universal vibration apparatus

7/27/2019 Universal Vibration Apparatus

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June 2011 Dr.-Ing. Amphon Jarasjarungkiat

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03501481 Marine Engineering Lab II

Universal Vibration Apparatus

TM 01


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CONTENTS

INTRODUCTION 1

GENERAL DESCRIPTION OF THE APPARATUS 1

Portal Frame 1

List of Components 3

EXPERIMENTS

Experiment 9: Transverse Vibration of a Beam with One or More Bodies Attached 4

Experiment 10: Forced Vibration of a Rigid Body - Spring System with Negligible Damping 10

Experiment 11: Free Damped Vibrations of a Rigid Body - Spring System 10

Experiment 12: Forced Damped Vibration of a Rigid Body - Spring System 14

References 16

APPENDIX: Data Tables 17


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1. INTRODUCTION

The TM01 Universal Vibration Apparatus enables students to perform acomprehensive range of vibration experiments with the minimum amount ofassembly time and the maximum adaptability. The experiments lead the studentthrough the basics of vibration theory by, initially, very simple experiments whichmake way for those of a more extensive nature as experimental aptitude increases.This manual primarily give details of the apparatus required and the experimentaltechniques involved for each experiment in turn. Each experiment starts with an'Introduction' dealing with the purpose and basic theory involved. Further sectionsdetail the apparatus and experimental method with reference to diagrams included inthe text. Finally, the form of calculations and results is given.

2. GENERAL DESCRIPTION OF THE APPARATUS

Figure 1TM0l Apparatus

Portal Frame

The apparatus shown in Figure 1, consists of a basic portal frame, robustlyconstructed from square, rolled hollow section, vertical uprights and double channelhorizontal members. The frame mounts on four castors for ease of mobility. Screwjacks allow the weight of the frame to transfer to the floor during experiments, which


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enables the entire rig to be leveled prior to the experimental work and guaranteesrigidity.

The frame has been fully machined for experiments. A cupboard is fitted atthe front to houses all the components when they are not in use.

Figure 2Front Panel and RearPanel of Control Box

A d.c. motor driven exciter is used for all forced vibrations experimentspowered by a control unit. This combination comprises of a control box and d.c.motor, which provides precision speed control of the motor up to 3000 rev/min. Thismotor drives the two unbalance discs to provide force excitation to the member

attached to this exciter assembly. The front panel of the unit contains a speed controland a period/frequency meter. The front panel also includes a start/stop switch fordrum recorder and a low speed/high speed selection switch for this recorder. Theindividual power on/off switches for two different kinds of sensor and plotter pens arealso included.

The back panel includes power sockets for mains input, power output to d.c.motor, power output to drum recorder motor, 2 sensor connection sockets labeledsensor names, 2 connectors for 2 pens and PC connection to AiD card inside PC.


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Part Number Description Relevant experiment

B1 pendulum sub-frame(cross beam) 1,2,3,4,5

B2 Simple pendulum-Wood ball 1

B3 B3 Simple pendulum-Steel ball 1

B4 Kater(adjustable) pendulum 4

B5 Wooden compound pendulum 3

B6 Simple bob pendulum 2,3

B7 Bifillar suspension 5

C1 Top adjusting assembly(Spring) 6,10,11,12C2 Guide bush assembly 6

C3 Loading platform 6

D1 Pivot mounting 9,10,11,12

D2 Damper assembly 10,11,12

D3 Damper bracket 10,11,12

D4 Out-Of-Balance disk 10,11,12

D5 Beam support 10,11,12

D6 Stylus and support 10,11,12

D7 Drum Plotter 10,11,12D8 pivot support for stylus 14

E1 Pivot mounting with lateral movement 9

E2 Damper Support 9

E3 Support for Linear Displacement Transducer 9

E6 Flexible Beam 9

E11 Exciter motor 9,10,12

H1 Rotor (254mm diameter) 7,9

H2 Rotor and addition 7

I1 Bracket 7

S1 LDT (Linear Displacement Transducer)

S4 Optical Sensor

M1 Magnetic Stand to hold optical sensor

Table 1 List of components


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3. EXPERIMENTS

Experiment 9: Transverse Vibration of a Beam with One or More BodiesAttached

lntroductionThe frequency of transverse vibrations of a beam with bodies attached is

identical to the critical (whirling) speed of a shaft of the same stiffness as the beam,carrying rotors of masses which correspond to those of the bodies on the beam.One has to think in terms of small size rotors, otherwise gyroscopic effects areinvolved.In the case of a beam with just one body attached, the basic theory is the same asthat in Experiment 6. For a beam with two or more bodies attached, other methodscan determine the frequency of free transverse vibrations. Examples are as follows:1. Rayleigh or energy method (gives good results);2. Dunkerley equation (only approximate, but quite adequate);3. Rigorous (accurate) analysis (arduous);4. Experimental analysis, using the equipment described below, (fairly simple quick)

ApparatusThe basic apparatus for this experiment is in Figure 20. A bar of steel of

rectangular cross-section (E6) is supported at each end. The left-hand support (D1)pivots in two ball bearings in a housing located on the inside face of the vertical

frame member.

Figure 20 Set-up for Experiment 9

The right-hand support consists of two roller bearings (E1), which are free tomove in a guide block located on the inside face. At the centre of the beam bolt asmall motor driving two 'out-of-balance' discs (Excitor Motor and Speed Control unit).Connect the motor via leads to the precision speed control unit, which applies a wide

range of exciting frequencies to the beam.


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Clockwise rotation of the control knob on the speed control unit will increase thespeed of the motor - thus increasing the out-of-balance rotating force produced bythe unbalanced discs. As the speed increases as indicated by the speed meter onthe control unit, the beam begins to vibrate transversely. Over a discrete band of

frequencies increasingly larger amplitudes of vibration are produced which reach apeak at a frequency corresponding to the frequency of free natural transversevibration of the system, i.e. beam plus added components.

Part A: Transverse Vibration of a Beam

ProcedureSuspend bodies of different size mass, m, below the motor. For each mass m,

adjust the speed control until the beam vibrates at its natural frequency. In order todetermine accurately the exact value on the speed meter, it is expedient to take thebeam through the range of excessive amplitudes several times, noting the limits of

the range. From these, we can locate the frequency at which the amplitude andresultant noise appears greatest. Record your observations in Table 12.

Table 12 Results

Mass m(kg) Frequency (Hz) 13.95

4.35

5.95

7.15

8.35

ResultsA graph of (1/f2) to a base of mgives a straight line, as in Figure 21.The intercept on the vertical axis is equal to (1/f2b)

= Natural frequency of the system, i.e. beam plus added components.

= Natural frequency of the beam by itself.Dunkerley's equation is applicable to this situation, and is given by

1 = 1 +1

Here, f1 stands for the natural frequency of a corresponding light beam with mass mattached. Clearly when m=0, f1=infinity, f= fb

Evaluate and compare with the theoretical value obtained from:


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= 2 where L = Length of the beam (m);

E = Modulus of elasticity of material of the beam (N/m2);I = Second moment of area of the beam section:mo = Mass of the beam by itself (kg); no masses attached.

Also, from the graph, when the system is not vibrating (period = 0) f = infinity and

1/f2= 0. The corresponding value of mass mis then equal to me, the equivalent mass

of the beam. me=m0, where is a constant.

Determine the value of . How does it compare with the generally accepted value of

0.5?

Figure 21 Graph of 1/f2versus m

Part B: Damped Transverse Vibration of a Beam

IntroductionDamping forces are counteracting forces in a vibration system, which

gradually reduce the motion. Damping occurs in all natural vibration and may becaused by coulomb friction (rubbing between one solid and another), or viscousresistance of a fluid as in this experiment on damped transverse vibration of a beamwhere a viscous damper is used.

ApparatusThis is shown in Figure 20 (the same set up as for Experiment 9A, but with

certain additions). In this experiment you will require the amplitude of vibration andphase angle. Fit a damper (D2) and its support (D3) to the beam to create damping.Use the linear transducer to determine the amplitude and phase angle very

accurately at any exciting frequency.


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ProcedureAllow the speed control unit time to warm-up, then adjust the linear transducer

vertical position so that it reading is zero on computer display. Energise the motor to

produce a definite amplitude at a predetermined frequency. Read the amplitude oncomputer display. You may also find the phase angle on computer display. Byfollowing this procedure for a range of frequencies, you can assess the effect ofdamping by varying the valve opening of the damper and thus altering the dampingcharacteristics of the system.

Compare the results obtained with these settings with an undamped condition(the system minus dashpot). Plot graphs of amplitude and phase angle against the

frequency ratio /n , i.e. (exciting frequency/natural frequency).

The results, in Tables 13 to 15, show the effect of increasing damping onamplitude and phase angle. For each damping condition a graph of amplitudeagainst frequency can be plotted, from which a value for the natural frequency foreach damping condition can be found. Figures 22 and 23 are typical graphs ofamplitude and phase angle plotted against frequency ratio.

Table 13 Results for the case without damping

Disc speed (Hz) /n Phase angle ()Max amplitude

(mm.)

Table 14 Results for the case of minimal damping

Disc speed (Hz) /n Phase angle () Max amplitude(mm.)


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Table 15 Results for the case of maximal damping

Disc speed (Hz) /n Phase angle ()Max amplitude

(mm.)


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Figure 22 Comparison of the damping ratio

Figure 23 Comparison of the phase lag


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References

1. Manual for Universal vibration apparatus TM01, Kinetics corporation limited.

2. Thomson W.T., Theory of Vibrations with Applications, 5th Edition, PearsonPrentice Hall, Inc., 1998.

3. Craig R.R., Kurdila A. J., Fundamental of Structural Dynamics, 2nd Edition,John Wiley & Sons, Inc., 2006.


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Appendix A


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