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Today. Vibrations measurements Case Study and Practice. Case study: Task objective. Identify the first three natural frequencies of a cantilever beam loaded with three masses Check for aliasing/leakage problems. Case study: theory review.

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Today

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  1. Today • Vibrations measurements • Case Study and Practice

  2. Case study: Task objective • Identify the first three natural frequencies of a cantilever beam loaded with three masses • Check for aliasing/leakage problems

  3. Case study: theory review • The movement of a cantilever beam holding a concentrated mass is regulated by the following DYNAMIC EQUILIBRIUM M F M where stifness and damping are given by geometrical and material properties of the beam This is a SECOND ORDER SYSTEM, therefore ONE NATURAL RESONATING FREQUENCY EXISTS ma cv kx

  4. Case study: theory review • Whereas the masses were two instead of one two different natural frequencies would be found, affecting two different position parameters M1 M2

  5. Case study: theory review • In our beam we have three masses therefore we expect three different natural frequencies for what concerns the motion. Our task is to find them experimentally. HOW? M1 M2 M3 we can look for the positions… …or for the accelerations as well

  6. Case study: meas. chain MEASURAND • Accelerometers • Amplification & Conditioning • DAQ board • PC / DAQ software MEASUREMENT RESULTS postelaboration analysis

  7. Case study: meas. chain • Accelerometers: type: piezoeletricbrand: wilcoxonmodel: 736sensitivity: 100mV/gfull scale: 50goutput: ICP/IEPE

  8. Case study: meas. chain • Amplification and conditioning: type: ICP/AC converterbrand: pcbmodel: 442B104gain: x1 x10 x100

  9. Case study: meas. chain • DAQ board: type: Simultaneous Analog Inputbrand: National Instrumentsmodel: 9215full scale: ±10Vs.frequency: 100 kS/s per channelresolution: 16 bit

  10. Case study: meas. chain • DAQ software:On-the-run made software to acquire 4 channels with an adjustable buffer and frequency, visualize and export in CSV for further elaboration.

  11. Case study: Objectives • We need to identify the natural frequencies of the system seeking for predominant armonics in the acceleration signals. • Analyze the acceleration signals spectrum and look for any peaks (peak-picking) • Keep in mind problems concerning ALIASING and LEAKAGE

  12. Case study: Flowchart • Set up the DAQ system. • Excite the system using a suitable input • Acquire the accelerometric signals • Select a proper interval of data • Use the DFFT algorithm to obtain the spectrum domain data • Find the first relevant natural frequencies

  13. Case study: Tools • DAQ on-the-run made software • Excel (for a non specialized analysis) • Signal analysis software (labview, mathlab, simulink…) PRACTICE

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