dom lab manual

DYNAMICS

OF MACHINE LAB

Class: B.Tech. 6 th Semester (Mechanical Engineering)

Mechanical Engineering Department

YMCA UNIVERSITY OF SCIENCE AND TECHNOLOGY FARIDABAD

Sr.

no.

Experiments Page

no.

1.

To perform experiments on Watt and porter governors to

prepare performance characteristics curves, and to find stability

and sensitivity.

1-5

2.

To perform experiment on proell governor to prepare

performance characteristics curve and to find stability and

sensitivity

6-9

3.

To perform experiment on Hartnell governor to prepare

performance characteristics curve and to find stability and

sensitivity.

10-13

4. To study Rope bake dynamometers 14-15

5. To determine gyroscopic couple on motorized gyroscope. 16-21

6. To perform the experiment for static balancing on static

balancing machine.

22-23

7 To perform the experiment for dynamic balancing on dynamic

balancing machine.

24-27

8

Determine the moment of inertia of connected rod by compound

pendulum method tri-flair suspension pendulum.

28-30

Experiment no.1

Objective:

To perform experiments on Watt and porter governors to prepare performance

characteristics curves, and to find stability and sensitivity.

Apparatus:

The apparatus is designed to exhibit the characteristics of the spring-loaded governor and

dead weight governor. The apparatus consists of a main spindle driven by a variable

speed D.C. Motor with variable speed control unit. The motor is connected through V

belt to drive shaft. Motor and main shaft are mounted on a rigid M.S. Base plate in

vertical fashion. The spindle is supported in ball bearings.

The optional governor mechanism can be mounted on spindle. Speed control unit

can control the spindle speed. And counter hole over the spindle shaft allows the use of

a hand tachometer to determine the speed. A graduated scale is fixed to the sleeve and

guided in vertical direction, which measures the sleeve displacement.

Experimental Procedure:

The governor mechanism under test is fitted with the chosen rotating weigr~... and spring,

where applicable and inserted into the drive unit. The following simple procedure may

then be follows:

Connect the motor to speed control unit using four way cable provided.

The control unit is switched ON and the speed control slowly rotated, increasing. the

governor speed unit the centre sleeve rises off the lower stop and aligns with the first

division on the graduated scale.

The sleeve position and speed are then recorded. Speed may be determined using a hand

tachometer on the spindle. The governor speed is then increased in steps to give suitable

sleeve movements, and readings repeated at each stage through out the range of sleeve

movement possible.

Watt Governor

Porter governor

Data Sheet

Length of each link, L, mm . = 125

Initial height of governor, ho, mm = 94

Initial radius of rotation, Ro, mm = 136

Weight of each ball, W, kg = 0.6

Sr. Sleeve Speed Height cos = h/L Radius of rotation, r Force

No displacement ,N h = ho-X/2 r = 50 + L Sin F(kg)

X (rpm) (mm) (cm)

(mm)

Results & Discussions:

(a) Graph to be plot:

(a) Fill up the data sheet.

(b) Note down sleeve displacement X at various speeds N.

(c) Find the radius of rotation r at any position.

(d) The result may be plotted as curves of speed (on y axis) against sleeve

displacement (on x axis).

(e) Plot the graph of force (on y axis) v/s radius of rotation (on x axis).

(f) Further tests are carried out changing the value of variable at a time to draw

curves.

(b) Calculations:

For Watt and Porter Governor Radius of rotation r can be calculated as follows: Find height h = (ho - x/2) Find by using cos = h/L Then, r = 50 + L Sin Force can be calculated as follows:

(a) Find the angular velocity of the arm and ball about the spindle axis.

sec/60

2rad

Npw =

Where N is the speed of the spindle

(b) Find the centrifugal force acting on the ball

Force, 02 r

gW

F = w in Kg

Where g is the acceleration due to gravity. g = 9.81 m/sec2

Precautions:

(a) Do not keep the mains "ON when trial is complete.

(b) Increase the speed gradually. .

(c) Take the sleeve displacement reading when the pointer remains steady.

(d) See that at higher speed the load on sleeve does not hit the upper sleeve of the

governor.

(e) While closing the test bring the dimmer to zero position and then switch "OFF"

the motor.

Experiment no.2

Objective:

To perform experiment on proell governor to prepare performance characteristics curve

and to find stability and sensitivity

Apparatus:













then be follows:








movement possible.

Data Sheet

In the Proell Governor, with the use of flyweight (Forming full ball) the governor

becomes highly sensitive. Under this conditions large sleeve displacement is observed for

very small change in speed. In order to make it stable, it is necessary to carry out the

experiments by using half ball flyweight on each side.

Length of each link, L, mm = 125

Initial height of governor, ho, mm =94

Initial radius of rotation, ro, mm =141.5

Weight of each ball, W, kg = 0.6

Weight of sleeve, kg = 0.6

Extension of Length BG, mm = 75

Sr. Sleeve Speed Height cos = h/L Radius of rotation, r Force

No displacement ,N h = ho-X/2 r = 50 + L Sin F(kg)

, X (rpm) (mm) (cm)

(mm)


Graph to be plot:

(g) Fill up the data sheet.

(h) Note down sleeve displacement X at various speeds N.

(i) Find the radius of rotation r at any position.

(j) The result may be plotted as curves of speed (on y axis) against sleeve


(k) Plot the graph of force (on y axis) v/s radius of rotation (on x axis).

(l) Further tests are carried out changing the value of variable at a time to draw

curves.

Precautions:

(f) Do not keep the mains "ON when trial is complete.

(g) Increase the speed gradually. .

(h) Take the sleeve displacement reading when the pointer remains steady.

(i) See that at higher speed the load on sleeve does not hit the upper sleeve of the

governor.

(j) While closing the test bring the dimmer to zero position and then switch "OFF"

the motor.

Experiment no. 3

Objective: To perform experiment on Hartnell governor to prepare performance characteristics curve

and to find stability and sensitivity

Apparatus:













then be follows:








movement possible.

Data Sheet

Arrangement is shown in figure

a. Length, a, mm . = 77

b. Length, b, mm = 122

c. Initial radius of rotation, r0, mm = 177.5

d. Weight of each ball, W, kg = 0.6

e. Weight of sleeve, kg = 0.6

f.. Free height of spring, mm = 102

g. Spring stiffness (P) = 10 & 5 kg/cm.

Sr. No. Sleeve displacement X Speed, N Radius of rotation, r Force, F

(mm) (rpm) = ro + X a/b (kg)

(cm)


Graph to be plot:

(m) Fill up the data sheet.

(n) Note down sleeve displacement X at various speeds N.

(o) Find the radius of rotation r at any position.

(p) The result may be plotted as curves of speed (on y axis) against sleeve


(q) Plot the graph of force (on y axis) v/s radius of rotation (on x axis).

(r) Further tests are carried out changing the value of variable at a time to draw

curves.

Radius of rotation r can be calculated as follows:

)()(

0 baX

rr +=

Where a and b are the length and X is the sleeve displacement

Precautions:

(k) Do not keep the mains "ON when trial is complete.

(l) Increase the speed gradually. .

(m) Take the sleeve displacement reading when the pointer remains steady.

(n) See that at higher speed the load on sleeve does not hit the upper sleeve of the

governor.

(o) While closing the test bring the dimmer to zero position and then switch "OFF"

the motor.

Experiment no. 4

Objective:

To study rope bake dynamometers

Introduction & Theory

The rope brake dynamometer consists of one or more ropes wound around flywheel or

rim of the pulley, fixed rigidly to the shaft of the prime mover. The end of the

ropes is attached to spring balance while the lower end is kept in position by applying a

dead weight. In order to prevent the slipping of the ropes over the flywheel, wooden

blocks are placed at intervals around the circumference of the flywheel. During

operation of the brake, the prime mover is made to run at a constant speed. The

frictional torque due to the ropes must be equal to the torque being transmitted by the

prime mover.

Let

W = dead load on the rope

S = spring balance reading

D = diameter of the pulley

d = diameter of the rope

N = speed of the pulley

Work done per minute = (W-S) (D +d) N

Brake power, ( ) ( )

KWX

NdDSWBP

100060+-

=p

Result:

Model of rope brake dynamometer have been visualized and studied.

Experiment no. 5

Objective:

To determine gyroscopic couple on motorized gyroscope

Theory:

Let a disc of weight Wand having a moment of inertia I be spinning with an angular

velocity ill about axis OX in an anti clockwise direction viewing from front. Therefore,

the angular momentum of disc is lill. Applying right hand screw rule, the sense of vector

representing the angular momentum of disc which is also a vector quantity will be in the

direction OX as shown. A couple, whose axis is OY perpendicular to OX and is in the

plane XOZ, is now applied to precess the axis OX.

Let axis OX turn through a small angular displacement 88 about axis OZ and in

the plane XOY, from OX to OX in time 8t. The couple applied produces a change in the

direction of angular velocity, the magnitude remaining constant. This change is due to the

velocity of precession. Therefore, OX represents the angular momentum after time 8t.

Change of angular momentum = OX - OX = XX

Rate of change of angular momentum= Angular Displacement/Time

tXXd

=

But rate of change of angular momentum = Couple applied, C

Where, dqOXxXX = in direction of XX

dqw)(I=

tIC

ddq

w=

and in the limit, t is very small

dtd

ICq

w=

where d /dt= P, the angular velocity of precession of yoke, which is uniform and is about

axis OZ.

Thus, we get

PIC ww=

The direction of the couple applied on the body is clockwise when looking in me

direction XX and in the limit this is perpendicular to the axis of and P

Apparatus

Schematic arrangement of the gyroscope is shown in Fig. 1. The motorized gyroscope

consists of a disc rotor mounted on a horizontal shaft rotates about XX axis in two ball

bearings of one frame. This frame can swing about YY axis in bearings provided in the

yoke type frame No.2. The rotor shaft is coupled to a motor mounted on a trunion frame

having bearings in a yoke frame, which is free to rotate about vertical axis ZZ. Thus

freedom of rotation about three perpendicular axis is given to the rotor (or the disc can be

rotated about three perpendicular axis). Angular scale and pointer fitted to frame helps to

measure precession rate. In steady position, frame No.1 is balanced by providing a weight

pan on the opposite side of the motor.

Experimental Work

Rule No 1

"The spinning body exerts a torque or couple in such a direction which tends to make the

axis of spin coincide with that of the precession"

To study the rule of gyroscopic behavior following procedure may be adopted

Step1: Balance the initial horizontal position of the rotor. .

Step 2: Start the motor by increasing the voltage with the autotransformer, and wait until

it attains constant speed.

Step 3: Precess the yoke frame No.2 about veliical axis by applying necessary force by

hand to the same (in the clockwise sense seen from above).

Step 4: 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 downward.

Step 5: Rotate the vertical yoke axis in the anti clockwise direction seen from above and

observe that the rotor frame swing in opposite sense (ns compared to that in previous case

following the above rule).

Rule No.2:

Step I: Balance the rotor position on the horizontal frame.

Step2: Start the motor by increasing the voltage with the autotransformer and wait till the

disc attains constant speed. Note down the speed.

Step3: Put weight (0.5 kg, 1 kg, or 2 kg) in the weight pan, and start the stop watch to

note the time in seconds required for precession, through 60 or 45 etc.

Step4: The vertical yoke precesses about OZ axis as per the rule No.2.

Step 5: Speed may be varied by the autotransformer provided on the control panel.

Data Sheet:

Weight of Rotor, kg: Rotor Diameter, mm: Rotor Thickness, mm Moment of inertia of the disc, coupling and motor rotor about central axis, I, kg cm sec2 : Distance of bolt of weight pan: from disc centre, L, cm

S. No.

Weight, W

(kg)

Time required for

precession, dt (sec)

Speed, N

(rpm)

Angle of precession,

d

( degree)


1. Fill up the data sheet.

2. Calculate the gyroscopic couple by the equation PIC ww= for different sets of

readings for different weight and different speed.

3. Compare the gyroscopic Couple calculated and observed.

Precautions

1. P is to be calculated for short duration of time, as the balance of rotation of disc about the horizontal axis YY due to application of torque, because of which P goes on reducing gradually.

2. A void using the tachometer while taking the reading of time as it will reduce the time taken for precession.

3. Autotransformer should be varied gradually.

APPENDIX-1: Critical data of experiment Weight of Rotor, kg: 6.7 Rotor Diameter, mm: 300 Rotor Thickness, mm: 10.5 Moment of inertia of the disc, coupling and motor rotor about central axis, I, kg cm sec2

( )768.0

830

9817.6

8

22

===D

gW

Distance of bolt of weight pan: from disc centre, L, cm :17.6

Motor: Fractional HP. single phase. 6000 rpm AC/DC Type Autotransformer provided for speed regulation. APPENDIX-2: Sample Experimental data Weight of Rotor, kg: 6.7 Rotor Diameter, mm: 300 Rotor Thickness, mm: 10.5 Moment of inertia of the disc, coupling and motor rotor about central axis, I, kg cm sec2 : : 0.768 Distance of bolt of weight pan: from disc centre, L, cm: 17.6

S. No. Weight, W Time required for Speed, N Angle of precession (kg) precession, dt (see) (rpm) ( degree)

1. 0.5 14 1730 45

APPENDIX-3: Data Analysis Angular velocity of disc in rad/sec

sec/17.1816017302

602

radN

=

==pp

w

Angular velocity of precession of yoke P in rad/sec

dtd

P

qw =

where d is in radian = rad785.0180

45 =p

sec/0561.014785.0

radP ==w

Experimental justification of the equation:

cmkgIC P .81.70561.017.181768.0 === ww KgCmLWCactual 8.86.175.0 ===

Experiment no.6

Objective:

To perform the experiment for static balancing on static balancing machine

Apparatus:

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

rectangular main frame. A set of four 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 and rim of this disc is grooved to take a light cord provided -Nith two

cylindrical metal containers of exactly the same weight.

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 230 volts single phase 50 cycles electric motor, mounted under

the main frame, through a belt.

For static balancing of individual weights the main frame is suspended to the supported

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.


Remove the drive belt. The value of Wr. For each block is determined by clamping each

block in turn on the shaft and with the cord and container system suspended over the

protractor disc, the number of steel balls, which are of equal weight, are placed into one

of the containers to exactly balance the blocks on the shaft. When the block becomes

horizontal, the number of balls N will give the value of Wr. for the block.

For finding out Wr during static balancing proceed as follows:

1. Remove the belt.

2. Screw the combined hook to the pulley with groove. (This pulley is different than

the belt pulley). .

3. Attach the cord-ends of the pans to the above combined hook.

4. Attach the block No.1 to the shaft at any convenient position and in vertical

downward direction.

5. Put steel balls in one of the pans till the block starts moving up. (Up to horizontal

position).

6. Number of balls gives the Wr value of block 1. Repeat this for 2-3 times and find

the average no. of balls.

7. Repeat the procedure for other blocks.

Precautions:

1. Do not run the motor for more time in unbalanced positions.

2. Place the weights/balls gently in the pan. While placing the balls the pan should

be hold gently and check that it should not jump its position.

3. Weight setting gauge should be check gently.

Experiment no.7

Objective:

To perform the experiment for dynamic balancing on dynamic balancing machine

Apparatus:

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

rectangular main frame. A set of four 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 and rim of this disc is grooved to take a light cord provided -Nith two

cylindrical metal containers of exactly the same weight. 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 230 volts single phase 50 cycles electric motor, mounted under

the main frame, through a belt.

For static balancing of individual weights the main frame is suspended to the supported

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.


It is necessary to leave the machine before the experiment. 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 position of the other block(s) for

balancing of the complete system. From the calculations, the student finally clamps all the

blocks on the shaft in their 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.

For dynamic balancing of 4 blocks

Obtain Dynamic Balance of a set of four blocks with unbalance as shown, by properly

positioning them in angular and lateral position on the shaft.

Block Unbalance (Wr Product)

NO.

1. 74

2. 71

3. 70

4. 76

Distance between each block is 3 cm. The arrangement is as shown in Fig.

(Plane 4 and 1 are unbalance planes and 3 and 2 are balancing planes)

First of all assume that reference plane is 3. Then find out the couples for blocks 4, 1 & 2

with respect to 3 and then draw couple polygon.

Plane Wr. Dist. From No.-3 Couple

3 70 0 0

4 76 3 228

1 74 6 444

2 71 9 639

Let us assume block no. 4 is in horizontal position. And also consider block No.1 is

at 36 to block NO.4. Now draw the couple polygon as shown

An angular position of block no. 2 is obtained from the couple polygon with respect to

block no 4.

Now draw the force polygon

Angular position of block NO.3 is obtained from the force polygon and its magnitude is

also obtained F3 = 70. Adjust all angular and lateral position properly and find the shaft

rotates without vibrations.

Precautions:

4. Do not run the motor for more time in unbalanced positions.

5. Place the weights/balls gently in the pan. While placing the balls the pan should

be hold gently and check that it should not jump its position.

6. Weight setting gauge should be check gently.

Experiment no.8 Objective:

To determine experimentally the mass moment of inertia by the help of trifilar suspension

apparatus

Introduction:

Many a time in engineering practice, the problem of finding out the mass moment of

inertia of a regular or irregular body arises. For this and allied problems, sometimes the

mathematical computation is tedious. Such problems can be solved by the method of

bifilar/ trifilar suspension.

Experimental Set Up:

The experimental set up consists of M.S. Channel frame at the bottom side and three

M.S. Pipes in vertical position. At top an angle frame is fitted. Three drill chucks are

fitted on each arm of this angle frame. String can be fixed in these chucks at the top and a

disc is fixed at the bottoms. The length of string can be easily varied. Two weights are

provided for experiment.

Theory:

The setup consists of a disc having a weight W is suspended by three long parallel

flexible cord of length I. The three strings being placed symmetrically about the center

of gravity G at a radius r and disposed at 1200 to each other. When the

disc is twisted through a small angle 8 about a vertical axis through the center of gravity

G, it will vibrate with simple harmonic motion in a horizontal plane.

Let

W = Weight of the body

k = Radius of gyration

I = Mass moment of Inertia of the body about a vertical axis through G

2kgW

=

l = length of each string

r = the distances of each wire from the axis of the disc

By measuring the frequency n actually we can find out radius of Gyration k and then

mass moment of inertia IG. Radius of gyration k can be found by lg

nrp2

Experimental Procedure

1. Fix all three strings (rope) to disc and drill chucks. Keep equal length of each cord.

2. Place weight centrally on disc (i.e. disc or ring weight).

3. Ensure that length of each cord is same.

4. Now apply equal and opposite torque to disc by hand and measure time required for 10

oscillations.

5. Repeat the same procedure for different lengths of cords and weights.

6. Take at least three readings for each set to minimize error.

Data Sheet

Weight of the Disc, W, kg =

I.D. of Ring, cm =

O.D. of Ring, cm =

Weight of Ring, kg Length of cord, l, cm=

r, cm =

S. No.

No. of Oscillation,

N (osc)

Time required, t ( sec)

Frequency n =tlN

osc/sec

Radius of gyration, k

(cm2)

Mass moment of inertia

I, kgcm.sec2

Precautions:

1. Apply carefully equal and opposite torque.

2. Length of the each cord should be same.

3. Place weight exactly at center of disc.

4. Keep the amplitude of torsional vibrations small and not more than about 5. 5. The

moment of inertia of the platform should be small as compared to the moment of

inertia of the mechanical part.

5. Ensure that there are no kinks in the wires.

6. Ensure that the vibrations are constrained in the horizontal plane.

7. The electric fan etc. situated near the trifilar suspension should be switched off and

ensure that guests of wind coming from a window opening in the room do not disturb

the experimental set up.

dom lab manual

Documents

governor speed unit

spindle speed

variable speed control

springloaded governor

proell governor

hartnell governor

sleeve speed height

initial height of governor