Torsional and Vibrational

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  • Topic: Torque, Moment of inertia, Angular momentum
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  • Published : May 8, 2013
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Torsion Vibration
Experiment Title: Introduction : Torsion Vibration. Torsion is the twisting of a metallic rod shaped object, when a torque is applied on two sides’ perpendicular to the radius of a uniform cross-sectional bar. To study the response of materials under a torsional force, the torsion test is performed by mounting the specimen onto a torsion testing machine, then applying the twisting moment till failure. The torque and degree of rotation are measured and plotted. It can be seen higher torsion force is required at higher degree of rotation. Normally the test specimens used are of a cylindrical rod type since the stress distribution across the section of the rod is the simplest geometry, which is easy for the calculation of the stresses. Both ends of the cylindrical specimen are tightened to hexagonal socket in which one is fitted to a torque shaft and another is fitted to an input shaft. The twisting moment is applied by turning the input hand wheel to produce torque until specimen fails. When the twisting moment is applied, the torque is reacted by a torque shaft, which moves in relation to the deflection arm. The movement of the deflection arm is measured by a linear potentiometer, which is connected to a calibrated TQ digital torque meter to give readout of the torque in unit of Nm or The move we turned the input hand wheel clockwise to increase the degree of rotation, the more torque is produced. At the initial stage, the graphical relationship of the torque and degree of rotation measured is linear as demonstrated. The specimen is elastically deformed and the recovery of the specimen to its original shape is possible if the specimen is unloaded. However, if a high degree of rotation is applied passing a proportional limit, the specimen starts to deform plastically and will not return to its original shape when the input hand wheel is turned anti-clockwise. Determining the natural frequency of a system undergoing torsional vibration. Using Newton’s second law of torsional system. o



Objective Theory 

: :

 T  I  …………………. (Equation 1)

Where Io = mass moment of inertia of the disk

 Hence,  k  I o ……..……... (Equation 2) Where k = torsional stiffness of the shaft Rearrange Equation 2

     n   0 .………..……... (Equation 3) 2

Where natural frequency of the system,

MD. Atiqur Rahman Faisal

Page 2

Torsion Vibration
n 
k …..…….…..……... (Equation 4) Io

From Simple Theory of Torsion,

T  G   J R L
J = Polar second moment of area R = Radius of shaft

Where T = Applied torque

 = Shear stress
G = Shear modulus L = Length of shaft As torsional stiffness k  Apparatus    :

 = Angle of twist


, it can be determined through k 

GJ ………….. (Equation 5) L

One solid circular disk with mass = 4.536kg, diameter = 150mm and thickness = 30mm. One annular circular disk with mass 1.89kg, outer diameter 150mm, inner diameter = 110mm and thickness = 30mm. Two chucks; one steel rod; one stopwatch.

MD. Atiqur Rahman Faisal

Page 3

Torsion Vibration
Procedure :

1. The diameter of the provided rod is measured at three different locations to get the average diameter of the rod. 2. The anchor is chucked tightly to the solid circular disk. 3. The length of the rod or the distance between the two chucks is initially kept 30cm. 4. The disk is displaced slightly, so that the rod can be twisted. 5. The disk is released and the stopwatch is switched on simultaneously. 6. The time taken is recorded according 10, 20, 30, 40 and 50 cycles of the disk. 7. From step 3 to step 6 is repeated by increasing the length between the two chucks from 35 cm to 40 cm. 8. The whole procedure is repeated by attaching the annular circular disk...
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