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Vibration isolation is one of the methods by which engineers combat the problem of harmonic resonance. It is the purpose of this lab to investigate how the resultant force of vibrations acting in a mechanical device may vary

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Introduction

Dynamics & Control Vibration Isolation William Annal Reg: 200334440 Contents Introduction 3 Theory 3 Experimental Work: 5 Procedure 5 Measurements 5 Calculations 6 Results 6 Discussions & Conclusions 7 Appendices A 9 B 10 Introduction Vibration isolation is one of the methods by which engineers combat the problem of harmonic resonance. It is the purpose of this lab to investigate how the resultant force of vibrations acting in a mechanical device may vary according to the frequency of oscillation that the device is subjected to, and how this relates to the natural frequency of the device. Theory Harmonic Resonance is the condition under which a mechanical device or structure is subjected to vibratory oscillations, the frequency of which, match the natural frequency of the device or structure. Under such conditions extreme amplitudes of vibration may be achieved and in some circumstances the structure may literally be shaken or shake itself to pieces. Vibrations of relevance are categorised into three main types; Free or natural vibrations, forced vibrations and self-excited vibrations. Free or natural vibrations are a result of random disturbances and remain until they are damped by either the systems own internal or other friction forces. These vibrations depend on the systems own balance between elastic and inertial forces which act during the oscillation.

Middle

Fig.3 As the shaft of the motor rotated the out-of-balance weights gave rise to a vibratory force that caused the test rig to oscillate. The vertical oscillations were measure by a transducer which was connected to the test rig. The transducer detected the vertical displacement by producing a voltage which was displayed on an oscilloscope. Measurements: Firstly, the voltage displacement transducer was calibrated using a slip gauge between the stylus of the displacement transducer and the base plate. The voltage change was observed on the oscilloscope on removal of the slip ring. This allowed a range of calculations to be undertaken using the output electrical signal properties. For a range of rotational speeds above and below resonance, the amplitudes of vibration were calculated. The rotational speeds were worked out using the sinusoidal oscilloscope trace as the time base settings were known. There measurements and calculated results were entered into the table available in appendix A. Also performed was a 'bump' or transient test. In this method the free or natural vibrations are measured by recording the 'transient' after striking the test rig. From the initial regular frequency of the transient, the natural frequency can be easily calculated. A wave form that was similar to the wave picture to the right, Fig 4 was observed on the oscilloscope.

Conclusion

In general, stiff light systems have high natural frequencies whereas soft heavy systems have low natural frequencies. To change the natural frequency of the system you can add or subtract weight or you can stiffen or soften the structure. Excitation Response ? P =mr?^2 (N) 2*x FF=kx ? of Periods Scope Screen q*T (cm) Time Base (s/cm) Period T (s) Frequency 1/T (Hz) angular Velocity 2?/T (1/s) Scope Screen (cm) Scope Gain (V/cm) Volts Trans. Calib. (mm/V) mm Total Stiffness (N/mm) FF (N) 9 8.8 0.20 0.1956 5.114 32.130 5.317 3.8 0.1 0.38 1.85 0.703 22.9 8.05 13 9.6 0.20 0.1477 6.771 42.542 9.321 3.0 0.5 1.50 1.85 2.775 22.9 31.77 15 9.6 0.20 0.1280 7.813 49.087 12.409 5.4 1.0 5.40 1.85 9.99 22.9 114.39 12 9.8 0.10 0.0817 12.245 76.937 30.484 1.6 0.5 0.80 1.85 1.48 22.9 16.95 15 9.2 0.10 0.0613 16.304 102.443 54.047 3.0 0.2 0.60 1.85 1.11 22.9 12.71 20 9.7 0.10 0.0485 20.619 129.550 86.434 2.6 0.2 0.52 1.85 0.962 22.9 11.01 10 8.7 0.05 0.0435 22.989 144.441 107.446 2.5 0.2 0.50 1.85 0.925 22.9 10.59 11 8.7 0.05 0.0395 25.287 158.885 130.009 2.4 0.2 0.48 1.85 0.888 22.9 10.17 13 9.2 0.05 0.0354 28.261 177.568 162.382 2.3 0.2 0.46 1.85 0.851 22.9 9.74 14 9.4 0.05 0.0336 29.787 187.159 180.396 2.2 0.2 0.44 1.85 0.8066 22.9 9.24 Appendices ?? ?? ?? ?? 1

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