EPS扭矩传感器-EPS传感器.rar_matlab_matlab例程_数值算法/人工智能下载-pudn.com

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/625f0ad02cc14f663627df84/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/625f0ad02cc14f663627df84/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">2006-01-0939 </div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls1 ws1">Development of a Cont<span class="_ _0"></span>actless Hall effect torque sensor for </div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls2 ws0">Electric Power S<span class="_ _0"></span>teering </div><div class="t m0 x4 h4 y4 ff1 fs2 fc0 sc0 ls2 ws2">Didier ANGLEVIEL </div><div class="t m0 x5 h5 y5 ff2 fs3 fc0 sc0 ls3 ws3">Moving Magnet Tec<span class="_ _1"></span>hnologies S.A. </div><div class="t m0 x6 h4 y6 ff1 fs2 fc0 sc0 ls4 ws4">Didier FRACHON, Gé<span class="_ _1"></span>rald MASSON </div><div class="t m0 x5 h5 y7 ff2 fs3 fc0 sc0 ls3 ws3">Moving Magnet Tec<span class="_ _1"></span>hnologies S.A. </div><div class="t m0 x7 h5 y8 ff2 fs3 fc0 sc0 ls5 ws0"> </div><div class="t m0 x8 h6 y9 ff2 fs4 fc0 sc0 ls6 ws5">Copyright © 2005 SAE International</div><div class="t m0 x8 h7 ya ff1 fs5 fc0 sc0 ls7 ws0">ABSTRACT </div><div class="t m0 x8 h8 yb ff3 fs3 fc0 sc0 ls8 ws6">In this paper, we will present an innovative torque </div><div class="t m0 x8 h8 yc ff3 fs3 fc0 sc0 ls9 ws7">sensor des<span class="_ _1"></span>ign which c<span class="_ _1"></span>ould be pre<span class="_ _1"></span>ferably used in Electric<span class="_ _1"></span> </div><div class="t m0 x8 h8 yd ff3 fs3 fc0 sc0 ls9 ws8">Power Assisted Steer<span class="_ _1"></span>ing (EPAS) application. This torqu<span class="_ _1"></span>e </div><div class="t m0 x8 h8 ye ff3 fs3 fc0 sc0 lsa ws9">sensor is<span class="_ _1"></span> a non-contact Ha<span class="_ _1"></span>ll effect design. Th<span class="_ _1"></span>e </div><div class="t m0 x8 h8 yf ff3 fs3 fc0 sc0 lsb wsa">specificity of this structure is its ability to measure the </div><div class="t m0 x8 h8 y10 ff3 fs3 fc0 sc0 lsc wsb">shift angle <span class="_ _1"></span>between <span class="_ _1"></span>two rotating shafts<span class="_ _1"></span> linked by<span class="_ _1"></span> a </div><div class="t m0 x8 h8 y11 ff3 fs3 fc0 sc0 lsc wsc">torsion bar<span class="_ _1"></span>. This measu<span class="_ _1"></span>rement is <span class="_ _1"></span>done with stat<span class="_ _1"></span>ionary </div><div class="t m0 x8 h8 y12 ff3 fs3 fc0 sc0 lsa wsd">electronic c<span class="_ _1"></span>omponents. This <span class="_ _1"></span>unique structur<span class="_ _1"></span>e generates<span class="_ _1"></span> </div><div class="t m0 x8 h8 y13 ff3 fs3 fc0 sc0 lsd wse">enough magnetic flux v<span class="_ _1"></span>ariation to measure<span class="_ _1"></span> angular shifts </div><div class="t m0 x8 h8 y14 ff3 fs3 fc0 sc0 lse wsf">from +/-1° to +/-8° with low-cost standard Hall ASICs </div><div class="t m0 x8 h8 y15 ff3 fs3 fc0 sc0 lsf ws10">available from var<span class="_ _1"></span>ious supplier<span class="_ _1"></span>s. This torque sensor<span class="_ _1"></span> has </div><div class="t m0 x8 h8 y16 ff3 fs3 fc0 sc0 ls10 ws11">convinced aut<span class="_ _0"></span>omotive industry du<span class="_ _0"></span>e to its good </div><div class="t m0 x8 h8 y17 ff3 fs3 fc0 sc0 ls11 ws12">performances, its<span class="_ _1"></span> compact dimension and a pric<span class="_ _1"></span>e </div><div class="t m0 x8 h8 y18 ff3 fs3 fc0 sc0 ls12 ws13">compatible with the <span class="_ _0"></span>mar<span class="_ _1"></span>ket expectation for this </div><div class="t m0 x8 h8 y19 ff3 fs3 fc0 sc0 lsf ws0">application. </div><div class="t m0 x8 h8 y1a ff3 fs3 fc0 sc0 ls5 ws14">This paper will explain the <span class="lse ws15">basic magnetic principle of </span></div><div class="t m0 x8 h8 y1b ff3 fs3 fc0 sc0 ls13 ws16">this torque sensor, the imp<span class="_ _0"></span>r<span class="_ _1"></span>ovements wh<span class="_ _0"></span>ich have lead to </div><div class="t m0 x8 h8 y1c ff3 fs3 fc0 sc0 lsd ws17">a structure co<span class="_ _1"></span>mpatible with automotive in<span class="_ _1"></span>dustry </div><div class="t m0 x8 h8 y1d ff3 fs3 fc0 sc0 lsa ws18">requirements, s<span class="_ _1"></span>ome measurement results<span class="_ _1"></span> and possible </div><div class="t m0 x8 h8 y1e ff3 fs3 fc0 sc0 ls11 ws19">sensor integr<span class="_ _1"></span>ation in the application. </div><div class="t m0 x8 h5 y1f ff2 fs3 fc0 sc0 ls5 ws0"> </div><div class="t m0 x8 h7 y20 ff1 fs5 fc0 sc0 ls14 ws0">INTRODUCTION </div><div class="t m0 x8 h5 y21 ff2 fs3 fc0 sc0 ls9 ws1a">Nowadays, for co<span class="_ _1"></span>st and pollution reaso<span class="_ _1"></span>ns, the </div><div class="t m0 x8 h5 y22 ff2 fs3 fc0 sc0 lsd ws1b">development <span class="_ _1"></span>of new vehicles <span class="_ _1"></span>is strongly driven by a </div><div class="t m0 x8 h5 y23 ff2 fs3 fc0 sc0 ls15 ws1c">research of fu<span class="_ _1"></span>el consumption r<span class="_ _1"></span>eduction. One<span class="_ _1"></span> interesting </div><div class="t m0 x8 h5 y24 ff2 fs3 fc0 sc0 lsf ws1d">way for such fuel ec<span class="_ _1"></span>onomies is the r<span class="_ _1"></span>eplacement of </div><div class="t m0 x8 h5 y25 ff2 fs3 fc0 sc0 ls11 ws1e">current hydrau<span class="_ _1"></span>lic power steering<span class="_ _1"></span> by EPAS using high </div><div class="t m0 x8 h5 y26 ff2 fs3 fc0 sc0 ls16 ws1f">power Brush<span class="_ _1"></span>less DC (BLDC) mo<span class="_ _1"></span>tors. The typical fuel </div><div class="t m0 x8 h5 y27 ff2 fs3 fc0 sc0 lsc ws20">economy rea<span class="_ _1"></span>lized by shifting <span class="_ _1"></span>from a hydr<span class="_ _1"></span>aulic power </div><div class="t m0 x8 h5 y28 ff2 fs3 fc0 sc0 ls16 ws21">steering to an EPAS is abou<span class="_ _1"></span>t 5 percent. With the </div><div class="t m0 x8 h5 y29 ff2 fs3 fc0 sc0 ls11 ws22">improvement of the<span class="_ _1"></span> BLDC motor s<span class="_ _1"></span>tructures an<span class="_ _1"></span>d the </div><div class="t m0 x8 h5 y2a ff2 fs3 fc0 sc0 ls9 ws23">increase of the elec<span class="_ _1"></span>tric power available<span class="_ _1"></span> with batteries, </div><div class="t m0 x8 h5 y2b ff2 fs3 fc0 sc0 lsa ws24">the market <span class="_ _1"></span>shares <span class="_ _1"></span>of EPAS should grow<span class="_ _1"></span> quickly in the </div><div class="t m0 x8 h5 y2c ff2 fs3 fc0 sc0 ls17 ws25">next few years [1]. </div><div class="t m0 x8 h5 y2d ff2 fs3 fc0 sc0 lsd ws26">In order to drive e<span class="_ _1"></span>fficiently the BLDC motor<span class="_ _1"></span>, the ECU </div><div class="t m0 x8 h5 y2e ff2 fs3 fc0 sc0 lsb ws27">requires accur<span class="_ _1"></span>ate informati<span class="ls11 ws28">on on the torque applied<span class="_ _1"></span> by </span></div><div class="t m0 x9 h5 y2f ff2 fs3 fc0 sc0 lsc ws29">the driver<span class="_ _1"></span> to the steerin<span class="_ _1"></span>g wheel. This tor<span class="_ _1"></span>que signal </div><div class="t m0 x9 h5 y30 ff2 fs3 fc0 sc0 ls18 ws2a">usually comes from<span class="_ _0"></span> the shift measurement <span class="_ _0"></span>between two </div><div class="t m0 x9 h5 y31 ff2 fs3 fc0 sc0 ls8 ws2b">shafts linked by a linear torsio<span class="ls9 ws8">n bar. The<span class="_ _1"></span> main concern in </span></div><div class="t m0 x9 h5 y32 ff2 fs3 fc0 sc0 ls19 ws2c">this meas<span class="_ _1"></span>urement is <span class="_ _1"></span>due to the fac<span class="_ _1"></span>t that these shafts<span class="_ _1"></span> are </div><div class="t m0 x9 h5 y33 ff2 fs3 fc0 sc0 ls3 ws2d">also rotating w<span class="_ _1"></span>ith the steerin<span class="_ _1"></span>g wheel and the in<span class="_ _1"></span>tegration </div><div class="t m0 x9 h5 y34 ff2 fs3 fc0 sc0 ls1a ws2e">of electron<span class="_ _1"></span>ic on rotating<span class="_ _1"></span> parts is <span class="_ _1"></span>definitely a blo<span class="_ _1"></span>cking </div><div class="t m0 x9 h5 y35 ff2 fs3 fc0 sc0 ls1b ws2f">point. An ex<span class="_ _0"></span>ample of BLDC motor and to<span class="_ _0"></span>rque sensor </div><div class="t m0 x9 h5 y36 ff2 fs3 fc0 sc0 lsa ws30">typical integr<span class="_ _1"></span>ation on th<span class="_ _1"></span>e steering co<span class="_ _1"></span>lumn is shown o<span class="_ _1"></span>n </div><div class="t m0 x9 h5 y37 ff2 fs3 fc0 sc0 ls1c ws31">the following draw<span class="_ _0"></span>ing. The BLDC exerts its torque t<span class="_ _0"></span>o the </div><div class="t m0 x9 h5 y38 ff2 fs3 fc0 sc0 ls9 ws32">steering column thro<span class="_ _1"></span>ugh a worm gear me<span class="_ _1"></span>chanism. </div><div class="t m0 xa h5 y39 ff2 fs3 fc0 sc0 ls5 ws0"> </div><div class="t m0 xb h9 y3a ff1 fs3 fc0 sc0 lsd ws33">Figure 1: Electric Pow<span class="_ _1"></span>er St<span class="_ _1"></span>eering </div><div class="t m0 x9 h5 y3b ff2 fs3 fc0 sc0 ls9 ws34">Moving Magnet Tec<span class="_ _1"></span>hnologies (MMT<span class="_ _1"></span>) has developed a<span class="_ _1"></span>n </div><div class="t m0 x9 h5 y3c ff2 fs3 fc0 sc0 ls1d ws35">innovative low cost structure answering all the </div><div class="t m0 x9 h5 y3d ff2 fs3 fc0 sc0 lsf ws36">requirements of torq<span class="_ _1"></span>ue sensing for EPAS. This torque </div><div class="t m0 x9 h5 y3e ff2 fs3 fc0 sc0 ls11 ws37">sensor is base<span class="_ _1"></span>d on a non-conta<span class="_ _1"></span>ct Hall effect princip<span class="_ _1"></span>le </div><div class="t m0 x9 h5 y3f ff2 fs3 fc0 sc0 ls11 ws38">and uses st<span class="_ _1"></span>andard progr<span class="_ _1"></span>ammable Hall ASICs available </div><div class="t m0 x9 h5 y40 ff2 fs3 fc0 sc0 ls16 ws39">on the mark<span class="_ _1"></span>et. MMT has a<span class="_ _1"></span>pplied for two<span class="_ _1"></span> patents </div><div class="t m0 x9 h5 y41 ff2 fs3 fc0 sc0 ls1e ws3a">regarding <span class="_ _1"></span>first a b<span class="_ _1"></span>asic structur<span class="_ _1"></span>e of this torqu<span class="_ _1"></span>e sensor an<span class="_ _1"></span>d </div><div class="t m0 x9 h5 y42 ff2 fs3 fc0 sc0 ls1f ws3b">then an op<span class="_ _0"></span>timized design [2] [3]<span class="_ _0"></span>. These torque sensor </div><div class="t m0 x9 h5 y43 ff2 fs3 fc0 sc0 ls3 ws3c">designs a<span class="_ _1"></span>re presente<span class="_ _1"></span>d hereafte<span class="_ _1"></span>r. </div><div class="t m0 xc h6 y44 ff2 fs4 fc0 sc0 ls20 ws3d">Torque sensor </div><div class="t m0 xd h6 y45 ff2 fs4 fc0 sc0 ls20 ws0">housing </div><div class="t m0 x1 h6 y46 ff2 fs4 fc0 sc0 ls21 ws3e">BLDC motor </div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/625f0ad02cc14f663627df84/bg2.jpg"><div class="t m0 x8 h7 y47 ff1 fs5 fc0 sc0 ls22 ws3f">BASIC DESIGN AND SENSOR PRINCIPLE </div><div class="t m0 x8 h5 y48 ff2 fs3 fc0 sc0 ls23 ws40">The MMT to<span class="_ _0"></span>rque sensor basic structure <span class="_ _0"></span>is shown </div><div class="t m0 x8 h5 y49 ff2 fs3 fc0 sc0 ls3 ws0">hereafter. </div><div class="t m0 xe h5 y4a ff2 fs3 fc0 sc0 ls5 ws0"> </div><div class="t m0 xf h9 y4b ff1 fs3 fc0 sc0 ls11 ws19">Figure 2: Exploded view<span class="_ _1"></span> of the MMT torqu<span class="_ _1"></span>e sensor </div><div class="t m0 x8 h5 y4c ff2 fs3 fc0 sc0 ls16 ws41">This sensor<span class="_ _1"></span> is made up of the followin<span class="_ _1"></span>g sub-assemb<span class="_ _1"></span>lies: </div><div class="t m0 x10 h5 y4d ff4 fs3 fc0 sc0 ls5 ws0">•<span class="ff2 ls11 ws42"> <span class="_ _2"> </span>The rotor (gr<span class="_ _1"></span>ey and red par<span class="_ _1"></span>ts), fixed on one </span></div><div class="t m0 x11 h5 y4e ff2 fs3 fc0 sc0 lsf ws43">rotary shaft of the stee<span class="_ _1"></span>ring column, is made by a </div><div class="t m0 x11 h5 y4f ff2 fs3 fc0 sc0 ls18 ws44">plurality of<span class="_ _0"></span> permanent magnets fixed on<span class="_ _0"></span> a soft </div><div class="t m0 x11 h5 y50 ff2 fs3 fc0 sc0 lse ws45">ferro-magnetic yoke. </div><div class="t m0 x10 h5 y51 ff4 fs3 fc0 sc0 ls5 ws0">•<span class="ff2 ls11 ws46"> <span class="_ _3"> </span>The stators<span class="_ _1"></span> (blue and yellow p<span class="_ _1"></span>arts) are fixed<span class="_ _1"></span> on </span></div><div class="t m0 x11 h5 y52 ff2 fs3 fc0 sc0 lsc ws47">the second ro<span class="_ _1"></span>tary shaft of th<span class="_ _1"></span>e steering column, </div><div class="t m0 x11 h5 y53 ff2 fs3 fc0 sc0 ls9 ws48">linked to the first one by a tor<span class="_ _1"></span>sion bar. These </div><div class="t m0 x11 h5 y54 ff2 fs3 fc0 sc0 lsc ws49">stators ar<span class="_ _1"></span>e fixed one towar<span class="_ _1"></span>d the other. They are </div><div class="t m0 x11 h5 y55 ff2 fs3 fc0 sc0 lsa ws4a">made of soft ferr<span class="_ _1"></span>o-magnetic material. </div><div class="t m0 x10 h5 y56 ff4 fs3 fc0 sc0 ls5 ws0">•<span class="ff2 lsd ws4b"> <span class="_ _4"> </span>One or two<span class="_ _1"></span> (for redundancy) H<span class="_ _1"></span>all ASICs fixed </span></div><div class="t m0 x11 h5 y57 ff2 fs3 fc0 sc0 lsf ws4c">stationary on th<span class="_ _1"></span>e housing. The Ha<span class="_ _1"></span>ll probe is </div><div class="t m0 x11 h5 y58 ff2 fs3 fc0 sc0 ls11 ws4d">inserted in a<span class="_ _1"></span> measurement <span class="_ _1"></span>slot created betwee<span class="_ _1"></span>n </div><div class="t m0 x11 h5 y59 ff2 fs3 fc0 sc0 ls24 ws4e">the two stat<span class="_ _0"></span>ors. With the MMT design,<span class="_ _0"></span> we </div><div class="t m0 x11 h5 y5a ff2 fs3 fc0 sc0 ls25 ws4f">generate <span class="_ _1"></span>enough flux <span class="_ _1"></span>variation to use th<span class="_ _1"></span>e Hall </div><div class="t m0 x11 h5 y5b ff2 fs3 fc0 sc0 ls26 ws50">ASICs available<span class="_ _0"></span> <span class="_ _1"></span>from Melexis (MLX <span class="_ _0"></span>90251 or </div><div class="t m0 x11 h5 y5c ff2 fs3 fc0 sc0 ls19 ws51">redundan<span class="_ _1"></span>t MLX 9027<span class="_ _1"></span>7) or M<span class="_ _1"></span>icronas (<span class="_ _1"></span>HAL 8XX). </div><div class="t m0 x8 h5 y5d ff2 fs3 fc0 sc0 ls3 ws52">The followi<span class="_ _1"></span>ng figure sh<span class="_ _1"></span>ows the se<span class="_ _1"></span>nsor in a w<span class="_ _1"></span>orking </div><div class="t m0 x8 h5 y5e ff2 fs3 fc0 sc0 ls27 ws0">configuration.<span class="_ _0"></span> </div><div class="t m0 x12 h5 y5f ff2 fs3 fc0 sc0 ls5 ws0"> </div><div class="t m0 x13 h9 y60 ff1 fs3 fc0 sc0 ls1c ws53">Figure 3: M<span class="_ _0"></span>MT torque sensor bas<span class="_ _0"></span>ic structure </div><div class="t m0 x9 h5 y61 ff2 fs3 fc0 sc0 ls11 ws54">On these two firs<span class="_ _1"></span>t views of the torque sen<span class="_ _1"></span>sor, the rotor is </div><div class="t m0 x9 h5 y62 ff2 fs3 fc0 sc0 ls28 ws55">realized with magnets of<span class="_ _0"></span> the same polarity (red parts) </div><div class="t m0 x9 h5 y63 ff2 fs3 fc0 sc0 ls16 ws56">alternated with ferro-<span class="_ _1"></span>magnetic areas fr<span class="_ _1"></span>om the yoke. This </div><div class="t m0 x9 h5 y64 ff2 fs3 fc0 sc0 ls11 ws57">magnet configur<span class="_ _1"></span>ation could b<span class="_ _1"></span>e replaced by a mor<span class="_ _1"></span>e </div><div class="t m0 x9 h5 y65 ff2 fs3 fc0 sc0 ls1c ws58">industrial ring<span class="_ _0"></span> magnet with alternat<span class="_ _0"></span>ed north and south<span class="_ _0"></span> </div><div class="t m0 x9 h5 y66 ff2 fs3 fc0 sc0 ls16 ws41">poles on its surfa<span class="_ _1"></span>ce as shown be<span class="_ _1"></span>low. </div><div class="t m0 x14 h5 y67 ff2 fs3 fc0 sc0 ls5 ws0"> </div><div class="t m0 x15 h9 y68 ff1 fs3 fc0 sc0 ls9 ws32">Figure 4: Rotor made w<span class="_ _1"></span>ith mult<span class="_ _1"></span>ipolar ring magnet </div><div class="t m0 x9 h5 y69 ff2 fs3 fc0 sc0 ls29 ws59">One couple of nort<span class="_ _0"></span>h <span class="_ _1"></span>and sout<span class="_ _0"></span>h poles of the magnet<span class="_ _0"></span> is </div><div class="t m0 x9 h5 y6a ff2 fs3 fc0 sc0 ls24 ws5a">associated to one tooth<span class="_ _0"></span> on each stator to create an </div><div class="t m0 x9 h5 y6b ff2 fs3 fc0 sc0 ls3 ws3c">elementary se<span class="_ _1"></span>nsor as s<span class="_ _1"></span>hown be<span class="_ _1"></span>low. </div><div class="t m0 x7 h5 y6c ff2 fs3 fc0 sc0 ls5 ws0"> </div><div class="t m0 x16 h9 y6d ff1 fs3 fc0 sc0 ls25 ws5b">Figure 5: View<span class="_ _5"></span> of an e<span class="_ _1"></span>lementary sensor in a<span class="_ _1"></span> </div><div class="t m0 x17 h9 y6e ff1 fs3 fc0 sc0 lsf ws5c">beginning of the stroke posit<span class="_ _1"></span>ion w<span class="_ _1"></span>ith flux lines </div><div class="t m0 x9 h5 y6f ff2 fs3 fc0 sc0 ls2a ws5d">A magnetic flux varia<span class="_ _0"></span>tion is generated in the stator teeth </div><div class="t m0 x9 h5 y70 ff2 fs3 fc0 sc0 ls15 ws5e">when the magn<span class="_ _1"></span>et transitions<span class="_ _1"></span> are moving in<span class="_ _1"></span> front of them. </div><div class="t m0 x9 h5 y71 ff2 fs3 fc0 sc0 ls2b ws5f">This flux variation is a linea<span class="_ _1"></span>r function of the magnet </div><div class="t m0 x9 h5 y72 ff2 fs3 fc0 sc0 lsd ws60">angular positio<span class="_ _1"></span>n and we have demonstrated<span class="_ _1"></span> the </div><div class="t m0 x9 h5 y73 ff2 fs3 fc0 sc0 ls1a ws61">following a<span class="_ _1"></span>nalytical equa<span class="_ _1"></span>tion: </div><div class="t m0 x18 ha y74 ff5 fs6 fc0 sc0 ls5 ws0">H<span class="_ _6"></span>.<span class="_ _7"></span>E<span class="_ _8"></span>.<span class="_ _9"></span>.<span class="_ _a"></span>Da<span class="_ _b"></span>.<span class="_ _c"></span>F<span class="_ _d"></span>.</div><div class="t m0 x19 ha y75 ff5 fs6 fc0 sc0 ls5 ws0">L<span class="_ _e"></span>D<span class="_ _f"></span>B</div><div class="t m0 x1a ha y76 ff5 fs6 fc0 sc0 ls5 ws0">B</div><div class="t m0 x1b hb y77 ff5 fs7 fc0 sc0 ls5 ws0">a<span class="_ _b"></span>r</div><div class="t m0 x1c hb y78 ff5 fs7 fc0 sc0 ls5 ws0">m</div><div class="t m1 x1d hc y74 ff4 fs8 fc0 sc1 ls5 ws0">σ<span class="_ _10"></span>α</div><div class="t m2 x1e hd y74 ff6 fs6 fc0 sc0 ls5 ws0">4</div><div class="t m2 x1f hd y75 ff6 fs6 fc0 sc0 ls5 ws0">4</div><div class="t m2 x20 he y79 ff6 fs7 fc0 sc0 ls5 ws0">1</div><div class="t m2 x21 hf y74 ff4 fs6 fc0 sc1 ls5 ws0">+</div><div class="t m2 x22 hf y75 ff4 fs6 fc0 sc1 ls5 ws0">Θ</div><div class="t m2 x23 hf y76 ff4 fs6 fc0 sc1 ls5 ws0">−<span class="_ _11"></span>=</div><div class="t m2 x24 h5 y7a ff2 fs3 fc0 sc0 ls5 ws0"> </div><div class="t m2 x9 h5 y7b ff2 fs3 fc0 sc0 ls16 ws0">Where: </div><div class="t m2 x25 h5 y7c ff4 fs3 fc0 sc0 ls5 ws0">•<span class="ff2 ls2c"> B</span></div><div class="t m2 x26 h10 y7d ff2 fs9 fc0 sc0 ls5 ws0">m</div><div class="t m2 x27 h5 y7e ff2 fs3 fc0 sc0 ls2d ws62"> is the flux m<span class="_ _0"></span>easured in the slot between two<span class="_ _0"></span> </div><div class="t m2 x28 h5 y7f ff2 fs3 fc0 sc0 ls27 ws63">stator teeth </div><div class="t m2 x25 h5 y80 ff4 fs3 fc0 sc0 ls5 ws0">•<span class="ff2 ls2c"> B</span></div><div class="t m2 x26 h10 y81 ff2 fs9 fc0 sc0 ls5 ws0">r</div><div class="t m2 x29 h5 y82 ff2 fs3 fc0 sc0 ls24 ws64"> is the magne<span class="_ _0"></span>t remanence </div><div class="t m2 x25 h5 y83 ff4 fs3 fc0 sc0 ls5 ws0">•<span class="ff2 ls2c"> D</span></div><div class="t m2 x26 h10 y84 ff2 fs9 fc0 sc0 ls5 ws0">a</div><div class="t m2 xb h5 y85 ff2 fs3 fc0 sc0 ls15 ws65"> is the average diameter<span class="_ _1"></span> of the air gap </div><div class="t m2 x25 h5 y86 ff4 fs3 fc0 sc0 ls5 ws0">•<span class="ff2 lsa ws4a"> <span class="_ _12"> </span>L is the magnet thick<span class="_ _1"></span>ness </span></div><div class="t m2 x25 h5 y87 ff4 fs3 fc0 sc0 ls5 ws0">•<span class="ff2"> <span class="_ _12"> </span></span>Θ<span class="ff2 ls26 ws66"> is the angular position of the magnet<span class="_ _0"></span> <span class="_ _1"></span>transition </span></div><div class="t m2 x25 h5 y88 ff4 fs3 fc0 sc0 ls5 ws0">•<span class="ff2"> <span class="_ _12"> </span></span>α</div><div class="t m2 x26 h10 y89 ff2 fs9 fc0 sc0 ls5 ws0">1</div><div class="t m2 x2a h5 y8a ff2 fs3 fc0 sc0 ls3 ws3"> is the angu<span class="_ _1"></span>lar length of one stato<span class="_ _1"></span>r teeth </div><div class="t m2 x25 h5 y8b ff4 fs3 fc0 sc0 ls5 ws0">•<span class="ff2 ls2e ws67"> <span class="_ _12"> </span>F is the thick<span class="_ _0"></span>n<span class="_ _1"></span>ess of th<span class="_ _0"></span>e slot between the two </span></div><div class="t m2 x28 h5 y8c ff2 fs3 fc0 sc0 ls27 ws63">stator teeth </div><div class="t m2 x25 h5 y8d ff4 fs3 fc0 sc0 ls5 ws0">•<span class="ff2"> <span class="_ _12"> </span></span><span class="ls2f">σ <span class="ff2 ls1e ws68">is the flux leakag<span class="_ _1"></span>e coefficient </span></span></div><div class="t m2 x25 h5 y8e ff4 fs3 fc0 sc0 ls5 ws0">•<span class="ff2 lsf ws5c"> <span class="_ _12"> </span>E is the radial air gap len<span class="_ _1"></span>gth </span></div><div class="t m2 x25 h5 y8f ff4 fs3 fc0 sc0 ls5 ws0">•<span class="ff2 ls16 ws41"> <span class="_ _12"> </span>H is the teet<span class="_ _1"></span>h radial length </span></div><div class="t m2 x2b h11 y90 ff3 fsa fc0 sc0 ls30 ws69">2 stators (ferromagnetic parts) fixed </div><div class="t m2 x2c h11 y91 ff3 fsa fc0 sc0 ls31 ws6a">on a rotary shaft </div><div class="t m2 x10 h11 y92 ff3 fsa fc0 sc0 ls32 ws6b">Rotor (ferro-magnetic </div><div class="t m2 x2d h11 y93 ff3 fsa fc0 sc0 ls33 ws6c">yoke+magnets) fixed on a </div><div class="t m2 x2e h11 y94 ff3 fsa fc0 sc0 ls34 ws6d">rotary shaft </div><div class="t m2 x2f h11 y95 ff3 fsa fc0 sc0 ls35 ws6e">Hall probe + Electronic (fixed </div><div class="t m2 x30 h11 y96 ff3 fsa fc0 sc0 ls36 ws6f">stationary on the housing) </div><div class="t m2 x31 h6 y97 ff2 fs4 fc0 sc0 ls37 ws70">Stator teeth (one of each </div><div class="t m2 x32 h6 y98 ff2 fs4 fc0 sc0 ls38 ws0">stator</div><div class="c x32 y99 w2 h12"><div class="t m2 x33 h6 y9a ff2 fs4 fc0 sc0 ls5 ws0">)</div></div><div class="t m2 x34 h6 y9b ff2 fs4 fc0 sc0 ls20 ws3d">Magnet poles of the rotor </div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div>