then put the

disc on the shaft and measure the critical speed in the same way. It will be seen that the experimental values are

quite different from theoretical ones. Explain why?

REFERENCE:

1) Elements of vibration analysis by L. Meirovitch

2) Mechanical vibration by Tse. Morse Henckle

3) Theory of machine by S.S. Rattan pp. 526-534


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EXPERIMENTAL NO: STUDY OF FORCED VIBRATION OF A PLATE SUPPORTED ON SPRINGS MODELLED AS

SINGLE D.O.F. SYSTEM

EQUIPMENT/EXPERIMENTAL SETUP NAME: DYNAMIC VIBRATION ABSORBER MODEL

A spring mass single degree of freedom model when excited by a steady state harmonic starts vibrating at the

same frequency as that of the excitation force. The vibration amplitude of the mass will depend upon the

excitation frequency and damping present in the system as given under

Where X is vibration response, F0 is applied harmonic force, r is the ratio of excitation frequency to natural

frequency of the system and ξ is damping ratio. In a system where damping present is very low, peak response

is noticed around its natural frequency.

EQUIPMENT DESCRIPTION: A square plate is supported on four springs at its four corners so that it can be

assumed as a single degree of freedom model in which m is the mass of the plate and K is the equivalent

stiffness of all the springs. An exciter placed below the plate at its centre provides the excitation. Exciter is

placed connected to an oscillator which provides the variable frequency harmonic signal for excitation. An

accelerometer with a vibration meter is used for vibration measurement.

PROCEDURE: Put an accelerometer on the plate and connect it to the vibration meter. Keep the selector knob of

vibration meter at displacement. Switch on the oscillator and vary the frequency from a low value say 5 HZ to

gradually further to at least 1.5 times the resonance frequency. Over this frequency interval note the vibration

reading at several frequency points and draw the response curve X vs w on a graph paper. From the response

plot find the natural frequency of the plate and calculating the mass of the plate find the spring stiffness k.


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EXPERIMENTAL NO: STUDY OF USE OF DYNAMIC VIBRATION ABSORBER ON A VIBRATING PLATE


In many industrial machine foundation systems, the vibration of the machine on the foundation can be modelled

as a spring mass system. In such arrangement if the excitation forces produce in the machine has a frequency

near to the natural frequency of the machine foundation system then excessively large vibration occurs due to

resonance. This happens when

If a secondary spring mass system with mass M1 and spring of stiffness K1 is added to the primary system such

that

Then the vibration of the primary foundation system gets reduced to zero. Hence the secondary spring mass

system is called dynamic vibration absorber system.

PROCEDURE: From experiment no. 13 we already know that the natural frequency of plate -spring system.

Excite the plate at this frequency and note the vibration displacement value. For this an accelerometer and a

vibration meter are to be connected as discussed before. Next attached the secondary spring mass system and

again excite the plate at the same old natural frequency. This time the vibration of the plate will be noticed to be

very less compared to previous value. Note the vibration reading now. Find out mass and stiffness of secondary

system and comment whether it is a tuned absorber or not. Suggest how you can tune it further to reduce the

vibration of the plate

REFERENCE:

1) Mechanical vibration by Rao & Gupta

2) Theory of vibration by W.T. Thomson


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EXPERIMENTAL NO: STUDY OF USE OF TUNABLE DYNAMIC VIBRATION ABSORBER ON A MOTOR

FOUNDATION BEAM


This experiment is similar to experiment no. 14 in the theoretical concepts but the setup is slightly different.

Instead of an exciter we have a motor at the centre of the supporting beam which is having some unbalance that

acts as the source of excitation at the rotating frequency. When the rotating frequency is close to the natural

frequency of the beam; which can be assumed to be simply supported; large vibration will be noticed in the

beam due to resonance. The tuneable absorber system consists of two small cantilever plates on which a mass

can move and thus vary the natural frequency of the secondary system. The position of the mass for which the

secondary system natural frequency matches with that of the primary system gives the tuned condition as then

the primary system will have zero or minimum vibration.

PROCEDURE: with a speed regulator gradually vary the speed of the motor and bring it to the resonance

condition when large vibration will be noticed in the supporting beam. Note the rotating frequency by a digital

tachometer. Switch off the motor and attach the absorber system and again run the motor to its resonating

natural frequency. Adjust the position of the mass so that vibration reduces to its minimum. Report the position

of the tuning mass from free end.


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EXPERIMENTAL NO: STUDY OF FORCE TRANSMISSIBILTY AT DIFFERENT EXCITATION

FREQUENCIES


Machines are often mounted on springs and dampers to see that the forces generated in the machine does not get

transmitted to the ground or foundation. This is required to protect other machines in the neighbourhood and to

ensure better operating environment for working personnel. If we consider a single degree of freedom spring

mass system in which F0 is the force applied on the mass Ft is the transmitted to ground then transmissibility is

defined as

Where, r is the ratio of excitation frequency to natural frequency. If the damping is absent or very low then

This means transmissibility will be low if r 2

PROCEDURE: The load cell connected with the exciter at the centre of the plate gives value of F0 whereas the

load cells connected with the supporting springs measure the transmissibility force Ft Connect all the load cells

to load indicator. Excite the plate with the help of oscillator at different frequencies and measure the load cell

readings

F0= load cell reading of one connected with exciter

Ft= sum of load cell readings of all connected with supporting springs

At various frequencies ranging from 6 Hz to 25 Hz note the value of F0 and Ft and calculate transmissibility TR.

Plot the variation of TR with frequency w on a graph paper.


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EXPERIMENTAL NO: STUDY OF GYROSCOPE

EQUIPMENT/EXPERIMENTAL SETUP NAME: GYROSCOPE

Whenever a spinning component has its spinning axis rotating about another axis called precession axis a

reaction couple acts on the component along third axis and this couple is known as gyroscopic couple is given

by

T is gyroscopic couple, I is moment of the spinning disc and and are respectively the precessional and

spin velocity.

This relationship is valid only under the condition that

a) Spin velocity is constant

b) Precessional velocity is constant, steady precession

c) Angle between axis of spin and axis of precession is 90 degree

PROCEDURE: Start the motor driving the spinning disc and bring the spinning velocity to a stable value.

Because of large inertia of the disc the acceleration of the disc will be slow. Measure the RPM of the disc with

digital tachometer. Bring the RPM to a value around 1500 RPM. Put a known mass on the pan of the gyroscope

which will result in active couple equal to mgl. This active couple will make the spinning disc precess around

the vertical axis. See that the precession is in a horizontal plane so that the angle between the axis of spin and

axis of precession is 90 degree. Note down the angle of precession over a time T and thus calculate precessional

velocity. Spin velocity is again measured with the tachometer and the average of two values is considered. Then

the moment of inertia of the spinning disc can be calculated from the relationship given below. Also the same is

calculated theoretically from the geometry of the disc.


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EXPERIMENTAL NO: STUDY OF JUMP-OFF PHENOMENON IN A CAM FOLLOWER MECHANISM

EQUIPMENT/EXPERIMENTAL SETUP NAME: CAM-FOLLOWER MECHANISM MODEL

In this experiment the setup consists of an eccentric cam and a roller follower with a follower spring whose

precession can be adjusted. When the cam rotates, several forces balance each other at the cam follower

interface. They are inertia force, spring force, weight of the follower, process load etc. If during the motion at

any time the contact force becomes zero then the follower will loose contact with the cam and move

independently till the contact is established. This phenomenon is called Jump-off speed. Jump-off speed

depends on cam profile, type of follower, spring stiffness and preload, follower mass etc. For different jump-off

speed for roller follower will be different from flat face follower even if cam and follower things are same.

PROCEDURE: Find out all required information like cam eccentricity, follower mass spring stiffness etc. Derive

the equation for contact force at the cam follower interface for this particular combination and calculate the

jump-off speed. Then start rotating the cam and gradually increase the speed till the noise characteristic changes

all of a sudden indicating jump-off. Measure the speed now which can be considered as the jump-off speed. A

better way of identifying the jump-off is to measure the follower motion by a non contact type probe and

observe the display on an oscilloscope. The derivation for the jump-off speed is to be done by the students and

to be reported along with a sketch of the cam follower mechanism.

Documents

Theory of Machines 2