KDM_1.3

IIT Gandhinagar, Dept. of Mechanical Engineering

ME312: Kinematics and Dynamics of Machines Laboratory (Structured Laboratory Component) V1.0/HPM/ Mar 2012

KDM-1.3: FREE AND FORCED VIBRATIONS 1. AIM: The aim of this experiment is to allow you to experiment with vibrations in mechanical elements. 2. APPARATUS: The forced and free vibrations equipment used for this study is shown in Figure 1, and its various components are marked in Figure 2.

Figure 1. Free and Forced Vibrations Apparatus

The Free and Forced Vibratiosn Apparatus permits study of a wide range of topics related to vibrations. The experimentation set-ups are mounted on an aluminium sectional frame. The oscillator

consists of a beam (part (2) in Figure 2), which can pivot at one end and is suspended by a helical spring (part (6) in Figure 2) at the other end. The beam has a hole grid that permits the attachment of springs, exciter (part (1) in Figure 2), damper (part (3) in Figure 2) in a variety of configurations. The apparatus also consists of an inductive proximity sensor that can be connected to a computer for measuring and viewing the vibrations of the beam. The apparatus also comes with an analog plotter (part (5) in Figure 2) that serves two purposes, that is, to record the vibration data and also provide a means for generating Coulomb friction (due to friction between the stylus and the paper). Finally, the excited control unit (part (4) in Figure 2) can be used to switch on the imbalance exciter and gradually change the frequency of excitation for forced vibration experiments.

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IIT Gandhinagar, Dept. of Mechanical Engineering

ME312: Kinematics and Dynamics of Machines Laboratory (Structured Laboratory Component) V1.0/HPM/ Mar 2012

Figure 2: Components of Free and Forced Vibrations Apparatus 3. PROCEDURE: The apparatus is already assembled and there is minimal setup procedure. Attachment of springs and dampers are easily changed by attaching these components at the desired location on the hole grid and tightening the attachment nut. For forced vibration experiments, the speed control knob is to be gradually increased to increase the speed of unbalance forcer and the vibrations of the unit are to be observed through the software installed on the computer connected to the system. Data recording procedure: Currently, capability to save the sensor data is not available, so it is suggested that for each experiment, you cature a screenshot of the plots displayed on the computer screen (using Alt+PrintScreen) and paste it on to a word document for future calculations and reference. 4. THEORY: The relevant course material pertaining to vibrations applies for this structured experiment and you are expected to refer to these lecture material, textbook and assigned resources for the course ME304. 5. EXPERIMENTAL TASKS ASSIGNED USING THE WHIRLING OF SHAFTS APPARATUS (a) Free vibrations - spring 1  Ensure that spring 1 is attached and that the damper is not attached to the oscillating bar.  Deflect the end of the beam by hand and release it. Observe the vibrations and caputre the time history of oscillations using Alt+PrintScreen. Calculate the natural frequency of

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IIT Gandhinagar, Dept. of Mechanical Engineering

ME312: Kinematics and Dynamics of Machines Laboratory (Structured Laboratory Component) V1.0/HPM/ Mar 2012

oscillations from the captured graphs. Warning: During these oscillations, take care that the bar does not contact the sensor.  Repeat the above step two more times with different initial amplitude. Do you obtain the same natural frequency of oscillations?  Attach the dashpot and repreat the above steps to set up free vibrations and calculate fequency of oscillations. Do you get the same frequency as without damping? Comment on any difference if any. Also comment on whether the damping ratio can be calculated from the observed oscillations.  Detach the dashpot from the bar and attach a stylus (pen) to generate coulomb friction due to contact between pen and paper. Again repeat the steps similar to previous steps to calculate frequency of oscillations. Do you obtain the same frequency as without coulomb friction? Comment on any differences if any. (b) Free vibrations - spring 2  Remove spring 1 and attach spring 2 to the bar.  Repeat the steps above for the five cases mentioned above (i-iii)with three different initial amplitudes (with no damping or friction), (iv) with the dashpot attached, and finally (v) with coulomb friction (pen attached). Comment on differences in results between both springs. Can you estimate from the results which one is a stiffer spring? Justify your answer. (c) Forced vibrations  Swith on the mass-imbalance exciter.  Gradually increase the frequency of excitation from 0 to 4 hertz.  At 4 hertz forcing frequency, note down the amplitude of vibrations.  Gradually increase frequency to 5 Hz and again note down the amplitude of oscillations. Repeat this by gradually increasing frequency to 6 Hz, 7 Hz, 7.5 Hz, 8 Hz, 8.4 Hz.  Warning: DO NOT go above 8.5 Hz when dashpot is not attached to the bar. This may cause serious damage to the apparatus. Take extreme care when going above 8 Hz and increase the frequency very gradually.  Fnally plot amplitude of oscillations versus frequency of oscillations. Can you roughly estimate the natural frequency of this oscillating system from this plot? 

Attach the stylus to add Coulomb damping, repeat the same steps above, noting down readings at 4, 5, 6, 7, 7.5, 8, 8.4 Hz, respectively. Again, generate an amplitude versus frequence plot and show both the plots (no damping and with Coulomb friction) on the same chart. Comment on any differences.

REFERENCES 1. Robert L. Norton, Kinematics and Dynamics of Machinery, SI Edition,2009, McGraw Hill ,ISBN: 0071278524, EAN: 9780071278522 2. Oleg Vinogradov, Fundamentals of Kinematics and Dynamics of Machines and Mechanisms,2000, CRC Press, ISBN: 0849302579,EAN: 9780849302572 3. S.S. Rao, Mechanical Vibrations, 4th Edition, Prentice-Hall, ISBN-13: 9780130489876, 2010 rd

4. Uicker J.J., Pennock G.R. and Shigley J.E., Theory of Machines and Mechanisms, 3 Edition, 2005, Oxford University Press, New York, rd

5. Rattan S.S., Theory of Machines, 3 Edition, 2009, 5

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Reprint 2010,Tata-McGraw Hill

IIT Gandhinagar, Dept. of Mechanical Engineering

ME312: Kinematics and Dynamics of Machines Laboratory (Structured Laboratory Component) V1.0/HPM/ Mar 2012

6. GUNT, Experiment Instructions: TM 155 Free and Forced Vibration Apparatus, Gutn- Hamburg Novermber 2011

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IIT Gandhinagar, Dept. of Mechanical Engineering

ME312: Kinematics and Dynamics of Machines Laboratory

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(Structured Laboratory Component) V1.0/HPM/ Mar 2012