VIB – LAB

Prof.Mahadve N Harkude VSMIT,Nipani Page 1

SIMPLE PENDULUM

AIM :

To verify the relation T = 2 L

G

Where, T = Periodic time in sec.

L = Length of Pendulum in mm.

Objective:

1.To develop an understanding the concept simple pendulum.

2.To develop an understanding the meaning of Periodic time.

3.Determine the natural frequency of oscillation of system.

Figure

DESCRIPTION

For conducting the experiment, each ball is supported by nylon thread into the hook. It is

possible to change the length of pendulum. This makes it possible to study the effect of variation

of length on periodic time. A small ball may be substituted for large ball to illustrate that the

period of oscillation is independent of the mass of the ball.


PROCEDURE

1. Attach the each ball to one end of the thread.

2. Allow the ball to oscillate and determine the periodic time T by knowing the time for say

10 oscillations.

3. Repeat the experiment by changing the length.

4. Complete the observation table given below.

OBSERVATION TABLE

Sr.

No.

Mass of the

Ball, m- gms

Length. of

string,

„L‟ mm.

No. of

Oscillation

„n‟

Time for

N Osc.

„t‟ Secs.

T (Expt) ,sec

T

Theoretical

sec

Weight of big ball : 230 gms., Dia. : 80mm

Weight of small ball : 170 gms., Dia. : 70mm

CALCULATIONS

TExpt. = ... secs.

t = Time required for „n‟ no. of oscillations.... secs.

n = No. of oscillations

L = Length of suspended string or Nylon rope .... mm.

... secs.

Plot the graph T2 Vs L. It should yield the straight line.

Conclusion: The length of simple pendulum is directly proportional to the square of the

period of oscillation.

Recommendations: As it related to basic concept of vibration and related to Unit 1 in theory.

TTheo = 2 x L

g

t

n


COMPOUND PENDULUM

AIM:

1. To determine the radius of gyration „k‟ of given compound pendulum.

2. To verify the relation T = 2 K

2 + (OG)

2

g (OG)

Where, T = Periodic time in sec.

K = Radius of gyration about C.G. ... cm.

OG= Distance of the C.G. of rod from support.

L = Free Length of suspended pendulum - cm.

g = 981 cm/sec2

Objective:

1.To develop an understanding the concept of gyration.

2.To develop an understanding the meaning of radius of gyration.

DESCRIPTION

The compound pendulum consists of steel bar. The bar is supported in the hole by the

knife edge.


PROCEDURE

1. Support the rod on knife edge.

2. Note the length of suspended pendulum and determine OG..

3. Allow the bar to oscillate and determine T by knowing the time for say 10

oscillations.


OBSERVATION TABLE

Sr.

No.

L

Cms

OG in

cm

No. of

Oscillation

Time req for

„n‟ Oscillations.

Secs.

T sec

(Expt)

t/n

K

Expt.

OG1 - a) Dist. between first point of suspension & CG1 - --- cm

b) Dist between second point of suspension & CG1 - ---- cm.

CALCULATIONS

01. Find „k‟ experimental from the relation

Where, T = Periodic time.

T = t/n

t = Time for „n‟ osc.

n = No. of osc.

Substituting for OG and T in the above formula...

Find K (theo) = L

2 3

Compare values of „K‟ obtained theo. and expt.


T = 2 K

2 + (OG)

2

g(OG)2


EXPERIMENT NO.3: BI-FILAR SUSPENSION.

AIM:

1. To determine the radius of gyration of given bar by using Bi-Filar suspension.

Objective:

1.To develop an understanding the concept of gyration of suspension.

2.To develop an understanding the moment of inertia of a horizontal rectangular drop bar

about its center mass using the bifilar suspension technique.

Figure: Bi-Filar Suspension system

DESCRIPTION

A uniform rectangular section bar is suspended from the pendulum support frame by two

parallel cords. Top ends of the cords are attached to hooks fitted at the top. Other ends are

secured in the Bi-filar bar. It is possible to change the length of the cord. The suspension may

also be used to determine the radius of gyration of any body. In this case the body under

investigation is bolted to the centre. Radius of gyration of the combined bar and body is then

determined.

PROCEDURE

1. Suspend the bar from hook. The suspension length of each cord must be the same.

2. Allow the bar to oscillate about the vertical axis passing through the centre and measure

the periodic time T by knowing the time for say 10 oscillations.

3. Repeat the experiment by mounting the weights at equal distance from the centre.



OBSERVATION TABLE

Sr.

No.

Weight L

Cms

“a”

cms.

No. of

Oscillations

Time for

n Osc.

t Secs.

Periodic

Time

K

Experimental

K

Theoretical

CALCULATIONS

For Bi-Filar suspension

Where, 2a = distance between two wires:__________ mm

k = Radius of gyration of bi-filar suspension.

Wt. of the flat = 2.05 kg.

Length. of the beam = 500mm

Weights a) 0.50 kg small. – 2 Nos.

b) 0.75kg. Big. – 2 Nos.

Find „k‟ experimental by using above formula.

K theoretical = L

2 3

SIZE OF SPANNER REQUIRED: 20 – 22


T = 2 x k L

a g


SPRING MASS SYSTEM

AIM :

To study the longitudinal vibrations of helical spring and to determine the

frequency or period of vibration (oscillations) theoretically and actually by

experiment

Objective:

1.To develop an understanding the longitudinal frequency.

2.Determination of helical spring stiffness (K).

3.Determination of natural period of oscillation and obtain natural undamped frequency.

DESCRIPTION

One end of open coil spring is fixed to the screw, which is firmly fixed to the upper bracket of

vertical frame. The spring is properly gripped by means of lock nut to the screw. Lower end of the

spring is attached to the platform carrying the weights. Thus the design of the system incorporates

vertical positioning of the unit to suit the convenience.


PROCEDURE

1. Fix one end of the helical spring to the screw provided to the horizontal bracket.

Fix the Weight pan to the other end of the spring and tighten the nut tightly to

hold the pan properly. Ensure it is not loose as it will come out while performing

experiment.

2. Measure the free length of the spring before putting the weight.

3. Put some, say 1Kgs weight on the platform and note down the deflection.

4. Stretch the spring through some distance, about 20 to 30 mm and release it.

5. Note down the time required (in sec.) for „n‟ (10 or 20) oscillations.

6. Determine the actual time period.

7. Repeat the above procedure for different weights 1, 2, 3 kgs etc...

OBSERVATIONS

OBSERVATION TABLE NO.1 ( For finding km. ) Static Reading.

Obs. No.

Wt. Attached in pan – Kg

- „W‟

Deflections of spring cm.

()

K

=

W

Km

.(mean)

01.

02.

03.

04.

05.

OBSERVATION TABLE NO.2 : Oscillations Method

Obs.No. Weight attached

Kg.( W )

No. of Osc.

N

Time required for n

osc. (sec)

Periodic time - T expt

= t/n


CALCULATIONS

01. Find Km. (mean stiffness) of the spring as follows

Where,

K1 = w1

, K2 = w2

, K3 = W3

1 2 3

N = number of readings

02. Find „T‟ theoretical by using relation

T theoretical = 2 w

Km x g

03.

Hence, f theoretical = 1

Hz

T (theo)

SIZE OF SPANNER REQUIRED: 16 - 17


Km = K1 + K2 + K3

…..Kg/cm. N

Check with experimental value T expt. = t

n


SINGLE ROTOR SYSTEM (UNDAMPED)

AIM :

To study the Torsional Vibration (un-damped) of single rotor shaft system.

Objective:

1.To develop an understanding the Torsional frequency.

2.To develop an understanding the torsional stiffness of shaft.

3.

DESCRIPTION

Figure shows the general arrangement for carrying out the experiments.

One end of the shaft is gripped in the chuck and heavy flywheel free to rotate in ball bearing is

fixed at the other end of the shaft. The bracket with fixed end of shaft can be clamped at any

convenient position along lower beam. Thus length of the shaft can be varied during the

experiments. Specially designed chucks are used for clamping ends of the shaft. The ball bearing

support to the flywheel provides negligible damping during experiment. The bearing housing is

fixed to side member of the main frame.

PROCEDURE

1. Fix the bracket at convenient position along the lower beam.

2. Grip one end of the shaft at the bracket by the chuck.

3. Fix the rotor on the other end of the shaft.

4. Twist the rotor through some length and release.


5. Note down the time required for 10 - 20 oscillations.

6. Repeat the procedure for different length of shaft.

7. Make the following observations.

a) Shaft dia. 'd' = 3 mm

b) Dia. Of Disc. A - 'D' = 225 mm (Big Disc)

c) Wt. Of the Disc. 'W' = 2.8 Kgs.

d) Modulus of rigidity for shaft = 0.8 x 106 Kg./cm

2

OBSERVATION TABLE

Obs Length of Shaft „L‟

cm.

No. of Osc.

„n‟

Time required for

„n‟ Osc. „t‟ secs.

Periodic time -

T expt. = t/n

CALCULATIONS

1. Determination of Torsional stiffness Kt

Kt = G IP

L

L = Length of the shaft.

IP = Polar M.I. of shaft = d

4

32

d = Shaft dia.

G = Modulus of rigidity of shaft = 0.8 x 106 Kg./cm

2


2. Determine T theoretical = Tth =

=2 I

Where, I = M.I. of disc = W

x D

2

Kt g 8

3. Determine T experimental

= Time for „n‟ osc.

= Sec. No. of osc. „n‟

RESULTS

Obs.

No. Length of Shaft Kt

T(Theo)

Secs.

T(Exp)

Secs.

F(Theo)

Secs.

F(Exp)

secs

CONCLUSIONS

FTheo = 1

FExp. = 1

TTheo TExp.

SIZE OF SPANNER REQUIRED: 20 – 22



TWO ROTOR SYSTEM ( Un-Damped )

AIM:

To study the free vibrations of two rotor system and to determine the natural frequency of

vibration theoretically and experimentally.

Objective:

1.To develop an understanding the Natural frequency.

2.To develop an understanding the moment of Inertia of rotors disc.

3.To develop an understanding the torsional stiffness of shaft.

4.Natural period of oscillation of the two degree of freedom system.

Figure

DESCRIPTION

Fig. shows the general arrangement for carrying out the experiment. Two disc having different

mass moment of inertia are clamped one at each end of shaft by means of collect and chucks.

Attaching the cross lever weights can change Mass moment of inertia of any disc. Both discs are

free to oscillate in the ball bearings. This provides negligible damping experiment.


PROCEDURE

1. Fix two discs to the shaft and fit the shaft in bearings.

2. Deflect the discs in opposite direction by hand and release.

3. Note down time required for particular number of oscillations.

4. Fit the cross arm to one of the discs say B and again note down time.

5. Repeat the procedure with different equal masses attached to the ends of cross arm and note

down the time.

OBSERVATIONS

1. Dia. Of disc A (Big Disc) = 225 mm.

2. Dia. Of disc B (Small Disc) = 190 mm.

3. Wt. Of disc A = 2.8 Kg.

4. Wt. Of disc B = 1.8 Kg.

5. Dia. Of shaft = 3 mm

6. Length of shaft between rotors L = mm

7. Weight Set : 1 – 0.750kgs – 2 Nos., 2 – 0.500kgs – 2 Nos.

OBSERVATION TABLE

Obs.

No.

No. of

oscillations -

„n‟

Time required

for „n‟ osc. –„t‟

secs

T expt = t/n secs.

CALCULATIONS

1. Find Kt of shaft as follows :

Kt = G IP

L

Where , G = modulus of rigidity of shaft = 0.8 x 106 Kg/cm

2


4

32


Let, IA = M.I. of disc A

IB = M.I. of disc B

( with wts. On cross arm)

d = shaft dia.

L = Length of the shaft

Then,

IA = WA

x (DA)

2

g 8

IB = WB x

(DB)2

+ 2 W1

X R

2

g 8 g 8

( neglecting effect of cross arm )

Where, W1 = Wt. Attached to the cross arm.

R = Radius of fixation of Wt. On the arm from disc centre=150mm.

T theoretical = 2 IA x IB

Kt (IA + IB)

T Experimental = Time for „n‟ osc

No. of osc. „n‟

FExp. = 1

FTher = 1

TExp TTher

RESULTS

IA IB T theo.

Sec.

F Theo.

Hz.

T Expt.

Secs.

F Expt.

Hz Kg. Cm2 Kg. Cm

2

SIZE OF SPANNER REQUIRED: 20 - 22



SINGLE ROTOR SYSTEM WITH VISCOUS DAMPING.

AIM: To study the damped Torsional oscillations and determine the damping co-efficient Ct.

Objective:

1.To develop an understanding determining the damping period of oscillation.

2.Determining the logarithmic decrement.

3.Determining the damping coefficient of oil

4.To develop an understanding the frequency of damped free vibrations.

5.Determining how damping coefficient depends on the depth immersion of the rotor in oil.

Figure

DESCRIPTION

Enclosed Fig. shows the general arrangement for the experiment. It consists of a long elastic shaft

gripped at the upper end by the chuck in the bracket. The bracket is clamped to the upper beam of

the main frame. A heavy steel flywheel clamped at the lower end of the shaft suspends from the

bracket. Damping drum is fixed to the lower face of the flywheel. This drum is immersed in the oil

which provides damping. Rotor can be taken up and down for varying the depth of immersion of

damping drum. Depth of immersion can be read from the scale. Recording drum is mounted to the

upper face of the flywheel. Paper is to be wrapped around the recording drum. Oscillations are

recorded on the paper with the help of specially designed piston of dash pot. The piston carries the

attachment for fixing the sketching pen.


SPECIFICATIONS :

01. Basic channel frame and stand.

02. Supports with drill chuck for fixing the shaft vertically.

03. Damper with pen holder arrangement fixed to main frame.

04. Flywheel assembly with recording drum and cone assembly.

05. Oil Drum with Piezometric tube. (PS : Lube Oil SAE 30/40 to be provided by college as per

requirement )

06. Stop watch and measuring tape.

PROCEDURE

1. With no oil in the container allow the flywheel to oscillate and measure the time for some (say 10)

oscillations.

2. Put thin lube oil (no. 30 or 40) in the drum and note the depth of immersion.

3. Put the sketching pen in its bracket.

4. Allow the flywheel to oscillate.

5. Allow the pen to descend. See that the pen always makes contact with the paper, and record

oscillations.

6. Measure the time for some oscillations by means of stop clock.

7. Determine Xn i.e. amplitude at any position and X n+r amplitude after „n‟ cycles.

OBSERVATION TABLE

Sr.No.

Length.of

suspension.

of shaft

L in (cms)

Depth of

Immersion

( mm. )

Time „t‟

for „n‟

oscillation

(secs.)

No.of

osc.

( n )

Periodic

time „Texpt.‟

„ t/n‟ secs

Xn

(cm)

Xn+r.

(cm)


CALCULATIONS

01. Calculate Torsional Stiffness „Kt‟ by using equation:

Kt = G IP

L

Where , G = modulus of rigidity of shaft = 0.8 x 106 Kg/cm

2


4

32

Let,

d = shaft dia. = 0.003m.

L = Length of the shaft = 1.29 mtr.

02. Calculate M.I. of flywheel by using equation …..

I I = W

x D

2

g 8

W = Weight of disc = 9.5 Kg.

D = Dia. Of disc. = 250mm = 0.25mtr

03. TTh = 2

T = Periodic time of oscillations in still air.

04. Calculate critical damping factor.

Ctc = 4 x I x Kt

05. Determine logarithmic decrement „‟ as follows:

= 1

log Xn

r Xn+r

Where, Xn = Amplitude of Vib. At the beginning of measurement to be found from

record.

Xn+r = Amplitude of Vib. After „n‟ cycles from record.

r = No. of cycles.

SIZE OF SPANNER REQUIRED: 20 – 22, 16 – 17 & 10 – 11.


I Kt


STATIC & DYNAMIC BALANCING MACHINE

Aim: This apparatus has been designed to allow the student “To check experimentally the

normal method of calculating the position of counter balancing weight in rotating mass

systems”.

Objective:

1.To develop an understanding static and dynamic balancing.

2.To develop an understanding the frequency of damped free vibrations.

DESCRIPTION:-

The apparatus basically consists of a steel shaft mounted in ball bearings in a stiff rectangular

main frame. A set of Five blocks of different weights is provided and may be clamped in any

position on the shaft, and also be easily detached from the shaft. A disc carrying a circular

protractor scale is fitted to one side of the rectangular frame. Shaft carries a disc. A scale is fitted

to the lower member of the main frame and when used in conjunction with the circular

protractor scale, allows the exact longitudinal and angular position of each adjustable block to be

determined. The shaft is driven by a 230v single-phase 50hz electric motor, mounted under the

main frame, through a belt. For static balancing of individual weights the main frame is

suspended to the support frame by chains and in this position the motor driving belt is removed.

For dynamic balancing of the rotating mass system the main frame is suspended from the

support frame by two short links such that the main frame and the supporting frame are in the

same plane.

SPECIFICATIONS :

01. Specimen Weights : 5 Nos. with different mass & Allen key.

02. Basic frame with central shaft fitted in bearings.

03. FHP AC Motor fitted to the base of basic frame support with counter balance

weight. A pedal type variac is provided to vary the speed of the motor.

04. Circular scale fitted to the central shaft.


05. Circular Disc with groove to fix the belt is mounted on the shaft.

06. Setting Gauge, Knob and rubber belt.

07. Sturdy main frame to hang the basic frame with weights.

PROCEDURE:-

STATIC BALANCING

We have taken into consideration the exact weight in grams of the specimen weights by weighing on the

weigh balance. The procedure is simplified by taking into consideration the weight of the specimen.

We are giving below table with specimen no. and its weight in gms.

Observation Table giving details of weight of specimen.

Sr. No. Specimen No. Weight in

„gms‟.

„wr‟

01. 1 without hole. 204

02. 2 200

03. 3 196

04. 4 190

05. 5 180

Now, with reference to the above specimen weights one has to select any four specimen weights

and should draw Couple Polygon & Force Polygon Diagram. Separate procedure is given to draw the

same.

PROCEDURE FOR DRAWING COUPLE AND FORCE POLYGON

( SAMPLE CALCULATIONS ONLY)

1. Select weight no.2, 3, 4 & 5 for balancing.

2. Take a specimen weight which is having maximum weight in horizontal position i.e. in

second position from reference weight say weight no.2.

3. Assume distance between 4 weights as shown in figure below

4 2 3 5

3cm 3cm 3cm


4. Now with reference to weight no.4 as ref. plane prepare following

Table

Wt. No. specimen

Weights in

„gms‟

Distance from

Wt.No.4

Couple

4 190 0 0 190x0=0

2 200 3 600 200x3=600

3 196 6 1176 196x6=1176

5 180 9 1620 180x9=1620

5. Now draw couple polygon with Weight No.2 in horizontal position.

a) Draw horizontal line of scale 1cm= 200grms.

b) Take 1176/200 = 5.88cm distance in compass and draw an arc of 5.88cm from second

point.

c) Take 1620/200 = 8.1cm distance in compass and draw an arc on the pervious arc from

initial point to meet the arc.

d) Mark the points where they are intersect with each other.

e) Measure the external angle as shown in figure.

6. Now draw force polygon as follows: (Actual weight).

a) Draw a horizontal line of scale 1cm = 50gms at 200

b) Draw a second line of 196gms (196/50) at angle of 510.

c) Draw a third line of 180(180/50) gms at angle of 2140

d) Intersect the both ends of 1st and 3

ed line with dotted line.

e) Measure the angle of resultant force value by force polygon.

Or

a) Draw a horizontal line C2 scale at 200 (Actual weight).

b) Draw a parallel line to C5 scale at 180.

c) Draw a parallel line to C3 scale at 196.

d) Join the line to form a polygon as shown in figure.

C5 C6

C2

C3

520

2150

Couple Polygon

1


7. As per the angles obtained from Force and Couple Polygons fix the weights accordingly in

the main shaft.

8. Suspend total main frame by chains.

9. Attach belt to main frame and shaft the motor at low speed and observe vibrations on the

frame. DYNAMIC BALANCING: (REFER FIG.NO.2)

It is necessary to suspend the machine before the experiments. Using the values of „Wr‟ obtained

as above, and if the angular positions and planes of rotation of three of four blocks are known,

the student can calculate the positions of other blocks for balancing of the complete system.

From the calculations, the student finally clamps all the blocks on the shaft in there appropriate

positions. Replace the motor belt; transfer the main frame to its hanging position and then by

running the motor, one can verify that these calculations are correct and the blocks are perfectly

balanced.

1. DYNAMIC BALANCING OF 4 BLOCKS

Obtain dynamic balance on a set of four blocks with unbalance as shown, by properly positioning them in

angular and lateral position on the shaft.

Sl.no Unbalanced(wr) product

1 2 180 200

2 3 196 196

3 4 190 190

4 5 200 180

Distance between each block is 3cm the arrangement is as shown in fig.

3 4 1 2

0 4

3cm 3cm 3cm

SIZE OF SPANNER REQUIRED: 16 – 17, 12 – 13 & Allen Key of 5 No.


F2 (192)

F4(182)

F3(186)

F5 (178) 197

0

Force Polygon 2


WHIRLING OF SHAFTS APPARATUS

Aim: To determine demonstration of whirling of shaft phenomenon for

different end conditions

Objective:

1.To develop an understanding concept of whirling.

2.To develop an understanding the whirling frequency An accurate analysis of the critical

whirling speed for the range of shaft geometry‟s, both loaded and unloaded and with

different combinations of end conditions.

Figure

DESCRIPTION

This apparatus is developed for the demonstration of Whirling phenomenon. The shaft can be tested for

different end conditions. The apparatus consists of a frame to support its driving motor, end fixing and

sliding blocks etc. 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 FIXING ENDS ( M and N )

These ends fix the shafts while it rotates. The shaft can be replaced within a short time with the

help of this unit. The fixing ends provide change of end fixing condition of the rotating shaft as per

the requirement.

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. 3 mm. 1000 mm.

02. 6 mm. 1000 mm.

03. 8 mm. 1000 mm.

D) END FIXING ARRANGEMENT

At motor end as well as tail end different end conditions can be developed by making use of

different fixing blocks.

1) Supported end condition : Make use of end block with single self aligning bearing.

2) Fixed end condition : Make use of end block with double bearing.

SPEED CONTROL OF DRIVING MOTOR

The driving motor is – A.C./D.C.Motor, F.H.P., 6000 rpm., 50 c/s., 250 volts and speed control unit is a

Dimmerstat of 240 V., 4 Amps., 50 c/s.

MEASUREMENT OF SPEED

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.

WHIRLING OF ELASTIC SHAFTS

If,

L = Length of the shaft = 1000mm or 1.0mtr.

E = Young‟s Modulus = 2.060 x 1011

N/m2

I = 2nd

moment of inertia of the shaft =6.362 x 10 -11

m4

W = Weight of the shaft per unit length Kg x 9.81/m = N/m

g = Acceleration due to gravity in m/sec2 = 9.81

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

f = k x E.I.g

W.L4

(R.P.S.)


The various values for K are given below :

End Condition Value of K

1st Mode 2

nd mode

Supported, Supported 1.57 6.28

Fixed, Supported 2.45 9.80

Fixed, fixed 3.56 -

DATA

Shaft Dia. I = m4 W = Kg/m W = N/m

3 mm 3.068 x 10-11

m4 0.15 Kg/m 1.47

6 mm 6.362 x 10-11

m4 0.24 Kg/m 2.35

8 mm 2.01 x 10-10

m4

0.38 Kg/m 3.72

OBSERVATION TABLE

Sr.No. End Condition Shaft Dia.(mm) 1st Mode (rps) 2

nd Mode (rps)

01. Free – Free 3 & 6 mm

02. Fixed - Free 6 mm

03. Fixed- Fixed 8mm

Typical Results Obtained after calculations

TYPICAL TEST OBSERVATIONS

1) Both ends of shaft free (supported) 1st and 2

nd mode of vibration can be observed on shafts with

3mm dia. and 6mm dia.

2) One end of shaft fixed and the other free; 1st and 2

nd mode of vibration can be observed on shaft

with 5mm dia.

3) Both ends of shaft fixed – 2nd

mode of vibration can not be observed on any of the shafts as the

speeds are very high and hence beyond the range of the apparatus.


4) There is a difference between theoretical speed of whirling and actual speed observed and

calculated, due to 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.

Tightness of the shaft will also affect the critical speed of the shaft while in operation.

PRECAUTIONS TO BE OBSERVED IN EXPERIMENTS

1) If the revolutions of an unloaded shaft are gradually increased it will be found that a certain 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 become 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

defection 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 of shaft rapidly and pass through the critical speeds 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 amplitude of vibration at 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 in comparison with the bending spring forces hence

possibility of build-up of dangerous amplitudes 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 behaviors

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.

5) Shaft should not be tightened too much as it will give erratic readings.

SIZE OF SPANNER REQUIRED: 16 – 17 & Allen Key No. 3

Recommendations: As it related to basic concept of vibration and related to Unit 3&4 in theory.


UNIVERSAL GOVERNOR APPARATUS 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…

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

can be studied. 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 characteristic 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 & main shaft are mounted on a rigid M.S. base frame in vertical fashion. The Governor

spindle is supported in a ball bearing. The unit has a unique facility of fixing optional Governor

Mechanisms on spindle, by removing the nut fitted on top of the spindle shaft. The Dimmerstat

provided with this unit achieves 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 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.


SPECIFICATIONS:-

1. Electric Motor : DC Motor, Capacity - ¼ hp, 1500rpm speed, Single Phase, 230 V AC.

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

3. Separate linkages with balls are provided for Watt & Porter type governor and proell

governor mechanism.

4. Spring loaded linkage for Hartnel Governor Mechanism.

5. Weights for Porter and Proell Governor.


100 A

ho

B B

W

ro


2) PORTER GOVERNOR

AIM: To study the behavior of porter governor at various speed.

Objective:

1.To develop an understanding how the rotational speed of the Porter Governor relates to the

displacement of the load that‟s being hoisted

2.To develop an understanding that, we are to compare the results of the experiment with the

theoretical values

Figure

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 the moving

parts and of the spindle shaft are properly tightened. Then following simple procedure is to

be followed.


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

2. Switch on the main supply and gradually go on increasing the speed of the motor. Due

to this the center sleeve rises 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 and 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

readings of sleeve displacement and the corresponding speed. All the readings are to be

entered in a tabular observation table.

5. This procedure is adopted for all the other three Governor mechanisms by properly

fitting the assembly to the spindle shaft.

6. After completing the experiment bring the knob of the dimmer stat to its original

position i.e. zero slowly and gradually. Then switch off the main supply.

7. Then the results may be plotted as.

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

b) Plot the graph of speed v/s governor height for Watt Governor.

c) Plot the Governor characteristic after doing the necessary calculations.

Go on increasing the speed gradually and take the readings of speed of rotation `N`

and corresponding sleeve displacement `X`.

OBSERVATIONS:

a) Length of each link - L = 0.125 m.

b) Initial height of Governor – ho = 0.105 m.

c) Initial radius of rotation – ro = 0.120 m.

d) Weight of each ball - W = 0.6 kgs.

e) Weight of Sleeve weight = 0.5 kgs.


CALCULATIONS:-

Radius of rotation `r` at any position could be found as follows

a) Find height h = ho – X/2--------------- mtr. ………. W.k.t ho = 0.105 m

b) Find “ “ by using = Cos –1

(h/L)--------------- in Degrees

c) Then r = 0.05 + L Sin -----------------mtr.

d) Angular Velocity „‟ = 2N/60-----------rad/sec

e) F=W/g .2.r--------------Kgf

OBSERVATION TABLE

Sr.No. Speed

“ N ” rpm

Sleeve Displacement

“ X ” in mm

Height

“ h” in mm

Radius of rotation

“ r ” in m

Force

F = (W/g) . 2.r

in Kgf

Following graphs to be plotted :

a) Force Vs Radius of rotation.

b) Speed Vs Sleeve Displacement.

Recommendations: As it related to basic concept of vibration and related to DOM Subject

in theory.


3) PROELL GOVERNOR

Aim: To study the behavior of proell governor at different speed.

Arrange the set-up as shown in Fig. above 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. 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.

Objective:

1.To develop an understanding how the rotational speed of the Porter Governor relates to the

displacement of the load that‟s being hoisted

2.To develop an understanding that, we are to compare the results of the experiment with the

theoretical values

OBSERVATIONS:

a) Length of each link - L = 0.125 m.

b) Initial height of Governor – ho = 0.100 m.

c) Initial radius of rotation – ro = 0.127 m.

d) Weight of ball - W = 0.6 kgs.

e) Extension of length BG = 0.075 m.

OBSERVATION TABLE

Sr.No.

Speed

“ N ” rpm

Sleeve Displacement

“ X ” in meter

Height

“ h ” in m

Radius of

rotation

“ r ” in mm

Force

F = (W/g) x 2 r

in Kgf


CALCULATIONS:--

a) Find height h = ho – ( X / 2 )

b) Angular Velocity „‟ = 2N/60-------------- rad/sec

c) Find “ “ by using = Cos –1

(h/L)--------------- in Degrees

d) Then r = 0.05 + L Sin -----------------mtr.

e) F=W/g .2.r--------------Kgf

Following graphs to be plotted:

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

b) Force Vs Radius of rotation 'r'.

c) Speed Vs Sleeve Displacement.

Recommendations: As it related to basic concept of vibration and related to DOM Subject

in theory.

Prof: Mahadev N Harkude VSMIT,Nipani Page 36

Proell Governor Assembly

Spindle Shaft

Ball

Drive Motor

Link

Scale

Sleeve Weight

Sleeve

Bearing

Block Dimmer start

Belt

ro

100

A

h0

B

100

BG

ro

ro

W

Sleeve Weight

L C


ROSETTE STRAIN GAUGE

Aim: For determining the Principal Stress & Principal strains

INTRODUCTION:

Measurement of Stress & Strain is getting much importance from academic syllabus point

of view. And the reason is very simple, because it is very important from practical testing

point of view or real life work. And keeping this exact requirement in view, we have

designed & developed this „ROSETTE STRAIN GAUGE SET-UP‟ with a sole intention

to enable the students to learn about the stress & strain measurement.

There are two versions of gauges simple foil type – single element and rosette gauges –

multi element. Electrical resistance strain gauges are normally employed on the free

surface of a specimen to establish the stress at a particular point on the surface. In general

it is necessary to measure three strains at a point to completely define either the stress or

the strain field. In terms of principal strains, it is necessary measure 1, 2, & direction of 1

relative to the X axis as given by the principal angle . Conversion of the strains into

stresses requires, in addition knowledge of the elastic constants E & of the specimen

material.

In most of general case, no knowledge of stress field or its directions is available before

the experimental as a analysis is conducted. Three element rosettes are required in these

instances to completely establish the stress field.

In actual practice three element rosettes with fixed angles are employed to provide

sufficient data to completely define the stress field. These rosettes are defined by the fixed

angles as the rectangular rosette, delta rosette & the Tee delta rosette.


DESCRIPTION:

In this set-up three-element rectangular rosette gauge placed at 00, 45

0, & 90

0 positions are

pasted on the specimen rectangular plate. A sturdy frame made from MS Channel is

provided with loading screw and handle. A spring balance is fixed in between specimen

and loading screw to indicate the given on specimen in kgs. A digital Strain Indicator is

provided which has three different tare pots. The readings observed on the indicator are in

micro strain. Specimen is hold properly in the clamps.

Objective:

1. To experimentally determine the normal stresses in a thin pressure vessel.

2. To experimentally determine the normal stresses in a Curved beams.

SPECIFICATIONS:

1. Rectangular Specimen with three-element rosette gauge pasted on it. – 2 No.

( Aluminium & MS Specimen 1 each )

02. Sample specimen with Rosette Gauge for study purpose – 1 No.

03. Base frame with vertical stand having loading screw and hand wheel.

04. Spring Balance – Range : – 0 – 50 Kgs.

05. Clamps for holding the specimen.

06. Digital Strain Indicator with following scope of supply.

* Range: 0 – 1999 units i.e. in micro strains.

* Least Count: 1 unit i.e. in micro strains.

* Display: Digital – Bright LED Type – 3 &1/2 Digit.

* Supply: 230V A.C. mains – Regulated.

* Gauge Inputs: Through Four-Pin Emphenol (1 No.).

* Control Inputs: 3 Tare Pots i.e. one per channel or arm.

* Sensor : a) M.S. Plate & b) Aluminium plate with Rosette Gauge pasted on It.

* Sensor Excitation – + 5V D.C. Regulated.


* Rosette Gauge : BE120-4CA.

* Zero Set: With Ten Turn Pot per channel Or arm.

* Enclosure: Powder Coated.

OPERATING PROCEDURE:

1. Clamp the specimen in between spring balance & the lower clamp fixed to the base

frame. Note that the loading screw should be in lower most position. Pointer of

spring should be on zero position after fixing the specimen.

2. Connect Supply Cable of Indicator to Stabilized 230V A.C. – Single Phase Supply.

3. Ensure that Good Quality Earthing is provided to the Indicator. It is must.

4. Connect shielded cable coming from Rosette Specimen to Indicator rear side,

through Four-Pin Emphenol.

5. Ensure that Specimen is free from any external loading.

6. Start up with 230 V A.C. mains actuation.

7. Wait for 10 to 15 min. to stabilize the Indicators internal conditioning circuits

before loading.

8. Then tare or nullify each channel for zero reading. It has to be adjusted for the all

three channels before starting the experiment.

9. Now Indicator is ready for Experiment Cycle with actual test Specimen & its

related exercise.

10. Now go on loading the specimen in steps of 4,8,12.. so on Kgs. Up to 20 kgs. only

for MS and 12Kgs for Aluminium .

11. ** Do not apply load to the specimen more than 20kgs. For MS specimen and

12 kgs. for Aluminium.

12. Simultaneously, note down the readings 1, 2, & 3, which is in micro strain for

each loading. Wait for few minutes before taking next reading after

loading specimen. Enter the reading in observation table.


OBSERVATION TABLE:

Sr.

No.

Applied

Load. Kgs. Strain in s Result

1 2 3 Prin. strain - s Prin. Stress – N/mm2

min max min max

1. 4

2. 8

3. …

CALCULATIONS:

01. Max. Principal Strain - max

1 1

= --- (1 + 3 ) + --- (1 - 3 )2 + [ 2 x 2 – (1 + 3 ) ]

2 = s

2 2

02. Min. Principal Strain - min

1 1

= --- (1 + 3 ) - --- (1 - 3 )2 + [ 2 x 2 – (1 + 3 ) ]

2 = s

2 2

1 2 2 – (1 + 3 )

03. = ---- tan-1

2 1 - 3

Where, is the angle between the direction of the maximum principal strain and the „X‟ axis

04. Max. Principal stress „max‟ in Psi

E 1 + 3 1

max = + (1 - 3 )2 + [ 2 x 2 – (1 + 3 ) ]

2

2 1 - 1+


05. Min. Principal Stress „ min‟ in Psi

E 1 + 3 1

min = - (1 - 3 )2 + [ 2 x 3 – (1 + 3 ) ]

2

2 1 - 1+

where, E = modulus of elasticity = 30 x 106 Psi

= possion‟s ratio = 0.3

06. Max. Principal Shear Strain max

max = (1 - 3 )2 + [ 2 x 2 – (1 + 3 ) ]

2 s

07. Max. Principal Shear Stress max

E

max = (1 - 3 )2 + [ 2 x 2 – (1 + 3 ) ]

2 Psi

2 (1+ )

SIZE OF SPANNER REQUIRED : 10 – 11.

Recommendations: As it related to basic concept of vibration and related to ESA subject

in theory.


PHOTOELASTICITY FOR SIMPLE COMPONENTS

AIM: Determine the stress difference at known point of circular disc with circular cut out

subjected uniaxial and compressive load.

Objective: 1.To develop an understanding Stress in different disc.

2.To develop an understanding the uni-axial stress in any component.

Figure:

OBSERVATION:

1) Angle in degree at which it the isoline passes through the point of intersect.

2) Frictional fringe order = N =

3) Stress intensity or difference = σ1 – σ2.

PROCEDURE:

1) Set the pin D-D position which gives plane polar scope arrangement.

2) Set the analysis to zero degree and switch on the white light.

3) Observe the black fringe [isoclinic pattern] which is zero order.

4) Pass the isoclinic fringe through the point of interest on free boundary by combine

rotation of polarizer and analysis which gives angle in degrees at which isoclined passes

through the point of interest.

5) Now the set arrangement to the circular frictional fringe order at any point can be

determined.

6) According to stress optic law we have σ1 – σ2 = N F σ / H

Where σ1 – σ2 = stress difference at a point of interest.

N =Frictional fringe value of F σ.

H= Thickness of the specimen.


OBSERVATION TABLE:

Sl

no

Load applied

W in Kg

Load

“P” = WY/X

Nf from N1

Nf= N1+ α/1800

Nf from N2

Nf= N1-β/1800

Nf mean = N F σ. Avg Kg/cm

Specimens calculation:

P = WY/X D = 55mm=5.5 cm; H=6mm= 0.6cm.

F σ avg = f σ1+ f σ2+ f σ3+ f σ4 / 4

Let σ1 – σ2 = N F σ / H

f σ1= 8P1/πDN1

Recommendations: As it related to basic concept of vibration and related to ESA subject

in theory.

Documents

VIB – LAB