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Autumn Semester 2012

ME 710 VibrationsHomework Assignment 6: Measurements

(Due date: Nov. 27)

General instructions: Write clearly and legibly, showing clearly the important steps in thesolution, including any assumptions and approximations.

1. A simulated experimental vibration signal is given in an accompanying file, that containscolumns for a time signal and the corresponding vibration signal measured at that instant.a. For the measured signal being velocity, obtain the displacement and acceleration signals.

From these time-domain signals, comment on the effect on noise of the transformationfrom velocity to the other derived quantities.

b. From a visual inspection of the time-domain signal of velocity (from the file), what are thephenomena that you can observe?

c. Obtain the frequency-domain representation of the displacement, velocity and

acceleration signals. Identify the various frequency components in the signal. Commenton the effect on noise of the transformation from velocity to the other derived quantities.[Hint: you can use the fft command in MATLAB.]

d. Select appropriate values of the sampling frequency and repeat part (c), commentingupon the effect of the sampling frequency on characteristics such as the noise, accurateidentification of the frequency components, the maximum frequency that can beidentified, aliasing, etc.

e. Create and apply a window to the three signals, and repeat part (c). Experiment withparameters of the window such as the weighting applied to the beginning and end of thesignal. Comment on the effect of the window on the frequency domain representation.

f. After identifying the key frequency components of the signal, recreate a time signalcontaining only these components, and plot it against the measured signal. Comment

on the differences between the two signals.

[Note: The file contains several measured signal columns. You must use only the onecorresponding to your roll number the column assignment is given separately. You are free todiscuss with your colleagues the generic aspects of the problem and its solution, but the finalwork must be your own!]

2. Consider a simulated experimental signal comprising a time signal, a rotational frequencysignal, and three measured vibration signals (x1, x2 and x3). This signal is similar to whatmight be obtained from a speed sweep of rotating machinery or a similar system where the

excitation frequency can be varied.a. Perform a time-frequency analysis of the above system. [Hint: you can use the MATLABspectrogram command.]

b. Identify and comment upon the key phenomena that you can observe, such as thenatural frequencies of the system.

c. The sampling frequency and the characteristics of the window used affect the resultsof the time-frequency analysis. Experiment with different cases/values of theseparameters and comment upon their effect.

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Signal Column Assignments for Question 1

Note: The students assigned to each signal (column) have to work separately, and turn inseparate reports. If N students are found to have copied from each other, the marks givenM shall be divided equally among these students, i.e. each student will be receive at mostonly M/N marks.

Signal Column Roll Number

1 8010005 (Apoorv), 10D100026, 113100029, 123100047

2 80xxxxx (Abhay), 10D100028, 113109007, 123100046

3 9004086, 10D100032, 123010025, 123100045,

4 9010012, 10D100041, 123014014, 123100056

5 9010024, 10D100043, 123100020, 123104006

6 9010058, 123100021, 123104007, 113100027

7 9010059, 123100023, 124100003, 113100052

8 9010068, 123100027, 124100005, 123100064

9 09D10018, 123100036, 113100023

10 09D10019, 123100043, 123100083