EXP LIST

Page

1

MECHANICAL MEASUREMENTS LAB MANUAL MECHANICAL ENGINEERING DEPARTMENT

Exp No:1 Calibration of Tachometer using Stroboscope

Aim:- To calibrate the given tachometer using stroboscope

Apparatus:- Tachometer, stroboscope, rotating shaft

PrincipleTachometer often fails in accurately reading the speed of the given shaft. This is mainly due to various losses incurred when the instrument is in contact with the shaft whose speed is to be measured. Often the results are erroneous on account of the extra load applied by the operator while recording the speed. The amount of error can be determined using a stroboscope which is an optical instrument, the reading is reliable since the apparatus does not come in contact with the rotating shaft and have no losses.

The term stroboscope is defined form the Greek word meaning whirling and to watch. These are most often used in experimental work. The principle of stroboscope is to synchronize a flashing light with the rotation of the shaft making it appear standstill. Usually a reference mark is put on the rotating body and the speed of the oscillation of the flash produced from the stroboscope itself is a measure of the rpm of the rotating body without requiring any contact. A stroboscope can be effectively used to calibrate the tachometer and a calibration curve can be plotted so that for any arbitrary reading of the tachometer the accurate value can be determined.

In a stroboscope high intensity light flashes are directed towards a rotating shaft on which a distinct marking has already been marked. The period of flashes can be varied immediately. The marking would appear stationary when time for one shaft revolution equals the flash period. This is the fundamental period. Also single stationary image will be seen if the flash period is an integral multiple of the above value. However for sub multiple flash period multiple stationary images will be seen. The fundamental period is used for speed measurements and this is identified as smallest period for which single stationary image is seen.

Procedure Start the machine Wait for some time as it may take time to reach the desired rpm Measure the rpm using stroboscope Now measure the rpm using tachometer Repeat the procedure for several speeds From the observations obtain the calibration equation using the curve fitting technique.

Sample calculation

Form table

x=

y=

x2 =

xy=

Curve fitting:

SCMS SCHOOL OF ENGINEERING AND TECHNOLOGY

Page

2


The method is used to plot graph between the x and y values. The method of least squares is

used to obtain the relation in the form of y = A + Bx

Solution is obtained by the following equations.

An + B∑ x = ∑ y ……………………… (1)

A∑ x + B∑ x2 = ∑ xy ……………………… (2)

Where n = No: of input variables, x is the input and y is the output

By solving the equations (1) and (2) by substituting the necessary values, we can obtain

the calibration equation.

Observations:

Sl No Speed measured using

Stroboscope

x rpm

Speed measured using tachometer

y rpm x2 xy

x= y= x2 = xy=

Result

Inference


Page

3


Exp no 2 Calibration of Strain Gauge .

Aim: To calibrate the given strain gauge using weights and to draw the calibration curve and hence determine an unknown load from the measured strain.

Apparatus: Strain gauge and weights.

Principle: Strain gauge is a passive transducer used to measure the lateral strain exerted on a

surface. This sensor converts the mechanical displacement into a change in resistance. An

optional external Wheatstone’s bridge is used to measure the bridge imbalance, which is a

measure of the strain. The sensors bonded on the surface of the rod in the apparatus converts

strain in the metallic rod in to a change in the resistance of the one arm of a balanced Wheatstone

bridge. If R1 is the change in resistance due to strain, the bridge which may be initially balanced

becomes unbalanced. This may be balanced again by changing the resistance of other arms of the

Wheatstone bridge says R3 or R4 which can be measured and computed to indicate the actual

strain suffered by the surface. Positioning and quality of bonding the sensor on the surface,

largely determine the accuracy of the strain gauge.

Strain suffered by the surface is given by

ε =

6 Px

Ebt2 ………………………………. (1)

P= weight applied at the free end of the rod in Newton;

x = span of the rod in ‘m’;

E= young’s modulus of material of surface in N/m2;

b = width of surface in m;

t = thickness of the surface in m.

Specifications:

Material of strip: stainless steel

Young’s modulus E: 2.1 * 1011 Pascal

Length of the strain gauge: 10 mm

Strip thickness: 3mm;

Supporting limb of loading point: 220mm;

Length of strip: 290mm;


Page

4


Width of strip: 25mm

Excitation voltage: 9V

Maximum weight: 1 kg

Observations:

Sl

No:

Weigh

t

X1

(kg)

Loading Unloading

x12 x1y1 x1y2

Strain gauge reading ‘a’

Actual strain gauge reading

y1=a/GF

Strain gauge reading ‘b’

Actual strain gauge reading

y2=b/GF

∑x1 ∑y1 ∑y2 ∑x12 ∑x1y1 ∑x1y2

Sample calculation

From table

∑x2 = 2∑x12 =………..

∑x = 2∑x1 = ………..

∑y = ∑y1+∑y2 =………

∑xy = ∑x1y1+∑x2y2 =………...

Curve fitting:

Equation of the curve, y = A + Bx


An + B∑ x = ∑ y ……………………… (1)

A∑ x + B∑ x2 = ∑ xy ……………………… (2)

Where n = No: of input variables.



For determining the unknown load:-

Strain suffered by the surface is given by


Page

5


ε =

6 Px

Ebt2

ε = strain from the calibration graph

P= weight applied at the free end of the rod in Newton;

x = span of the rod in ‘m’;

E= young’s modulus of material of surface in N/m2;

b = width of surface in m;

t = thickness of the surface in m.

Procedure:

Switch on the instrument using on/off switch provided on rear side. Let cantilever part of strain gauge be freely suspended. Observe the digital display reading. Ensure it is to be zero, otherwise adjust the

zero of the potentiometer. Add weights of 100 gm each sequentially and record the readings. Repeat the procedure for unloading the cantilever. Put the unknown weight and record its strain. Switch off the apparatus. From the observations, obtain the calibration equation using the curve fitting

technique. Determine the strain corresponding to unknown load from the graph and verify.

Result:

Inference:


Page

6


Exp no 3 Determination of the taper angle using sine bar and slip gauges

Aim ; To determine the taper angle of the given taper rod

Apparatus : surface plate ,taper rod ,sine bar slip gauges etc

Principle:A sine bar is s tool that is used to measure the angle accurately. It consists of a straight edge having two rollers located at or near the ends as shown in figure. The rollers must be of the same diameter. The center distance of sine bar preferably be an even number. The center distance of the sine bar of the common use is 200mm. The sine bar is used with surface plate and precision gauges or alternate measuring equipments to locate the work for mechanical or inspection operations by raising one end of the bar at the plate to form a right angled triangle. Since the sine of the angle is measured, its name is sine bar.

SpecificationsDistance between the rollers of the sine bar L = 200mmMaximum diameter of the taper rod = 30mmMinimum diameter of the taper rod = 20mmLength of the taper rod = 100mm

ProcedureClean the surface plate using cotton wool and place the given taper rod over it. Align and place the sine bar over the taper rod. Fill in the space between the rollers of the sine bar and the surface plate using the slip gauges. This process requires immense trial and error technique. The slip gauges should fit exactly in the space by bringing them properly. The thickness of the used slip


Page

7


gauges are recorded. The procedure is repeated for different sets of slip gauges. The average value of all these trails may be taken as the required angle of the taper.

Observations

Trial

Left side Right sideh1-h2(mm)

Taper anglesin-1((h1-h2)/L)

Slip gauge thickness

(mm)

Slip gauge no

Total thickness

(mm)

Slip gauge

no

Slip gauge thickness

(mm)

Total thickness

(mm)

Sample calculationh1 = ……mmh2 = ……..mmh1-h2= ……..mmL = ……..mmSin θ = (h1-h2) hence θ = …… LResult

Inference


Page

8


Expt. No. 4

Temperature Measurement Using Thermocouple

OBJECTIVE:-

To measure the temperature using Thermocouples J/K/T types and Mercury Thermometer, plot the calibration curve for the thermocouples and to verify the various thermocouple laws.

APPARATUS:-

1. Temperature transducers

2. Digital temperature indicator

3. Thermometer and

4. Electric Sterilizer

BASIC PRINCIPLE:-

Pair of dissimilar metals that are in physical contact with each other, form a thermocouple. The operation of a thermocouple is based on Seebeck effect. When heat is applied to a junction (hot junction) of two dissimilar metals, an emf is generated which can be measured at the other junction (cold junction).The two dissimilar metals form an electric circuit, and a current flows as a result of the generated emf.

Thermocouples are available in different combination of metals. The most common types are J, K, T and E. Each has a different temperature range and environment, although the maximum temperature varies with the diameter of the wire used in the thermocouple.

Thermocouple Type and Range:

TypeMetal

Range oFPositive Negative

J Iron Constantan -300 to 1600K Chromel Alumel -300 to 1400T Copper Constanton -300 to 650

Thermocouples provide an economic means of measuring temperature with many practical following advantages for the user.

1. They can be extremely robust, by using thick wire.

2. Fine wire thermocouples respond very rapidly to temperature changes (less than 0.1 seconds). For ultra fast response (10µ seconds typical), foil thermo-couples are used.

3. Capable of measuring over very wide temperature ranges, from cryogenics to engine exhausts.


Page

9


4. Thermocouples are easy to install and are available in many packages, from Probes to bare wires or foil.

The number of free electrons in a piece of metal depends on both temperature and composition of the metal, therefore pieces of dissimilar metal in isothermal contact will exhibit a potential difference that is a repeatable function of temperature. The resulting voltage depends on the temperatures, T1 and T2, in a repeatable way as shown in Figure 1.

Since the thermocouple is basically a differential rather than an absolute temperature measuring device, one junction must be at a known temperature if the temperature of the other junction is to be found from the value of the output voltage.

An alternative measurement technique is illustrated in Figure 2. This is used in most practical applications. The reference junction temperature is allowed to change but some type of absolute thermometer carefully measures it. A measurement of the thermocouple voltage combined with knowledge of the reference temperature can be used to calculate the measurement junction temperature. Usual practice, however, is to use a convenient thermoelectric method to measure the reference temperature and to arrange its output voltage so that it corresponds to a thermocouple referred to 0°C. Thermocouples are available in different combinations of metals. The four most common types are J, K, T and E. Each type has a different temperature range and environment, although the maximum temperature varies with the diameter of the wire used in the thermocouple.

Figure 1 Figure 2

Thermocouple selection:

Following criteria are used in selecting a thermocouple.

Temperature range

Chemical resistance of the thermocouple or sheath material

Abrasion and vibration resistance

Installation requirements (may need to be compatible with existing equipment; existing holes may determine probe diameter).

Thermocouple Effects:-

a. Seebeck effect:-

When the junctions of two dissimilar metals forming a closed circuit are exposed to different temperatures, a new thermal electromotive force is generated which induces a continuous electric current. The emf produced is proportional to the difference in temperature and further, to the


Page

10


difference in the metallic thermal transport constants. Thus, if the metals are the same, the emf is zero, and if the temperatures are the same, the emf is also zero.

Figure 3

emf produced in Volts (ε) = α(T2 - T1)

where, α = constant in volts /°C, and

T1, T2 = junction Temperatures in °C

b. Peltier effect:-

Figure 4

When an electric current flows across a junction of two dissimilar metals, heat is liberated or absorbed. When the electric current flows in the same direction as the Seebeck current, heat is absorbed at the hotter junction and liberated at the colder junction. The Peltier effect is defined as the change in heat content when a quantity of charge (1 coulomb) crosses the junction. See figure 4. This is the basis for thermoelectric refrigeration and heating.

c. Thomson effect:-

The Thomson effect is defined as the change in the heat content of a single conductor of unit cross section when a unit quantity of electricity flows through it along a temperature gradient of 1 Kelvin.


Page

11


CHARACTERISTICS OF THERMOCOUPLE:-

PROCEDURE:-

1. Select the J/K/T Thermocouples by selector switch.

2. Connect the J/K/T Thermocouples to the sensor socket provided at the front panel.

3. Set the min pot to read the ambient temperature in display.

4. Insert the J/K/T Thermocouples in the HOT bath.

5. 3½ Digit LED display shows the temperature obtaining at the HOT bath directly in oC.

6. If necessary adjust the MAX pot for the maximum level temperature.

7. Recorder Red and Green terminals for the analog output.

8. Fuse holder provided to protect the circuit from the over load (500 Ma).

9. Plot the graph of

a. Thermometer reading Vs J type reading

b. Thermometer reading Vs J type reading

c. Thermometer reading Vs J type reading

OBSERVATIONS:-

Sl No:J type Readingin

oCK type Reading

in oCT type Reading

in oCThermometer reading in oC

CALIBRATION OF THERMOCOUPLE:-

For getting the best fit and calibrated equation, y = mx + c

and

where x = Theoretical o/p voltage w.e.t temperature indicator reading

y = actual O/P of thermocouple

m = slope

c = y intercept of best fit line


Page

12


Temp indicator reading oC

Theoretical o/p voltage wet temperature indicator

reading (x)

actual O/P of thermocouple

(y)mVxy x2

RESULT:-

Calibration equation thermocouple, y = mx + c =

INFERENCE:-


Page

13


Expt. No. 5

CALIBRATION OF LVDT USING MICROMETER

Aim: To calibrate the given Linear variable differential transformer (LVDT) using micrometer and to plot the calibration curve.

Apparatus: LVDT- micrometer setup

Principle:

LVDT consists of a cylindrical, insulating, non-magnetic form that has primary coil in the mid segment and a secondary coil symmetrically wound in the two end segments. The two secondary coils are connected in series opposition, so that the


Page

14


potentials induced in the two coils segments oppose each other. A core of ferromagnetic material is inserted coaxially in the cylindrical form without actually touching it.

PROCEDURE

1. Connect the o/p of LVDT to the Analog transducer Amplifier.2. Adjust the micrometer to 0mm,note the corresponding reading from LVDT .3. Take readings for increasing value of displacements 4. Similarly take the readings for decreasing value of displacement till 0 reading of micrometer.

Tabulation Column

Sl

No:

Displacement in

micrometer

X(mm)

Displacement measured by LVDT

X2 XYLoading Unloading Mean Y

mm mm mm


Page

15


∑X =

∑ X2 = ∑ XY =

Sample calculation

Curve fitting:

Equation of the curve, Y = A + BX


An + B∑ x = ∑ y ……………………… (1)

A∑ x + B∑ x2 = ∑ xy ……………………… (2)

Where n = No: of input variables.



Result:

Inference:

Expt.6 TORSIONAL VIBRATION OF A SINGLE ROTOR SYSTEM

AIM: To determine the natural frequency of undamped torsional vibration of a single rotor shaft system.APPARATUS:


Page

16


SPECIFICATIONS:Shaft diameter, d = mm Diameter of disc, D = mm Weight of the disc, W = N Modulus of rigidity for shaft, C = N/m2

THEORY: When the particles of the shaft or disc move in a circle about the axis of the shaft, then the vibrations are known as torsional vibrations. The shaft is twisted and untwisted alternatively and the torsional shear stresses are induced in the shaft. Since there is no damping in the system these are undamped vibrations. Also there is no external force is acting on the body after giving an initial angular displacement then the body is said to be under free or natural vibrations. Hence the given system is an undamped free torsional vibratory system.

PROCEDURE: 1. Fix the brackets at convinent position along the beam. 2. Grip one end of the shaft at the bracket by chuck. 3. Fix the rotor on the other end of the shaft. 4. Twist the rotor through some angle and release. 5. Note down the time required for 10 oscillations.

6. Repeat the procedure for different length of the shaft.

Tabulation :


Page

17


Sample calculations:

Results:

Inference:

Expt.7


Page

18


STUDY OF SURFACE ROUGHNESS

INTRODUCTIONSurface topography is of great importance in specifying the function of a surface. A significant proportion of component failure starts at the surface due to either an isolated manufacturing discontinuity or gradual deterioration of the surface quality. The most important parameter describing surface integrity is surface roughness. In the manufacturing industry, surface must be within certain limits of roughness. Therefore, measuring surface roughness is vital to quality control of machining work piece.

Fig.1 : Surface texture includes roughness and wavinessROUGHNESS – a quantitative measure of the process marks produced during the creation of the surface and other factors such as the structure of the material. The action of the cutting tool, chemical action, polishing, lapping, and the structure of the material all contribute to the roughness of the surface.

WAVINESS – a longer wavelength variation in surface away from its basic form (e.g. straightline or arc). . It may result from such factors as machine or work deflection, vibration, chatter,heat treatment, or warping strainsLAY refers to the predominant direction of the surface texture. Ordinarily lay is determined bythe particular production method and geometry used.Turning, milling, drilling, grinding, andother cutting tool machining processes usually produce a surface that has lay

PROFILE is, mathematically, the line of intersection of a surface with a sectioning plane which is (ordinarily) perpendicular to the surface. It is a two-dimensional slice of the threedimensional surface. Almost always profiles are measured across the surface in a direction perpendicular to the lay of the surface. Shortly saying, it's the graphical representation of the surface.CENTER LINE (Mean line) : mathematically it's positioned in such a way that within the sampling length the sum of areas enclosed by the profile above & below the center line are equal.

FORM of a surface is the profile of the surface under consideration ignoring variations due toroughness and waviness. Deviations from the desired form result from clamping marks orsliding marks machining guide errors etc.

SAMPLE LENGTH : after the data has been filtered with a cut –off, we then sample it.


Page

19


Sampling is done by breaking the data into equal sample lengths. The sample lengths have thesame numeric value as the cut-off. In other words, if you use a 0.8mm cut-off, then the filtereddata will be broken down into 0.8mm sample lengths. These sample lengths are chosen in sucha way that a good statistical analysis can be made of the surface. In most cases, five samplelengths are used for analysis.

Roughness parameters

EXPERIMENT NO: 8


Page

20


Autocollimator

AIM: measurement of the straightness using Autocollimator

APPARATUS: autocollimator,

THEORY: definition of straightness: - A plane is to be said straight over a given length if the variation or distance of its points from two planes perpendicular to each other and parallel to the generation direction at of the line remains within specified tolerance limits the reference planes being so chosen that there intersection is parallel to the straight line joining two points suitably located on the line to be tested and two points being close ends of the length to be measured.

PRINCIPLE OF AUTOCOLLIMATOR: - it works on the principle that if the light source is placed in the focus of a collimating lens then the light is projected as a parallel beam .If this beam is made to strike a plane reflector normal (perpendicular) to the optical axis then it is reflected back along its own path and brought to the same focus.But if reflector is tilted through a small angle 0 the parallel beam is reflector through twice that angle and is brought to focus in same plane as a light source but to one side at a distance x=20f.f =focal length of collimating lens

CONSTRUCTION:-A line diagram of injected reticule autocollimator consists of three parts as micrometer microscope, lighting unit and collimating lens.

WORKING: - When the lamp is illuminated then ray from lamp passes through condenser, target reticule and strilus on 45 transparent beam splitter. Beam splitter then reflects the image on collimating lens which projects the rays as parallel beam. Now a plane reflector is placed normal to optical axis which reflects the rays along its own path and an image is collected at target graticale . But while reflectors some of the rays crosses the 45 transparent beam splitter and the image is seen through eye piece of microscopic on external reflector. Now we tilt the plane reflector by a small angle 0 the rays will reflect back but twice the angle and in this condition we couldn’t find the image on microscope eye piece. Therefore in order to obtain an image operate micrometer microscope till the image is seen or collected on an external reflector. Stop rotatingmicrometer, note down the reading. The reading are directly in angular value that is in


Page

21


minutes 1’, 2’, 3’ and 10 on.Hence the difference in two readings of micrometer gives the value of ‘x’.Therefore we can calculate from equation x= 2f0Where f is focal length of collimating lens.Auto collimator is quite accurate and read unto 0.1 sec andused for distance 30 m.

PROCEDURE:-(1)Mark the distance of 50mm internal on the w/p.(2)Set the cross wire so that the two cross wire will coincide.(3)Set the mirror so that the cross wire will be visible.(4)Move the reflector on next 50 mm mark and adjust it to see reflection of cross wire.(5)Take the reading of reflected crosswire deviated or moved up or down. Measure the distance between two crosswire.

RESULT:-

Inference

Expt.9Tool maker’s microscope

Aim- Measurement of cutting tool angles using tool maker’s microscope.


Page

22


Apparatus: - Tool maker’s microscope, cutting tool.

Tool maker’s microscope:-Tool maker’s microscope is versatile instrument that measures by optical means with no pressure being involved .it is thus a very useful instrument for making measurements on small and delicates parts . the tool maker’s microscope is designed for the following measurements; measurements on parts of complex form for example, the profile of external thread as well as for the tools, templates and gauges ,measuring centre to centre distance of holes in any plane and other wide variety of linear measurements and accurate angular measurements.

A tool maker’s microscope is as shown in fig. the optical head can be moved up or down the vertical column and can be clamped at any height by means of a clamping screw .The table which is mounted on the base of the instruments can be moved in two mutually perpendicular horizontal directions (longitudinal and lateral) by means of accurate micrometers screws having thimble scale and vernier.A ray of light from light source (fig- 2) is reflected by a mirror through 90.it is then passes through a transparent glass plate (on which flat parts may be placed). A shadow image of the outline or contour of the work piece passes through the objective of the optical head and is projected by a system of three prisms to a ground glass screen. Observations are made through an eyepiece. Measurements are made by means of cross-lines engraved on the ground glass screen. The screen can be rotated through 360 the angle of rotation is read through an auxiliary eyepiece.


Page

23


Procedure:-The use of tool maker’s microscope for the taking the various angular measurements is explained below-To determine the tool angle, the screen is rotated until a line on the angle of screen rotation is noted. The screen is further rotated until thesame line coincides with the other side. The angle of tool on the screen will be difference in two angular readings. Different types of graduated and engraved screens and corresponding eye piece are used for measuring different elements.

Result:-

Inference:-

Expt.10

CALIBRATION OF BOURDON TUBE PRESSURE GAUGE USING DEAD WEIGHTS

Aim: To calibrate bourdon tube pressure gauge and plot the following graphs.


Page

24


Gauge pressure Vs true pressure using dead weightCalibration curve

Apparatus:- pressure gauge tester, Dead weight piston and standard weights.

Description:-

Needle valve:There are two needle valve, one on right side to fill oil pump and left side to pressure gauge.Main block:-House, Piston cylinder assembly and plunger piston and cylinder. It consists of a main cylinder and piston supported by a handle By moving the handle up and down, pressure builds inside the cylinder will cause pumping of oil from cylinder through non return valve to the fulcrum which will move needle in the pressure gauge simultaneously pressure developed will lift load placed.Set of weights:-All weights marked in terms of pressure equivalent weights.Oil:- SAE 20 or 30 is used. The oil should be clean.Principle:-

Procedure:-Before starting the experiment, the cup is filled with oil. The entrapped air is removed by lifting the handle up and down, one or two times, until trapped air is removed from oil completely .The valve of oil pump is closed and floating plunger is made vertical by adjusting leveling screw using spirit level.Place a known weight on the carrier and slowly pump by moving the handle up and down. This increase the pressure inside the system and pressure gauge indicates the same. Rotate the weight career in order to reduce friction of plunger due to offset. move handle up and down such that plunger lift weights unto 7mm.The weight and pressure gauge reading are noted. Now some more weights are added and the above procedures repeated and pressure gauge readings are noted. Repeat for more weights up to maximum.Now the weight added is removed one by one and corresponding pressure gauge readings are noted. Then the mean of pressure gauge readings is taken as the output pressure gauge readings.


Page

25


Result:-

Inference:-

Expt.11

DAMPED TORSIONAL OSCILLATIONS

Aim: To study the damped torsional oscillations and to determine the damping coefficient


Page

26


Equipment setup: It consists of a long elastic shaft gripped at the upper end by chuck in the bracket. The bracket is clamped to upper beam of the main frame. A heavy steel flywheel clamped at the lower end of the Shaft suspends form bracket. Damping drum is fixed to the lower face of the flywheel.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 dashpot. The piston carries the attachment for fixing sketch penPrinciple:

The torsional stiffness of shaft

where C= modulus of rigidity of shaft =0.8 x 106 kg/cm2

J = polar moment of inertia of shaft = d= shaft dia =3mm

= length of shaft=98cm

Moment of inertia of flywheel

M=mass of disc =9.844kg r= radius of disc=12.5cm

Periodic time of oscillations in still air

Critical damping coefficient

Logarithmic decrement

where = amplitude of vibration at the beginning of measurement

= amplitude of Vibration after n cycles from recordDamping factor or damping ratio

where c= damping coefficient

Procedure:


Page

27


1. Arrange the set up as shown in fig2. Put the sketch pen in its bracket3. Allow the flywheel to vibrate4. Allow the pen to descend. See that the pen always makes contact with paper and record

oscillations.5. Measure the time for some oscillations by means of stop clock

6. Determine and

Observation Table

No of oscillations Time for n oscillations(s)

(cm)(cm)

Expt.11

VERIFICATION OF DUNKERLEYS PRINCIPLE


Page

28


Aim: To verify the Dunkerley’s rule

Principle :The Dunkerley’s equation is given by the formula

1/F2 = (1/f B 2) + (1/f L 2)

Where F=Natural frequency of given beam (considering the weight of beam) with central load W.FL= Natural frequency of given beam (neglecting the weight of beam) with central load W.Fb= Natural frequency of given beam.

General equation for natural frequency f n of beam =

Deflection of beam due to load is δ

Where W 1 = Central load on the beam ,or weight attached.

W 2 is the weight per unit length L = Length of the beam.

I=M I of beam section=bh3/12E= Modulus of elasticity of beam material (to be taken as 2x106 kg/cm2).

Experimental time period, Texpt = t/nWhere n= Number of oscillations.t = Time for n oscillations.Experimental Natural frequency, Fexpt= 1/ Texpt

Procedure: Arrange the set up as shown in Fiq with some weight W clamped to weight platform. Pull the platform and release it to set the system in to natural vibrations. Find periodic time T and frequency of vibrations F by measuring time for some

oscillations. Repeat experiment by putting additional masses on weight platform


f n=12π √ gδL

δL=W 1 l

3

48 EI

f B=π2 L2 √ gEIW 2

Page

29


Plot graph of 1/F2 Vs W. Intercept of the graph with W=0 gives the value of frequency Fb

of the beam. Compare the values of natural frequency of the beam obtained by using theoretical

expression and obtained form graph.

Observation:

Length of beam, L=Weight of the beam W=Weight per cm of the beam=w2=W/L=Section of the beam (bxh)=

Sl.No Weight Attached(kg)

No of Oscillations N

Time for ‘n’ oscillations

Texpt

(s) Fexpt

(Hz) f L (Hz)

f B (Hz)

1/F2

12

Sample calculation:

I= bh3/12

1/F2 = (1/f B 2) + (1/f L 2) =

From Graph y intercept=1/F2 =


f L=12π √ gδL

δL=W 1 l

3

48 EI

f B=π2 L2 √ gEIW 2

Date post:	22-Jan-2016
Category:	Documents
Upload:	adhilabdulazeez
View:	218 times
Download:	0 times

EXP LIST

Documents