# CU-Boulder MCEN 3037 - 26 (20 pages)

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- Pages:
- 20
- School:
- University of Colorado at Boulder
- Course:
- Mcen 3037 - Data Analysis

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EXAMPLE In order to measure the vibration of a test part the output of an air coupled transducer is sent into a spectrum analyzer The spectrum analyzer display is shown in the figure to the right Note that the spectrum analyzer displays the magnitude of the signal versus frequency an output analogous to the FFT of a time domain signal The measurement is made using a transducer second order system with a resonance frequency of 15kHz a damping ratio of 0 8 and a static sensitivity of 10V mm You note that the part seems to be vibrating strongly at two resonance frequencies and you are interested in quantifying the magnitude of the displacement at each frequency a Estimate the dynamic error at each frequency b Estimate the actual magnitude of the displacement in mm of the part at each frequency c Estimate the time delay at the lowest frequency WOW WE NEED TO DECIDE HOW TO ATTACK THIS PROBLEM y t A sin t System 1 K1 M 1 Frequencies 1 2 f1 2 4 9 x103 30 78 x103 rad s 2 2 f 2 2 20 x103 125 66 x103 rad s System Parameters n 2 f n 2 15 x103 94 24 x103 rad s 0 8 K 10V m m y t AK1M 1 sin t NOW WE CAN CALCULATE THE DYNAMIC ERROR The magnitude responses are M 1 M 2 1 2 3 2 3 30 78 x10 2 0 8 30 78 x10 1 3 94 24 x103 2 94 24 x10 1 2 2 3 2 3 125 66 x10 2 0 8 125 66 x10 1 3 3 2 94 24 x 10 94 24 x10 2 What is the dynamic error at each frequency 1 M 1 1 0 034 2 M 2 1 0 562 1 0 966 0 7980 0 2730 1 0 438 0 6502 4 551 HOW ABOUT THE INPUT AMPLITUDE y t A sin t System 1 K1 M 1 AK1M 1 0 32V 1 0 25V 2 A 1 0 32V 1 0 033mm 10V mm 0 96 A 2 0 25V 1 0 058mm 10V mm 0 43 y t AK1M 1 sin t FINALLY WE HAVE THE TIME DELAY AT THE LOWEST FREQUENCY What do we need first 3 2 0 8 30 78 x10 2 3 94 24 x 10 5225 n Arc tan Arc tan 0 5292rad Arc tan 2 2 8933 1 30 78 x103 1 2 3 2 n 94 24 x10 What is the time delay 5292 17 2m s 3 30 78 x10 Using computerized data acquisition measurements are taken at discrete set of times The time interval between measurements is quantified by the sample rate 1 t How do we choose

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