EXPERIMENT ON TORSIONAL VIBRATION OF A

SINGLE ROTOR SHAFT

AIM :: To study the torsional vibration of single rotor shaft system.

APPARATUS :: Vibration test rig , vernier caliper , scale, stopwatch…

THEORY :: When the particles of the shaft or disc moves in a circle about the axis of the shaft  i.e if the shaft gets alternatively twisted and untwisted on amount of vibratory system then the vibrations are known as torsional vibrations consider a shaft of negligible weights fixed at one end of and carries a rotor on the free end the amplitude of torsional vibration is maximum at the force end i.e at B and zero at fixed end i.e at A the point of section at the shaft whose amplitude of torsional vibration is zero .

Torsion of circular shaft :

          Mt/J = J/R = Gθ                                        Mt = Mt = Ip/R  .J   -Strength equation

Mt/J = J/R = Gθ/L                                              Mt=Mt =  Ip/L = Gθ –Stiffness equation

                                                                            Mt= Ip =πd˄4/32 mm4

Where …Mt= the torque that produces the twist  θ

               G = Shear modulus

              L = Length of the shaft

Ip = polar moment of inertia of cross section of shaft

If the disc is displaced by an amount θ from its equilibrium position the shaft provides resisting torque of magnitude Mt. thus shaft act as torsional spring with a torsional spring constant.

          

OBSERVARTIO::

·        Diameter of shaft  , d=4.00mm

·        Diameter of disc , D=224mm

·        Mass of the disc , m= 3.286kg

·        Thickness of disc , t= 10.8mm

·        Modulus of rigidity of the shaft material ,G=78.48GPa

TABULAR COLUMN

SL..NO	LENGTH OF SHAFT	Time For’n’ Oscll..	NO.OF OSCILLATION	Texp In(s)	(ωn)exp rad/sec	(ωn)th rad/sec	(fn)th Hz	(fn)exp Hz
1	245	2.12	5	0.424	14.81	18.071	3.125	2.358
2	350	2.31	5	0.462	13.59	16.391	2.608	2.164
3	430	2.44	5	0.488	12.84	14.788	2.358	2.048

PROCEDURE::
·        Fix the bracket at convenient position along the lower beam
·        Grip one end of the shaft at the bracket by using chucks
·        Fix the rotor on the other end of the shaft
·        Note down the time required for  n oscillation
·        Repeat the above procedure for different shaft length.

RESULT:

              Shaft length= 245

v Natural frequency (fn)the = 3.124 Hz

v Natural frequency (fn)exp= 2.358 Hz

                       Length =350

v  Natural frequency (fn)the = 2.608 Hz

v Natural frequency (fn)exp=2.164 Hz

Length  =430

v Natural frequency (fn)the = 2.358 Hz

v Natural frequency (fn)exp = 2.048 Hz   

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QUESTIONS AND ANSWER ON TORSIONAL VIBRATION OF SINGLE ROTOR SHAFT

·        Define periodic motion ?

The motion which repeats after a regular interval of time is called periodic motion.

·        Define frequency?

The number of cycle completed in a unit time is called frequency.its unit is cycles per second or hertz.

·        Define time period ?

Time taken to complete one cycle is called periodic time . it is represented in seconds/cycle.

·        Define  amplitude ?

The maximum displacement of a vibration system or body from the mean equilibrium position is called amplitude.

·        Define free vibration ?

When a s/m is disturbed, it starts vibrating and keeps on vibrating there after without the action of external force .such vibration are called free vibration.

·        Define forced vibration ?

The vibration of the s/m under the influence of an external force are called forced vibration. The frequency of forced vibration is equal to the forced frequency.

·        What are the harmful effects of vibration .

1.    Excessive wear of bearings

2.    Formation of cranks in machines ,building & structure ,etc…

3.    Loosening of fasteners in mechanical s/m.

4.    Structure and mechanical failures of machines and buildings.

5.    Frequent and costly maintenance of machines.

6.    Electronic malfunctions through failure of solder joints.

7.    Abrasion of insulation around electric conductors, causing soots.