emm &dom lab

5/21/2018 emm &dom lab

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UEPME35P METROLOGY AND MESASUREMENTS LAB AND DYNAMICS LAB

PONNAIYAH RAMAJAYAM INSTITUTE OF SCIENCE & TECHNOLOGY

PRIST UNIVERSITYCENTRE FOR HIGHER LEARNING & RESEARCH

(Under Section 3 of UGC Act, 1956)TRICHY CAMPUSTAMILNADU

FACULTY OF

CERTIFICATE

Certified that this is the bonafide of practicals

done by Selvan/Selvi

(Reg. No. ..) . Year/Branch in the

lab . During .

Staff In charge Head of faculty

Submitted to the university practical held on

Internal Examiner External Examiner


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CONTENTS

Sl. No. Date Name of the experiments Page No. Marks Signature


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CONTENTS

Average Marks Scored

Faculty In charge

Sl. No. Date Name of the experiments Page No. Marks Signature

Completed Not Completed


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METROLOGY AND MESUREMENTS LAB


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CALIBRATION OF VERNIER CALIPER

Ex. No.: Date:

Aim:

To calibrate the given Vernier Caliper by using a slip gauges.

Apparatus required:

1. Vernier caliper

2. Slip gauge

Formula:

Error

Percentage of error = x 100

Slip gauge value

Where,

Error = Slip Gauge value ~ Vernier caliper value

Theory:

A vernier caliper consists of a fixed part and a moveable jaw.

The fixed part includes a stem, that has a linear scale (called the main scale)

engraved on it. The moveable jaw is free to slide along the fixed stem and has a

small auxiliary scale (called the vernier scale) etched on it.

A vernier caliper can be used to measure the inside diameter of a cylinderby inserting the jaws into the cylinder and opening them until they are in snug

contact with the inner walls.

A vernier caliper is also useful in determining the depth of an opening in

an object, such as the depth of a cup. This is accomplished by first placing the

right end of the stem in contact with the top surface of the opening. Then extend

the blade (which is protruding out of the right end of the stem) until it is in

contact with the bottom of the opening. The depth of the opening is then given

by the reading of the vernier caliper.


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Vernier caliper

1. Out side measuring jaws

2. Inside measuring jaws

3. Depth bar4. Main scale reading in mm

5. Main scale reading in inch6. Vernier scale reading in mm

7. Vernier scale reading in inch

8. Sliding Grip

Observation:

Least count of Micro meter = 0.02mm

Tabulation:

Sl. No. Vernier value Vernier value Error % of Error


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Procedure:

1. Check the Vernier Caliper for smooth running over full range.

2. Clean the jaws and the measuring tip carefully and remove the protective

grease from the gauges with the clean cloth.3. Set the dimensions slightly higher the value of the slip gauge and slide the

jaws against the slip gauges.4. Use the following series of slip gauges for testing errors throughout the

range. They are 5, 5.5, 6, 6.510 mm.

Result:

Thus the given Vernier is calibrated and is found to have error in range of5mm to 10mm.


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CALIBRATION OF MICROMETER

Ex no.: Date:

Aim:

To calibrate the given micrometer by using a standard slip gauges.

Apparatus required:

1. Micro meter

2. Slip gauge

Formula:

Percentage of error =

Where,

Error

Slip gauge value

Error = Slip gauge reading ~ micrometer value

Theory:

A micrometer caliper, commonly called a "mike", is used for makingaccurate measurements of short lengths (less than 2.5 cm). It consists of aframe, which is semicircular in shape, a moveable rod which fits inside a sleeve(which looks like a barrel), and a thimble which rotates over the sleeve.

A precision thread is machined on one end of the rod, such that the rod ismoved by rotating the thimble. The jaws of a micrometer caliper are the anvil

(which is a fixed surface) and the left end of the movable rod.

The object to be measured is first placed loosely between the anvil andthe rod. The final adjustment is then made by rotating the ratchet at the end of

the micrometer. The ratchet allows the screw mechanism to slip in order to

prevent too much force from being applied on the jaws, such that no damage isdone to the precision threads, jaws, and the object being measured.


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Observation:


Tabulation:

Sl. No. Slip gauge

value

Micrometer value Error % of Error


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Procedure:

1. Check the micrometer for smooth running over its full range.

2. Clean the anvil and measuring tip carefully and remove the protective grease

from the gauges with clean cloth.3. Set the micrometer dimensions slightly larger than the size of the slip gauge

and slide the slip gauge gently over the contact surface of the micrometer.

4. Turn the thimble till the measuring tip just touches the slip gauge and gives

the final movement by ratchet, so that uniform pressure is applied.5. Use the following series of slip gauges for testing errors throughout the

range. They are 0.5,1 and 1.5 5mm.

Graph:1. A graph is drawn taking percentage of error in Y-Axis and slip gauge value

in X-Axis

Result:

Thus the given micrometer is calibrated and found the error in the range of

0.5mm to 5mm


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CHECKING DIMENSION OF PART USING SLIP GAUGE

EX.NO.: DATE:

Aim:

To measure the given job using slip gauge.

Apparatus required:

1. Slip gauge

2. Type A measuring jaw

THEORY:

Slip gauges are also called as JOHANSON GAUGES. The measuring

surface of gauges is perfectly flat and accurate, so that any two faces may bewrung together.

As per IS: 2984-1966, slip gauges are available in three different grades

i.e. grade O, grade I, and grade II.

Grade ISlip gauges are used in inspection departmentGrade IISlip gauges are used in workshopGrade 0Slip gauges are used in laboratories & standard rooms

Some available sets of slip gauges are M112, M105, M50, M33, M27, M45,etc.

Wringing phenomenon:

When two clean & perfectly flat surfaces are slide together under

pressure, they adhere firmly. This phenomenon is called as WRINGING ofslip gauges. The phenomenon of wringing occurs due to molecular adhesion

between liquid film & the mating surface.


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slip Gauge

Observation:


Tabulation:

Sl. No. Name of the job Dimensions

measured by

vernier

Dimensions

measured by slip

gauge


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Procedure:

1. Clean the faces of the measuring jaw with a cloth.

2. Clamp the given job in the measuring jaw.

3. Measure the job dimension by vernier caliper and note the dimensions.

4. Build the slip gauge to the required dimensions and insert in the jaw.

5. Find the total value of slip gauges used for building required dimensions.

6. The total value of the slip gauges are the dimension of the given job.

RESULT:

Thus the job is measured using slip gauges and the dimension of

the job is


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SINE BAREx No.: Date:

Aim:

To Measure the included angle of a taper plug gauge using a SINE BAR.

Apparatus required:

1. Taper plug gauge (Small gauge with included angle of less then 30).2. Sine Bar.

3. Set of slip gauges.4. Vernier Caliper

5. Surface plate.

6. Dial indicator with Stand.

Formula:

1. Taper angle of Plug Gauge = Tan -1 (h1-h2)LWhere,

h1 = Major height on the taper plug gauge.

h2 = Minor height on the taper plug gauge.

2. Approximate value of slip gauge = Length of sine bar x Sin

3. Included angle of gauge,

Sin = Accurate Value of slip gauges / Length of the sine bar

Theory:

Sine bar is always used in conjunction with datum support (e.g. surface

plate) and auxiliary equipments such as slip gauges, dial indicator, angle plateand height gauge. It consists of a steel bar containing two rollers of equal

diameter attached at the end of it as shown in fig. The axes of these two rollers

are mutually parallel to each other and are also parallel to and at equal distance

from the upper surface of sine bar. The distance between the axes of roller

known as length of sine bar is usually 100mm, 200mm & 300mm. Some holes

are drilled in the body of the bar to reduce the weight and to facilitate the

handling. It is made up of high carbon, high chromium, and corrosion resistancesteel, hardened ground & stabilized steel.


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Sine bar:

Observation:

1. Major height on the taper plug gauge (h1) = mm

2. Minor height on the taper plug gauge (h2) = mm

3. Length of the taper plug gauge (L) = mm

4. Length of the sine bar (center distance of rollers) (l) = mm

Tabulation:

Sl.

No.:

Trial Value of Slip

Gauge (mm)

Result of different

reading (mm)Action


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Procedure:

1. In order to have a near value of the slip gauge. Measure the larger andsmaller diameter and also the length of the taper plug gauge.

2. Place the sine bar. Which is nothing but a horizontal bar with two rollers

at the bottom over the surface plate.

3. Set the taper plug gauge on the surface of the sine bar. Which is now

known as Sine bar. While doing so, the center line of the gauge must be

accurately aligned with that of the bar.

4. Different slip gauges are placed underside of the sine bar to make the

taper plug gauge horizontal to the surface plate.

5. The straightness of the gauge is tested using a dial indicator. The slip

gauges are altered until there is a negligible deflection in the dial gauge.

CALCULATION

Result:

The included angle () of the given taper plug gauge is found


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MEASUREMENT OF VIBRATIONEx No.: Date:

Aim:

To measure velocity, Acceleration and displacement by using Vibration

measurement Trainer

Apparatus required:

1. Vibration measurement trainer.

Theory:

Accelerometer:

When the piezoelectric elements are stained by an external force,

displaced electrical charge accumulates on opposing surfaces due to thedefection of the lattice in a naturally piezoelectric quartz crystal.

Accelerometers typically have a seismic mass, which is represented by gray

color. Two piezo-crystals are placed between the mass and the base. Inaccelerometers, which measure motion, the invariant seismic mass, M isforced by the crystals to follow the motion of the base and structure to which it

is attached. The resulting force on the crystals is easily calculated usingNewtons second law of motion: F=MA. The output charge from sensor is fedto charge amplifier and to signal conditioner.

Vibration generator:

Vibration comprise of a permanent magnet mounted to the base. A coil is

fitted to the diaphragm which is fitted rigidly to the magnet at the

circumference. As the coil is excited the coil vibrates depending on the

frequency and the amplitude applied to the coil. Sensor is fitted on the stud

provided at the center of the diaphragm.

Procedure:


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1. Connect the sensor to the instrument through the BNC socket provided on

the rear mentioned Sensor.

2. Connect the vibration generator to the instrument through the cable

provided at the rear panel of the instrument marked EXCTER.

3. Connect the instrument to the 230V 50Hz. Supply through cable provided

at the rear panel.

4. Keep the FREQ. Port and the VOLT port in the minimum position.

5. Switch on the instrument, the display glows to indicate the power is on.

6. Turn the VOLT port the max position.

7. Now turn the FREQ. port in steps of 100Hz. And note down the reading

of acceleration, Velocity and Displacement by selecting the MODE throughselector switch.

8. Tabulate the readings in the tabular column. Experiment can be repeated

for different voltage levels settable through VOLT knob provided.

Graph:

1. Frequency Vs Acceleration

2. Frequency Vs Velocity

3. Frequency Vs Displacement

Tabulation:

Sl. No.: Frequency Acceleration Velocity Displacement

1

2

3

4

5

6

7


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Result:

Thus the velocity, Acceleration and displacement are measured and tabulated

by using vibration measuring Trainer.


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MEASUREMENT OF DISPLACEMENT USING LVDT

Ex No.: Date:

Aim:

To study &use liner Variable Differential Transformer for measurement

of displacement up to 20mm.

Apparatus required:

1. LVDT Trainer kit.

Formula:

Input displacement ~ Output displacement

1. % of Error = x 100

Input displacement

Theory:

It uses Transformer principal & hence the name LVDT. The output

voltage produced by the displacement of the core is liner over a considerable

range, but flattens out at both ends. The voltage phase changes by 180 as the

core moves through the center position LVDT provides continuous resolution &shows low hysterics & hence repeatability is excellent under all condition. It is

sensitive to vibration & temperature.


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1. Input Displacement Vs Output Displacement

2. Input Displacement Vs % Error

Procedure:

1. Connect the LVDT module to the main unit.

2. Initially set the core position at zero.

3. Note the corresponding displacement as the input displacement.

4. Note the corresponding output displacement.

2. Now, adjust the micrometer position so that the core moves towards the

right & left of the zero position.

3. Note down the corresponding displacement for each displacement on the

right & left of the zero position.

4. The readings are tabulated.

Graph:


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Tabulation:

Sl.

No.:

Input Displacement

(mm)

Output

Displacement(mm)

Error % of Error

1

2

3

4

5

6

7

8

9

10

Result:Thus LVDT was used to measure displacement up to 20mm.

lvdt:


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MEASUREMENT OF TORQUE

Ex No.: Date:

Aim:

To measure torque using strain gauge.

Apparatus required:

1. Torque measurement trainer kit.

2. Different load.

Theory:

Torque is defined as the force, which tends to change the linear or of a

body. It may also be defined as the turning or twisting moment of force about an

axis. Torque is given as T=FD where T Torque FForce D Perpendiculardistance from the axis of rotation of the force.

Basically, rotating are two types of torque sensor1. Inline rotating torque sensor2. Inline stationary torque sensorReaction torque sensors are those that measure the torque on machine

housing rather then on shaft, are generally not suitable measurement because

connecting power & pipelines affect the torque.The in line rotating sensor is used for torque measurement of rotating

equipments, it consist of a metal with bonded strain gauges electrically

connected in the form of a Wheatstone bridge.

The strain gauges are kept on the shaft at precisely 45 to the shaft axis tosense compressive and tensile deformation due to torsion. The strain gauges

1&3 must be diametrically opposite as must strain gauges 2 & 4.

IN one direction at a 45 angle to the axis, pure ten side stress exists,

whereas 45 in the other direction pure compressive stress is extant the rotor

shaft are elastic and will deflected minutely under the imposed stresses. The out

of the Wheatstone bridge is in proportion to the torsion and hence to the appliedtorque on the shaft.

The torque is used for the measurement of relative angular

displacement, Variable inductance and Magnetostrictive effects.


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Procedure:

1. Connect one end of the 4 core shielded cable connection to thetransducer and other end to the digital torque indication.

2. Switch on the instrument.

3. Keep READ CAL switch in read position without any torque applied.

Adjust the zero control pot till the display read zero.

4. Keep READ CAL switch in CAL position for calibration. Adjust the

Cal control pot till display reads given range of torque.

5. Switch back the READ CAL switch to read.

6. The display now ready to accept torque applied directly.

7. Repeat the above steps with different loads.

Graph:

1. LOAD Vs Torque


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WHEATSTONES BRIDGE:

Tabulation:

Sl. No.: Load (Kg) Torque (Kgm)

1

2

3

4

5

6

Result:

Thus the torque was measured using strain gauge and the graph was plotted

with the load Vs torque.


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MEASUREMENT OF TEMPERATURE USING

THERMOCOUPLE

Ex No.: Date:

Aim:

To Measure the temperature by using Thermocouple.

Apparatus required:

1. Instrumentation TrainerThermocouple.

2. Heat Source.

1. Thermometer.

2. Thermocouple sensor.

Formula:

Actual Temperature ~ Indicated Temperature

1. % of Error = x 100Actual Temperature

Theory:

When two metals or semiconductors of dissimilar characteristics are

joined together, an emf is induced between them. The junction of the metals iscalled thermocouple. Thermocouple is based on the principal of See backeffectin Thermocouple one junction is subjected to heating. The difference intemperature is directly proportional to the emf induced usually the reference

junction is maintained at 0 C


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Procedure:

1. Connect the heat source box to the socket provided on the backside of the

main unit.

2. Plug the three pin input socket of the main unit to standard single phase ac

220V, 50Hz plug point.

3. Connect the leads from the Thermocouple Sensor to the main unit.

4. The display will indicate the room temperature.

5. Place the thermometer inside the hole in heat source box.

6. Record the thermometer reading & the display reading.

7. Adjusting the knob of the phase controller to select the temperature level of

the experiment.

8. Record the corresponding temperature reading.

9. The readings Tabulated.

Graph:

The graph is drawn to % of error Vs Actual temperature


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Tabulation:

Sl.

No.:

Actual value in

thermometer

Indicated value in

thermometer% of Error

1

2

3

4

5

6

7

8

9

10

Result:

Thus the temperature is measured by using Thermocouple.

Thermocouple sensor:


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DYNAMICS LAB


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CAM JUMP PHENOMENON

Ex No.: Date:

Aim:

To determine the speed at which follower jump occurs.

Apparatus required:

1. Experimental setup

Formula:

1. 2e = f/m + g

2. = 1/e X {(f/m) + g}

3. N = 60/21/e X {(f/m) + g}

Where,

m = Mass of the follower in Kg

g = Acceleration due to gravity in m/s2

e = Eccentricity of cam in m

f = Force required by spring = K

Where,

= Deflection in mK = Stiffness of spring = Gd

4/ 8D

3n

N/m

Where,

G = Rigidity of coil in md = Diameter of coil in m

D = Mean diameter of spring in mN = Number of coil in spring


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Theory:

A reciprocating (or) oscillating cam is subjected to acceleration orangular acceleration and retardation. During retardation the contact between

cam and follower is maintained by spring force. The force required forretardation is F = m X f where mis the mass of the follower and f is theretardation force.

If the F is less then mX f then the follower will not follow the camprofile and gap will be crated. This phenomenon is called cam jump. Theretardation f depends on the square of angular velocity of cam (). In other

words the angular speed is increased, at one particular speed cam occurs can bedetermined.

Procedure:

Measure the dimension of the spring such asd, D, nand free length. The motor is started, initially the follower will follow the cam profile but

as the speed is increased the follower starts in jumping.

The speed of which the follower jumps is noted and is called the critical

speed. Set the various values of and compare with calculated values.


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Graph:

Defection of Spring Vs Speed

Observation:

1. Diameter of coil (W) = m

2. Mean diameter of spring (D) = m

3.Number of coil in spring (n) = Nos.

4. Modulus of rigidity of steel (G) = N/mm2

5. Acceleration due to gravity (g) = m/s2

6. Mass of follower (m) = Kg

7. Eccentricity of cam (e) = m

Tabulation:

Sl.

No.:

Spring

defection ()Spring force (F)

Actual critical

speed (Nact)

Theoretical critical

speed (Nth)

Mm N Rpm Rpm

01

0203

04

05

Result

Thus the cam jump phenomenon is determined

CAM JUMP PHENOMENON:


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FREE BEAM

EX.NO.: DATE:

Aim:

To find the natural frequency of the given free beam setup.

Apparatus required:

1. Free beam setup

2. Hangers

3. Dial gauge.

4. Dead weight.

Formula:

Natural frequency (n) = K / m Hz

Where,

m = Mass of the bar + Mass of hanger + Added mass

K = Stiffness of bar = P/y

Where,P = Load applied on the bar.( Mass of the bar + Mass of hanger)

y = Deflection measured from dial gauge

THEORY:

The bench mounted apparatus has a steel base with a fixed support atboth the ends. A steel beam and two hangers are placed at the top of the

supports. A dial gauge is mounted for measuring the deflection of beam.


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PRIST UNIVERSITY


Procedure:

1. The mass of the beam and the mass of the hangers are measured.

2. The dial gauge is fixed at the centre of the bar.

3. The hangers are placed at the particular distance from the centre(dial gauge) on both sides.

4. Equal loads are applied on the hanger and the deflection of the

beam is measured.

5. Natural frequency of the system is found using (n) = K / m

6. Experiment is repeated for different load and for various position ofhangers.


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PRIST UNIVERSITY

Observations:

1. Mass of the bar = Kg

2. Mass of the Hanger = Kg. (each)

Tabulation:

Length

WeightaddedinHanger

1(m1)

WeightaddedinHanger

2(m2)

To

talweightaddedin

be

am(P=m1+m2+mh)

De

flectionofbeam(y)

Stiffnessofthebar(K)

Weightonthebar(P+mb)

Naturalfrequencyofthe

beam(n

)

L1 L2

Mm mm Kg Kg Kg mm Kg/mm Kg Hz


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PRIST UNIVERSITY

RESULT:

Thus the natural frequency is determined by using given free beam setup.

FREE BEAM:


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PRIST UNIVERSITY

GEAR TRAIN

Ex No.: Date:

Aim:

To draw the speed / Ray diagram by using the gear box.

Apparatus required:


Formula:

1. Gear ratio =

No. of revolution in output shaft

No. of revolution in input shaft

2.Deviation =Preferred gear ratioActual gear ratio

Theory:

Preferred gear ratio

In multi speed gear box, different output speeds can be obtained bychange gears. With two numbers of three positions sliding gears in intermediateshaft 3 x 3 = 9 different speeds can be obtained in the output shaft for a constant

input shaft speed. These types of gear boxes are widely used in machine tools,automobiles and number of machines, where speed change is required. This

speed will in geometric progressive inversely proportional to speed ratio forconstant power transmission. This also can be verified by this setup.

The gear train arrangement consists of three shafts. In shaft 1&3 (Input

and Output), Three fixed gears are provided. In intermediate shaft (No.2)2sliding gears are provided for selectively engaged with gears in 1&3 . All shafts

are mounted on ball bearing. All items are mounted on single base. The speed

can be achieved by manual shifting of sliding gears. If 1,2&3 are positions of

slide gear 1, and 4,5&6 are position of slider gear 2, then the following

combinations are posible1-4,1-5,1-6,2-4,2-5,2-6,3-4,3-5,3-6.


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PRIST UNIVERSITY

UEPME35P METROLOGY AND MESASUREMENTS LAB AND DYN

Testing Procedure:

1. Check the sliding gear is perfectly mesh with its meshing gears.

2. Check the number of teeth for the all gears.

3. Check the bearings shafts and key position.

4. Check the gear numbers are perfectly.

Experimental procedure:

1. The number of teeth in each gear is counted.

2. Module of gear is calculated and is verified.

3. Centre distance between the shafts is measured.

4. Gear ratio in each combination 1-4,1-5,1-6,ect is estimated.

5. Different position of 1/2/3&4/5/6 are set and give revolution to input shaftand measure the output revolution. Gear ratio is estimated and is verified

with calculated value.

6. Speed diagram is drawn.

7. Speed in geometric progression is calculated and the relations are noted.

Geometric Progression ()n-1 = Nmax / Nmin

Gear tra

in:

AMICS LAB


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PRIST UNIVERSITY

Observation:

1. Z1, Z3, Z5 - Input shaft gears - 34,30,38

2. Z2, Z4, Z6 - Intermediate shaft gears - 34,38,30

3. Z7, Z9, Z11 - Intermediate shaft gears - 30,40,20

4. Z8, Z10, Z12 -Output shaft gears - 30,20,40

Tabulation:

Gearposition

Calculated gear ratioPreferredgear ratio

Deviation in

%Inputrevolution in

Deg

Outputrevolution in

Deg

Output /

Input

1-4

1-5

1-6

2-4

2-5

2-6

3-4

3-5

3-6

Result:

Thus the speed diagram/ ray diagram are drawn by using the gear trainand compared with its preferred value.



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PRIST UNIVERSITY


GYROSCOPIC COUPLEEx No.: Date:

Aim:

To verify the law of gyroscope and to find the gyroscopic couple

Apparatus required:

1. gyroscope2. Stop watch

3. Dead weight4. Auto transformer

5. Tachometer

Formula:

1. gyroscopic couple (C) = I. . p

Theory:

Where,

I = Moment of inertia of the disc = (W/g) x K2

= Angular velocity of spin = 2N/60 rad/secp = Velocity precessionW = Weight of the disc in Kgf

K = Radius of the disc in cm

G = Acceleration due to gravity in cm/sec

N = Speed of the disc in radian

= Angle turned in radiant = Time taken for angle turned in sec

When a body moves along a curved path with a uniform linear velocity, a force

in the direction of centripetal acceleration (know as centripetal force) has to be

applied externally over the body, so that it moves along the required curvedpath. This external force applied is known as active force. When a body, itself.

Is moving with uniform linear velocity along a circular path, it is subjected to


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PRIST UNIVERSITY

U AND DYNAMICS LABEPME35P METROLOGY AND MESASUREMENTS LAB

the centrifugal force radially outwards. This centrifugal force is called reactive

force.

The change is angular momentum is known as active gyroscopic couple

(I. . p). When the axis of spin itself moves with angular velocity p, the discis subjected to reactive couple whose magnitude is same (i.e. I. . p) butopposite in direction to that of active couple.

Gyroscopic laws:

a. Axis of the spin, precession and active gyroscopic couple are

mutually perpendicular to each other.

b. Reactive gyroscopic couple is equal in magnitude and opposite in

direction to the active gyroscopic couple.

Procedure:

1. Measure the distance Lbetween the centres of the disc and the point ofapplication of load.

2. Rotate the disc at a known speed N rpm, and measure it using atachometer.

3. Add the load and note the time taken (t sec) for a known angle of rotation

of the disc about the axis of spin.

4. Angle of precisions (p) can be found using the relation = / t and theangular velocity of spin () can be found using the relation() = 2N / 60.

5. Calculate the gyroscopic couple using the relation C = I . . p

Graph:

Draw the curve to the following

Gyroscopic couple Vs Applied couple


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PRIST UNIVERSITY


Observation:

1. Weight of the Disc (W) = Kgf

2. Radius of the Disc (K) = m

Tabulation:

S

l.No.:

Addedmass

(W1)

Distance(L)

Applied

couple(AC)

Angle

turned()

Time(t)

Velocityof

precession

(p

)

Speed(N)

Angular

velocityof

spin()

Gyroscopic

couple(C)

Kg m Kgf.cmDeg.()

Rad.

sec rad/sec rpm rad/sec Kgf.m

Calculations


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PRIST UNIVERSITY


\

Result:

Gyroscopic couple of the given gyroscope is determined.Gyroscope


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PRIST UNIVERSITY


HARTNELLGOVERNOREx No.: Date:

Aim:

To draw the characteristics curve and to determine sensitively and effort of the

Hartnell governor

Apparatus required:


2. Tachometer

3. Auto transformer

Formula:

1. Radius of rotation (R1) = r + h X (x/y) m

Where,

r = Distance of fulcrum from governor in m

h = Distance of sleeve in m

x = Length of vertical arm in m

y = Length of horizontal arm in m

2. Centrifugal force (fc) = m X 2 X r1


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PRIST UNIVERSITY


Where,

m = Mass of the fly ball in Kg

r1 = Radius of the rotation in m

= Angular velocity of ball = 2N / 60N = Speed of governor in rpm

3. Stiffness of spring (S) =

4. Sensitivity of governor =

2(fc2 - fc1) X x/y

h2h1

2(N2N1)

(N1 + N2)

5. Spring force (Sf) = 2 X Fc X (x/y)

6. Effort (p) = (Sf2Sf1) / 2

7. Power = P X h

Theory:

A Hartnaell Governor is a spring loaded Governor. It consists of two bell

crank lever pivoted at the end of the frame. The frame is attached to thegovernor spindle and therefore rotates with it. Each lever carries a ball at the

end of the vertical arm and a roller at the end of the horizontal arm. A helical

spring in compression provides equal downward forces on the two rollers

through a collar on the sleeve. The spring force may be adjusted by screwing anut up or down on the sleeve.

As the speed increases the moves away from the spindle axis the crank

levers moves on the pivot and the sleeve against spring force, if the speed

deceased then the sleeve moves downward


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Procedure:

1. The Hartnall Governor configuration is setup wit given spring.

2. The distance r, x, y are measured.

3. Using the auto transformer, the governor is rotated at the given speed.

4. The deflection of the sleeve (h) is noted.

5. For each speed, radius of rotation (r1) and the centrifugal force are

calculated.

6. The stiffness of the spring is found using the below relation

Stiffness of spring (S) =

2(fc2 - fc1) X x/y

h2h1

7. Then mean value of stiffness of the spring is calculated.

8. The sensitivity efforts and power are found by using the tabulated values

using the corresponding relations.

Graph:

Deflection of sleeve Vs Speed

Effort Vs Speed


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:


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Observation:

1. Mass of the fly Ball (M) = mm

2. Readies of fulcrum from Governor (r) = Kg

3. Length of the vertical arm (x) = mm

4. Length of the horizontal arm (y) = m

Tabulation:

Sl.N

o.:

Spe

ed(N)

Sleevedeflection(h)

Radius

ofrotation

(r1)

Centrif

ugalforce

(fc)

Stiffnes

sofspring

(S)

Sensitivityof

governor

Spring

force(Sf)

Effort(P)

Power

rpm m m Kg Kg/m Kg Kg Kg-m

1

2

3

4

5

6

7


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Calculation

Result:

The stiffness of spring, sensitivity, effort and power of the Hartnell

Governor are found.


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VIBRATION TABLE

Ex No.: Date:

Aim:

To determine the natural frequency and critical speed of the given

vibration table and compare with its theoretical values.

Apparatus required:

1. Vibration table setup

2. Motor with tacho disc

3. Local cell

4. Spring

5. Rpm indicator and bar graph

Formula:

1. Transmissibility ratio (T) =Force Transmitted

Force excited

2. Force exited = m X X e

Where,

m = Mass of disc in Kg

= Angular velocity = 2N/60

e = Time Eccentricity of disc in m


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N = Speed of the motor in Rpm

i.e., Force transmitted = 0.125 X Number of plinking LED

3. Theoretical natural frequency (th) = K/M HZ

Where,

M = Mass of the motor and its base in Kg

Gd4

K = Stiffness of spring = 8D3n


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PRIST UNIVERSITYG = Rigidity modulus in N/mm

2

D = Diameter of coil in m

N = Number of turns in coil

4. Theoretical critical speed (Nth) = n X (60/2) Rpm

5. Actual natural frequency (act) = 2Ncri/60 Hz

Where,

Ncri = Actual critical speed of system (from speed Vs T graph)

Theory:

Rotating machine such as engine, blower, etc., will have unbalancedabout its axis f rotation. It can be represented by mass with eccentricity atangular speed of Radius per second. This will produce unbalance force of mX 2 X e if directly mounted on floor; it will transmitted this to the ground,which is not desirable. However, if the spring is placed between machine andfloor, the force transmitted to the ground will vary.

Procedure:

1. The motor, unbalance wheel and guide rod are weighed.

2. The spring dimension are measured such d, D, n, free length etc.,

3. From the above readings, the theoretical natural frequency and

critical speed are calculated.

4. The spring is placed on the table and motor switched on.

5. The force transmitted values are noted as a function of speed.

6. Force Excited, force transmitted and transmissibility ratio are

calculated from the above noted values.

7. Graph is drawn to transmissibility ratio Vs Speed.

8. From the above graph values actual critical speed is notedwhere transmissibility is maximum

9. The actual nature frequency is calculated from the critical speed.


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1. Output diameter of spring (D) = m

2.Coil diameter of spring

(d)

= m

3.Number of turns (n) =4. Modulus of rigidity (G) = N/m2

5. Mass of the motor (M) = Kg

6. Mass of the disc (m) = K

7. Eccentricity (e) = m

Graph:

Transmissibility ratio (T) Vs Speed

(N) Observation:

Tabulation:

Sl.

No.:

Speed

(N)

No. of

LED

Transmitted

forceExcited force

Transmissibility

ratio (T)

01

02

03

04

05

06

Result:

Thus the Moment natural frequency and critical speed of thegiven vibration table and compare with its theoretical values.

1. Theoretical natural frequency of the system (th) = Hz

2. Actual natural frequency of the system (nact) = Hz

3. Theoretical critical speed (Nth) = Rpm

4. Actual critical speed (Nact) = Rpm

VIBRATION TABLE:


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TRANSVERSE VIBRATION

Ex No.: Date:

Aim:

To determine the natural frequency of the cantilever beam.

Apparatus required:

1. Experimental Setup

2. Steel rule

3. Align Key

Formula:

1. Correction factor for length(K) = l / L

Where,l = The length at which the load is applied in mm.L = Total length of beam in mm.

2. Theoretical natural frequencyE . I . 1000

(nTH) =

Where, L3 . 3 {(0.026)m1 + m2(K

2 / 2K3 / 6)2}

K = Correction factor for length.m1 = Mass of the beam in Kg.

m2 = Mass of the motor in Kg.

E = Youngs modulus of steel in N / mm2

I = Area moment of inertia of beam = (1 / 12)Bd3

Where,


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PRIST UNIVERSITY

DYNAMICS LABUEPME35P METROLOGY AND MESASUREMENTS LAB AND

B = Breath of the beam in mm.

d = Thickness of beam in mm.

3. Theoretical Critical speed (NTH) = nTH . 60 / 2

4. Actual natural frequency (nACT) = 2. NACT / 60

Theory:

When the practical of the shaft or disc move approximately perpendicular

to the axis of the shaft, then the vibrations are known transfers vibration. In this

case the shaft is straight and bends alternately and bending stresses are inducedin the shaft.

This experimental setup consists of a flat, which is fixed at one end. Thevariable speed motor is mounted on the flat.

Procedure:

1. Measure the cross section of the beam.

2. Weigh the mass of the beam.

3. Fix the motor at known distance and vary the speed.

4. Observe speed at which amplitude is maximum.(Do not run at this speed

for long time.)

5. Increase the speed for this and check that amplitude is less at high speed.

6. Do this for various values of land compare with calculated values.

7. Calculate the theoretical frequency and compare the values.

Graph:

Actual critical speed (Nact) Vs Length (l)

Theoretical critical speed (Nth) Vs Length (l)

Transverse vibration


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Sl.

No.:

Length

(l)

Correction

factor for

length(K)

Actualcritical

speed

(N )

Theoreticalcritical

speed (Nth)

ActualNaturalfrequency

(nACT)

TheoreticalNaturalfrequency

(nTH)

mm rpm rpm Hz Hz

Observation:

1. Total length of the cantilever beam (L) = mm

2. Breath of the beam (B) = mm

3. Thickness of the beam (d) = mm

4. Mass of the beam (m1) = Kg

5. Mass of the motor (m2) = Kg

6. Youngs Modules of steel (E) = N / mm2

Tabulation:

act


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Result:

Thus the natural frequency of the cantilever beam is determined.

emm &dom lab

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