2019-05-13 13:22:11 +02:00
<?xml version="1.0" encoding="utf-8"?>
< !DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
< html xmlns = "http://www.w3.org/1999/xhtml" lang = "en" xml:lang = "en" >
< head >
2020-04-27 11:35:57 +02:00
<!-- 2019 - 10 - 31 jeu. 16:19 -->
2019-05-13 13:22:11 +02:00
< meta http-equiv = "Content-Type" content = "text/html;charset=utf-8" / >
< meta name = "viewport" content = "width=device-width, initial-scale=1" / >
< title > Vibrations induced by the Slip-Ring and the Spindle< / title >
< meta name = "generator" content = "Org mode" / >
< meta name = "author" content = "Dehaeze Thomas" / >
< style type = "text/css" >
<!-- /* --> <![CDATA[/*> <!-- */
.title { text-align: center;
margin-bottom: .2em; }
.subtitle { text-align: center;
font-size: medium;
font-weight: bold;
margin-top:0; }
.todo { font-family: monospace; color: red; }
.done { font-family: monospace; color: green; }
.priority { font-family: monospace; color: orange; }
.tag { background-color: #eee; font-family: monospace;
padding: 2px; font-size: 80%; font-weight: normal; }
.timestamp { color: #bebebe; }
.timestamp-kwd { color: #5f9ea0; }
.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
.org-left { margin-left: 0px; margin-right: auto; text-align: left; }
.org-center { margin-left: auto; margin-right: auto; text-align: center; }
.underline { text-decoration: underline; }
#postamble p, #preamble p { font-size: 90%; margin: .2em; }
p.verse { margin-left: 3%; }
pre {
border: 1px solid #ccc;
box-shadow: 3px 3px 3px #eee;
padding: 8pt;
font-family: monospace;
overflow: auto;
margin: 1.2em;
}
pre.src {
position: relative;
overflow: visible;
padding-top: 1.2em;
}
pre.src:before {
display: none;
position: absolute;
background-color: white;
top: -10px;
right: 10px;
padding: 3px;
border: 1px solid black;
}
pre.src:hover:before { display: inline;}
/* Languages per Org manual */
pre.src-asymptote:before { content: 'Asymptote'; }
pre.src-awk:before { content: 'Awk'; }
pre.src-C:before { content: 'C'; }
/* pre.src-C++ doesn't work in CSS */
pre.src-clojure:before { content: 'Clojure'; }
pre.src-css:before { content: 'CSS'; }
pre.src-D:before { content: 'D'; }
pre.src-ditaa:before { content: 'ditaa'; }
pre.src-dot:before { content: 'Graphviz'; }
pre.src-calc:before { content: 'Emacs Calc'; }
pre.src-emacs-lisp:before { content: 'Emacs Lisp'; }
pre.src-fortran:before { content: 'Fortran'; }
pre.src-gnuplot:before { content: 'gnuplot'; }
pre.src-haskell:before { content: 'Haskell'; }
pre.src-hledger:before { content: 'hledger'; }
pre.src-java:before { content: 'Java'; }
pre.src-js:before { content: 'Javascript'; }
pre.src-latex:before { content: 'LaTeX'; }
pre.src-ledger:before { content: 'Ledger'; }
pre.src-lisp:before { content: 'Lisp'; }
pre.src-lilypond:before { content: 'Lilypond'; }
pre.src-lua:before { content: 'Lua'; }
pre.src-matlab:before { content: 'MATLAB'; }
pre.src-mscgen:before { content: 'Mscgen'; }
pre.src-ocaml:before { content: 'Objective Caml'; }
pre.src-octave:before { content: 'Octave'; }
pre.src-org:before { content: 'Org mode'; }
pre.src-oz:before { content: 'OZ'; }
pre.src-plantuml:before { content: 'Plantuml'; }
pre.src-processing:before { content: 'Processing.js'; }
pre.src-python:before { content: 'Python'; }
pre.src-R:before { content: 'R'; }
pre.src-ruby:before { content: 'Ruby'; }
pre.src-sass:before { content: 'Sass'; }
pre.src-scheme:before { content: 'Scheme'; }
pre.src-screen:before { content: 'Gnu Screen'; }
pre.src-sed:before { content: 'Sed'; }
pre.src-sh:before { content: 'shell'; }
pre.src-sql:before { content: 'SQL'; }
pre.src-sqlite:before { content: 'SQLite'; }
/* additional languages in org.el's org-babel-load-languages alist */
pre.src-forth:before { content: 'Forth'; }
pre.src-io:before { content: 'IO'; }
pre.src-J:before { content: 'J'; }
pre.src-makefile:before { content: 'Makefile'; }
pre.src-maxima:before { content: 'Maxima'; }
pre.src-perl:before { content: 'Perl'; }
pre.src-picolisp:before { content: 'Pico Lisp'; }
pre.src-scala:before { content: 'Scala'; }
pre.src-shell:before { content: 'Shell Script'; }
pre.src-ebnf2ps:before { content: 'ebfn2ps'; }
/* additional language identifiers per "defun org-babel-execute"
in ob-*.el */
pre.src-cpp:before { content: 'C++'; }
pre.src-abc:before { content: 'ABC'; }
pre.src-coq:before { content: 'Coq'; }
pre.src-groovy:before { content: 'Groovy'; }
/* additional language identifiers from org-babel-shell-names in
ob-shell.el: ob-shell is the only babel language using a lambda to put
the execution function name together. */
pre.src-bash:before { content: 'bash'; }
pre.src-csh:before { content: 'csh'; }
pre.src-ash:before { content: 'ash'; }
pre.src-dash:before { content: 'dash'; }
pre.src-ksh:before { content: 'ksh'; }
pre.src-mksh:before { content: 'mksh'; }
pre.src-posh:before { content: 'posh'; }
/* Additional Emacs modes also supported by the LaTeX listings package */
pre.src-ada:before { content: 'Ada'; }
pre.src-asm:before { content: 'Assembler'; }
pre.src-caml:before { content: 'Caml'; }
pre.src-delphi:before { content: 'Delphi'; }
pre.src-html:before { content: 'HTML'; }
pre.src-idl:before { content: 'IDL'; }
pre.src-mercury:before { content: 'Mercury'; }
pre.src-metapost:before { content: 'MetaPost'; }
pre.src-modula-2:before { content: 'Modula-2'; }
pre.src-pascal:before { content: 'Pascal'; }
pre.src-ps:before { content: 'PostScript'; }
pre.src-prolog:before { content: 'Prolog'; }
pre.src-simula:before { content: 'Simula'; }
pre.src-tcl:before { content: 'tcl'; }
pre.src-tex:before { content: 'TeX'; }
pre.src-plain-tex:before { content: 'Plain TeX'; }
pre.src-verilog:before { content: 'Verilog'; }
pre.src-vhdl:before { content: 'VHDL'; }
pre.src-xml:before { content: 'XML'; }
pre.src-nxml:before { content: 'XML'; }
/* add a generic configuration mode; LaTeX export needs an additional
(add-to-list 'org-latex-listings-langs '(conf " ")) in .emacs */
pre.src-conf:before { content: 'Configuration File'; }
table { border-collapse:collapse; }
caption.t-above { caption-side: top; }
caption.t-bottom { caption-side: bottom; }
td, th { vertical-align:top; }
th.org-right { text-align: center; }
th.org-left { text-align: center; }
th.org-center { text-align: center; }
td.org-right { text-align: right; }
td.org-left { text-align: left; }
td.org-center { text-align: center; }
dt { font-weight: bold; }
.footpara { display: inline; }
.footdef { margin-bottom: 1em; }
.figure { padding: 1em; }
.figure p { text-align: center; }
.equation-container {
display: table;
text-align: center;
width: 100%;
}
.equation {
vertical-align: middle;
}
.equation-label {
display: table-cell;
text-align: right;
vertical-align: middle;
}
.inlinetask {
padding: 10px;
border: 2px solid gray;
margin: 10px;
background: #ffffcc;
}
#org-div-home-and-up
{ text-align: right; font-size: 70%; white-space: nowrap; }
textarea { overflow-x: auto; }
.linenr { font-size: smaller }
.code-highlighted { background-color: #ffff00; }
.org-info-js_info-navigation { border-style: none; }
#org-info-js_console-label
{ font-size: 10px; font-weight: bold; white-space: nowrap; }
.org-info-js_search-highlight
{ background-color: #ffff00; color: #000000; font-weight: bold; }
.org-svg { width: 90%; }
/*]]>*/-->
< / style >
< link rel = "stylesheet" type = "text/css" href = "../css/htmlize.css" / >
< link rel = "stylesheet" type = "text/css" href = "../css/readtheorg.css" / >
< link rel = "stylesheet" type = "text/css" href = "../css/zenburn.css" / >
< script type = "text/javascript" src = "../js/jquery.min.js" > < / script >
< script type = "text/javascript" src = "../js/bootstrap.min.js" > < / script >
< script type = "text/javascript" src = "../js/jquery.stickytableheaders.min.js" > < / script >
< script type = "text/javascript" src = "../js/readtheorg.js" > < / script >
< script type = "text/javascript" >
/*
@licstart The following is the entire license notice for the
JavaScript code in this tag.
Copyright (C) 2012-2019 Free Software Foundation, Inc.
The JavaScript code in this tag is free software: you can
redistribute it and/or modify it under the terms of the GNU
General Public License (GNU GPL) as published by the Free Software
Foundation, either version 3 of the License, or (at your option)
any later version. The code is distributed WITHOUT ANY WARRANTY;
without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
As additional permission under GNU GPL version 3 section 7, you
may distribute non-source (e.g., minimized or compacted) forms of
that code without the copy of the GNU GPL normally required by
section 4, provided you include this license notice and a URL
through which recipients can access the Corresponding Source.
@licend The above is the entire license notice
for the JavaScript code in this tag.
*/
<!-- /* --> <![CDATA[/*> <!-- */
function CodeHighlightOn(elem, id)
{
var target = document.getElementById(id);
if(null != target) {
elem.cacheClassElem = elem.className;
elem.cacheClassTarget = target.className;
target.className = "code-highlighted";
elem.className = "code-highlighted";
}
}
function CodeHighlightOff(elem, id)
{
var target = document.getElementById(id);
if(elem.cacheClassElem)
elem.className = elem.cacheClassElem;
if(elem.cacheClassTarget)
target.className = elem.cacheClassTarget;
}
/*]]>*///-->
< / script >
< / head >
< body >
< div id = "org-div-home-and-up" >
< a accesskey = "h" href = "../index.html" > UP < / a >
|
< a accesskey = "H" href = "../index.html" > HOME < / a >
< / div > < div id = "content" >
< h1 class = "title" > Vibrations induced by the Slip-Ring and the Spindle< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
2020-04-27 11:35:57 +02:00
< li > < a href = "#orga44a9d5" > 1. Experimental Setup< / a > < / li >
< li > < a href = "#orgb5a2f1a" > 2. Data Analysis< / a >
2019-05-13 13:22:11 +02:00
< ul >
2020-04-27 11:35:57 +02:00
< li > < a href = "#org239b200" > 2.1. Load data< / a > < / li >
< li > < a href = "#org66889bf" > 2.2. Voltage to Velocity< / a > < / li >
< li > < a href = "#orgd049ddc" > 2.3. Time domain plots< / a > < / li >
< li > < a href = "#orgfee57e5" > 2.4. Frequency Domain< / a > < / li >
< li > < a href = "#org7d3ac71" > 2.5. Relative Motion< / a > < / li >
< li > < a href = "#org1464a72" > 2.6. Conclusion< / a > < / li >
2019-05-13 13:22:11 +02:00
< / ul >
< / li >
< / ul >
< / div >
< / div >
2020-04-27 11:35:57 +02:00
< div id = "outline-container-orga44a9d5" class = "outline-2" >
< h2 id = "orga44a9d5" > < span class = "section-number-2" > 1< / span > Experimental Setup< / h2 >
2019-05-13 13:22:11 +02:00
< div class = "outline-text-2" id = "text-1" >
< p >
2020-04-27 11:35:57 +02:00
< b > Setup< / b > :
2019-05-13 13:22:11 +02:00
All the stages are OFF.
< / p >
< p >
Two geophone are use:
< / p >
< ul class = "org-ul" >
< li > One on the marble (corresponding to the first column in the data)< / li >
< li > One at the sample location (corresponding to the second column in the data)< / li >
< / ul >
< p >
Two voltage amplifiers are used, their setup is:
< / p >
< ul class = "org-ul" >
< li > gain of 60dB< / li >
< li > AC/DC switch on AC< / li >
< li > Low pass filter at 1kHz< / li >
< / ul >
< p >
A first order low pass filter is also added at the input of the voltage amplifiers.
< / p >
2020-04-27 11:35:57 +02:00
2019-05-13 13:22:11 +02:00
< p >
< b > Goal< / b > :
< / p >
< ul class = "org-ul" >
< li > Identify the vibrations induced by the rotation of the Slip-Ring and Spindle< / li >
< / ul >
2019-05-14 14:11:31 +02:00
2019-05-13 13:22:11 +02:00
< p >
2019-05-14 14:11:31 +02:00
< b > Measurements< / b > :
2019-05-13 13:22:11 +02:00
Three measurements are done:
< / p >
2019-05-13 22:36:14 +02:00
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Measurement File< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > < code > mat/data_024.mat< / code > < / td >
< td class = "org-left" > All the stages are OFF< / td >
< / tr >
< tr >
< td class = "org-left" > < code > mat/data_025.mat< / code > < / td >
< td class = "org-left" > The slip-ring is ON and rotates at 6rpm. The spindle is OFF< / td >
< / tr >
< tr >
< td class = "org-left" > < code > mat/data_026.mat< / code > < / td >
< td class = "org-left" > The slip-ring and spindle are both ON. They are both turning at 6rpm< / td >
< / tr >
< / tbody >
< / table >
< p >
Each of the measurement < code > mat< / code > file contains one < code > data< / code > array with 3 columns:
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-right" > Column number< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > Geophone - Marble< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > Geophone - Sample< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > Time< / td >
< / tr >
< / tbody >
< / table >
2019-05-13 13:22:11 +02:00
< p >
2020-04-27 11:35:57 +02:00
A movie showing the experiment is shown on figure < a href = "#org1669ed1" > 1< / a > .
2019-05-13 13:22:11 +02:00
< / p >
2020-04-27 11:35:57 +02:00
< div id = "org1669ed1" class = "figure" >
2019-05-13 13:22:11 +02:00
< p > < img src = "./img/VID_20190510_155655.gif" alt = "VID_20190510_155655.gif" width = "300px" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Movie of the experiment, rotation speed is 6rpm< / p >
< / div >
< / div >
< / div >
2020-04-27 11:35:57 +02:00
< div id = "outline-container-orgb5a2f1a" class = "outline-2" >
< h2 id = "orgb5a2f1a" > < span class = "section-number-2" > 2< / span > Data Analysis< / h2 >
2019-05-13 13:22:11 +02:00
< div class = "outline-text-2" id = "text-2" >
< p >
2020-04-27 11:35:57 +02:00
< a id = "org73b6124" > < / a >
2019-05-13 13:22:11 +02:00
< / p >
< div class = "note" >
< p >
All the files (data and Matlab scripts) are accessible < a href = "data/spindle_slip_ring_vibrations.zip" > here< / a > .
< / p >
< / div >
< / div >
2020-04-27 11:35:57 +02:00
< div id = "outline-container-org239b200" class = "outline-3" >
< h3 id = "org239b200" > < span class = "section-number-3" > 2.1< / span > Load data< / h3 >
2019-05-13 13:22:11 +02:00
< div class = "outline-text-3" id = "text-2-1" >
< div class = "org-src-container" >
2020-04-27 11:35:57 +02:00
< pre class = "src src-matlab" > of = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_024.mat'< / span > , < span class = "org-string" > 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; of = of.data;
sr = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_025.mat'< / span > , < span class = "org-string" > 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; sr = sr.data;
sp = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_026.mat'< / span > , < span class = "org-string" > 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; sp = sp.data;
< / pre >
< / div >
< div class = "warning" >
< p >
There is a sign error for the Geophone located on top of the Hexapod.
The problem probably comes from the wiring in the Slip-Ring.
< / p >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > of< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = < span class = "org-type" > -< / span > of< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
sr< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = < span class = "org-type" > -< / span > sr< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
sp< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = < span class = "org-type" > -< / span > sp< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
< / div >
< / div >
2020-04-27 11:35:57 +02:00
< div id = "outline-container-org66889bf" class = "outline-3" >
< h3 id = "org66889bf" > < span class = "section-number-3" > 2.2< / span > Voltage to Velocity< / h3 >
2019-05-13 13:22:11 +02:00
< div class = "outline-text-3" id = "text-2-2" >
2020-04-27 11:35:57 +02:00
< p >
We convert the measured voltage to velocity using the function < code > voltageToVelocityL22< / code > (accessible < a href = "../src/index.html" > here< / a > ).
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > gain = < span class = "org-highlight-numbers-number" > 60< / span > ; < span class = "org-comment" > % [dB]< / span >
of< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< span class = "org-rainbow-delimiters-depth-1" > (< / span > of< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , of< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
sr< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , sr< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
sp< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< span class = "org-rainbow-delimiters-depth-1" > (< / span > sp< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , sp< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
of< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< span class = "org-rainbow-delimiters-depth-1" > (< / span > of< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , of< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
sr< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , sr< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
sp< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< span class = "org-rainbow-delimiters-depth-1" > (< / span > sp< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , sp< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< / div >
< / div >
< div id = "outline-container-orgd049ddc" class = "outline-3" >
< h3 id = "orgd049ddc" > < span class = "section-number-3" > 2.3< / span > Time domain plots< / h3 >
< div class = "outline-text-3" id = "text-2-3" >
2019-05-13 13:22:11 +02:00
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
2020-04-27 11:35:57 +02:00
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > sp< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , sp< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , 'Spindle < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6rpm< / span > < span class = "org-type" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , sr< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , 'Slip< span class = "org-type" > -< / span > Ring < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6rpm< / span > < span class = "org-type" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > of< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , of< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
2019-05-13 13:22:11 +02:00
hold off;
2020-04-27 11:35:57 +02:00
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Time < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > s< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; ylabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Velocity < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > m/s< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > , < span class = "org-highlight-numbers-number" > 100< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'northeast'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
2020-04-27 11:35:57 +02:00
< div id = "org4e9bed0" class = "figure" >
2019-05-13 13:22:11 +02:00
< p > < img src = "figs/slip_ring_spindle_marble_time.png" alt = "slip_ring_spindle_marble_time.png" / >
< / p >
2020-04-27 11:35:57 +02:00
< p > < span class = "figure-number" > Figure 2: < / span > Velocity as measured by the geophone located on the marble - Time domain< / p >
2019-05-13 13:22:11 +02:00
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
2020-04-27 11:35:57 +02:00
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > sp< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , sp< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Spindle and Slip-Ring'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , sr< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'Only Slip-Ring'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > of< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , of< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
2019-05-13 13:22:11 +02:00
hold off;
2020-04-27 11:35:57 +02:00
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Time < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > s< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; ylabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Velocity < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > m/s< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > , < span class = "org-highlight-numbers-number" > 100< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'northeast'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
2020-04-27 11:35:57 +02:00
< div id = "org8be7963" class = "figure" >
2019-05-13 13:22:11 +02:00
< p > < img src = "figs/slip_ring_spindle_sample_time.png" alt = "slip_ring_spindle_sample_time.png" / >
< / p >
2020-04-27 11:35:57 +02:00
< p > < span class = "figure-number" > Figure 3: < / span > Velocity as measured by the geophone at the sample location - Time domain< / p >
< / div >
< div id = "orgfc19876" class = "figure" >
< p > < img src = "figs/slip_ring_spindle_sample_zoom.png" alt = "slip_ring_spindle_sample_zoom.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Velocity as measured by the geophone at the sample location - Time domain< / p >
2019-05-13 13:22:11 +02:00
< / div >
< / div >
< / div >
2020-04-27 11:35:57 +02:00
< div id = "outline-container-orgfee57e5" class = "outline-3" >
< h3 id = "orgfee57e5" > < span class = "section-number-3" > 2.4< / span > Frequency Domain< / h3 >
< div class = "outline-text-3" id = "text-2-4" >
2019-05-13 13:22:11 +02:00
< p >
We first compute some parameters that will be used for the PSD computation.
< / p >
< div class = "org-src-container" >
2020-04-27 11:35:57 +02:00
< pre class = "src src-matlab" > dt = of< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > of< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % [s]< / span >
2019-05-13 13:22:11 +02:00
Fs = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
2020-04-27 11:35:57 +02:00
win = hanning< span class = "org-rainbow-delimiters-depth-1" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 10< / span > < span class = "org-type" > *< / span > Fs< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % Window used< / span >
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
< p >
Then we compute the Power Spectral Density using < code > pwelch< / code > function.
< / p >
< p >
First for the geophone located on the marble
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxof_m, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > of< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxsr_m, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxsp_m, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sp< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
And for the geophone located at the sample position.
< / p >
< div class = "org-src-container" >
2020-04-27 11:35:57 +02:00
< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxof_s, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > of< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
2019-05-13 13:22:11 +02:00
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxsr_s, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxsp_s, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sp< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
2020-04-27 11:35:57 +02:00
And we plot the ASD of the measured velocities:
2019-05-13 13:22:11 +02:00
< / p >
< ul class = "org-ul" >
2020-04-27 11:35:57 +02:00
< li > figure < a href = "#org704b4b4" > 5< / a > for the geophone located on the marble< / li >
< li > figure < a href = "#orga078b66" > 6< / a > for the geophone at the sample position< / li >
2019-05-13 13:22:11 +02:00
< / ul >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
2020-04-27 11:35:57 +02:00
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsp_m< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , 'Spindle < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6rpm< / span > < span class = "org-type" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsr_m< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , 'Slip< span class = "org-type" > -< / span > Ring < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6rpm< / span > < span class = "org-type" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxof_m< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
2019-05-13 13:22:11 +02:00
hold off;
2020-04-27 11:35:57 +02:00
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale'< / span > , < span class = "org-string" > 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Frequency < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; ylabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'ASD of the measured velocity $\left< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > \frac< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > {< / span > < / span > < span class = "org-string" > m/s< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > }{< / span > < / span > < span class = "org-string" > \sqrt< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-4" > {< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-4" > }< / span > < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < / span > < span class = "org-string" > \right< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > $'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'southwest'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 500< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
2020-04-27 11:35:57 +02:00
< div id = "org704b4b4" class = "figure" >
2019-05-13 13:22:11 +02:00
< p > < img src = "figs/sr_sp_psd_marble_compare.png" alt = "sr_sp_psd_marble_compare.png" / >
< / p >
2020-04-27 11:35:57 +02:00
< p > < span class = "figure-number" > Figure 5: < / span > Comparison of the ASD of the measured velocities from the Geophone on the marble< / p >
2019-05-13 13:22:11 +02:00
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
2020-04-27 11:35:57 +02:00
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsp_s< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , 'Spindle < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6rpm< / span > < span class = "org-type" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsr_s< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , 'Slip< span class = "org-type" > -< / span > Ring < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6rpm< / span > < span class = "org-type" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxof_s< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
2019-05-13 13:22:11 +02:00
hold off;
2020-04-27 11:35:57 +02:00
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale'< / span > , < span class = "org-string" > 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Frequency < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; ylabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'ASD of the measured velocity $\left< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > \frac< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > {< / span > < / span > < span class = "org-string" > m/s< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > }{< / span > < / span > < span class = "org-string" > \sqrt< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-4" > {< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-4" > }< / span > < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < / span > < span class = "org-string" > \right< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > $'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'southwest'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 500< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
2019-05-13 13:22:11 +02:00
< / pre >
< / div >
2020-04-27 11:35:57 +02:00
< div id = "orga078b66" class = "figure" >
2019-05-13 13:22:11 +02:00
< p > < img src = "figs/sr_sp_psd_sample_compare.png" alt = "sr_sp_psd_sample_compare.png" / >
< / p >
2020-04-27 11:35:57 +02:00
< p > < span class = "figure-number" > Figure 6: < / span > Comparison of the ASD of the measured velocities from the Geophone at the sample location< / p >
< / div >
< p >
We load the ground motion to compare with the measurements (Fig. < a href = "#org71cc947" > 7< / a > ).
We see that the motion is dominated by the ground motion below 20Hz.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > gm = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > '../ground-motion/mat/psd_gm.mat'< / span > , < span class = "org-string" > 'f'< / span > , < span class = "org-string" > 'psd_gv'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsp_m< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , 'Spindle < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6rpm< / span > < span class = "org-type" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsr_m< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , 'Slip< span class = "org-type" > -< / span > Ring < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6rpm< / span > < span class = "org-type" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxof_m< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > gm.f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > gm.psd_gv< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'k-'< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale'< / span > , < span class = "org-string" > 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Frequency < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; ylabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'ASD of the measured velocity $\left< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > \frac< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > {< / span > < / span > < span class = "org-string" > m/s< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > }{< / span > < / span > < span class = "org-string" > \sqrt< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-4" > {< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-4" > }< / span > < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < / span > < span class = "org-string" > \right< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > $'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'southwest'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 500< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div id = "org71cc947" class = "figure" >
< p > < img src = "figs/ty_comp_gm.png" alt = "ty_comp_gm.png" / >
< / p >
< p > < span class = "figure-number" > Figure 7: < / span > Comparison of the ground velocity with the measured velocity (< a href = "./figs/ty_comp_gm.png" > png< / a > , < a href = "./figs/ty_comp_gm.pdf" > pdf< / a > )< / p >
2019-05-13 13:22:11 +02:00
< / div >
< / div >
< / div >
2020-04-27 11:35:57 +02:00
< div id = "outline-container-org7d3ac71" class = "outline-3" >
< h3 id = "org7d3ac71" > < span class = "section-number-3" > 2.5< / span > Relative Motion< / h3 >
< div class = "outline-text-3" id = "text-2-5" >
< p >
The relative velocity between the sample and the marble is shown in Fig. < a href = "#org21be4d0" > 8< / a > .
The velocity is integrated to have the relative displacement in Fig. < a href = "#org2d58d24" > 9< / a > .
< / p >
< div id = "org21be4d0" class = "figure" >
< p > < img src = "figs/rz_relative_velocity.png" alt = "rz_relative_velocity.png" / >
< / p >
< p > < span class = "figure-number" > Figure 8: < / span > Relative velocity between the hexapod and the marble (< a href = "./figs/rz_relative_velocity.png" > png< / a > , < a href = "./figs/rz_relative_velocity.pdf" > pdf< / a > )< / p >
< / div >
< p >
Time domain: Integration to have the displacement
< / p >
< div id = "org2d58d24" class = "figure" >
< p > < img src = "figs/rz_relative_motion.png" alt = "rz_relative_motion.png" / >
< / p >
< p > < span class = "figure-number" > Figure 9: < / span > Relative displacement between the Hexapod and the marble (< a href = "./figs/rz_relative_motion.png" > png< / a > , < a href = "./figs/rz_relative_motion.pdf" > pdf< / a > )< / p >
< / div >
< p >
We compute the PSD of the relative velocity between the sample and the marble.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxof_r, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > of< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > of< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxsr_r, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > sr< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxsp_r, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sp< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > sp< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
The Power Spectral Density of the Granite Velocity, Sample velocity and relative velocity are compare in Fig. < a href = "#org0cfb4b3" > 10< / a > .
< / p >
< div id = "org0cfb4b3" class = "figure" >
< p > < img src = "figs/rz_psd_sample_granite_relative_comp.png" alt = "rz_psd_sample_granite_relative_comp.png" / >
< / p >
< p > < span class = "figure-number" > Figure 10: < / span > Comparison of the PSD of the velocity of the Sample, Granite and relative velocity (< a href = "./figs/rz_psd_sample_granite_relative_comp.png" > png< / a > , < a href = "./figs/rz_psd_sample_granite_relative_comp.pdf" > pdf< / a > )< / p >
< / div >
< p >
Then, we display the PSD of the relative velocity for all three cases in Fig. < a href = "#org9d08176" > 11< / a > .
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsp_r< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , 'Spindle < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6rpm< / span > < span class = "org-type" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsr_r< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , 'Slip< span class = "org-type" > -< / span > Ring < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6rpm< / span > < span class = "org-type" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxof_r< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale'< / span > , < span class = "org-string" > 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Frequency < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; ylabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'ASD of the relative velocity $\left< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > \frac< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > {< / span > < / span > < span class = "org-string" > m/s< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > }{< / span > < / span > < span class = "org-string" > \sqrt< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-4" > {< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-4" > }< / span > < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < / span > < span class = "org-string" > \right< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > $'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'southwest'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 500< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div id = "org9d08176" class = "figure" >
< p > < img src = "figs/sr_sp_psd_relative_compare.png" alt = "sr_sp_psd_relative_compare.png" / >
< / p >
< p > < span class = "figure-number" > Figure 11: < / span > Comparison of the ASD of the relative velocity< / p >
< / div >
< p >
The Cumulative Power Spectrum of the relative velocity is shown in Fig. < a href = "#org76a9b23" > 12< / a > and in Fig. < a href = "#org61e2e4a" > 13< / a > (integrated in reverse direction).
< / p >
< div id = "org76a9b23" class = "figure" >
< p > < img src = "figs/dist_rz_cps.png" alt = "dist_rz_cps.png" / >
< / p >
< p > < span class = "figure-number" > Figure 12: < / span > Cumulative Power Spectrum of the relative velocity (< a href = "./figs/dist_rz_cps.png" > png< / a > , < a href = "./figs/dist_rz_cps.pdf" > pdf< / a > )< / p >
< / div >
< div id = "org61e2e4a" class = "figure" >
< p > < img src = "figs/dist_rz_cps_reverse.png" alt = "dist_rz_cps_reverse.png" / >
< / p >
< p > < span class = "figure-number" > Figure 13: < / span > Cumulative Power Spectrum of the relative velocity (integrated from high to low frequencies) (< a href = "./figs/dist_rz_cps_reverse.png" > png< / a > , < a href = "./figs/dist_rz_cps_reverse.pdf" > pdf< / a > )< / p >
< / div >
< p >
Finally, the Cumulative Amplitude Spectrum of the relative position between the hexapod and the marble is shown in Fig. < a href = "#org454a2a7" > 14< / a > .
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > flip< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > -< / span > cumtrapz< span class = "org-rainbow-delimiters-depth-4" > (< / span > flip< span class = "org-rainbow-delimiters-depth-5" > (< / span > f< span class = "org-rainbow-delimiters-depth-5" > )< / span > , flip< span class = "org-rainbow-delimiters-depth-5" > (< / span > pxsp_r< span class = "org-type" > ./< / span > < span class = "org-rainbow-delimiters-depth-6" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f< span class = "org-rainbow-delimiters-depth-6" > )< / span > < span class = "org-type" > .^< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-5" > )< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , 'Spindle < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6rpm< / span > < span class = "org-type" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > flip< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > -< / span > cumtrapz< span class = "org-rainbow-delimiters-depth-4" > (< / span > flip< span class = "org-rainbow-delimiters-depth-5" > (< / span > f< span class = "org-rainbow-delimiters-depth-5" > )< / span > , flip< span class = "org-rainbow-delimiters-depth-5" > (< / span > pxsr_r< span class = "org-type" > ./< / span > < span class = "org-rainbow-delimiters-depth-6" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f< span class = "org-rainbow-delimiters-depth-6" > )< / span > < span class = "org-type" > .^< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-5" > )< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , 'Slip< span class = "org-type" > -< / span > Ring < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 6rpm< / span > < span class = "org-type" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > flip< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > -< / span > cumtrapz< span class = "org-rainbow-delimiters-depth-4" > (< / span > flip< span class = "org-rainbow-delimiters-depth-5" > (< / span > f< span class = "org-rainbow-delimiters-depth-5" > )< / span > , flip< span class = "org-rainbow-delimiters-depth-5" > (< / span > pxof_r< span class = "org-type" > ./< / span > < span class = "org-rainbow-delimiters-depth-6" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > f< span class = "org-rainbow-delimiters-depth-6" > )< / span > < span class = "org-type" > .^< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-5" > )< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > 'OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale'< / span > , < span class = "org-string" > 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Frequency < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; ylabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'CAS of the relative displacement $\left< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > \frac< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > {< / span > < / span > < span class = "org-string" > m< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > }{< / span > < / span > < span class = "org-string" > \sqrt< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-4" > {< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-4" > }< / span > < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < / span > < span class = "org-string" > \right< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > $'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location'< / span > , < span class = "org-string" > 'southwest'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 500< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div id = "org454a2a7" class = "figure" >
< p > < img src = "figs/dist_rz_cas.png" alt = "dist_rz_cas.png" / >
< / p >
< p > < span class = "figure-number" > Figure 14: < / span > Cumulative Amplitude Spectrum of the relative motion Hexapod/Granite (< a href = "./figs/dist_rz_cas.png" > png< / a > , < a href = "./figs/dist_rz_cas.pdf" > pdf< / a > )< / p >
< / div >
< p >
The Power Spectral Density of the relative velocity is saved for further analysis.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > save< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/pxsp_r.mat'< / span > , < span class = "org-string" > 'pxsp_r'< / span > , < span class = "org-string" > 'f'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< / div >
< / div >
< div id = "outline-container-org1464a72" class = "outline-3" >
< h3 id = "org1464a72" > < span class = "section-number-3" > 2.6< / span > Conclusion< / h3 >
< div class = "outline-text-3" id = "text-2-6" >
2019-05-13 13:22:11 +02:00
< div class = "important" >
< p >
2020-04-27 11:35:57 +02:00
The relative motion below 20Hz is dominated by another effect than the rotation of the Spindle (probably ground motion).
< / p >
< p >
The Slip-Ring rotation induce almost no relative motion of the hexapod with respect to the granite (only a little above 400Hz).
2019-05-13 13:22:11 +02:00
< / p >
< p >
2020-04-27 11:35:57 +02:00
The Spindle rotation induces relative motion of the hexapod with respect to the granite above 20Hz.
2019-05-13 13:22:11 +02:00
< / p >
2020-04-27 11:35:57 +02:00
< / div >
< div class = "important" >
< p >
There is a huge peak at 24Hz on the sample vibration but not on the granite vibration
< / p >
< ul class = "org-ul" >
< li > The peak is really sharp, could this be due to magnetic effect?< / li >
< li > Should redo the measurement with piezo accelerometers.< / li >
< / ul >
2019-05-13 13:22:11 +02:00
< / div >
< / div >
< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
2020-04-27 11:35:57 +02:00
< p class = "date" > Created: 2019-10-31 jeu. 16:19< / p >
2019-05-13 13:22:11 +02:00
< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
< / div >
< / body >
< / html >
