DoM Lab Manual_Cycle I

SNS COLLEGE OF TECHNOLOGY

Department of Mechanical Engineering

ME3219

MACHINE DYNAMICS LABORATORY

Compiled by

Dr. T. Balasubramani, ASP/MC

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Sl. No. Name of the Experiment Signature

1 Governor – Determination of sensitivity, effort, etc. for Watt, Porter, Proell, Hartnell governors.

2 Cam – Study of jump phenomenon and drawing profile of the cam.

3 Motorised Gyroscope – Verification of law’s – Determination of gyro-scopic couple.

4 Whirling of shaft – Determination of critical speed of shaft with concen-trated loads.

5 Determination of Moment of inertia by oscillation method for connect-ing rod and flywheel.

6 Determination of influence co–efficients for multidegree freedom sus-pension system.

7 Balancing of reciprocating masses.

8 Balancing of rotating masses.

9 Vibrating system Spring mass – system – Determination of damping co – efficient of single degree of freedom system.

10 Determination of transmissibility ratio – vibrating table.

11 Determination of torsional frequencies for compound pendulum and fly-wheel – system with lumped Moment of inertia.

12 Transverse vibration – free – Beam. Determination of natural frequency and deflection of beam.

Content beyond the Syllabus

1 Kinematics of universal joint

2 Determination of velocity and acceleration of four bar mechanism

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Expt. No.: Date:

1. Governor – Determination of sensitivity, effort, etc. for 1) Watt, 2) Porter, 3) Proell, and 4) Hartnell governors.

UNIVERSAL GOVERNOR APPARATUS

INTRODUCTION and DESCRIPTION

This equipment is designed & developed to enable the students to study the characteristics of various types of governors by fixing the mechanisms properly to the spindle shaft. On this apparatus four types of Governors can be studied.

1) Watt 2) Porter 3) Proell 4) Hartnell

Characteristics curves of the dead weight Governors and spring loaded Governor can be drawn.

The apparatus can perform following experiments

1. Determination of characteristic curve of sleeve position against controlling force and speed.

2. Plotting of characteristics curve of radius of rotation.

The drive unit consists of a small electric motor connected by a 'V' belt to drive the shaft. The motor and main shaft are mounted on a rigid M.S. base the frame in vertical fashion. The Governor spindle is supported in a ball bearing.

The unit has a unit has a facility of fixing optional Governor Mechanisms on spindle , by removing the nut fitted on top of the spindle shaft. The Dimmersat is provided with this unit chives precise speed control. A counter hole over the spindle shaft allows the use of a hand tachometer to measure the speed of the shaft. (Tachometer is not in the scope of supply). A graduated scale to the bracket and guided in vertical direction to measure the lift.

The center sleeve of the Porter and Proell Governors incorporates a weight sleeve to which weights can be added. In the Hartnell Governor spring rate & initial compression level can be varied. This enables the Hartnell Governor, to be operated as a counter hole the spindle shaft allows the use of hand tachometer to measure the speed of the shaft. (Tachometer is not the scope of supply). A graduated scale is fixed to the bracket and guided in vertical direction to measure the lift.

The center sleeve of the porter and Proell governors incorporates a weight sleeve to which weights can be added. In the Hartnell Governor spring rate and initial compression level can be varied. This enables the Hartnell Governor, to be operated as a stable or unstable Governor.

EXPERIMENTAL PROCEDURE

The Governor mechanism as desired, to be tested is fitted with the chosen weights and spring, where applicable, to the spindle shaft. Ensure that the nut & bolts of all moving parts and of the spindle shaft are properly tightened. Then following simple procedure is to be followed.

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1. Keep the knob of the dimmerstat in zero position before switching on the main supply.

2. Switch on the main supply and gradually go increasing the speed of the motor. Due to this the center sleeve rise from the lower stop aligning with the marking on the scale. This is initial lift of the sleeve.

3. Note down the readings of the sleeve position &speed for this initial lift. Speed of the motor is to be measured by hand tachometer, from the counter hole provided on the spindle.

4. Then increase the speed in steps to give suitable sleeve movement and note down the corresponding speed. All the readings are to be entered in a tabular observation table.

5. This procedure is adapted for all other three Governor Mechanisms by properly fitting the assembly to the spindle shaft.

6. After completing the experiment bring the knob of the dimmerstat to its original position i.e. zero slowly & gradually. Then switch off the main supply.

7. Then the result may be plotted as.

a) The graph of speed v/s sleeve displacement for Watt, Porter & Proell Governor.

b) Plot the Governor characteristics after doing the necessary calculations.

PRECAUTIONS

1. Do not keep the mains ON when the trail is complete.

2. Make proper connections of field of armature of the DC motor.

3. Increase the speed slowly & gradually. Avoid abrupt use of dimmerstat for controlling the speed.

4. Take the sleeve displacement readings when the pointer is steady.

5. See that higher speed the load on the sleeve does not hit the upper sleeve of the Governor.

6. While closing the test bring the dimmer to zero position & then switch OFF the motor.

7. Put some lubricating oil on the spindle shaft before it is driven.

EXPERIMENTS

AIM

To determine the sensitiveness and effort of various governors

APPARATUS REQUIRED

1. Governors

2. Speed control unit

3. Digital Tachometer

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1) WATT GOVERNOR

Arrange the set-up as shown in fig by using the proper linkages provided. Tighten the bolts and nuts properly. The assembly is ready for conducting the experiment. Now follow experimental procedure as mentioned above.

Go on increasing the speed gradually and take the readings of speed of rotation 'N' and corresponding sleeve displacement 'X’.


The Governor mechanism as desired, to be tested is fitted with the chosen weights and spring, where applicable, to the spindle shaft. Ensure that the nut & bolts of all moving parts and of the spindle shaft are properly tightened. Then following simple procedure is to be followed.

1. Keep the knob of the dimmerstat in zero position before switching on the main supply.

2. Switch on the main supply and gradually go increasing the speed of the motor. Due to this the center sleeve rise from the lower stop aligning with the marking on the scale. This is initial lift of the sleeve.

3. Note down the readings of the sleeve position &speed for this initial lift. Speed of the motor is to be measured by hand tachometer, from the counter hole provided on the spindle.

4. Then increase the speed in steps to give suitable sleeve movement and note down the corresponding speed. All the readings are to be entered in a tabular observation table.

5. This procedure is adapted for all other three Governor Mechanisms by properly fitting the assembly to the spindle shaft.

6. After completing the experiment bring the knob of the dimmerstat to its original position i.e. zero slowly & gradually. Then switch off the main supply.

7. Then the result may be plotted

The graph of speed v/s sleeve displacement for Watt, Porter and Proell Governor.

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Plot the Governor characteristics after doing the necessary calculations

DIMENSIONS

a) Length of each link – L = 125 mm.

b) Initial height of Governor –h0 = 090 mm

c) Initial radius of rotation –r0 = 136 mm

d) Weight of each ball-w = 500 gms

(No need to consider sleeve weight) Radius of rotation 'r' at any position could be found as follows

a) Find height h= h0-X/2

b) Find 'α' by using α = cos-1(h/L) in degrees

c) Then r = 0.05 + Lsinα in meter.

d) Angular velocity 'ω' = 2πN/60 rad/sec

S. No.Speed, N,

rpm

Sleeve Displacement,

X (m)

Height, h

(m)

Radius of Rotation,

r (m)

Force, F=mω²r

kgf

Following graphs to be plotted:

a) Force vs Radius of rotation.

b) Speed vs Sleeve Displacement.

2) PORTER GOVERNOR:

Arrange the set-up as shown in Fig by using the proper linkages & weights provided. Tighten the bolts and nuts properly. The assembly is ready for conducting the experiment. Now flow experimental procedure as mentioned above.

Go on increasing the speed gradually and take the readings of speed of rotation 'N' and corresponding sleeve displacement 'X'.

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(Same as watt governor)

Dimensions:-

a) Length of each link – L = 125 mm

b) Initial height of Governor –h0 = 090 mm

c) Initial radius of rotation –r0 = 136 mm

d) Weight of each ball-w = 500 gms

e) Weight of sleeve weight = 500gms

Radius of rotation 'r' at any position cloud be found as follows

a) Find height h= h0-X/2

b) Find 'α' by using α = cos-1(h/L) in degrees

c) Then r = 0.05 + Lsinα in meter

d) Angular Velocity 'ω' = 2πN/60 rad/sec

S. No.Speed, N,

rpm


X (m)

Height, h

(m)

Radius of Rotation,

r (m)

Force, F=mω²r

kgf

Following graphs to be plotted:

a) Force Vs Radius of rotation.

b) Speed Vs Sleeve Displacement.

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3) PROELL GOVERNOR

Arrange the set-up in Fig

In the Proell governor, with the use of fly weights (forming full ball) the governor becomes highly sensitive. Under these conditions large sleeve displacement is observed for very small change in speed. Hence, it is suggested that increase the speed of the motor very slowly and carefully to get the lift.

PROCEDURE:

(Same as watt governor)

Dimensions

a) Extension of length BG = 075mm

b) Length of each link – L = 125mm.

c) Initial height of Governor –h0 = 090mm.

d) Initial radius of rotation –r0 = 141 mm.

e) Weight of each ball-w = 500 gms.

Go on increasing the speed gradually and take the readings of speed of rotation 'n' and corresponding sleeve displacement 'X'.

Complete the following observation table.

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S. No.Speed, N,

rpm


X (m)

Height, h

(m)

Radius of Rotation,

r (m)

Force, F=mω²r

kgf

a) Find Weight h= h0-X/2

b) Find r in static condition for different sleeve displacement

c) Angular Velocity 'ω'=2πN/60 rad/sec

Following graphs to be plotted:9

a) Sleeve Disp. 'X' Vs 'r' Radius of rotation.

To draw this graph proceeds as follows:

1. Keep the Governor in static position.

2. By lifting the Governor Mechanism manually measure the sleeve displacement and corresponding radius of rotation 'r' of balls.

b) Force Vs Radius of rotation 'r'.

c) Speed Vs sleeve Displacement.

4) HARTNELL GOVERNOR

a) Length-a = 75 mm

b) Length-b = 125mm.

c) Weight of ball-W = 500 gms.

d) Initial radius of rotation –r0 = 177.5 mm.

e) Spring stiffness –P = 2 Kg/cm.

f) Free Length of spring = 100 mm.

1) Measure initial compression of the spring.

2) Go on increasing the speed gradually and take the readings of speed of rotation 'N' and corresponding sleeve displacement 'X'. radius of rotation 'r' at any position could be found as follows:

r = r0 + x (a/b) mtr.

3) Angular Velocity 'ω'= 2πN/60 rad/sec

4) Spring force = Free Length of Sprig- Compressed Length of Spring)× spring Stiffness in Kgs.

Following graphs then be plotted to study governor characteristics :

a) Force Vs Radius of rotation.

b) Speed Vs Sleeve Displacement

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S. No.Speed, N,

rpm


X (m)

Height, h

(m)

Radius of Rotation,

r (m)

Force, F=mω²r

kgf

Schematic layout of governor apparatus – Set up – spring controlled Hartnell governor.

SAMPLE CALCULATIONS

WATT GOVERNOR

Initial height of Governor (Ho) = 94mm

Initial radius of Governor(ro) =136mm

Weight of ball(W) =700gms

Length of each link(L) =125mm

X in mm N in RPM ω h in mm α r in mm F in kgs11

in rad/sec10 158 16.54 89 44o36’ 137.77 2.6820 164 17.17 84 47046’ 142.5 3.030 171 17.9 79 50048’ 146.8 3.3540 177 18.53 74 53o42’ 150.7 3.7Calculation for reading No:1

1. ω = = = 16.54rad/sec.

2. h = ho - =89 mm

3. α = cos-1( ) = 44036’

4. r = 50+Lsin = 50+125sin(44036’) = 137.77mm

5. F= mω2r= 0.7×16.542×.137 = 2.68 Kg.PORTER GOVERNOR

Initial height of Governor (Ho) = 94mm

Initial radius of Governor(ro) =136mm



X in mm N in RPM ω in rad/sec

h in mm α r in mm F in kgs

10 158 16.54 89 44o36’ 137.77 2.6820 164 17.17 84 47046’ 142.5 3.030 171 17.9 79 50048’ 146.8 3.3540 177 18.53 74 53o42’ 150.7 3.7Calculation for reading No:1

1. ω = = = 18.74rad/sec.

2. h = ho - =89 mm

3. α = cos-1( ) = 44036’

4. r = 50+Lsin = 50+125sin(44036’) = 137.77mm

5. F= mω2r= 0.7×16.542×.137 = 2.68 Kg.

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PROELL GOVERNOR

X in mm N in RPM ω in rad/sec r in mm F in KgTable 1- Weight on sleeve -1 kg10 127 13.29 150 1.920 129 13.5 158 2.05Table 2- Weight on sleeve -2 kg10 140 14.66 150 2.320 143 14.97 158 2.5230 146 15.28 165 2.74Calculation for reading No:1

ω = = = 13.29rad/sec

F= mω2r= 1×16.542×.137 = Kgs.

HARTNELL GOVERNOR

Initial radius of Governor(ro) =177.5mm



Length of extended arm (a) = 77mm

Length of link (b) = 122 mm

Spring stiffness = 2Kg/cm

Free length of spring = 103 mm

Initial spring force = (10.3-9.4)×2 = 1.8Kg.

X in mm N in RPM ω in rad/sec r in mm F in KgTable 1- Spring force -1.8 kg4 227 23.77 180.02 7.268 258 27.01 182.54 9.5Table 2- Weight on sleeve -3.2 kg4 269 28.16 180.02 10.188 280 29.32 182.54 11.1912 300 31.41 185.07 13.01

1. ω = = = 23.77rad/sec.

2. r= ro+ X( ) = 177.5+(4×(77/122) = 180.02mm

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3. F= mω2r= 0.7×16.542×.137 = 2.68 Kg.[Note: 0.7 Kg is not weight of the ball. It is weight of the sleeve.]

RESULT

Thus the sensitiveness and effort of various governors are determined.

SPECIFICATIONS

1. Electric Motor :DC Motor, capacity-1/4hp, 1500rpm speed, single phase, 230V AC.

2. Dimmerstat-2Amp.,DC Type- for controlling the speed.

3. Separate linkages with balls are provided for Watt &Potter Type governor mechanism.

4. Spring loaded linkage for Hartnell Governor Mechanism.

5. Weights for Porter and Proell Governor

VIVA VOCE

1. What is the function of governor?The function of a governor is to maintain the speed of an engine within specified lim-

its whenever there is a variation of load. Governors control the throttle valve and hence the fuel supply to cater the load variations on the engines.2. What is the principle of working of centrifugal governor?

These are based on balancing of centrifugal force on the rotating balls by an equal and opposite radial force.3. Differentiate between governor and flywheel?

S.NO Governor Flywheel1 The function of a governor is to regu-

late the mean speed of an engine, when there are variations in the load.

The function of flywheel is to reduce the fluctuations of speed caused by the fluctuation of the engine turning mo-ment during each cycle of operation.

2 It is provided on prime movers such as engines and turbines.

It is provided on engine and fabricating machines.

3 It works intermittently, i.e., only when there is change in load.

It works continuously from cycle to cy-cle.

4 It has no influence over cyclic speed fluctuation.

It has no influence on mean speed of the prime mover.

4. What is the principle of inertia governors?In inertia governors the balls are so arranged that the inertia forces caused by an an-

gular acceleration or retardation of the shaft tend to alter their positions.5. What is controlling force?

An equal and opposite force to the centrifugal force acting radially inward is termed as controlling force.6. What do you mean by governor effort?

The mean force acting on the sleeve for a given percentage change of speed for lift of the sleeve is known as governor effort.7. What is the effect of friction on the governor?

The effect of friction on the governors is to increase the range of speed, governor effort, and power of the governor.

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8. What is meant by hunting?The phenomenon of continuous fluctuation of the engine speed above and below the

mean speed is termed as hunting. This occurs in over-sensitive governors.9. What is controlling force diagram?

When the graph is drawn between the controlling force as ordinate and radius of rotation of the balls as abscissa, the graph so obtained is called controlling force diagram.

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Expt. No.: Date:

2. Cam – Study of jump phenomenon and drawing profile of the cam

AIM

To plot n – θ (follower displacement Vs. angle of cam rotation) curve for different cam follower pairs.

APPARATUS REQUIRED

Cam machineEccentric cam Knife edge followerSpeed controlled motor

OPERATING PROCEDUREThe n – θ plot can be used to find out the velocity and acceleration of the follower system. For this experiment, arrange the set op as shown in Fig. the exact profile of the cam can be obtained by taking observations ‘n’ vs. ‘θ’, where n= displacement of the follower from rotation initial po-sition and θ = angle of am rotation with reference from axis of symmetry chosen. By differentiat-ing the n – θ curve once and twice, the velocity and acceleration curves can be plotted for the fol-lower and cam under study.

a. Select any one pair of cam and follower.b. Fix the follower to the push rod and fix the cam in the cam shaft.c. Keep the cam at the lower most position.(Nose of the cam is downward position)

And now tighten the follower in such a way that the follower and cam are in just contact.

d. Fix dial gauge to stand and rotate the base plate, in order to e. touch displacement rod of gauge.

f. Also, note while fixing cam position angular scale pointer is at zero and even dial gauge pointer is at zero

g. Now go on rotating the cam shaft by hand through 30 or 45 degree and note down the dial gauge reading. This is taken till 360 degree

h. To observe phenomenon of speed keep initial setting of spring compression at a certain level and observe jump speed for different follower weights by adding them successively and plot the graph

i. Similarly go on increasing the spring force and observe the jump speed and fill the reading in the table

CAM ANALYSIS

Angular rotation of cam

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Cam Rotation Deflection020406080100120140160180200220240280300320340360

Sl. No Weight on follower (kg) Jump Speed (rpm)1234

RESULT

The jump phenomenon and displacement of follower of the cam has been determined.

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Extra

A) Eccentric cam with Knife edge followerB) Circular arc cam with Mushroom followerC) Tangent cam with Roller follower

Cam Rotation A B C0 0.0 0.0 0.0

20 5.11 0.02 0.0140 5.56 0.03 0.0260 6.72 0.04 0.0680 7.95 0.05 0.035100 9.39 0.05 0.035120 10.48 0.23 0.4140 12.03 1.9 1.13160 12.72 5.16 5.17180 12.95 6.18 8.58200 12.65 4.88 5.65220 11.7 1.64 1.18240 10.38 0.35 0.23280 7.62 0.17 0.18300 6.48 0.10 0.10320 5.6 0.08 0.06340 5.11 0.02 0.02360 0.0 0.01 0.01

EXPERIMENT (II)

CAM ANALYSIS

AIM: To observe Jump phenomenon of various cam and follower assembly.

Eccentric cam with Knife edge follower

No Weight on follower (kg) Jump Speed (rpm)1 0 15002 0.250 12253 0.50 10054 0.750 9335 1.00 8686 1.50 733

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Circular arc cam with Mushroom follower


Tangent cam with Roller follower


EXPERIMENT III

CAM ANALYSIS

AIM: To study the effect of Spring compression on jump speed with constant follower weight

Eccentric cam with Knife edge follower

No Spring Lt – mm Spring force Jump Speed (rpm)1 33 4.26 9202 36 3.42 8603 40 1.90 8054 43 0.76 725

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Expt. No.: Date:

3. Motorised Gyroscope – Verification of law’s – Determination of gyroscopic couple.

MOTORISED GYROSCOPEAIMTo determine the gyroscopic couple by using motorized gyroscope

INTRODUCTIONA) AXIS OF SPINIf a body is revolving about an axis the latter is known as axis of spin. (Refer Fig. 1 where OX is the axis of spin).

B) PRECESSION Precession means the rotation about the third axis OZ (Refer Fig. 1) Which is perpendicular to both the axis of spin ‘OX’ and that of couple ’OY’.

C) AXIS OF PRECESSIONThe third axis OZ is perpendicular to both the axis of spin “OX” and that of couple “OY” is known as axis of precession.

D) GYROSCOPEIt is a body, which, while spinning about an axis, is free to rotate in either directions under the action of external forces.EXAMPLESLocomotive, automobile and aero-plane making a turn. In certain cases the gyroscopic forces are undesirable whereas in other cases the gyroscopic effect may be Utilized in developing desirable forces.

E) GYROSCOPIC EFFECTTo a body, revolving (or spinning) about an axis say ‘OX’ (Refer fig.1), if a couple represented by a vector OY perpendicular to ‘OX’ is applied, the body tries to Precess about an axis ‘OZ’ which is perpendicular both to ‘OX’ and ‘OY’. Thus the plane of spin, plane of precession and plane of gyroscopic couple are mutually perpendicular. The above combined effect is known as precession or gyroscopic effect.

DESCRIPTION AND WORKING INSTRUCTIONSSchematic arrangement of Gyroscope is as shown in the Figure . The motor is coupled to the disc rotor, which is balanced. The disc shaft rotates about ‘X-Y’ axis in two- ball bearing housed in the frame No. 1. This frame can swing about ‘y-y’ axis in bearings provided in the yoke type frame No. 2. While in a steady position. Frame No.1 is balanced. The yoke frame is free to rotate about vertical axis ‘z’. Thus freedom of rotation about three perpendicular axis is given to the ro-tor.

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PRECAUTIONS1. While measuring the speed with tachometer do not exert pressure on rotor shaft.Use of

Non- contact type tachometer or stroboscope for measurement of motor speed will give better results.

2. When the speed of rotor spin is changed, it takes some time to attain the constant speed due to rotor inertia. Hence, it is advised to wait until the rotor spin reaches constant speed.

TECHNICAL DATA

1) Weight of Rotor (W) : 6.5 Kgs.2) Rotor Diameter (D) : 300 mm (30 cm.)3) Rotor Thickness : 10mm (1 cm)

4) Moment of inertia of :

the disc, coupling andmotor rotor about central axis (I)

5) Distance of bolt of : 18.0 cm.Weight pan from disc

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Center (L)6) Motor : AC/DC, Fractional HP, Single phase, 6000 rpm.

RULE NO.1“The spinning body exerts a torque or couple in such a direction which tends to make the

axis of spin coincides with that of the precession.”To study the rule of gyroscopic behavior following procedure may be adopted.

a) Balance the initial horizontal position of the rotor.b) Start the motor by increasing the voltage with the dimmer, and wait until it attains Con-

stant speed. c) Process the yoke frame No.2 about vertical axis by applying necessary force by hand

To the same (in the clockwise sense seen from above).d) It will be observed that the rotor frame swings about the horizontal axis ‘YY’. Motor

Side is seen coming upward and the weight pan side going downwards.e) Rotate the vertical yoke axis in the anti- clockwise direction seen from above and

Observe that the rotor frame swing in opposite sense (as compared to that in Previous case following the above rule).

RULE NO.2 “The spinning body processes in such a way as to make the axis of spin coincide withthat of the couple applied, through 90 turn axis

a) Balance the rotor position on the horizontal frame.b) Start the motor by increasing the voltage with the dimmer and wait till the disc attains

constant speed.c) Put weight (1 kg., 1.5 kg. or 2 kg) in the weight pan, and start the stop watch to note the

time in seconds required for precession, through 90 or 180 etc.d) The vertical yoke processes about OZ axis as per the rule No.2.e) Speed may be measured by the tachometerf) Enter the observation in the table.

OBSERVATION TABLEN

(rpm)Load

(w) (kgs)Time

(dt) secDegrees

(d)ωp

(rad/sec)Tact

(kg.cm)Tth

(kg.cm)

GYROSCOPIC RELATIONT actual = I ×ω × ωp, where (kg. cm) (Gyroscopic couple)I = M. I. of disc kg.cm.sec.2

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ω = Angular velocity of precession of disc in radians per secondN = RPM of disc ωp = Angular velocity of precession of yoke about vertical axis radians per second. = (d/dt)×(π/180) rad/sec.

From above findTactual = Iω ωp kg.cmL = Distance of weightTth = w×L (kg. cm) w = weight applied in kgs.ωp is to be calculated for short duration of time, as the balance of rotation of disc about

the horizontal axis yy is due to application of torque, and because of which wp goes on reducing gradually.

RESULT Thus the gyroscopic couple has been determined.

MOTORISED GYROSCOPESample CalculationsOBSERVATIONS

1) Dia. Of disc :300 mm = 30 cm (D)2) Weight of Rotor : 6.85 kg. (w)×9.81 N3) Distance of Bolt :18.4 cm(L)

From Disc Moment of Inertia = I = w/g × (D)2/8 or mR2 /2 Moment of Inertia = I = 6.85/981 × (30)2/8 = 6.98 ×10-3 ×112.5 I = 0.78 Kg.cm. sec2

OBSERVATION TABLEN

(RPM)Load(w)

(kgs)

Time(dt) sec

Degrees(d)

wp(rad/sec)

Tact

(kg.cm)Tth

(kg.cm)

2932 0.5 7 15O 0.037 8.86 9.2

1.0 3.5 150 0.0743 17.79 18.4

1800 0.5 5 150 0.052 07.64 09.2

1.0 2.5 150 0.10 14.70 18.40

Specimen calculations for reading No. 1- 2932 rpm for 0.5 kg. Load.1) T act = I × ω × ωp

2) ωp =(d/dt)×(π/180) = (15/7)×π/180 = 0.037rad/sec.

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3) ω =

4) Tact = 0.78×307.03×0.037= 8.86 Kg.cm5) Tth =w×L = 0.5 ×18.4 = 9.2 Kg.cm

1. Give the applications of gyroscopic principle.It is used:

1. in instrument or toy known as gyroscope,2. in ships in order to minimize the rolling and pitching effect of waves, and3. in aero planes, monorail cars, gyrocompasses , etc.

2. Give the applications of gyroscopic principle.It is used

1. in instrument or toy known as gyroscope,2. in ships in order to minimize the rolling and pitching effect of waves, and3. in aero planes, monorail cars, gyrocompasses , etc.

3. What is gyroscopic torque?When ever a rotating body changes its axis of rotation, a torque is applied on the rotating

body. This torque is known as gyroscopic torque.

What is the effect of gyroscopic couple on rolling of ships? Why?We know that, for the effect of gyroscopic couple to occur, the axis of precession should always be perpendicular to the axis of spin. In case of rolling of a ship, the axis of precession is always parallel to the axis of spin for all positions. Hence there is no effect of the gyroscopic couple act -ing on the body of the ship during rolling.Discuss the effect of the gyroscopic couple on a two wheeled vehicle when taking a turnThe gyroscopic couple will act over the vehicle outwards. The tendency of this couple is to over turn the vehicle in outward directionWhat is gyroscopic torque?Whenever a rotating body changes its axis of rotation, a torque is applied on the rotating body. This torque is known as gyroscopic torque

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Expt. No.: Date:

4. Whirling of shaft – Determination of critical speed of shaft with concentrated loads

WHIRLING OF SHAFT APPARATUSAIMTo determine the whirling speed of the shaft for various diameters and lengths and to compare its theoretical and actual speeds.APPARATUS REQUIRED:

1. Test Shafts2. Auto Transformer3. Tachometer4. Meter Scale

DESCRIPTIONThis apparatus is developed for the demonstration of Whirling phenomenon. The shaft can be tested for free - free end conditions.The apparatus consists of a frame to support its driving motor, end fixing having bearing blocks. A special design is provided to clear out the effects of bearings of motor spindle from those of testing shafts. The special design features of this equipment are as follows…

A) COUPLING A flexible shaft is used to drive the test shaft from motor.

B) BALL BEARING FIXED ENDS These ends fix the shafts while it rotates. The shaft can be replaced within a short time with the help of this unit.

C) SHAFT SUPPLIED WITH THE EQUIPMENT Polished steel shafts are supplied with the machine, the dimensions being as under..Shaft No. Dia.(approx) Length(approx)

01. 5mm 900mm 02. 4mm 900mm

D) END FIXING ARRANGEMENT 1) Supported end condition : Make use of end block with single Self aligning bearing.

GUARDS D1 AND D2The guards D1 and D2 (Fig.1) is fixed permanently to the base frame. Rotating shafts are to be fitted in blocks in A and B stands.SPEED CONTROL DRIVING MOTOR

The driving motor is – A.C./D.C.Motor,F.H.P.,6000rpm.,50c/s.,250 volts and speed con-trol unit is a Dimmer stat of 240V.,2 amps.,50c/s.MEASUREMENT OF SPEED

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To measure the speed of the rotating shaft a simple tachometer may be used (tachometer not in scope of supply). A provision is provided on the opposite side of the shaft of the motor for measuring the speed.

PROCEDURE1. The test shaft diameter length is fixed on the supports of the apparatus.2. The static deflection of shaft is noted in the form of nodes.3. Then the speed of the shaft is controlled with the help of an autotransformer4. The shaft is rotated until a bob is formed in the shaft and note the corresponding speed.5. Calculate the frequency of vibration.6. To find two node frequency increase the speed of the shaft until two bob is formed in the

shaft and note the corresponding speed. Calculate the corresponding speed.WHIRLING OF ELASTIC SHAFTSIf,

L=Length of the shaft in cms.E=Young’s Modulus = 2.060 x 106 Kg/cm²I=2nd moment of inertia of the shaft cm4 W=Weight of the shaft per unit length Kg/cm.g=Acceleration due to gravity, 981 cm/sec2

Then the frequency of vibration for the various modes is given by the equation26

The various values for K are given below :End condition Value of K

1st Mode 2nd modeFree, Free 1.57 6.28

DATA Shaft Dia. I=cm4 W=Kg/cm0.5cm 3.068 x 10-3 0.14 x 10-2

0.4cm 2.512 x 10-3 0.1 x 10-2

TYPICAL TEST OBSERVATIONS1) Both ends of shaft free (supported) 1st and 2nd mode of vibration can be observed on

shafts with 4mm dia and 5mm dia.2) There is a difference between theoretical speed of whirling and actual speed observed,

due to the following reasons… The end conditions are not so exact as assumed in theory. Pressure of damping at the end bearings. Assumptions made in theoretical predictions. Lack of knowledge of exact properties of shaft material. A uniformly loaded shaft has, theoretically infinite no.of natural frequencies of

transverse vibration for fundamental mode observation of the first mode of whirling is therefore not so defined and thus difficult.2nd mode can be very easily observed.

PRECAUTIONS TO BE OBSERVED IN EXPERIMENTS1) If the revolutions of an unloaded shaft are gradually increased it will be found that a cer-tain speed will be reached at which violent instability will occur, the shaft deflecting into a single bow and whirling round like a skipping rope. If this speed is maintained, the deflection will be-come so large that the shaft will be fractured. But if this speed is quickly run through, the shaft will become straight again and run true until at another higher speed the same phenomenon will occur. The deflection now however, being in a double bow and so on. Such speeds are called critical speeds of whirling.2) It is advisable to increase the speed first rather than observing the 1st critical speed which increases the speed of rotation slowly. In this process there is a possibility that the amplitude of vibration will increase suddenly bringing the failure of the shaft. If, however, the shaft speed is taken to maximum first and then slowly reduced, (thus not allowing time to build-up the ampli-tude of vibration resonance) higher mode will be observed first and the corresponding speed noted and then by reducing the speed further the next mode of lower frequency can be observed without any danger or rise in amplitude as the speed is being decreased and the inertia forces are smaller

27

in comparison with the bending spring forces hence possibility of build-up of dangerous ampli-tudes at resonance or near resonance is avoided.3) Thus it can be seen that it is a destructive test of shafts and it is observed that the elastic be -haviors of the shaft material changes a little after testing it for a few times and it is advisable therefore, to use fresh shaft samples afterwards.4) Fix the apparatus firmly on the suitable foundation.

OBSERVATION TABLE:

S.No End conditionShaft diame-

ter, dSpeed for 1st

Mode – RPMSpeed for 2nd

Mode - RPMLength of Shaft -mm

01. Free – Fixed 5mm 800

02. Supported & Supported (free)

5mm 800

03. Free – Fixed 4mm 800


4mm 800

CALCULATIONS FOR SUPPORTING & SUPPORTED (FREE) SR.NO.2 READING :FOR FIRST MODE – 3/16” DIA SHAFT :Observed speed – ----------- RPM, Length of shaft – 900mmTheoretical speedWhirling of elastic shafts (f) – Frequencyf = K x (√ (E x I x g) / (W x L^4))where, K = 1.57 E = 2.06 x 106 Kg/cm2

g = Acceleration due to gravity = 981 cm/sec2

W = 0.15 x 10-2

I = 25.39 x 10-6

f = ---------- (RPS) ×60= ------------ (RPM)

RESULT:The whirling speed of the shaft for various diameters and lengths has been determined

and its theoretical and actual speeds are compared.

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SAMPLE CALCULATIONObservation Table:S.No End condition Shaft size Speed for 1st Mode

– RPMSpeed for 2nd

Mode - RPMLength of Shaft -mm

01. Free – Fixed 3/16” – 4.76mm

1146 4440 800


3/16” – 4.76mm

720 3000 800

03. ----do---- 1/4” – 6.35mm

1100 3615 800

04. Fixed – fixed 3/16” – 4.76mm

1680 - 800

05. ----do---- 1/4" – 6.35mm

2150 - 800

06. ---do--- 5/16” – 7.93mm

2760 - 800

CALCULATIONS FOR SUPPORTING & SUPPORTED (FREE) SR.NO.2 READING :FOR FIRST MODE – 3/16” DIA SHAFT :

Observed speed – 720 RPM, Length of shaft – 800mmWhirling of elastic shafts (f) – Frequency

f = K x ( √ E x I x g / W x L4)where

K = 1.57 E = 2.06 x 106 Kg/cm2

g = Acceleration due to gravity = 981 cm/sec2

W = 0.15 x 10-2

I = 25.39 x 10-6

f = 14.34 RPS = 14.34×60 = 860 RPM

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Expt. No.: Date:

5. Determination of Moment of inertia by oscillation method for connecting rod and flywheel.

(a) MOMENT OF INERTIA OF FLY WHEELAIMTo determine the moment of inertia of connecting rod and flywheel by oscillation method.FORMULA

whereT = periodic time in secK = Radius of gyration about C.G. in cmOG = Distance of the C.G. of rod from support = 122mmL = length of suspended pendulum cm = 206mm

PROCEDURE1. support the rod on knife edge2. allow the bar to oscillate and determine periodic time ‘T’ 3. complete the observation table given below.

OBSERVATION TABLE ( with lumped mass)Sl.No.

OG (Cms) No. of Osc ‘n’ Time for ‘n’Osc. t (sec)

t - sec(Expt)t/n

KExperimental

CALCULATIONFind ‘K’ experimentally from the relation

where, Tex = periodic time. Tex = t/n t = Time for ‘n’ osc. n = No. of osc.

Find moment of inertia of connecting rodMI of connecting rod = m x K2 in Nm2

where, m = mass of connecting rod = 0.95 Kg x 9.81 = 9.31 RESULT

The moment of inertia of the given connecting rod has been determined.

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(b) MOMENT OF INERTIA OF FLY WHEELDESCRIPTION

The pendulum consists of flywheel. The fly wheel is supported by the knife edge.PROCEDURE

1. support the flywheel on knife edge.2. allow the fly wheel to oscillate and determine periodic time ‘T’, by knowing the time

‘t’ for say ‘n’ oscillations.3. complete the observation table given below.

OBSERVATION TABLE. Sr.No.

OGCms

No. of Osc‘n’

Time for ‘n’Osc.‘t’ secs

t- sec(Expt)t/n

KExperimental

CALCULATIONFind ‘K’ experimental from the relation

where, T = periodic time in sec (t/n) K = radius of gyration about C.G. in cm OG = distance of the C.G of wheel from support = 12.5cm

Tex = periodic time. Tex = t/n

t = Time for ‘n’ osc. n = No. of osc.

Find K theoretical K = D/ (2 3 )

whereD = Diameter of the flywheel = 25cm

Compare values of ‘K’ obtained theoretical and experimental and verify the same

02. Find moment of inertia of FLY WHEELMI of fly wheel = m x K2 in Nm2

Where, m = mass of connecting rod = 0.95 Kg x 9.81 = 9.31 NK = Internal radius of the fly wheel.

RESULT:

The radius of gyration ‘K’ and moment of inertia of the given flywheel has been de-termined.

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SPECIMEN CALCULATIONEXPT. NO. 2 :- COMPOUND PENDULUM

i) To determine the raduius of gyration ‘K’ of given compound pendulum.ii) To verify the relation-

OBSERVATION TABLESr.No.

Center of gravity in cms

No. of Osc

Time for ‘n’ Osc

T-sec(Expt)

KExperimental

KTheoretical

OG ‘n’ ‘t’ secs t/n01 37.5 10 14 1.4 21.65 20.5002 27.5 10 12 1.2 15.87 15.06

CALCULATION FOR READING N0. 01Tex = 2π√(K2 + (OG)2) / (g(OG)2)1.4 = 2π√(K2 + (37.5)2) / (981(37.5)2)Kexp = 20.5 LFind K theoretical = 2√3

= 75 / (2√3) = 21.65.

32

Expt. No.: Date:

6. Determination of influence co–efficients for multi degree freedom suspension system.

AIMTo determine influence numbers/influence coefficients and natural frequency of a multi

degree freedom system.

APPARATUS REQUIREDSpring support, springs, Meter scale, Weights and Bolts

INTRODUCTIONConsider that a spring is suspended to the spring support and this system is fixed on a

channel base frame. To this spring, there is a bolt fitted to the bottom side of the spring and to this bolt weight is fitted. Due to the weight, there will be a certain deflection in the spring, say δ11. The second spring is fixed to the 2nd Bolt and again weight is fitted to the 3rd bolt fitted to the bottom of the second spring. Due to this, there will be some deflection on the First and second spring, say δ12 on the first spring and δ21 on the second spring. These deflections on the corresponding springs - δ11 δ12 δ13 ..., δ21 δ22 δ23 etc. are called as INFLUENCE NUMBERS or INFLUENCE COEFFICIENT.DESCRIPTION:

This system consists of a base frame to which, centrally, a support frame of MS Channel is fixed vertically. Bolts with hole frilled on top and bottom side are provided for fixing springs. Four springs of different wire diameter and spring stiffness are supplied. Please refer Fig – 1. Springs are suspended vertically in downward direction.

All the springs are suspended to one another with bolts and nuts in between the two springs. Desired weights are fixed to the bolts as shown in the Fig – 1. With the help of measuring scale, deflection in the springs1, springs 2, springs 3 etc is measured. Stop watch is provided to measured the number of oscillations of the system.

OPERATING PROCEDURE1. Springs will be suspended vertically downward to the central spring support.2. Fix the spring with heavy wire Dia. to the spring support by bolt.3. Add weight to the bolt and spring assembly. Note down the first spring deflection ' δ11' in

the observation table.4. Place the second spring to the bottom of the bolt fixed first to first spring. Add some

weight to the second bolt. Note down the deflection in the first spring as δ12 & δ21 of the second spring in the observation table.

5. Repeat the above procedure for third and fourth spring and note down the deflection of the springs - δ13, δ22, δ31 etc. in the observation table.

6. After measuring all the deflections, by giving some pressure to bottom spring make the system to oscillate. Measure the time required for 'N' oscillations of the system. Repeat this procedure for 3 to 5 times and take mean of these readings.

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OBSERVATION TABLE

S. No.Deflection / Influence

No. or influence coefficient, 'δ'

Time Required

for 'N'

oscillations, s

Natural

Frequency

- Expt, f Ne

Natural Frequency

- Theo, f Nt

1 δ 11

2 δ12

3 δ 13

4 δ 21

5 δ22

6 δ23

7 δ----

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CALCULATIONS Data / Constants :S.NO SPRING WIRE DIAMETER STIFFNESS1 2mm 0.1 kg/cm2 2.5mm 0.25kg/cm3 3mm 0.76kg/cm4 3.5mm 0.93kg/cm a) Spring wire dia.

i) 2mmii) 2.5 mmiii) 3mmiv) 3.5mm

Natural Frequency – Experimental:f Ne = N / twhere N = No. of oscillations

t = Time required for Oscillations in sec.

Natural Frequency – Theoretical:For single degree of freedom

f Nt = f1 =

For multi degree of freedom f Nt = f1+ f2 + f3 .....

f1 =

f2 =

where K = Spring StiffnessM = Weight on the base plate

RESULTThe influence numbers/influence coefficients and natural frequency of a multi degree

freedom system is determined.

35

W3

W1

W2

DoM Lab Manual_Cycle I

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