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T.E. MECH (SEM-I) Dynamics of Machine Lab

DYNAMICS OF MACHINES LABDYNAMICS OF MACHINES LAB

MANUALMANUAL

Department of Mechanical Engineering DIEMS, Aurangabad.


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CONTENTS

Exp.No Name of the Experiment Page No

1. Governor 9

2. Gyroscope 14

3. Vibration (Longitudinal) 24

4. Vibration (Torsional) 29

5. Gear Train 77

6. Gears 88

Experiment No: 1 Governor



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1.1 Objective, 1.2 Apparatus, 1.3 Theory, 1.4 Description of Apparatus, 1.5 Procedure, 1.6 Specification,

1.7 Observation Table 1.8 Calculation, 1.9 Graph, 1.10 Result & Discussion, 1.11 Precautions, 1.12

Viva-voce questions.

1.1 Objective:To find the controlling force (Fc) for porter governor and proellgovernor.

1.2 Apparatus:Governor Arrangements, vary volt, tachometer,

1.3 Theory:Definitions of

Sensitivity:

Stability:

Hunting:

Isochronisms:

Effort & power:

Insensitiveness:

1.4 Description of Apparatus:



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Fig.1.1 Porter Governor

Fig.1.2 Hartnell Governor

1.5 Procedure:-



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1. Check the instrument for the proper connections.

2. Place the governor assembly in position along with balls and arms.

3. Tighten the screws, nut and bolt gently.

4. Measure the initial height of the governor.

5. Switch on the supply.

6. Vary the height of the governor and corresponding speed with the

help of vary-volt.

7. Bring back the governor to initial position and switch off the supply.

8. Measure the weight of the ball, sleeve and length of the links.

1.6 Specification:

Weight of the sleeve =-----------------------Kg

Mass of the ball =-----------------------Kg

Length of the link =-----------------------mm

Initial height of the governor, h i =-----------------------mm

Weight placed on the sleeve =-------------------------Kg

Hartnell Governor :

Weight of the sleeve =---------------------------Kg

Mass of the ball =---------------------------Kg

Length of the link =---------------------------mm

Initial height of the governor, h i =---------------------------mm

Weight placed on the sleeve =----------------------------Kg

1.7 Observation table:Porter Governor:



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Weight placed on the sleeve-----------------Kg.

S. No. Speed, N

(rpm)

Angular

speed (rad

/sec)

Sleeve

displacement,

x in mm

Height of

Governor

h=hi-x/2

Radius ofrotationr= 12- h2

Controlling

Force,

Fc=m 2r

Remark

1.2.3.4.5.

HartnellGovernor:

Weight placed on the sleeve-----------------Kg.

S. No. Speed, N

(rpm)

Angular

speed (rad

/sec)

Sleeve

displacement,

x in mm

Height of

Governor

h=hi-x/2

Radius ofrotationr= 12- h2

Controlling

Force,

Fc=m 2r

Remark

1.2.3.4.5.

1.8 Calculations:

1.9 Graph:Plot a graph between the angular speed and sleeve displacement for both the

governors.

Plot a graph between the controlling force and radius of rotation for both thegovernors.

1.10 Result & Discussion:



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1.11 Precautions:

1. Reading should be taken carefully.2. Speed should be increased gradually and slowly noting that sleeve may not

come out.

Experiment No.: 4 Gyroscope


1.7 Observation Table 1.8 Calculation, 1.9 Graph, 1.10 Result & Discussion, 1.11 Precautions, 1.12

Sources of error, 1.13 Viva-voce questions.

1.1 Objective:To verify the law of gyroscopic couple, C=I p with the help

of motorized Gyroscope.



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1.2 Apparatus:Motorized Gyroscope, weights, stopwatch & tachometer

1.3 Theory: Fig. 4.1 shows motorized gyroscope.

Fig.4.1 Gyroscope

The various terms involved are:

GYROSCOPE: It is rotating body, which processes perpendicular to plate of

rotation, i.e. axis of rotation also changes its direction under the action ofexternal forces.

Axis of Spin: Is the axis about which a disc/rotor rotates as shown in figure

Precession: It means the rotation of axes in other plane or about other axis

(axis of precession) which is perpendicular to both the axis i.e. axis of spin

and axis of couple.

Gyroscopic Couple: it is applied couple needed to change the angular

momentum vector of rotating disc/Gyroscope when it processes. It acts in

the plane of coupe which is perpendicular to both the other planes (plane of

spin and plane of precession) it is given as:-

C= I p



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Where,

I = Moment of inertia of rotor.

= Angular velocity of rotor.

p= Angular velocity of precession.1.4 Description of Apparatus:

1.5 Procedure:-

1. Balance the initial horizontal position of the rotor.

2. Start the motor by increasing the voltage with the transformer & watch

until it attains a constant speed.

3. Process the yoke frame no.2 about vertical axis by applying necessary

force by hand to the same.

4. It will be observed that the rotor frame swing about the horizontal axis Y-

Y. Motor side is seen coming upward and the weight pan side doing

downwards.

5. Rotate the vertical Yoke axis in the anti-clock wise direction seen from

above & observe that the rotor frame swing in opposite sense.

6. Balance the rotor position on the horizontal frame.

7. Start the motor by measuring the voltage with the autotransformer & wait

till it attains constant speed.

8. Put weight in the weight pan & start the stopwatch to note the time in sec

required

9. Speed may be measured by the tachometer provided on control panel.

10 Enter the observation in the table.

1.6 Specification:

1. Weight of rotor - 6.25 kg

2. Rotor diameter - 301 mm



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3. Rotor thickness - 100.45 mm

1.7 Observation table:

Speed of

discC for 90o

precession

0.5 1 1.5 2 2.5

LoadTime

1.8 Calculations:

1. I=2. =

3. p= d / dt = /2/E 2 S / 22

1.9 Graph:1.10 Result & Discussion:

1.11 Precautions:

1. At starting the pointer should be at zero mark.2. For comparison of Gyroscopic couple angular displacement for different

loads should be insured before conducting the experiment.

3. Proper lubrication should be placed gently and without impact.

1.12 Sources of Errors:

1. Rotor should run at a steady speed.

2. Rotor should rotate in a vertical plane.



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Experiment No: 7 Vibration (Longitudinal)


1.7 Observation Table 1.8 Calculation, 1.9 Result & Discussion, 1.10 Precautions.

1.1 Objective: To study the longitudinal vibration of helical spring and todetermine the frequency of period of vibrator theoretically & actually byexperiment.

1.2 Apparatus:Vibration apparatus, stopwatch, weights, stand scale etc.

1.3 Theory:

Longitudinal vibration:



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Spring stiffness:


Fig. 7.1 shows the line diagram of vibration apparatus.

Fig.7.1, Vibration apparatus

1.5 Procedure:-

1. Fix one end of helical spring by upper screw.2. Determine the free length.3. Put some weight on platform & note down the deflection.4. Stretch spring length some distance & release.5. Count the time required in sec. for say 10,20 oscillations.6. Determine the actual period.7. Repeat the procedure for different weights.

1.6 Specification:

Axial length of spring =



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Mean diameter of spring =Wire diameter =

1.7 Observation table:For Mean Stiffness

S.No. Wt. attachedW= (m x 9.81) N

Deflection ofspring (cm)

Stiffness (k)(N/cm)

1.

2.

3.

4.

For Mean Period

S.No. Wt. attachedW= (m x 9.81)

N

No.ofoscillations

(n)

Time foroscillations

(t)

Period (t/n)

1.

2.

3.

4.

1.8 Calculations:


1.10 Precautions:

1. Note down the time correctly.2. Note down the oscillations properly.3. Dont stretch spring very much.



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Experiment No: 8 Vibration (Torsional)


1.7 Observation Table 1.8 Calculation, 1.9 Result & Discussion, 1.10 Precautions.

1.1 Objective:To study the torsional vibration (undamped) of single rotor shaftsystem.

1.2 Apparatus:Torsional vibration apparatus, stopwatch etc.

1.3 Theory:

Torsional vibration:

Modulus of rigidity:

Polar moment of inertia:

Fig. 8.1 shows the line diagram of a torsional vibration apparatus.



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Fig.8.1, Torsional vibration apparatus


One end of the shaft is gripped in the chuck and heavy flywheel free torotate in ball bearing is fixed at the other end of the haft. The bracket withfixed end of the shaft can be clamped at any convenient position alonglower beam. Thus length of the shaft can be varied during theexperiments.The ball bearing housing is fixed to side member of the mainframe.

1.5 Procedure:-

1. Fix the bracket at convenient position along the lower beam.2. Grip one end of the shaft at bracket by chuck.3. Fix the rotor on other end of the shaft.4. Twist the rotor through some angle and release.5. Note down the time required for 10,20 oscillation.6. Repeat the procedure in different length of the shaft.

1.6 Specification:(a) Shaft diameter=(b) Diameter of disc=(c) Weight if the disc=



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(d) Modulus of rigidity for shaft= 0.8*106 Kg/cm2

1.7 Observation table:

S.No. Length of shaft (L) No. of Oscillations (n) Time taken forn oscillations(t)

Periodictime(T=t/n)

1.2.3.4.5.

1.8 Calculations:i. Find the torsional stiffness KtKt= GIP/L Where L= length of shaft

D= Diameter of shaftIp= P.I. of shaftG= Modulus of rigidity

ii Theoretical

T=2 I/kt

Where, I= M.I. of disc=

iii Experimental

Time of oscillatingT=

No. of oscillation


1.10 Precautions:



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1. The chuck should properly tighten the shaft.2. Note down the time correctly .


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