Final Manual Edited Pramod

7/28/2019 Final Manual Edited Pramod

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Design Lab Manual

AIET, Mijar, Moodbidri 1

TORSIONAL VIBRATION (Un-damped)

Aim: To determine the natural frequency of Torsional vibrations and compare with

theoretical value.

Apparatus: Stand, Torsional wire with rotar, scale, vernier caliper, recorder drum with

motor

Theory: Torsional (Angular) Vibration:

Vibration is a dynamic phenomenon observed as an oscillatory motion around an

equilibrium position. Vibration is caused by the transfer or storage of energy within

structures, resulting within structures, resulting from the action of one or more forces. This

obviously applies equally well to translational vibrations (in one or several linear degrees of

freedom) as it does to Torsional vibrations (in one or several angular degrees of freedom). Inthe latter case, the forcing function is one or more moments instead of linear force acting

on the test structure.

Accurate analysis of torsional plays an increasingly important role when

troubleshooting or designing rotating machinery, yet Torsional vibrations remain, without

modern day laser Doppler-based techniques, notoriously difficult to measure. It is important

to be able to measure and analyse Torsional vibration accurately because the vibrations in

rotations in rotating shafts are well-known sources of numerous vibration problems.

I

dL

Procedure:

Fix the one end of the shaft to the above bracket, and the other end is attached withthe rotor disc.

The length of the shaft can be varied by moving the bracket to any convenientposition along the frame, and then clamping it.

Note down the diameter, & length of the shaft with the help of vernier caliper andscale.

Note down the diameter of the disc, mass of the disc, and rigidity modulus of the disc.


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Attach the graph sheet to recorder drum with marker arrangement, this recorder drumis attached to the motor. Before twisting on the motor.

Twist the rotor through some angle and then release. The amplitude of vibration can be seen on the graphs, take on complete revolution. Measure the distance Y in the graph, as shown in figure

Figure:

Observation: Diameter of disc D = mm Mass of disc M = kg Diameter of shaft d = mm Length of the shaft L = mm Rigidity modulus of shaft material G = N/m2 Diameter of recorder drum dr = mm Speed of drum n = rpm

Calculations: Theoretical frequency of Torsional vibrations is given by:

fn(the) =

= Hzwhere,

J = Polar moment of inertia of the shaft = = m

4

I = Mass moment of inertia of the disc =

= kg.m2

Experimental frequency for Torsional vibrations is given by:fn(exp) =

where,

T = where, Y = distance/cycle on graph (m)

V = velocity of the recorder drum =

m/secSl. No fn(the) Distance(Y) % error =

X 1001

2Results:


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TORSIONAL VIBRATION (DAMPED VIBRATION)

Aim:To determine the logarithmic decrement, Damping ratio and damping coefficient for

the given Torsional pendulum.

Apparatus: Stand, Torsional wire with rotar, scale, vernier caliper, recorder drum with

motor, oil container.

Theory:

In general all physical systems are associated with one or the other type of damping.

Damping is the resistance to the motion of a vibration body. Types of damping are:

i) Viscous damping (for small velocities in lubricated sliding surfaces, dashpots etc.,and in case of eddy current damping). The damping resistance is proportional to

the relative velocity. Analysis is simpler as the differential equation is linear

ii) Dry friction damping is constant and independent of velocityiii) Solid or structural damping is due to internal friction of moleculesiv) Slip or interfacial damping is due to microscopic slip on the interfaces of machine

parts in contact under fluctuating loads.

Differential equation of motion for a damped free vibration for degree of freedom system

figure a is,

where c = damping coefficientGeneral solution of above equation can be obtained as,

where,

c1 and c2 can be evaluated by applying boundary condition

Critical damping coefficient (Cc):

For critical damping, condition is (C = Cc)

or

Damping factor or Damping ration ():

It is the ratio of the damping coefficient to critical damping coefficient


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Over damping : > 1

Critical dampig : = 1

Under damping : < 1

Damped Natural Frequency for the above type is,

Logarithmic Decrement:

It is the ration of any two successive amplitude for an underdamped system vibrating

freely and is a constant and function of damping only.

( )Also,

Fig (a) Free vibration with viscous damping


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1x

2x

x3

Under damped vibrations(Viscous Damping)

I

dL

I

dL

I

dL

Oil

Procedure:

Fix the one end of the shaft to the above bracket, and the other end is attached withthe rotor disc.

The length of the shaft can be varied by moving the bracket to any convenientposition along the frame, and then clamping it.

Note down the diameter, & length of the shaft with the help of vernier caliper andscale.

Note down the diameter of the disc, mass of the disc, and rigidity modulus of the disc. Dip that disc into the oil container, until the disc is in the oil Attach the graph sheet to recorder drum with marker arrangement; this recorder drum

is attached to the motor. Before twisting on the motor.

Twist the rotor through some angle and then release.


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The amplitude of vibration can be seen on the graphs, take on complete revolution. Measure the distance Y in the graph, as shown in figure

Observations:

1. Diameter of the disc D= ------ meters2. Mass of the disc M = -------- kg3. Diameter of the wire or shaft d = -------- m4. Length of wire L =---------meters5. Rigidity modulus of wire material (Steel) G = 84 GPa= 84x109N/m26. Diameter of the recorder drum dr= --------- mm7. Rotational Speed of the drum n=6 rpm.

Tabular column (Undamped Vibration)

Sl.No Theoretical

frequency fn(the)

Hz

Ratio of

Successive

amplitudes

Logarithmic

decrement

Damping

ratio

Damping

coefficient

C

Frequency of

Damped

vibrations fd

Specimen calculations:

Theoretical frequency of Torsional vibrations is given by:fn(the) =

= Hz

where,

J = Polar moment of inertia of the shaft = = m

4

I = Mass moment of inertia of the disc =

= kg.m2

Ration of successive amplitudes = = . Circular frequency n= 2 fn(the) = rad/sec

Logarithmic decrement = . Damping ratio = . Damping coefficient = N-sec/m Frequency of damped vibration = HzResults:


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SPRING MASS SYSTEM (UNDAMPED VIBRATIONS)

Aim: To determine the natural frequency of vibrations experimentally & compare with thetheoretical value.

Apparatus: Spring, Weight, Scale, Graph sheet.

Theory:

Degree of freedom (D.O.F):

The number of independent coordinates required to specify completely the geometric

location of the mass of the system in space. Single degree of freedom means only one

coordinate is required to define the geometric configuration of the system.

Differential equation of motion:

Differential equation of motion for a simple spring mass system for undamped freevibration is given by,

0kxxm Or 0xm

kx

Where 2n

m

k

Where n = circular frequency in rad/s

f = n/2 linear frequency in cycles/s (or Hz.)

f

1 Time period in seconds.

m

k k

Dm

k

x

Undamped Free vibrations

Procedure:

Fix one end of the given spring to the upper screw. Note down its free length. Attach the known weight to the lower end of the spring Note down the stretched length of the spring Place a graph sheet on the recorder drum and fix the marker to attached to it On the motor, then pull down the platform gently and then releases, thus setting the

spring into free vibration.

The amplitude of vibration can be seen on the graphs, take on complete revolution. Measure the distance Y in the graph, as shown in figure


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Observation:

Free length of spring lo= meters Mass attached to the spring, m = kg Elongation of the spring l= meters

Diameter of recorder drum dr= mm Rotational speed of the drum n = rpm.Tabular column (Undamped Vibration)

Sl.No Theoretical frequencyfn (the) Hz

Distance Y percycle from graph,

mm

Experimentalfrequency fn (exp)

Hz

% error = X 100


Static deflection of spring = (ll0) Theoretical frequency = Hz , where g = 9.81 m/sec2 Experimental frequency is given by:

fn(exp) =

where,

T = where, Y = distance/cycle on graph (m)V = velocity of the recorder drum =

m/sec

Percentage of error = X 100

Results:


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SPRING MASS SYSTEM (DAMPED VIBRATIONS)

Aim: To determine the logarithmic decrement, damping ratio & damping coefficient for the spring

mass system with viscous damping.

Apparatus: Spring, Weight, Scale, Graph sheet, viscous oil

Observations:

Free length of spring lo= meters Mass attached to the spring, m = kg Elongation of the spring l= meters Diameter of recorder drum dr= mm Rotational speed of the drum n = rpm.

Tabular column (damped Vibration)

Sl.No Static

deflectionDMeters

Ratio ofSuccessiveamplitudes

Logarithmicdecrement

Damping ratio

Damping coefficient

C

Frequency of Dampedvibrations fd


Static deflection of spring = (ll0) Theoretical frequency = Hz , where g = 9.81 m/sec2 Ration of successive amplitudes = = . Circular frequency n= 2 fn(the) = rad/sec Logarithmic decrement = . Damping ratio = . Damping coefficient = N-sec/m Frequency of damped vibration = Hz


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1x

2x

x3

Under damped vibrations(Viscous Damping)

k

m

C

x

Damped Free vibrations

Results:


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R.P

100mm 100mm 100mm

A B C D

rA

Problem 2: A rotating shaft carries four equal masses A, B, C and D of 50 gms each which

are placed in planes as shown in figure. The radius of rotation of masses B is 70 mm and the

angle between B & C is 900 and between B & D is 2400. Find the radii of rotation of masses

A, C & D and also the angular position of masses A for complete dynamic balance. Check for

the balance graphically.


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CRITICAL SPEED OF SHAFT (WHIRLING OF SHAFT)

Aim: To determine the critical speed of the given shaft theoretically and verify the same

through experiment

Apparatus: shaft, vernier caliper, scale, tachometer, Dimmer stat,

Theory:Whirling of shafts

In many practical applications such a turbines, compressors, electric motors and

pumps, a heavy rotor is mounted on a light weight flexible shaft that is supported between

bearings. The mass centre of rotor does not coincide with the centre line of the shaft. Thus

there will be unbalance in the rotor due to manufacturing errors. When the shaft rotates

centrifugal force is induced on the shaft, which makes it to bend in the direction of

eccentricity of rotor.

In addition to this other effects such as stiffness and damping of the shaft, hysteresis

damping, gyroscopic effects, and fluid friction in bearings also cause the shaft to bend. This

bending further increases eccentricity and hence the centrifugal force. This effect is

cumulative and ultimately the shaft may even fail. The extent to which the shaft bends

depends upon the eccentricity of the rotor mass and speed of the shaft. At certain rotational

speeds the shaft tends to vibrate violently in transverse direction. At these speeds the shaft

has a tendency to bow-out and whirl in a complicated manner.

This phenomenon is called whirling or whipping of shafts and the corresponding

speeds are referred as whirling or whipping or critical speeds of shafts. These critical speeds

are found to coincide with the natural frequencies of lateral (transverse) vibrations of the

shaft.

Figure:


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Procedure:

The experimental set-up is as shown in figure. Measure the diameter (d), length (l), and mass per unit length (m) of the shaft. Make the shaft to rotate (using motor) about its axis. Increase the speed slowly with

the help of the dimmer stat.

Immediately whirling of shaft is observed. During whirling, when the shaft deflects into single bow (1 st mode) of maximum

deflection. Note down the value of critical speed Nc1.

On further increasing the speed of the shaft, when the shaft deflects into two bows(2nd mode) of maximum deflection, note down its corresponding experimental value

of critical speed for that mode.

Compare the above values with that of theoretical critical speed for 1 st and 2nd modeby calculating with the help of equations or formulae.

Observation:

Diameter of the shaft d = mm Length of the shaft L = mm Density of the shaft material = kg/m3 Elastic modulus of shaft material E = GPa

Calculations:

I mode:

Critical frequency for first mode (Single loop) is given by:fc1 = 2.45 = Hz

where,

I = Moment of inertia of circular cross section of the shaft = = m

4

m =Mass per unit length of shaft =

= kg/m


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Theoretical critical speed of shaft for first mode is given by:Nc1 = 60 X fc1 = rpm

From experimentally the critical speed of shaft for first mode is given by:Nc1 = rpm

II mode

Critical frequency for second mode (Two loops with a node) is given by:fc2 = 7.95 = Hz

where,

I = Moment of inertia of circular cross section of the shaft =

= m

4

m =Mass per unit length of shaft =

= kg/m Theoretical critical speed of shaft for first mode is given by:

Nc2 = 60 X fc1 = rpm

From experimentally the critical speed of shaft for first mode is given by:Nc2 = rpm

Result:

For I Mode:

Theoretical critical speed of shaft Nc1 = rpm Experimental critical speed of shaft Nc1 = rpm

For II Mode:

Theoretical critical speed of shaft Nc2 = rpm Experimental critical speed of shaft Nc2 = rpm


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Design Lab Manual


FRINGE CONSTANT USING PHOTOELASTIC

Aim: Determination of fringe constant of photoelastic material using:

a) Circular disc subjected to diametral compressionb) Pure bending specimen (four point bending)

Apparatus: Vernier calipers, circular polariscope and its accessories including light

source, polariscope and loaded model.

Theory:

Photoelasticity is an experimental method to determine stress distribution in a

material. The method is mostly used in cases where mathematical methods become quite

cumbersome. Unlike the analytical methods of stress determination, photoelasticity gives a

fairly accurate picture of stress distribution even around abrupt discontinuities in a material.

The method serves as an important tool for determining the critical stress points in a material

and is often used for determining stress concentration factors in irregular geometries. The

method is based on the property of birefringence, which is exhibited by certain transparent

materials. Birefringence is a property by virtue of which a ray of light passing through a

birefringent material experience two refractive indices. The property of birefringence or

double refraction is exhibited by many optical crystals. But photoelastic materials exhibit the

property of birefringence only on the application of stress and the magnitude of the refractive

indices at each.

Procedure:

Set up the apparatus. Measure all the magnitude of the model Switch on the apparatus Apply the load till first fringe formed Note down the value of applied load Repeat the procedure for more fringe lines Calculate the fringe constant

Observation:

Diameter of the disc d = mm Thickness of the disc h = mm Magnification factorm = b/a =


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Tabular column:

SL. No Load at the

end of

lever, FL,

(Newton)

Load on

Model, F

(Newton)

Fringe

order at

center of

the disc, nc

Slope of

calibration

curve,

F/nc

Material

fringe

value,

f

Model

fringe

value of

fm1

2

3


Load on the model F = FL X m = N Slope from calibration curve (Load v/s fringe order) = N/fringe Material fringe value = N/mm-fringe

Model fringe value N/mm

2

-fringe

Calibration curve

Result:


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Calibration of photoelastic specimen subjected to pure bending

Aim: To determine the material fringe constant and model fringe constant for the given

photoelastic specimen under four-point bending

Observation:

Depth of the model d = mm Moment arm x = mm Thickness of the disc h = mm Magnification factor m = b/a= .

Procedure:

Setup the specimen under four point bending condition Measure all the magnitude of the specimen Switch on the main Apply the load until the first fringe is formed Note down the load reading Repeat the experiment for more fringe values Calculate the fringe constant

Tabular Column:

SL. No Load at theend of

lever, FL,

(Newton)

Load onModel, F

(Newton)

Fringeorder at

center of

the disc, nc

Slope ofcalibration

curve,

F/nc

Materialfringe

value,

f

Modelfringe

value of

fm

1

2

3


Load on the model F = FL . m = N Slope from calibration curve (Load v/s fringe order) = N/fringe Material fringe value = N/mm-fringe Model fringe value = N/mm2-fringe


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Calibration curve

Result:


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Determination of stress concentration factor in a plate with a hole using

photoelasticity

Aim: To determine stress concentration factor for the given photoelastic specimen subjected

to tensile load.

Observation:

Width of the model w = mm Diameter of the hole d = mm Thickness of the plate h = mm Magnification factor m = b/a = . Material constant f = N/fringe

Procedure:

Measure all the dimensions in the plate with a hole Set the experimental setup Apply load till the formation of stress concentration around the hole Note down the load applied Calculate the stress concentration factor

Tabular column:

SL. No Load at the

end of

lever, FL,

(Newton)

Load on

Model, F

(Newton)

Fringe

order, nc

Maximum

stress max

Nominal

stress nom

Stress

concentration

factor K

1

2

3

Specimen calculation:

Load on the model F = FL . m = N Maximum stress induced in the neighborhood of the circular hole = N/mm2Nominal stress induced in the specimen based on c/s area at hole section

= N/mm2 Stress concentration factor


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Calibration curve

Result:


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PORTER GOVERNOR

Aim: To determine the frictional resistance at the sleeve, centrifugal forces on the governor

balls & to draw the controlling force diagram for porter governor

Apparatus:Porter Governor, Tachometer, dimmer stat, measuring scale.

Theory: Governors are used for maintaining the speeds of the engines within prescribed

limits from no load to full load. In petrol engines; governors control the throttle valve of

carburetor and in diesel engines; they control position of fuel pump rack.

Most of the governors are of centrifugal type. These governors use flyweights to create

centrifugal force. Depending upon the speed, position of weights change, which is

transmitted to sleeve through governor links. Ultimately, the sleeve operates the throttle or

fuel pump.

The apparatus consists of a spindle mounted in bearings vertically. Three types of governors

can be mounted over the spindle, namely Porter, Proell and Hartnell on the existing

apparatus. A sleeve attached to governor links is lifted by outward movement of balls, due to

centrifugal force. Lift of the sleeve is measured over a scale. The spindle is rotated by a

variable speed motor.

The governors may broadly be classified as:

1. Centrifugal governor2. Inertia governor

The centrifugal governors may further be classified as follows;

1. Pendulum typeWatt governor2. Loaded type

i) Dead weight type governor (Porter governor and Proell governor)ii) Spring controlled governors (Hartnell governor, Hartung governor, Wilson

Hartnell governor and Pickering governor)

In the porter governor, added weight is mounded on the sleeve. As the speed increasesdue to centrifugal force, the sleeve is lifted, and when the speed decreases the centrifugal

force decreases and the sleeve comes down.

In the hartnell governor the spring is used as the loading member. It consists of a two

bell crank levers pivoted to the frame. The frame is attached to the governor spindle and

is rotates with it. Each lever carries a roller at the end of horizontal arm and the vertical

arm carries the balls. A vertical compression spring provides a downward force on the

two collers through a coller on sleeve. The spring force may be adjusted tightening and

loosening the nut.


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In the proell governor the ball is fixed at the extensional of the lower links and upper

links are pivoted on the top. The weight are added at the centre of spindle in order to

obtain more equilibrium speed should be smaller and lower mass balls.

Figure:

Procedure:

Arrange the set up as a Porter or Hartnell governor. This can be done by removing theupper sleeve on the vertical spindle of the governor and using proper linkages

provided.

Make the proper connections of the Motor.

Switch on the control unit and rotate the dimmer stat knob slowly increasing the speedof the governor until the central sleeve rises off the lower stop and aligns with the first

division of the graduated scale.

Increase the speed in steps to give suitable sleeve movement Note down the sleeve displacement on the scale and the corresponding speed using

tachometer.

Repeat the sleeve displacement for different displacement and note down the speed.


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Compute the controlling force and radius of rotation for each speed. A graph with controlling force on y axis and radius of rotation on x axis is plotted.

This is the controlling force diagram.

Observation:

Mass of governor fly balls m = Kg Mass of central sleeve assembly M = Kg Length of upper links = Length of lower links L = meters Offset of links pivots from axis of rotation y = meters Initial vertical distance between top & bottom pivots H = meters

Tabular Column:

TrialNo

SpeedNrpm

SleeveLiftxmts

Distance'c'meters

Distance's'meters

Radiusofrotation

'r' mts

Angle''degrees

Height ofgovernor'h' mts

FrictionalForce 'f'Newton

Centrifugalforce'Fc' Newton

EffortENewton

PowerP, Nm

1

2

3

4

Specimen calculation:

i) Distance c = = mii) Distance s = = miii) Radius of rotation r = = miv) Angle = degv) Height of governor

= m

vi) Frictional force: we know that the equilibrium speed of a porter governor with equallink length and equal offset of the upper and lower links is given by:

{ }

Hence,

vii) Effort of the governor is the mean force exerted at the sleeve for a fractional changein speed, for 1% change in speed.

viii)Power = Effort x sleeve lift = E x = Nm


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ix) Angular velocity of the spindle = = rad/secx) Centrifugal force or controlling force = NPlot:

Radius of rotation r

centrifugalforce

Fc

Controlling force curve

Result:


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DETERMINATION OF PRESSURE DISTRIBUTION IN

JOURNAL BEARING

Aim: To determine the load carrying capacity, co-efficient of friction & power lost in

viscous friction and to draw the circumferential pressure distribution curve

Apparatus: Scale, tachometer, oil, apparatus setup model

Theory:

A journal bearing sometimes referred to as a friction bearing, is a simple bearing in which a

shaft, or journal, or crankshaft rotates in the bearing with a layer of oil or grease separating

the two parts through fluid dynamic effects. The shaft and bearing are generally both simple

polished cylinders with lubricant filling the gap. Rather than the lubricant just reducing

friction between the surfaces, letting one slide more easily against the other, the lubricant isthick enough that, once rotating, the surfaces do not come in contact at all. If oil is used, it is

generally fed into a hole in the bearing under pressure, as is done for the most heavily-loaded

bearings (main connecting rod big-end and camshaft) in an automobile engine. Simple oil

slinger in the sump and an appropriate feed hole in the bearing shell are considered

adequate for small single-cylinder engines, such as those used in lawnmowers.

A journal bearing works on the principle that, over an infinitesimally small length of the shaft

circumference, the theory of a lubricant pair can be applied. The convergence as well as the

viscosity and velocity of fluid generate a pressure film. As one surface moves, it drags oil

into the gap that is made between it and the other. As the oil moves forward, the space

decreases. The oil can be considered to be incompressible enough to generate pressure. This

pressure prevents oil from entering the gap created. The oil within the gap reaches a pressure

limit after which it pushes oil through the smaller space.

Procedure:

Fill the oil tank by using SAE-20 grade of SAE-40 grade oil in the reservoir and positionthe reservoir at appropriate height (above the level of the journal bearing)

Drain out the air bubbles from all the tubes on the manometer and check level balancewith supply level

Check that some oil leakage is there, some leakage of oil is necessary for cooling purpose Set that speed and the journal sum for about half an hour. Until the oil in the bearing is

warmed up and check the steady oil level at various tapings

When the manometers levels are settled down, take the pressure reading on manometertubes for circumferential pressure distribution and takes for axial pressure distribution

Repeat the experiment for various speeds After the test is over set diameter to zero position and switches off main supply Keep the oil tank at lower most position so that there will be number leakage in the idle

period


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Observation:

Diameter of shaft (Journal) d = m Diameter of bearing D = m Speed of journal n = rpm Viscosity of oil used (SAE 40) = Pa-sec Length of the bearing L = m Attitude of Eccentricity ratio = .

Tabular Column:

Tube

Number

Angular position

deg

Initial head of

oil hi , cm of oil

Final head of

oil hf, cm of oil

Actual head h = (hf-hi),

cm of oil

1 302 60

3 90

4 120

5 150

6 180

7 210

8 240

9 270

10 300

11 33012 360

Calculation:

i) Linear speed of the journal m/secii) Diametral clearance ratio .iii) Load carrying capacity * + Niv) Frictional force [ ] Nv) Coefficient of friction .vi) Power lost in viscous friction KW

To draw the circumferential pressure distribution

Draw a circle with initial head hi, as radius taking a suitable scale Divide the circle into 12 equal parts (of 300) each and mark the tube numbers 1,2,3 etc

on the divisions in the same sense as the equipment.


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Draw radial lines along the divisions Mark actual head (hf hi) (to the same scale selected earlier) along the respective

radial lines from the divisions 1,2,3 etc

If (hfhi) is positive mark outside the circle and if negative, mark within Join all the points thus obtained by a smooth curve.


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DETERMINATION OF PRINCIPAL STRESSES AND

STRAINS IN A MEMBER SUBJECTED TO

COMBINED LOADING USING STRAIN ROSETTES

Aim: To conduct experiment on a member subjected to combined bending and torsion usingRectangular & DeltaRosettes and to determine;

(iv) Principal Strains & their orientations(v) Principal stressesApparatus required: Strain rosettes, Cantilever shaft with torsion arm, Weights, Wheatstone bridge circuit, and Strain indicator.

Theory:When a machine or structural member is subjected to a system of load, stresses will

be induced in the member, which will result in strain and deformation. Strain gages whenmounted at any point on the surface of the body will enable to measure the strain at that point

in the direction of axis of the gage. If xx & yy are the normal strains along X & Y

direction and xy is the shear strain, then the strain in an arbitrary direction XX is

xx= xx Cos2 + yy Sin2 + xy Sin Cos

Where is the angle between X & Y axis .

In a general case we have to measure strain in three directions to obtain xx , yy and

xy in equation (1) . There are two types of gage rosettes:

1. Rectangular Rosette2. Delta Rosette

Observations: Elastic modulus of the material of the beam E = GPa Poisson's ratio v = . Type of strain gauges: Electrical resistance type : Rectangular & Delta arrangement

Procedure:Connect the rosette strain gauges to the strain indicator by using wires. Ensure that dummy resistance are connected properly ON the indicator and keep the indicator for at least 5 minutes, till the gauges heats up

and get stabilized.

Set the gain to 50 for each indicator by using multiturn gain control pot provided overthe indicator.

Balance the indicator. Ensure pressure gauge reading at zero. Tight the check valves of the hand pump and apply the pressure in the pressure vessel

cylinder.

Load the pressure vessel in step like 2/4/6/8/10/12/14 kg / cm2 Read the strain values from the indicator.


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Tabular column: (Rectangular Rosette)

Tabular Column


Principal Strains:

( ) +ve sign for 1 (major principal strain) andve sign for 2(Minor principal strain)

(Note: i f any of the individual strain values are negative, substi tute them as it i s)

Principal Stresses:

(

)

( )

Tria

l No

Load,

Newton

Micro

Strain

''x(10

-6)

Micro

Strain

''x(10

-6)

Micro

Strain

'C'x(10

-6)

Major

Principal

strain

1

Minor

Principal

strain

2

Major

Principal

stress

1

Minor

Principal

stress

2

1 2

1

2

3


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Where, 1and 2 are the major and minor principal stresses.

Principal angle : ( )

and, Maximum Shear stress:

Delta Rosette:

Tabular column:


Principal Strains:

+ve sign for 1 (major principal strain) andve sign for 2(Minor principal strain)

(Note: i f any of the individual strain values are negative, substi tute them as it i s)

Principal Stresses:

Trial

No

Load,

Newton

Micro

Strain

''x(10

-6)

Micro

Strain

''x(10

-6)

Micro

Strain

'C'x(10

-6)

Major

Principal

strain

1

Minor

Principal

strain

2

Major

Principal

stress

1

Minor

Principa

l stress

2

1 2

1

2


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( )

(

)

Where, 1and 2 are the major and minor principal stresses.

Principal angle:

and, Maximum shear stress:

Result:

1) For Rectangular RosettePrinciple Strains: 1 =

2 =

Principle Stresses: 1 =

2 =

Principle angle: 1 =

2 =

Maximum shear stress: max =

2) For Delta Rosette:Principle Strains: 1 =

2 =

Principle Stresses: 1 =

2 =

Principle angle: 1 =

2 =

Maximum shear stress: max =


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STRESSES IN A CURVED BEAM

Aim:To determine the stresses in inner and outer fibers of a curved beam of square crosssection using strain gauges.

Apparatus: Curved beam, Strain gauges (Electrical resistance type) mounted at inner,middle and outer radii of the semicircular beam, Strain indicator, Dead weights.

Theory:The apparatus consists of a main frame which is mounted on a working table & fixed to

the table top. The frame is placed on the table in vertical position with the shorter side

vertical. Five types of curved beams are provided which can be clamped to the vertical sides

of the main frame. Brackets are provided to fix one end of the curved beam to the main frame& the free end is provided with a hook, so that load may be attached in either vertical

position. A magnetic dial gauge stand is provided which can be attached to the main frame &

will measure the deflection of the desired point in mm.

Weight pan with suitable is provided for applying the load to the curved beam. Loads can

be placed in loading pan. Standard specimen with rectangular cross section of the curved

beam supplied with the apparatus is:

Semicircle Quadrant Curved Davit Angle Davit Circular ring.

Strain gauges are mounted on the beam at proper location to measure the strain by

using a digital strain indicator.

In mechanical engineering, crane hooks, proving ring and chain links are typical examples of

a curved beam.

The apparatus includes different beams, borne on statically determinate supports: a

circular beam, a single davit (curved & straight) etc.

All the beams have the same cross section and so the same 2nd moment of area. This

enables test results to be compared directly. Castiglianos theorem rule is employed

Procedure:

Fix one end of the curved beam as shown in the figure, to the curved beam as shownin the main frame, with the help of brackets provided.

Fix the dial gauge stands provided to measure the deflection at the required point ofinterest.

Make connection of the strain gauges to the strain gauge indicator. Apply load at the required point of loading and note the, deflection values. Also note the strain values as indicated in the strain gauge indicator.

Observations:

Outer radius of the curved beam ro= mm, Inner radius of curvature of the beam ri= mm Cross section , 15 x 15 mm square


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Length of straight portion L = mm. Elastic modulus of material of the beam E= N/mm2

180 mm

A

R27

.5

A

Section A-A

Load

R42.5

132

Tabular Column:

Trial

No

Load

F,

Newton

Strain

(x10-6)

Total Stress

Mpa

(Experimental

)

Stress ,Mpa

(N/mm2)

(Theoretical)

Total Stress

Mpa

(Theoretical)

(Inner)

(Outer)

(Middle)

i 0 bi bo d i 0

1 1 x 9.81

2 2 x 9.81

3 3 x 9.81

4 4 x 9.81

5 5 x 9.81

Specimen Calculations:

Bending moment about Centroidal axis M=F (L+rc)Where rc= radius of Centroidal axis = (r0+ri)/2

For the given beam, rc =35 m, L=180mm

Total stress at the inner fiber 1 1where is the strain in the inner gaugei E Total stress at the outer fiber 2 2where is the strain at the outer gaugeo E Direct stress


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Where 3 is the strain in the middle gauge

Theoretical bending stress at the inner fiber ibi

i

Mc

Aer

Theoretical bending stress at the outer fiber oboo

Mc

Aer

Theoretical direct stressd

F

A

Theoretical value of total stress at the inner fiber as both areopposite in sign

Theoretical value of the total stress at the outer fiber as both areopposite in sign

15

15

7.5

27.5

centre line

of curvature

180

Load line

r

C

A

N

A

rn

o iC C

NA=Neutral axis

CA=Centroidal axis

c

For the given beam of square section 15 mm 15 mm, from Data hand book,

15( ) 35 (35 34.4575)

42.5loglog

27.5

Eccentricity 0.5424

Also ( ) (34.4575 27.5) 6.9575

a

c n c

oee

i

i n i

he r r r

r

r

e mm

c r r mm

0 0nd ( ) (42.5 34.4575) 8.0425nc r r mm

3 6

1

3

0 3

Load F=2 kg=2 9.81=19.62 N

Bending moment M=19.62(35+65)=1962 N-mm.

, =207 10 5 10 =1.035 Mpa

= 207 10 (

bi

b

E

E

Experimentally

Sample Calculations : (For tr ial No 2)

6

3 6

2

-2) 10 = 0.414 Mpa

Direct stress 207 10 (1) 10 0.207 Mpa

19.6215 15

d

d

E

FA


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Design Lab Manual


GYROSCOPE

Aim: To conduct an experiment on motorized gyroscope and to determine; Gyroscopic couple Applied couple and To demonstrate the effect of gyroscopic couple using right hand screw

rule

Observations:

Mass of the spinning disc M= ------------ kg Diameter of the disc D= ----------- meters Distance of the weights added from the fulcrum of the motor x= -------

meters

Tabular column:

Trial

No

Weight

added,

'W'

Newton

RPM

of the

disc

'N'

Angular

velocity

of spin

''rad/sec

Angle

''deg

Time

taken t

(for

precession

of'') sec

Angular

velocity of

precession

'p' rad/sec

Gyroscopic

couple Cg,

Nm

Applied

couple

Ca , Nm

12

3

4


Mass moment of inertia of the disc = kg-m8

MDI

22

Angular velocity of spin 2 = rad/sec60

N

Angular velocity of precession = rad/sec180

pt

Gyroscopic couple Cg= =pI Nm Applied couple Ca= X =W Nm


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Design Lab Manual

gC

aC

gCaC

Oa

a'

Characteristic curve Spin Vector diagram

As the disc is spinning counterclockwisewhen viewed from the front, theapplied couple acts so as to tilt the spin vector to oa'. The reactive couple tends

to rotate the entire system clockwisewhen viewed from the top, which is

evident from the Right hand screw rule.

DISC

FULCRUM

WEIGHT

WX

Documents

Final Manual Edited Pramod