design lab material 2

8/12/2019 Design Lab Material 2

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K. L. E. Society'sBV.Bhoomaraddi College of Engineering & Technology, Hubli - 31

DEPARTMENT OF MECHANICAL ENGINEERING

Experiment No.: Q1(~Title of Experiment: Moment of a system subjected to free Torsional VibrationAim: To detemrine moment of inertia of a combine system by subjecting thesystem to the vibration and to check the validity of equation Wn = . y KIIApparatus:. Torsional vibration apparatus contains a disc of diameter 8.25 em, Wire ofknown diameter 0.051 em, shop watch

Parts of the apparatus:1) Adjusting screws2) Wire3) Bush4) Disc with scale5) Rotor6) Stand

Theory:Consider a system consistmg of rotor of mass moment of inertia 10 ,connected to a shaft of torsional stiffness K as shown.When the rotor is displaced slightly in the angular manner about the axisof shaft and released, it executes torsional oscillations. Its nature frequency canbe obtained as follows.

When at any instant the rotor occupies a position 0 with reference tothe equilibrium position, the torque acting on the rotor through the twisted shaftis=K + e .The -ve sign is included because the torque on the rotor acts in adirection opposite to its twist.

.. From Newton s II law of motion10 8; = { Jo) 8=0 (1) --::: .~ -

Put W2n = Kt / Join ----------- (1):. Equation (1) ---------- 8 + W2n 8 = 0:. Natural frequency of vibration of this system is Wn = j Kt / Jo


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.K. L. E. Society's

B.V.Bhoomaraddi College of Engineering & Technology, Hubli - 31DEPARTMENT OF MECHANICAL ENGINEERING

Formulae Required: 4-1) Stiffness of wire Kt = JIL Where J =1C~d 4/322) Theoretical moment of inertia In = 1/2g Z J W ~ i n 2 I ViLI;D \\r4 2 J C W t r ~ + W 2 - - r ; : -t :3) Theoretical natural frequency Wn = - V Kt /Io JProcedure:1) Experimental setup is arranged properly as shown in figure2) Now adjust the pointer on the disc to zero position using the two

screws provided on top of device3) After adjusting tighten the screw4) Now disc is displaced to known angle which can be read from the discscale and record this reading from this position the disc is allow to

oscillate5) When the disc makes back r\turn at the other end, the reading isrecorded. Five such reading are taken

6) Time taken for each oscillation is recorded7) Plot the graph of amplitude Vs time

Nature of Graph:

, ,


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K. L. E. Society's .B.V.Bhoomaraddi College of Engineering & Technology, Hubli - 31DEPARTMENT OF MECHANICAL ENGINEERING

bservation1) Weight of disc WI = 260 gms2) Weight of bush + screw W2 = 50 gms3) Length of wire L = 40 em4) Density of wire p =1 gm m5) Weight of wje W3 = 40 gms .6) Weight of ~otor W4 = 292 gllis7) Diameter of disc dl = 8.25 ems8) Diameter of bush d2 = 1.27 ems9) Diameter of wire d3 =0.051 ems10) Diameter ofttbtor d4 = 4.24 ems11) Modules of rigidity of wire = G=0.84 x 106 kg em

TabulationSl. No. No. of Amplitude Time for Time Nature freq.oscillations LHS RHS 5 period Wn=21t~(n) oscillation T= tIn Rad/sec(t) - . ..see

120 120120 110

1 5 105 105 14 2.8 2.244100 10095 95

I 130 130 I125 1252 5 120 115 14 2.8 2.244

115 110105 105

Mean Wn = 2.244 rad/sec.


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K. L. E. Society'sB.v.Bhoomaraddi College of Engineering & Technology, Hubli - 31 .

DEPARTMENT OF MECHANICAL ENGINEERING

Specimen Calculation:Stiffness of wire Kt = G.JIL

=Gnd34/32t-= 0.84 x 106 x n x (0.051) 4 /40 x 32Kt = 0.01395 Kg - em

Theoretical moment of inertia10 =~1 r12 +w2 r2 2 +w3 r3 2 +w4 r4 2]

~= 1 /2 x 981 [ 260 x 4.125 2~o x 0.635 2 + 40 x 0.0255 2 + 292 x 2.12 2 ] x 10-3

..-:

Theoretical natural frequencyWn = Kt / 10

~.01395 /2.935 x 10-3[Wn = 2.180 rad / see]

Conclusion:BY seeing the graph the apparatus is verified i.e without damping effectthe rotor rotates with equal angle and amplitude.

. .


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t < L E, Society s8, J,t: or iaradd CJI~Sgeof Engineering Technology, Hubli - 31JEPARTi 1ENT OF MECHANICAL ENGINEERING

XPERIl\IEl T T 0 .: ot. ATitle of Experiment: Balancing of rotating massesAim: To bale-ice four ci fferent rotating masses rotating in a single plane byanother massApparatus:

1) Weiuhts2 ) Stud = 5 - 1 - gms3) Washer =\l1l1S- 1 - Nuts = 1 0 gms5) DYE_.mi : balancing machine

Balancingmachine has four planes, each plane having radii of rotations as 8ems. 10 ems. . 2 ems and 1-1-ems. Motor: Speed in rpm = 1425, voltage in volts= 230. current n amp =4.3Theory: The hj~ 1 1 speed of engines and other machines are common. It istherefore vel essential that all the rotating and reciprocating parts should becompletely 1- ir c(l .:S r . r as possible. If these parts are not properly balancedthe dynamic . re-s are set up. These forces not only increase the loads on thebearings and -;: SS c5 111 the various members but also produce up pleasant anddangerous \ ~ 'C' ~ S . The process of providing the mass in order to counter outtne effect of nt rfugal forces of the existing masses rotating in a single planebut at differc (1 ;1(,5 is called balancing of several masses by a single mass inthe s~me )L., .There are twr .ne xls to find the mass and angle of the balancinz mass.'-' '-'1) Am t t al methorl

2) Gr.. L .al methodCon.::ider fo ::.::es o rrngnitude 1111, 1112, 1113 and m4 at distances ofr1, r2,1 3 . . .md 1 4 t . a is (J f otating shaft. Let e I. 82, 83 and 84 be the angles ofthese masses .r, rhe horizontal line ox. Let these masses rotate about an axisthrough ,. J. err .n.licular to the plane of paper with constant angularvelocir v 01 -\Analytic: t

1) Fin

2) Res

(I:t the prodrct of mass and its radius of rotation exerted by each. tie rotat 19 shaft. the centrifugal force horizontally and vertically and find theirsun- i.e. f. - + & p. .,


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BK L E Socety 5

II~ge of Engineering Technology. Hubli - 31C-=PAr, 1ENT OF MECHANICAL ENGINEERING---.-- -

21 1 2C ~ I...... m2, r2 cas 82 ...L. ' ..

. rl ~ si: llL~2~ S i1182 ~


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K. L E Society sS.v.8hoom81_.ddi College of Engineering Technology, Hubli - 31DEPARTMENT OF MECHANICAL ENGINEERING

: 2 ) Select a suitable plane of rotation on the rotating shaft of the balancingmachine

3) Arrange the various masses at their respective positions on the planeof rotation and also arrange the balancing mass of calculated weight atthe given posing using stud, washers and nuts

4) Suitable on the balancing machine, if shaft and the suspension systemon the machine are correctly balanced then there will be no vibrations.i.e. system is balanced.

Record of observations1) Mass of one stud + two washers + Two nuts =86 gms

No. : Mass 111 in gins Radiusrotation rcms

of I Angle of rotation I Force F = mr in Iin I 8 in deg rees I gm cm I

I I I1 586) 286. . . , 486J

386~5

I 12 30 703210 ,100 i 2860

1 8 210 13888I 14 260 5404I 10 85 10m5

Specimen alculationsScale 1em = 1000 units1 ) Solution by graphical approach

2) Solution by analytical methodF = Ymrv;2 = 0-- ~IFx = Imrl.os 8 = 0F\=)1 sin8=00 .. - .,i ~ .. )111rcos u = 0i.e. m l r l c is e 1 + m2r2 cos 82 + m3r3 cos 83 T1114r4cos 84 + m5r5cos 85 = n.586 x 12 - ( cos 30 x + 286 x 10 x cos 100 + 486 x 8 x cos (210) +386x 14 cos260-rm5x 10cos85=0. . 1115co 85 =- 1287.75/10 =- 128.77 -------~----(l).. Imrsin 8 = 0


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E soc.etv sB.V Bncorna 10dl Colleye of Engineering Technology, Hubll - 31DEPARTMENT OF MECHANICAL ENGINEERING

i.e 111 11 1 sin e 1 7 1112r2 sin e 2 - r sin e 3 - m-lr-l sin 84 -;-1115r5sine.:; =0:.:86 x 12. cos 30u x -r 286 x 10 x sin 100u -;-~86 x 8 x sin (210)-386 x 14 x sin 260 U - mS x 10 sin e5 =0:. 1115 sin A5 =933.35 / 10 =93.33 ------------(2)Diving (2) C ) (1).. Tan e5 =93.33 / 128.77 = 0.7247. . e =14~ 06 --------------)Substitute \ alve of e5 in (1) we get111 - os (1..1-.06 0) =- 128.71115= 159 .05 gms

onclusion The analytical method gives the correct masses required forbalancing of rotation masses as compared to the graphical method solution.

design lab material 2

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