<html><body><span style="font-family:Times New Roman; color:#000000; font-size:12pt;"><div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">Paul,<o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">Basically, FFT then find the peak.<SPAN style="mso-spacerun: yes"> </SPAN><o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">The difficulties with any digital system (sampled data) which is always what we have when we are performing an analysis on a digital computer (these could be bypassed if we used an analog recording and computers).<SPAN style="mso-spacerun: yes"> </SPAN><o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">Sampling data from a system produces what is called the Gibbs phenomena.<SPAN style="mso-spacerun: yes"> </SPAN>Analytically, when we jump into a data steam and take a dataset, we are convolving a square window with the input data.<SPAN style="mso-spacerun: yes"> </SPAN>There is no getting around it - that is a sampled data system.<SPAN style="mso-spacerun: yes"> </SPAN><o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">To get an idea of what this does, take a signal that is constant, say a value of 1 all the way through the sample time.<SPAN style="mso-spacerun: yes"> </SPAN>FFT this data.<SPAN style="mso-spacerun: yes"> </SPAN>We will see a function the peaks at zero (constant value) but the extends out and drops to zero, passing through zero, bottoms out, goes back up and wiggles up and down with less and less amplitude.<SPAN style="mso-spacerun: yes"> </SPAN>In fact, it is the function sin(x)/x.<SPAN style="mso-spacerun: yes"> </SPAN><o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">This is most disruptive if the frequency content of the signal is low enough and our sample window (duration) is short enough.<SPAN style="mso-spacerun: yes"> </SPAN>An additional sample conditioning process can be applied <SPAN style="mso-spacerun: yes"> </SPAN>which is called windowing.<SPAN style="mso-spacerun: yes"> </SPAN>This is a window to help suppress some of the 'wiggles' experienced with the rectangular window of standard sampling.<SPAN style="mso-spacerun: yes"> </SPAN>Rather than the 'square edge' or rapid rise of the standard sample process, a window is designed to smooth the transition. <SPAN style="mso-spacerun: yes"> </SPAN>There are many window designs such as the raised cosine and Hamming window.<SPAN style="mso-spacerun: yes"> </SPAN>See Richard Hamming's book 'Digital Signals' for specific details.<SPAN style="mso-spacerun: yes"> </SPAN><o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><a href="http://www.amazon.com/Digital-Filters-Richard-W-Hamming/dp/048665088X">http://www.amazon.com/Digital-Filters-Richard-W-Hamming/dp/048665088X</a><o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">The frequency resolution depends upon the number of samples taken.<SPAN style="mso-spacerun: yes"> </SPAN>The larger number can be real signal or you can pad the signal with zeros or some 'windowed' solution.<SPAN style="mso-spacerun: yes"> </SPAN><o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">The Nyquist’s samping theory says that the sampling rate must be at least 2 times the highest frequency contained in the signal.<SPAN style="mso-spacerun: yes"> </SPAN>This does not mean the highest frequency you are interested in but the highest frequency contained.<SPAN style="mso-spacerun: yes"> </SPAN>So if your vibration process has as its highest frequency 50 kHz, you must sample at 100 kHz or higher.<SPAN style="mso-spacerun: yes"> </SPAN>If there is a noise source, say an inductive heater operating at 100 kHz and that noise gets into your measurement circuit, that becomes signal content.<SPAN style="mso-spacerun: yes"> </SPAN>This noise signal will be aliased by the digital system and appear as many signals inside the desired signal band.<SPAN style="mso-spacerun: yes"> </SPAN>This aliased signal can not be filtered by a filter algorithm.<SPAN style="mso-spacerun: yes"> </SPAN>The only thing to do is to put an analog filter in front of the sampling system to make sure the higher frequency noise does not get into the sample.<o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">So the key is to define everything you are going to do to be doing with the data, the entire analysis system and understand what will be required by each step.<SPAN style="mso-spacerun: yes"> </SPAN>Then work up the sampling systems and processes.<o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><st1:PersonName w:st="on"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">Ray <st1:City w:st="on">Joseph</st1:City></SPAN></st1:PersonName><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">, <st1:State w:st="on">PE</st1:State><o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">832 586-5854<o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;MARGIN: 0in 0in 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><a href="mailto:ray@aarden.us">ray@aarden.us</a><o:p></o:p></SPAN></div>
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<BLOCKQUOTE id=replyBlockquote style="PADDING-LEFT: 8px; FONT-SIZE: 10pt; MARGIN-LEFT: 8px; BORDER-LEFT: blue 2px solid; COLOR: black; FONT-FAMILY: verdana" webmail="1">
<DIV id=wmQuoteWrapper>-------- Original Message --------<BR>Subject: [scilab-Users] vibration test analysis<BR>From: "Paul CARRICO" <<a href="mailto:paul.carrico@free.fr">paul.carrico@free.fr</a>><BR>Date: Sun, October 10, 2010 3:02 pm<BR>To: <<a href="mailto:users@lists.scilab.org">users@lists.scilab.org</a>><BR><BR>
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<div class=MsoNormal style="font-size:12pt;">All,<o:p></o:p></div>
<div class=MsoNormal style="font-size:12pt;"><o:p> </o:p></div>
<div class=MsoNormal style="font-size:12pt;"><SPAN lang=EN-US>Does somebody has ever wrote/coded (under Scilab but not necessary) a program that analyses the vibration tests results (i.e. automatically find the natural frequencies) ? <o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;"><SPAN lang=EN-US><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;"><SPAN lang=EN-US>I do it manually but studying the transmissibility’s and the phase changes but I would like to code it under Scilab and of course there won’t be any human appreciation/analysis<o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;"><SPAN lang=EN-US><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;"><SPAN lang=EN-US>The purpose of this email is not to have this code but to have advices/information’s on the method / algorithm and so on !<o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;"><SPAN lang=EN-US><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;"><SPAN lang=EN-US>In any way It’s a good challenge for me<o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;"><SPAN lang=EN-US><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;"><SPAN lang=EN-US><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;"><SPAN lang=EN-US>Thanks for any help<o:p></o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;"><SPAN lang=EN-US><o:p> </o:p></SPAN></div>
<div class=MsoNormal style="font-size:12pt;"><SPAN lang=EN-US>Paul<o:p></o:p></SPAN></div></DIV></DIV></BLOCKQUOTE></span></body></html>