The Smart Motion Cheat Sheet


 Barnaby Long
 9 months ago
 Views:
Transcription
1 Srt otion "Cht" Sht 8.1 AutotionSolutions offrs full lin of otion control nd fctory utotion products nd srvics, ckd y n princd t of utotion nginrs. For ssistnc with your ppliction, cll to rch th AutotionSolutions offic nrst you or visit our wsit t: AutotionSolutions AutotionSolutions W k Tchnology Work Th Srt otion Cht Sht $10.00 Srt otion Systs r dfind, for our purposs, s otion systs whr spd, cclrtion rt, nd position (nd sotis torqu) cn digitlly progrd. Srt otion Systs consist of thr sic functionl locks: Brins, uscl, nd Lod. Th Brins (controls) slctd will dpnd significntly upon ppliction dtils, th fturs dsird y th syst dsignr or usr, nd prsonl prfrnc. Th Lod nd th otion chnis usd r dicttd y th ppliction rquirnts nd th chin dsignr. But th uscl (th otor & driv) is th ssntil lnt of Srt otion Syst whr it is possil for dgr of scinc to tk ovr. For n ppliction with givn Lod (nd chnis) with th ppropritly slctd Brins, s long s th torqu vill (t spd) fro th slctd otordriv syst cds th torqu rquird to prfor th dsird otion, th ppliction should succss. Th Srt otion Cht Sht ws crtd to provid th syst dsignr th infortion ost coonly usd to proprly dtrin th uscl (torqu t spd) rquird y givn ppliction nd to giv so guidlins for slcting th ost pproprit otordriv syst to dlivr tht rquird torqu t spd. Whil it is dsirl to hv sic knowldg of th diffrnt srt otion tchnologis currntly vill, it is not ssntil. Wht is ssntil is tht th ppliction rquirnts wll dfind, tht th torqu t spd rquirnts dtrind with fir dgr of ccurcy, nd tht th uscl (otordriv) slctd sd upon its ility to roustly dlivr th rquird torqu t spd. Whil it y intrsting nd vn usful, it is not ssntil to know wht hppns insid givn srt otor or driv in ordr to proprly slct nd utiliz it. Hving sid tht, short discussion of th chrctristics of th jor corcilly vill uscl for srt otion systs is pproprit. Thr r two coonly usd clsss of srt uscl: stppr systs nd srvo systs. Stppr systs (otor & driv) r fundntlly opnloop systs which ccpt digitl conds. Thy rspond to digitl stp & dirction inputs providd y n indr or otion controllr (Brin) which is siclly progrl puls gnrtor. This squnc of pulss is trnsltd into otion of th otor y th driv ( trnsltor ). Th rsult is vry costffctiv lldigitl Srt otion Syst. PAGE 1 Stppr otors r rushlss otors tht includ prnnt gnt, vril rluctnc, nd hyrid typs. Within ths typs thr r ny diffrnt vritions of otor construction including , 3, 4, nd 5phs windings with ny diffrnt pol counts nd chnicl stp ngls. Ovrll, th function of th stppr driv is to squntilly rgult th currnt into th otor phs windings in ordr to produc th dsird otion. Th switching sch usd in driv (full, hlf, ini, icrostp) in cointion with th chnicl construction of th otor dtrins th syst rsolution (stps/rv). Whil ht considrtions ultitly liit th iu torqu fro givn otor/driv syst, th torqu t spd is lrgly function of th driv s ility to ovrco th inductnc of th windings nd push th iu currnt into th phs windings s quickly s possil without ovrhting. Thr r ny diffrnt typs of drivs dsignd to ccoplish this tsk (L/R, unipolr, ipolr, choppr, rcirculting choppr, tc.) ll of which hv dvntgs. Thr is discussion of ths in nufcturrs litrtur. For ost stppr drivs, ing opn loop y ntur, th currnt snt to th otor is th s, indpndnt of lod vritions. Whil ny drivs now provid rducd currnt lvl whn no otion is condd, sinc otor currnt is lwys high, ost gt vry hot, vn whn stoppd. Anothr rsult of switching (coutting) currnt twn windings without knowldg of th rotor vlocity or position is to produc rsonnc. Rsonnc is th culintion of th copl opnloop dynic intrctions twn otor, driv, lod, nd th condd otion profil, nd cn rduc vill torqu significntly t so spds. An iportnt chrctristic of stppr systs (on frquntly isundrstood) is tht thir coonly pulishd torqu vs. spd curvs rprsnts th torqu t which syst will stll undr idl conditions. Du to th rsonnc ffcts ntiond ov, stppr syst will typiclly stll t 050% low this curv, dpnding upon spd. (S discussion on torqu vs. spd curvs on Pg 5.) Th Srt otion Cht Sht, crtd y Brd Grnt, P.E.; Copyright 1999 y AutotionSolutions Intntionl, LLC
2 Srt otion "Cht" Sht 8. Srvo Systs: Whil stppr systs could clld typ of tchnology, srvo is or proprly tr, not dvic or tchnology. A srvo is y dfinition syst tht ks corrctions sd upon fdck. It is lso y dfinition closdloop. In th following discussion, w will rfrring to srvos s th ny fors of lctric otors nd plifirs (p) usd s closdloop systs. Thr r thr sic loops in Srt (positioning) lctric srvo syst: th torqu (currnt) loop; th vlocity loop; nd th position loop. Th currnt loop is intrnl to th p. Sinc thr is linr rltionship twn currnt nd torqu in (ost) srvo otors, th p knows th torqu ing dlivrd fro th otor sd upon th currnt it is snding. Snsors on th otor nd/or lod provid vlocity nd/or position infortion to th p nd/or Brin. Snsors coonly usd for oth spd nd position r ncodrs nd rsolvrs. Erlir, tchotrs wr usd for vlocity, ut dvncs in digitl lctronics llow driving th vlocity dt fro ncodrs nd rsolvrs. Also, lctroniclly couttd (rushlss) otors rquir couttion loop (fdck of rotor position in ordr to proprly coutt). Ultitly, th rsult of th otion conds coing fro th Brin is to chng th torqu (currnt) snt to th otor in rspons to dvition fro th dsird vlu of th surd spd nd/or position. How uch currnt (torqu) should th p snd? It dpnds upon th rror(s) twn th dsird spd nd/or position, nd upon th gins (ount of corrction rltiv to ount of rror) tht r st (ithr y nlog pots or digitl sttings) in th fdck loops. Th highr th gin stting, th lrgr th chng in th loop output for givn rror. To digrss into n utootiv nlogy: Your cr is srvosyst. It hs otor (ngin), plifir (crurtor), nd Brin (cruis control & you or trip coputr). It lso hs torqu loop (within th crurtor: ngin output proportionl to gs flow), vlocity loop (spdotr nd you, or cruis control), nd position loop (odotr nd you, or trip coputr). Lik n lctric srvo, if th spd or position diffrs fro th dsird, chng in torqu is d. If you r high gin drivr (or if your crurtor nd cruis control gins r high), your syst cn high rspons. Howvr, s with n lctric srvo, whn th gins r too high for th lod nd otion profil, n unstl condition cn rsult (wrck). Action: dtun. If your syst is sluggish for th lod nd th dsird otion, incrs th gins, or gt highr prfornc syst. ost corcilly vill srvos still us nlog intrfcs (not to confusd with nlog hrdwr) to rciv ithr vlocity or torqu conds fro Brin. Howvr, srvos r incrsingly coing vill with digitl intrfcs (not to confusd with digitl hrdwr) which ithr ult stppr otor intrfc (nd fro th Brin viwpoint, cn controlld opnloop lik stppr otors), or which rciv torqu, vlocity, or position conds dirctly in digitl for. Siilr to stpprs, thr r vrity of iplnttions of lctric srvos, ch of which hv dvntgs. Th or coon distinguishing (or rkting) trs usd for th vrious typs of srvos includ: DC rushtyp; AC rushlss; DC rushlss; Vctor...; EC (lctroniclly couttd otors.... i.. rushlss), switchd rluctnc, synchronous srvo, induction srvo, tc. So trs rfr to otor construction; so to plifir chrctristics; so to oth. For or infortion on th diffrncs twn srvo nd stppr tchnologis, consult th nufcturrs litrtur, AIE, NEA PC Group, or ttnd lncd gnric clss on Srt otion. Agin, whil th dtils of givn tchnology y intrsting nd vn hlpful to know, s syst dsignr, your slction should not sd upon th tchnologis ployd, ut on thir rsult: i.., th torqu t spd thy roustly produc nd thir vlu (prfornc vs. cost) rltiv to your ppliction rquirnts. Whn you tk this pproch, gnrlly th ost pproprit tchnology will slct itslf. 1. Estlish otion Ojctivs 1.. Clcult Criticl otion Prtrs Spd Acclrtion Rt Itrt 3. Clcult Acclrtion Torqus. Dfin/Slct otion chnis.. Clcult Syst Inrtis (oving ojcts) 1. Estlish otion Ojctivs (ost Iportnt!): Ovrll distnc vs. ti rquirnts? Vlocity vs. Ti for ntir cycl? Worstcs ov? (L distnc in t ti) Any iposd. spd constrints? Rquird ov rsolution? Rquird positioning rptility? Rquird positioning ccurcy? 1.. Clcult Criticl ov Prtrs:. ov spd ω?. ccl rt α?. Dfin/Slct otion chnis: Dirct Driv? Scrw? Tngntil Driv? Rducr? Typ?.. Clcult inrti of ll oving coponnts chnis coponnts; Rducr; Coupling Rflct inrti s to otor Srt otor Sizing/Slction FlowChrt Ecpt otor 4. Clcult NonInrtil Forcs Grvity? Friction? PrLods? PushPull? Tool? 5. Clcult Totl Torqu (inus otor inrti) Rpt Procdur 6. k (nw) otor/driv Slction 3. Clcult Acclrtion Torqu t otor shft du to rflctd inrti (lod & chnis only) 4. Clcult ll noninrtil forcs, torqus Forcs, torqus du to grvity? Torqus du to othr trnl forcs? Friction? Prlods? 5. Clcult Totl Torqu rflctd to otor Acclrtion/Inrtil (T=J L α) torqus Plus ll othr Torqus Pk torqu for worst cs ov Also rs torqu for ntir ov cycl 6. k (initil) otor/driv slction Torqu vill ust cd pk nd rs Rr, otor inrti hsn t n ddd 7. Clcult Torqu ddd y otor inrti Lrgr th ccl rt = > highr significnc Chck Assuptions Chck Units! Rdo Clcultions Chng chnis No Us Torqu vs. Spd Curvs! Not just Dt. 8. Torqu Avill > Rquird Torqu? 7. Add Torqu du to otor Inrti Ys 10. Try Agin! No 9. Pss Snity Tst? Ys Don! Good Jo. 8. Torqu Avill cds Torqu Rquird? At ll spds? Pk torqu during ccl? RS (continuous) ovr ntir cycl? Us Torqu vs. Spd Curvs, not just Dt! If No, rturn to 6, nd slct nw otor 9. If Ys, dos slction pss th Snity Tst? Snity Tst = Dos this k sns? Forgt th nurs... Us your coon sns, intuition & judgnt! If Ys, you r don! Good Jo! Iplnt! 10. If No, Try Agin... Rpt th procdur Doulchck your ssuptions Rdo your clcultions Triplchck your units!! Try chnging your chnis dtils PAGE
3 Srt otion "Cht" Sht 8.3 T c T + T c = T Totl Torqu vs. Ti T c t t c t d t h t ttotl d Rottion vs. Ti Vlocity vs. Ti T d + T c d c Totl T H Ky otion Rltionships NOTE: Ths foruls r sily drivd knowing th r undr th vlocity vs. ti curv is distnc nd its slop is cclrtion. If you cn clcult th r of rctngls, tringls, nd th slop of lin (ris ovr run), you cn rr nd/or sily driv ths foruls!! Units Syol Dfinition SI English C G Circufrnc of Gr (or c) in (or ft) C P: 1,, 3 Circufrnc of Pullys, 1,, or 3 D Ditr of cylindr or... (or c) in (or ft) D G...(pitch di.) of Gr D PL...(pitch di.) of Pullys on Lod D P...(pitch di.) of Pullys on otor D P:1,, 3...(pitch di.) of Pullys 1,, or 3 fficincy of chnis or rducr % % F Forcs du to... N l F tr...friction (F fr = µw L cos γ) F g...grvity (F g = W L sin γ) F p...push or Pull forcs For Trpzoidl ovs t t d θ Totl = θ + θ c + θ d = ω + t c + θ Totl ω = t t ( + t d c + ) For Tringulr ovs (if t c = 0) t t θ d Totl = θ + θ d = ω ( + ) θ Totl θ Totl ω = t ; if t = t d, ω = t d t ( + ) Acclrtion (ω  ω o ) α = π t or d linr ccl or dcl rt s  ins  α ngulr cclrtion rt rds  rds  g grvity ccl constnt s ins  J ss ont of inrti for... kg lin J B...Blt rflctd to otor or or J C...Coupling gc ozin J G...Gr tc. or J L...Lod inls J L...Lod rflctd to otor or...otor inozs J PL...Pully on th Lod tc. J P...Pully on th otor J PL...Pully on Lod rflctd to otor J P: 1,, 3...Pully or sprockt 1,, or 3 J r...rducr (or gro) J Totl...Totl of ll inrtis J S...ld Scrw N r Nur rtio of rducr non non N t Nur of tth on gr, pully, tc. P G Pitch of Gr, sprockt or pully tth/ tth/inch P S Pitch of ld Scrw rvs/ rvs/inch t ti... sc sc t, c, or d...for ccl, constnt spd or dcl t...for ov t Totl...for Totl Cycl t h...for hold ti (dwll ti) Syols & Dfinitions AutotionSolutions Uniforly Acclrtd Rotry otion Unknown Known Eqution θ ω o, t, α θ = ω o t + αt / (rdins) ω, ω o, t θ = (ω + ω o )t/ ω, ω o, α θ = (ω  ω o )/(α) ω, t, α θ = ω t  αt / ω ω o, t, α ω = ω o + αt (rdsc 1 ) θ, ω o, t ω = θ/t  ω o θ, ω o, α ω = ω o + (αθ) θ, t, α ω = θ/t + αt/ ω o ω, t, α ω o = ω  αt (rdsc 1 ) θ, ω, t ω o = θ/t  ω θ, ω, α ω o = ω  (αθ) θ, t, α ω = θ/t  αt/ t ω, ω o, α t = (ω  ω o )/α (sc) θ, ω, ω o, t = θ(ω + ω o ) α θ, ω, ω o α = (ω  ω o )/(θ) (rds  ) ω, ω o, t α = (ω  ω o )/t θ, ω o, t α = (θ/t  ω o /t) θ, ω, t α = (ω /t  θ/t ) Units Syol Dfinition SI English T Torqu...(for rquird Clcultions) N inl T,c, or d...during ccl, constnt, or dcl or T CL...Constnt t Lod inoz T C...Constnt rflctd to otor T H...Holding (whil otor stoppd) T L...t Lod (not yt rflctd to otor) T P...du to Prlod on scrw nut, tc. T RS...RS ( vrg ) ovr ntir cycl T Totl...totl fro ll forcs V L linr Vlocity of Lod s 1 ins 1 ω O initil ngulr/rottionl vlocity rds 1 rps or rp ω ngulr/rottionl vlocity of otor ω iu ngulr/rottionl vlocity W L Wight of Lod N (or kg) l W B Wight of Blt (or chin or cl) W T Wight of Tl (or rck & oving prts X L Distnc X trvld y Lod (or c) in (or ft) θ rottion... rdins rvs θ, c, or d...rottion during ccl, dcl, tc. θ L...rottion of Lod θ...rottion of otor θ Totl Totl rottion of otor during ov π PI = non non π rottionl unit convrsion (rds/rv) rd/rv rd/rv µ cofficint of friction non non γ lod ngl fro horizontl dgrs dgrs Th following Dfinitions pply to th Torqu vs. Spd Curvs...typicl torqu trs usd with srvos.. N inl T PS Pk Torqu t Stll (zro spd) or T PR Pk Torqu t Rtd Spd inoz T CS Torqu vill continuously t Stll T CR Continuous Torqu Rting rtd spd)...typicl torqu trs usd with Stpprs... T H Holding Torqu (t zro spd) ω R Rtd Spd (srvos) rds 1 rps or rp ω iu Spd (srvos & stpprs) ω 1 Spd t Pk Torqu (not coonly usd) ω H High spd...rl iu (not coon) PAGE 3
4 Srt otion "Cht" Sht 8.4 Ky chnis Rltd Equtions otion chnis nd otion Equtions Gring, J GL, NtL J G, N t L, L, T L N r = N tl N t θ = N r θ L ω = N r ω L T L N r Inrti, Torqu Equtions J Totl = + J G + J GL + J L J GL = 1 J GL J L = 1 () N r () N r J L Othr Fctors To Considr Luricnt viscosity (oil or grs hs jor ffct on drg torqu!) Bcklsh Efficincy Rducr, L, L, T L θ N r = = θ L θ = N r θ L ω ω L J Totl = + J r + J L () J L = 1 J L T L N r N r Coupling inrti Gr nd/or rflctd rducr inrti J r, Nr, r J L ω = N r ω L J r = inrti of rducr rflctd to input Tiing Blt N TL D PL Rck & Pinion X L, V L, F p, F g Convyor X L, V L, F p, Fg Ldscrw J F fr J C W L, W L X L, V L, F p, Fg J PL, rpl W T, J P, rp W L W B, F fr, L, L, T L D G W T Ffr J P, D J P1, D1 J L J G, P G J S, P S W B J P3, D 3 N r = = N t θ = N r θ L ω = N r ω L C G = π D G = θ = P S X L ω = P S V L D P C P1 = π D P1 = N t P G θ = θ = X L C G ω = V L C G X L C P1 ω = V L C P1 N t P G J Totl = + J P + J PL + J B + J L () J PL = 1 J PL W J B = B D P N r g () J L = 1 J L N r J Totl = + J G + J L J L = F g = (W L + W T ) sinγ F fr = µ (W L + W T ) cosγ F g = (W L + W B ) sinγ T L N r D J Totl = + J P1 + P1 J P D + P1 J P3 + J D L P D P3 J L = (W L + W B ) g F P + F g + F fr D ( P1 ) F fr = µ (W L + W B ) cosγ D ( P1 ) J Totl = + J C + J S + J L (W J L = L + W T ) 1 g ( π P S ) F g = (W L + W T ) sinγ F fr = µ (W L + W T ) cosγ (W L + W T ) g F P + F g + F fr F P + F g + F fr π P S D G D ( G ) + T P Pully inrtis Inrti is proportionl to r 4! Blt/chin inrti Bcklsh Pinion inrti Bring friction Countrlnc vrticl lods if possil Brk on vrticl lods Linr ring spd liit Pully inrtis Blt/chin inrti Countrlnc vrticl lods if possil Brk on vrticl lods Linr ring spd liit Scrw inrti Coupling inrti Nut prlod Bring friction Ldscrw whip. ll spd. ring spd Typicl Friction Cofficints (F fr = µw L cosγ) tril Dnsitis chnis Efficincis trils µ chnis µ tril g/c 3 l/in 3 Acscrw w/rss nut ~ Stl on Stl ~0.58 Bll Bushings <.001 Aluinu ~.66 ~0.096 Acscrw w/plstic nut ~ Stl. On Stl. (grsd) ~0.15 Linr Brings <.001 Brss ~8.30 ~0.300 Bllscrw ~ Aluinu on Stl ~0.45 DovTil Slids ~0.++ Bronz ~8.17 ~0.95 Prlodd BllScrw ~ Coppr on Stl ~0.30 Gi Wys ~0.5++ Coppr ~8.91 ~0.3 Spur or Bvl Grs ~0.90 Brss on Stl ~0.35 Plstic ~1.11 ~0.040 Tiing Blts ~ Plstic on Stl ~ Stl ~7.75 ~0.80 Chin & Sprockt ~ Hrd Wood ~0.80 ~0.09 Wor Grs ~ PAGE 4
5 Srt otion "Cht" Sht 8.5 Fundntl uscl Slction Rltionships AutotionSolutions Th fundntl rltionship tht ust t for succssful srt otion ppliction is tht th Torqu Avill (t ll spds) fro th srt uscl (otordriv syst) ust Grtr Thn th Torqu Rquird y th ppliction. T Avill > T Rquird (t ll spds) Thus, th procdur to follow is to first dtrin th totl torqu rquird (oth Pk nd Continuous or RS), thn copr it to th torqu vill fro th otordriv systs ing considrd. For vill torqu, us th otordriv torqu vs. spd prfornc curvs whnvr possil!! 1) T Pk (Rquird) = T TOTAL = T + T c : Totl Rquird Torqu (N or inl) = Acclrtion Torqu (N or inl) + Constnt Torqus (N or inl). T = J Totl * α : Acclrtion Torqu (N or inl) = Torqu Inrti (kg or inls ) * Acclrtion Rt (rdinssc  ) 1. J Totl = otor inrti plus chnis inrtis rflctd to otor (s foruls on Pg 4). α = ω /t * π : Angulr Acclrtion (rdinssc  ) = (or chng in) Spd/ccl ti (rps/sc) * unit convrsion (π rd/rv). T C = Torqu du to ll othr noninrtil forcs such s grvity, friction, prlods, tool, nd othr pushpull forcs (VERY IPORTANT: Us Consistnt Units!! S unit convrsions on Pg 6) ) T RS (Rquird) = Root n Squrd : (~vrg) torqu ovr ntir cycl (rfr to figurs on pg 3. Not: Wtch your signs... As vctor quntity, T d = T ) T PS T PR T CS T CR T 0 Typicl Torqu vs. Spd for Srvos (Aint Tp = 40 C) Intrittnt Duty Zon Continuous Torqu Lin Continuous Duty Zon 0 R T RS = Intrprttion of Srvo & Stppr Torqu vs. Spd Curvs Pk Torqu Lin (T = T c ) t + T c t c + (T d + T c ) t d + T h t h t + t c + t d + t h Srvos: Th figur t lft rprsnts typicl torqu vs. spd curvs for oth rush nd rushlss lctric srvo systs. Srvos typiclly hv two zons: on in which continuous oprtion is possil; th scond in which oprtion is possil only on n intrittnt sis (fro.05 to 30+ sc., dpnding on th nufcturr). Srvos typiclly hv pk torqu (ithr stll T PS or rtd T PR ) tht is to 3 tis highr thn th continuous torqu (ithr stll T CS or rtd T CR ). ost krs list iu spd ω (usully 3000 to 6000 rp) which would th spd t full voltg nd no lod (T 0 ). So krs list rtd torqus, which r th intrsction of th Pk nd Continuous Torqu curvs with rtd spd ω R (coonly rp). Sinc srvos r closdloop y dfinition, s long s th pk torqu rquird is low th Pk Torqu (vill) Lin nd th rs torqu rquird dos not cd th Continuous Torqu Lin, oprtion up to th Pk Torqu Lin is possil without fr of stlling or fulting. Ky Considrtions whn copring curvs twn vrious nufcturrs with spcific ppliction includ: Alwys try to us th torqu vs. spd curvs! If only tulr dt is vill, clrly undrstnd wht th dt points rprsnt. For pl, is T t 0 spd or t. spd? Etc... Is th curv for th otor nd driv tht you will using? Wht int tprtur is ssud (5 vs. 40 C ks significnt diffrnc in rl prfornc!)? Also, wht voltg is ssud (vill voltg ffcts th top spd)? T H T 0 Typicl Torqu vs. Spd for Stpprs (Aint Tp = 40 C, otor Cs Tp < 100 C) Rlistic Oprting Zon (~050%) Stll Torqu Lin Rlistic Oprting Torqu Lin 0 1 H Stpprs: Stppr otordriv systs r usd vry succssfully in ny offic nd industril utotion pplictions. Proprly pplid thy r typiclly th ost costffctiv solution to Srt otion ppliction. If thir chrctristics r isundrstood nd thy r ispplid, costly pplictions filurs frquntly rsult. Th Stll Torqu Lin t lft rprsnts th typicl idl prfornc curv pulishd y krs of stppr otors nd driv systs. This curv ust intrprtd vry diffrntly thn srvo curvs. Du to th opnloop ntur of stppr systs nd th copl dynic intrctions twn otor, driv, lod, nd otion profil, stppr otor will frquntly stll wll for rching this idl stll torqu lin. And unlss fdck is providd, th control syst will not l to rspond. Also, vn th idl torqu flls off rpidly ov ω 1 (typiclly rp) to only 510% of holding torqu T H t ω H (typiclly <3000 rp). Thus, whn slcting stppr otordriv systs, unlss n ppliction is trly wll dfind nd th lods do not significntly vry, it is rcondd tht th usr us rducd torqu spd curv siilr to th Rlistic Oprting Lin shown t th lft (which is sowht ritrrily dfind s 50% of th Stll Torqu Lin). Th rsulting slctions will uch or roust nd your ppliction will usully uch or succssful. T PS T PR T H T CS T CR T Srvo nd Stppr Coprison Torqu t Spd Epls A. Stppr Oky B. Stppr Qustionl C. Srvo Rquird H, R Stpprs vs. Srvos: If stppr syst will roustly prfor n ppliction, it will gnrlly lowr cost thn coprl srvo. Th prol is dfining vlid, consistnt sis on which to copr th. Th figur t lft illustrts on sis on which to copr th. It is n ovrly of torqu vs. spd curvd. Also shown r th torqu vs., spd rquirnts for 3 diffrnt ppliction pls. Not tht th holding torqu T H for th stppr syst is ovr twic s uch s th rtd torqu T CR of th srvo. Also not tht th iu spd for th stppr ω is grtr thn th rtd spd of th srvo ω R. Study of this figur will show tht slction sd upon zrospd torqu lon (T H vs. T CS or T CR, which is vry coon) will ld to rronous conclusions. Appliction A shows tht stppr would ttr choic for low spd pplictions rquiring firly high continuous nd/or pk torqu. Appliction B illustrts tht vn t odrt spds stppr y not hv th torqu to do th s ppliction tht th srvo shown cn do vn without utilizing th srvo s intrittnt torqu. Appliction C is t highr spd nd rquirs srvo, vn though it rquirs lss thn third of T H nd is t spd lss thn ω H of th stppr. It cn not ovrphsizd tht coprisons of ll systs should don on th sis of rlistic torqu vs. spd infortion, not just holding or rtd torqu dt! PAGE 5
6 Srt otion "Cht" Sht 8.6 L L Rctngulr Block L r h Solid Cylindr ro Hollow Cylindr w ri Ars, Volus, nd Inrtis for Sipl Shps A nd = h w; A sid = L h; V = L h w J  = 1 ( h + w ) J  = 1 ( 4L + w ) (if short) J  = 3 ( L ) (if h & w <<L) A nd = π r ; V = A L r Wr πlρr 4 J  = = = g g J  = ( 3r + L ) 1 J  = r 0 + r ( i ) A nd = π r 0 r i ; V = A L πlρ W = g r 0 + r i = g r 4 0 r 4 i J  = 3r 0 + 3r i + L 1 Coon Enginring Unit Convrsions Prtr Syst Intn s (SI) Units Coon English/Aricn Units N Syol Unit N Unit N Bsic Units ss kg kilogr l pound ss lngth (distnc) L tr ft (or in) foot (or inch) ti t s scond s scond currnt l A Apr A Apr Drivd Units Forc (wight) F (W) N Nwton lf (or oz) pound (or ounc) Torqu T N Nwtontr ftl (or inl) footpound Work (nrgy) W (E) J Joul ftl (or inl) footpound Powr P W Wtt hp (or W) horspowr Voltg, EF V V Volt V Volt Rsistnc R Ω ohs Ω ohs Inrti J kg kilogrtr inls (+othrs) inchpoundscond pln ngl α, β, γ, tc. rd rdin dg or rd dgr or rdin rottion θ rv rvolution rv rvolution vlocity (linr) v s 1 tr pr sc. ins 1 inch pr scond cclrtion s  tr pr sc. ins  inch pr scond vlocity (ngulr) ω rds 1 rd pr scond rds 1 rd pr scond vlocity (rottionl) ω rp rv pr inut rp rv pr inut ccl (ngulr) α rds  rd pr scond rds  rd pr scond Bsic Dfinitions & Forul Dfinition/Forul Syst Intn l (SI) Units English/Aricn Units Forc (ccl) F = * 1 N = 1 kg * 1 s  1 lf = 1 lf/(386 ins  ) * 386 ins  Torqu (ccl) T = J * α 1 N = 1 kg * 1 rds  1 inl = 1 inls * 1 rds  Voltg (EF) V = I * R 1 V = 1 A * 1 Ω 1 V = 1 A * 1 Ω Work (Enrgy) E = F * L 1 J = 1 N * 1 1 inl =.113 N =.113 Ws =.113 J Enrgy (lct.) E = V * l * t 1 J = 1 V * 1 A*1 s 1 J = 1 V * 1 A * 1 s Powr P = F * v 1 W = 1 N * 1 s 1 1 hp = 550 ftls 1 = W or P = T * ω 1 W = 1 N * 1 rds 1 (not: rdins r unitlss vlus) or P = V * I 1 W = 1 V * 1 A 1 W = 1 V * 1 A or P = E * t 1 1 W = 1 J * 1 s 1 1 W = 1 J * 1 s 1 or P = I * R 1 W = 1 A * 1 Ω 1 W = 1 A * 1 Ω otor Constnts Torqu Const. K t = T/I K t = N/A K t = inl/a Voltg Const. K = V/ω K = V/(rd/s) K = V/krp T = 0) K = (V/(rd/s)) = K t (N/A) K (V/krp) = K t (inl/a) Srvo otor Forul Currnt Drw I = T * K 1 t 1 A = 1 N * (N/A) 1 1 A = 1 inl * (inl/a) 1 Voltg Rq d V = IR + K * ω 1 V = AΩ +V/(rd/s)*(rd/s) 1 V = AΩ +V/(krp)*(krp) PAGE 6 Coon Units Syol Dfinition SI A/English L Lngth of solid or c in or ft w width of solid or c in or ft h hight of solid or c in or ft A Ar of shp or c in or ft V Volu of solid 3 or c 3 in 3 or ft 3 W Wight of solid N lf ss of solid kg l = lf / g J ,  Inrti out is ,  kg inl=s (& othrs) r, r 0 outr rdius or c in or ft r i innr rdius or c in or ft g ccl or grvity, s lvl s ins  ρ ss dnsity of tril gc 3 lin 3 / g Gnrl Forul: ss: = Wight / grvity (y dfinition, 1 N = 1 kgs  ) (kg) = W (9.81 N) / g (9.81 s  ) (l) = (lfs /386 in) = W (lf) / g (386 ins  ) (s lvl) Wight: W = Volu * dnsity (t s lvl) W (N) = V (c 3 ) * ρ (gc 3 ) * (.001 kg/g * s  ) W (l) = V (in 3 ) * ρ (lin 3 /g) * (386 ins  ) Wight: W = * grvity (t s lvl) W (N) = (.10 kg) * g (9.81 s  ) W (l) = (l/386 ins  ) * g (386 ins  ) Coon Unit Convrsions Lngth 1 in = in =.54 c = in = 5,400 µ (icrons) 1 µ = * 106 in 1 ft =.3048 ; 1 = in 1 il = 580 ft 1 il = k ss, Wight, Forc 1 l = kg 1 l = N 1 l = 16 oz 1 kg = 9.81 N Grvity Constnt g (s lvl) g = 386 ins  = 3.1 fts  = s  Torqu 1 inl = 16 inoz =.113 N 1 ftl = 1 inl = N 1 ftl =.138 kg 1 inoz = N Inrti 1 lin =.93*104 kg 1 inls = kg 1 ozin = 1.83*105 kg 1 inozs = 7.06*103 kg 1 lft = 4.1*10  kg 1 ftls = kg 1 kgc = 104 kg Rottion 1 rv = 360 dg 1 rv = π rdins 1 rv = 1,600 rcin 1 rv = 1.96*10 6 rcsc Enrgy 1 inl =.113 N =.113 J 1 BTU = 1055 J 1 BTU = 5 cloris Powr 1 hp ~ 746 W = 746 Js 1 1 hp = 550 ftls 1 1 hp ~ 550 ftlrp SI Prfis & ultipls Tr T 10 1 Gig G 10 9 g 10 6 kilo k 10 3 hcto h 10 dk d 10 1 dci d 101 cnti c 10  illi 103 icro µ 106 nno n 109 pico ρ 101 To Convrt Units ultiply y 1 if 1 l = 16 oz, thn 1 = 16 oz/l or 1 =.065 l/oz Epl: 5 l =? oz... 5 l * (16 oz/l) = 80 oz Convrting Inrti Don t confus ss inrti with wight inrti. ss inrti is wight inrti dividd y grvity constnt g... inls (ss inrti) = lin /(386in/s ) Not: rdins r unitlss vlus! Hint: convrt to SI units nd ll will co out corrctly!
Instructions for Section 1
Instructions for Sction 1 Choos th rspons tht is corrct for th qustion. A corrct nswr scors 1, n incorrct nswr scors 0. Mrks will not b dductd for incorrct nswrs. You should ttmpt vry qustion. No mrks
More informationMaxwellian Collisions
Maxwllian Collisions Maxwll ralizd arly on that th particular typ of collision in which th crosssction varis at Q rs 1/g offrs drastic siplifications. Intrstingly, this bhavior is physically corrct for
More informationLecture 11 Waves in Periodic Potentials Today: Questions you should be able to address after today s lecture:
Lctur 11 Wvs in Priodic Potntils Tody: 1. Invrs lttic dfinition in 1D.. rphicl rprsnttion of priodic nd priodic functions using th xis nd invrs lttic vctors. 3. Sris solutions to th priodic potntil Hmiltonin
More informationECE602 Exam 1 April 5, You must show ALL of your work for full credit.
ECE62 Exam April 5, 27 Nam: Solution Scor: / This xam is closdbook. You must show ALL of your work for full crdit. Plas rad th qustions carfully. Plas chck your answrs carfully. Calculators may NOT b
More informationUNIT # 08 (PART  I)
. r. d[h d[h.5 7.5 mol L S d[o d[so UNIT # 8 (PRT  I CHEMICL INETICS EXERCISE # 6. d[ x [ x [ x. r [X[C ' [X [[B r '[ [B [C. r [NO [Cl. d[so d[h.5 5 mol L S d[nh d[nh. 5. 6. r [ [B r [x [y r' [x [y r'
More informationTheoretical Study on the While Drilling Electromagnetic Signal Transmission of Horizontal Well
7 nd ntrntionl Confrnc on Softwr, Multimdi nd Communiction Enginring (SMCE 7) SBN: 97865954585 Thorticl Study on th Whil Drilling Elctromgntic Signl Trnsmission of Horizontl Wll Yhuo FAN,,*, Ziping
More informationUsing the Printable Sticker Function. Using the Edit Screen. Computer. Tablet. ScanNCutCanvas
SnNCutCnvs Using th Printl Stikr Funtion Onokin stikrs n sily rt y using your inkjt printr n th Dirt Cut untion o th SnNCut mhin. For inormtion on si oprtions o th SnNCutCnvs, rr to th Hlp. To viw th
More informationDefinition1: The ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions.
Dirctivity or Dirctiv Gain. 1 Dfinition1: Dirctivity Th ratio of th radiation intnsity in a givn dirction from th antnna to th radiation intnsity avragd ovr all dirctions. Dfinition2: Th avg U is obtaind
More informationExam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.
Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r
More informationperm4 A cnt 0 for for if A i 1 A i cnt cnt 1 cnt i j. j k. k l. i k. j l. i l
h 4D, 4th Rank, Antisytric nsor and th 4D Equivalnt to th Cross Product or Mor Fun with nsors!!! Richard R Shiffan Digital Graphics Assoc 8 Dunkirk Av LA, Ca 95 rrs@isidu his docunt dscribs th four dinsional
More informationGradebook & Midterm & Office Hours
Your commnts So what do w do whn on of th r's is 0 in th quation GmM(1/r1/r)? Do w nd to driv all of ths potntial nrgy formulas? I don't undrstand springs This was th first lctur I actually larnd somthing
More informationEE1000 Project 4 Digital Volt Meter
Ovrviw EE1000 Projt 4 Diitl Volt Mtr In this projt, w mk vi tht n msur volts in th rn o 0 to 4 Volts with on iit o ury. Th input is n nlo volt n th output is sinl 7smnt iit tht tlls us wht tht input s
More information22/ Breakdown of the BornOppenheimer approximation. Selection rules for rotationalvibrational transitions. P, R branches.
Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th BornOppnhimr approximation. Slction ruls for rotationalvibrational transitions. P, R branchs. CHE_P8_M
More informationThe pn junction: 2 Current vs Voltage (IV) characteristics
Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V ptyp Dpltion rgion ntyp Elctron movmnt across th junction: 1. n
More informationThe van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012
Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor
More informationIVE(TY) Department of Engineering E&T2520 Electrical Machines 1 Miscellaneous Exercises
TRANSFORMER Q1 IE(TY) Dpartmnt of Enginring E&T50 Elctrical Machins 1 Miscllanous Exrciss Q Q3 A singl phas, 5 ka, 0/440, 60 Hz transformr gav th following tst rsults. Opn circuit tst (440 sid opn): 0
More informationOn the Hamiltonian of a MultiElectron Atom
On th Hamiltonian of a MultiElctron Atom Austn Gronr Drxl Univrsity Philadlphia, PA Octobr 29, 2010 1 Introduction In this papr, w will xhibit th procss of achiving th Hamiltonian for an lctron gas. Making
More informationDesigning A Concrete Arch Bridge
This is th mous Shwnh ri in Switzrln, sin y Rort Millrt in 1933. It spns 37.4 mtrs (122 t) n ws sin usin th sm rphil mths tht will monstrt in this lsson. To pro with this lsson, lik on th Nxt utton hr
More informationSearch sequence databases 3 10/25/2016
Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an
More informationPush trolley capacities from 1 2 through 10 Ton Geared trolley capacities from 1 2 through 100 Ton
H o i s t n T r o l l y C o m i n t i o n s Push trolly cpcitis from 2 through 0 Ton Gr trolly cpcitis from 2 through 00 Ton CB n CF hn chin hoists cn suspn from ithr PT push trollys or GT gr trollys.
More informationINC 693, 481 Dynamics System and Modelling: Linear Graph Modeling II Dr.Ing. Sudchai Boonto Assistant Professor
INC 69, 48 Dynamics Systm and Modlling: Linar Graph Modling II Dr.Ing. Sudchai Boonto Assistant Profssor Dpartmnt of Control Systm and Instrumntation Enginring King Mongkut s Unnivrsity of Tchnology Thonuri
More informationEngineering 323 Beautiful HW #13 Page 1 of 6 Brown Problem 512
Enginring Bautiful HW #1 Pag 1 of 6 5.1 Two componnts of a minicomputr hav th following joint pdf for thir usful liftims X and Y: = x(1+ x and y othrwis a. What is th probability that th liftim X of th
More informationMEASURING HEAT FLUX FROM A COMPONENT ON A PCB
MEASURING HEAT FLUX FROM A COMPONENT ON A PCB INTRODUCTION Elctronic circuit boards consist of componnts which gnrats substantial amounts of hat during thir opration. A clar knowldg of th lvl of hat dissipation
More informationErrata for Second Edition, First Printing
Errt for Scond Edition, First Printing pg 68, lin 1: z=.67 should b z=.44 pg 71: Eqution (.3) should rd B( R) = θ R 1 x= [1 G( x)] pg 1: Eqution (.63) should rd B( R) = x= R = θ ( x R) p( x) R 1 x= [1
More informationDEVELOPING COMPUTER PROGRAM FOR COMPUTING EIGENPAIRS OF 2 2 MATRICES AND 3 3 UPPER TRIANGULAR MATRICES USING THE SIMPLE ALGORITHM
Fr Est Journl o Mthtil Sins (FJMS) Volu 6 Nur Pgs 8 Pulish Onlin: Sptr This ppr is vill onlin t http://pphjo/journls/jsht Pushp Pulishing Hous DEVELOPING COMPUTER PROGRAM FOR COMPUTING EIGENPAIRS OF MATRICES
More informationDUET WITH DIAMONDS COLOR SHIFTING BRACELET By Leslie Rogalski
Dut with Dimons Brlt DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Lsli Roglski Photo y Anrw Wirth Supruo DUETS TM from BSmith rt olor shifting fft tht mks your work tk on lif of its own s you mov! This
More informationNotes on Finite Automata Department of Computer Science Professor Goldberg Textbooks: Introduction to the Theory of Computation by Michael Sipser
Nots on Finit Automt Dprtmnt of Computr Scinc Profssor Goldrg Txtooks: Introduction to th Thory of Computtion y Michl Sipsr Elmnts of th Thory of Computtion y H. Lwis nd C. Ppdimitriou Ths nots contin
More informationSteadystate tracking & sys. types
Stytt trcking & y. ty Unity fck control: um CL tl lnt r C y  r  o.l. y y r ol ol o.l. m m n n n N N N N N, N,, ut N N, m, ol.. cloloo: y r ol.. trcking rror: r y r tytt trcking: t r ol.. ol.. For
More informationCS 6353 Compiler Construction, Homework #1. 1. Write regular expressions for the following informally described languages:
CS 6353 Compilr Construction, Homwork #1 1. Writ rgular xprssions for th following informally dscribd languags: a. All strings of 0 s and 1 s with th substring 01*1. Answr: (0 1)*01*1(0 1)* b. All strings
More informationMore Foundations. Undirected Graphs. Degree. A Theorem. Graphs, Products, & Relations
Mr Funtins Grphs, Pruts, & Rltins Unirt Grphs An unirt grph is pir f 1. A st f ns 2. A st f gs (whr n g is st f tw ns*) Friy, Sptmr 2, 2011 Ring: Sipsr 0.2 ginning f 0.4; Stughtn 1.1.5 ({,,,,}, {{,}, {,},
More informationPaths. Connectivity. Euler and Hamilton Paths. Planar graphs.
Pths.. Eulr n Hmilton Pths.. Pth D. A pth rom s to t is squn o gs {x 0, x 1 }, {x 1, x 2 },... {x n 1, x n }, whr x 0 = s, n x n = t. D. Th lngth o pth is th numr o gs in it. {, } {, } {, } {, } {, } {,
More information1997 AP Calculus AB: Section I, Part A
997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs for which f () is a ral numbr.. (4 6 ) d= 4 6 6
More informationDesign Guidelines for Quartz Crystal Oscillators. R 1 Motional Resistance L 1 Motional Inductance C 1 Motional Capacitance C 0 Shunt Capacitance
TECHNICAL NTE 30 Dsign Guidlins for Quartz Crystal scillators Introduction A CMS Pirc oscillator circuit is wll known and is widly usd for its xcllnt frquncy stability and th wid rang of frquncis ovr which
More informationA 1 A 2. a) Find the wavelength of the radio waves. Since c = f, then = c/f = (3x10 8 m/s) / (30x10 6 Hz) = 10m.
1. Young s doublslit xprint undrlis th instrunt landing syst at ost airports and is usd to guid aircraft to saf landings whn th visibility is poor. Suppos that a pilot is trying to align hr plan with
More informationMath 8 Winter 2015 Applications of Integration
Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl
More informationCSC Design and Analysis of Algorithms. Example: ChangeMaking Problem
CSC 801 Dsign n Anlysis of Algorithms Ltur 11 Gry Thniqu Exmpl: ChngMking Prolm Givn unlimit mounts of oins of nomintions 1 > > m, giv hng for mount n with th lst numr of oins Exmpl: 1 = 25, 2 =10, =
More informationExam 2 Thursday (7:309pm) It will cover material through HW 7, but no material that was on the 1 st exam.
Exam 2 Thursday (7:309pm) It will covr matrial through HW 7, but no matrial that was on th 1 st xam. What happns if w bash atoms with lctrons? In atomic discharg lamps, lots of lctrons ar givn kintic
More informationWhy the Junction Tree Algorithm? The Junction Tree Algorithm. Clique Potential Representation. Overview. Chris Williams 1.
Why th Juntion Tr lgorithm? Th Juntion Tr lgorithm hris Willims 1 Shool of Informtis, Univrsity of Einurgh Otor 2009 Th JT is gnrlpurpos lgorithm for omputing (onitionl) mrginls on grphs. It os this y
More informationME311 Machine Design
ME311 Machin Dsign Lctur 4: Strss Concntrations; Static Failur W Dornfld 8Sp017 Fairfild Univrsit School of Enginring Strss Concntration W saw that in a curvd bam, th strss was distortd from th uniform
More informationPipe flow friction, small vs. big pipes
Friction actor (t/0 t o pip) Friction small vs larg pips J. Chaurtt May 016 It is an intrsting act that riction is highr in small pips than largr pips or th sam vlocity o low and th sam lngth. Friction
More informationLecture 6 Thermionic Engines
Ltur 6 hrmioni ngins Rviw Rihrdson formul hrmioni ngins Shotty brrir nd diod pn juntion nd diod disussion.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to ltril nrgy Convrsion WARR M. ROHSOW HA AD MASS
More information1 Introduction to Modulo 7 Arithmetic
1 Introution to Moulo 7 Arithmti Bor w try our hn t solvin som hr Moulr KnKns, lt s tk los look t on moulr rithmti, mo 7 rithmti. You ll s in this sminr tht rithmti moulo prim is quit irnt rom th ons w
More informationPROOF OF FIRST STANDARD FORM OF NONELEMENTARY FUNCTIONS
Intrnational Journal Of Advanc Rsarch In Scinc And Enginring http://www.ijars.com IJARSE, Vol. No., Issu No., Fbruary, 013 ISSN3198354(E) PROOF OF FIRST STANDARD FORM OF NONELEMENTARY FUNCTIONS 1 Dharmndra
More information11: Echo formation and spatial encoding
11: Echo formation and spatial ncoding 1. What maks th magntic rsonanc signal spatiall dpndnt? 2. How is th position of an R signal idntifid? Slic slction 3. What is cho formation and how is it achivd?
More informationSEE PAGE 2 FOR BRUSH MOTOR WIRING SEE PAGE 3 FOR MANUFACTURER SPECIFIC BLDC MOTOR WIRING EXAMPLES EZ SERVO EZSV17 WIRING DIAGRAM FOR BLDC MOTOR
0V TO 0V SUPPLY GROUN +0V TO +0V RS85 ONVRTR 9 TO OM PORT ON P TO P OM PORT US 9600 U 8IT, NO PRITY, STOP, NO FLOW TRL. OPTO SNSOR # GROUN +0V TO +0V GROUN RS85 RS85 OPTO SNSOR # PHOTO TRNSISTOR TO OTHR
More informationSection 11.6: Directional Derivatives and the Gradient Vector
Sction.6: Dirctional Drivativs and th Gradint Vctor Practic HW rom Stwart Ttbook not to hand in p. 778 # 4 p. 799 # 45 7 9 9 35 37 odd Th Dirctional Drivativ Rcall that a b Slop o th tangnt lin to th
More informationContinuous Random Variables: Basics
Continuous Rndom Vrils: Bsics Brlin Chn Dprtmnt o Computr Scinc & Inormtion Enginring Ntionl Tiwn Norml Univrsit Rrnc:  D.. Brtss, J. N. Tsitsilis, Introduction to roilit, Sctions 3.3.3 Continuous Rndom
More informationObserver Bias and Reliability By Xunchi Pu
Obsrvr Bias and Rliability By Xunchi Pu Introduction Clarly all masurmnts or obsrvations nd to b mad as accuratly as possibl and invstigators nd to pay carful attntion to chcking th rliability of thir
More informationDifferentiation of Exponential Functions
Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of
More informationChapter 11 Calculation of
Chtr 11 Clcultion of th Flow Fild OUTLINE 111 Nd for Scil Procdur 112 Som Rltd Difficultis 113 A Rmdy : Th stggrd Grid 114 Th Momntum Equtions 115 Th Prssur nd Vlocity Corrctions 116 Th PrssurCorrction
More informationa b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued...
Progrssiv Printing T.M. CPITLS g 4½+ Th sy, fun (n FR!) wy to tch cpitl lttrs. ook : C o  For Kinrgrtn or First Gr (not for prschool).  Tchs tht cpitl lttrs mk th sm souns s th littl lttrs.  Tchs th
More informationCrosssection section of DC motor. How does a DC Motor work? 2 Commutator Bars N X. DC Motors 26.1
DC Motors 26.1 How does DC Motor work? Crosssection section of DC motor Mgnetic field vector, B oft Iron Core (otor) Wire length vector, dl Force vector, df Current, i Permnent Mgnet (ttor) Crosssection
More informationCHAPTER 1. Introductory Concepts Elements of Vector Analysis Newton s Laws Units The basis of Newtonian Mechanics D Alembert s Principle
CHPTER 1 Introductory Concpts Elmnts of Vctor nalysis Nwton s Laws Units Th basis of Nwtonian Mchanics D lmbrt s Principl 1 Scinc of Mchanics: It is concrnd with th motion of matrial bodis. odis hav diffrnt
More informationThe SuperFET: A HighPerformance GaAs VoltageControlled Current Source for Cryogenic Applications
The SuperFT: HighPerormace Gas VoltageCotrolled Curret Source or Cryogeic pplicatios.v.cami, G.Pessia,.Previtali ad P. Ramaioli*. ipartimeto di Fisica dell'uiversita' ad Istituto Nazioale di Fisica Nucleare,
More information15. StressStrain behavior of soils
15. StrssStrain bhavior of soils Sand bhavior Usually shard undr draind conditions (rlativly high prmability mans xcss por prssurs ar not gnratd). Paramtrs govrning sand bhaviour is: Rlativ dnsity Effctiv
More informationIXBT22N300HV IXBH22N300HV
High Voltag, High Gain BIMOSFT TM Monolithic Bipolar MOS Transistor Advanc Tchnical Information IXBTNHV IXBHNHV V CS = V = A V C(sat). TO6HV (IXBT) Symbol Tst Conditions Maximum Ratings V CS = 5 C to
More information5.4 The QuarterWave Transformer
4//9 5_4 Th Qurtr Wv Trnsformr.doc / 5.4 Th QurtrWv Trnsformr Rdg Assignmnt: pp. 7376, 443 By now you v noticd tht qurtrwv lngth of trnsmission l ( λ 4, β π ) pprs oftn microwv ngrg prolms. Anothr
More information2. Laser physics  basics
. Lasr physics  basics Spontanous and stimulatd procsss Einstin A and B cofficints Rat quation analysis Gain saturation What is a lasr? LASER: Light Amplification by Stimulatd Emission of Radiation "light"
More informationPreliminary Fundamentals
1.0 Introduction Prliminary Fundamntals In all of our prvious work, w assumd a vry simpl modl of th lctromagntic torqu T (or powr) that is rquird in th swing quation to obtain th acclrating torqu. This
More information1 Finite Automata and Regular Expressions
1 Fini Auom nd Rgulr Exprion Moivion: Givn prn (rgulr xprion) for ring rching, w migh wn o convr i ino drminiic fini uomon or nondrminiic fini uomon o mk ring rching mor fficin; drminiic uomon only h o
More informationCHAPTER 3 MECHANISTIC COMPARISON OF WATER CONING IN OIL AND GAS WELLS
CHAPTER 3 MECHANISTIC COMPARISON OF WATER CONING IN OIL AND GAS WELLS Wtr coning in gs lls hs n undrstood s phnomnon similr to tht in oil ll. In contrst to oil lls, rltivly f studis hv n rportd on spcts
More informationSimilarity Search. The Binary Branch Distance. Nikolaus Augsten.
Similrity Srh Th Binry Brnh Distn Nikolus Augstn nikolus.ugstn@sg..t Dpt. of Computr Sins Univrsity of Slzurg http://rsrh.unislzurg.t Vrsion Jnury 11, 2017 Wintrsmstr 2016/2017 Augstn (Univ. Slzurg) Similrity
More informationModel neurons!!the membrane equation!
Modl nurons!!th bran quation! Suggstd rading:! Chaptr 5.15.3 in Dayan, P. & Abbott, L., Thortical Nuroscinc, MIT Prss, 2001.! Modl nurons: Th bran quation! Contnts:!!!!!! Ion channls Nnst quation GoldanHodgkinKatz
More informationSeebeck and Peltier Effects
Sbck and Pltir Effcts Introduction Thrmal nrgy is usually a byproduct of othr forms of nrgy such as chmical nrgy, mchanical nrgy, and lctrical nrgy. Th procss in which lctrical nrgy is transformd into
More informationModule 2 Motion Instructions
Moul 2 Motion Instrutions CAUTION: Bor you strt this xprimnt, unrstn tht you r xpt to ollow irtions EXPLICITLY! Tk your tim n r th irtions or h stp n or h prt o th xprimnt. You will rquir to ntr t in prtiulr
More informationAn undirected graph G = (V, E) V a set of vertices E a set of unordered edges (v,w) where v, w in V
Unirt Grphs An unirt grph G = (V, E) V st o vrtis E st o unorr gs (v,w) whr v, w in V USE: to mol symmtri rltionships twn ntitis vrtis v n w r jnt i thr is n g (v,w) [or (w,v)] th g (v,w) is inint upon
More information3 Finite Element Parametric Geometry
3 Finit Elmnt Paramtric Gomtry 3. Introduction Th intgral of a matrix is th matrix containing th intgral of ach and vry on of its original componnts. Practical finit lmnt analysis rquirs intgrating matrics,
More informationTap Changer Type MHZ Specification, Assembly and Materials
Tap Changr Typ MH Spcification, ssmbly and Matrials Dscriptions Gnral Spcifications Rmarks availabl in on, two or thr phas application multi layr typs upon rqust shaft lngth availabl in variabl sizs driving
More informationThe Mathematics of Harmonic Oscillators
Th Mhcs of Hronc Oscllors Spl Hronc Moon In h cs of onnsonl spl hronc oon (SHM nvolvng sprng wh sprng consn n wh no frcon, you rv h quon of oon usng Nwon's scon lw: con wh gvs: 0 Ths s sos wrn usng h
More informationPHA 5127 Answers Homework 2 Fall 2001
PH 5127 nswrs Homwork 2 Fall 2001 OK, bfor you rad th answrs, many of you spnt a lot of tim on this homwork. Plas, nxt tim if you hav qustions plas com talk/ask us. Thr is no nd to suffr (wll a littl suffring
More informationu 3 = u 3 (x 1, x 2, x 3 )
Lctur 23: Curvilinar Coordinats (RHB 8.0 It is oftn convnint to work with variabls othr than th Cartsian coordinats x i ( = x, y, z. For xampl in Lctur 5 w mt sphrical polar and cylindrical polar coordinats.
More informationSection 14.3 Arc Length and Curvature
Section 4.3 Arc Length nd Curvture Clculus on Curves in Spce In this section, we ly the foundtions for describing the movement of n object in spce.. Vector Function Bsics In Clc, formul for rc length in
More informationWaves in cavities such as vehicle compartments, rooms or ducts
7.1 Wavs in cavitis such as vhicl compartmnts, rooms or ducts Sound propagation from sourcs into th fr fild is rlativly simpl. At a rciving position in a distanc to th sourc th sound will arriv dlayd by
More informationA L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!
More informationMotion. Acceleration. Part 2: Constant Acceleration. October Lab Phyiscs. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.
Motion ccelertion Prt : Constnt ccelertion ccelertion ccelertion ccelertion is the rte of chnge of elocity. =  o t = Δ Δt ccelertion = =  o t chnge of elocity elpsed time ccelertion is ector, lthough
More informationExam 1 Solution. CS 542 Advanced Data Structures and Algorithms 2/14/2013
CS Avn Dt Struturs n Algorithms Exm Solution Jon Turnr //. ( points) Suppos you r givn grph G=(V,E) with g wights w() n minimum spnning tr T o G. Now, suppos nw g {u,v} is to G. Dsri (in wors) mtho or
More informationDISParity. Search for New Physics Through Parity Violation In Deep Inelastic Electron Scattering. The Physics Case
DISParity Sarch for Nw Physics Through Parity Violation In Dp Inlastic Elctron Scattring Th Physics Cas R. Arnold for th DISParity Collaboration Exprimnt Plan by Stv Rock will follow 12 Jun 2003 DISParity
More informationSECTION where P (cos θ, sin θ) and Q(cos θ, sin θ) are polynomials in cos θ and sin θ, provided Q is never equal to zero.
SETION 6. 57 6. Evaluation of Dfinit Intgrals Exampl 6.6 W hav usd dfinit intgrals to valuat contour intgrals. It may com as a surpris to larn that contour intgrals and rsidus can b usd to valuat crtain
More informationPhysics 312 First Pledged Problem Set
Physics 31 First Pldgd Problm St 1. Th ground stat of hydrogn is dscribd by th wavfunction whr a is th Bohr radius. (a) Comput th charg dnsity Ã (r) = 1 p ¼ µ 1 a 3 r=a ; ½ (r) = jã (r)j : and plot 4¼r
More informationu( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 218, pp 4448): Determine the equation of the following graph.
nlyzing Dmped Oscilltions Prolem (Medor, exmple 218, pp 4448): Determine the eqution of the following grph. The eqution is ssumed to e of the following form f ( t) = K 1 u( t) + K 2 e!"t sin (#t + $
More informationLinear Algebra Existence of the determinant. Expansion according to a row.
Lir Algbr 2270 1 Existc of th dtrmit. Expsio ccordig to row. W dfi th dtrmit for 1 1 mtrics s dt([]) = (1) It is sy chck tht it stisfis D1)D3). For y othr w dfi th dtrmit s follows. Assumig th dtrmit
More informationSplitplot Experiments and Hierarchical Data
Splitplot Exprimnts nd Hirrchicl Dt Introduction Alx Stlzlni invstigtd th ffcts of fding rgim for bf nimls nd muscl typ on th tndrnss of mt. H ssignd ight nimls to ch of thr trtmnts. Th trtmnts wr th
More informationWhat are those βs anyway? Understanding Design Matrix & Odds ratios
Ral paramtr stimat WILD 750  Wildlif Population Analysis of 6 What ar thos βs anyway? Undrsting Dsign Matrix & Odds ratios Rfrncs Hosmr D.W.. Lmshow. 000. Applid logistic rgrssion. John Wily & ons Inc.
More informationSystem variables. Basic Modeling Concepts. Basic elements single and. Power = effort x flow. Power = F x v. Power = V x i. Power = T x w.
Basic Modling Concpts Basic lmnts singl and multiport t dvics Systm variabls v m F V i Powr F x v T w Powr T x w Powr V x i P Q Powr P x Q Powr ort x low Eort & low ar powr variabls Eorts t... Flows...
More informationCalculus concepts derivatives
All rasonabl fforts hav bn mad to mak sur th nots ar accurat. Th author cannot b hld rsponsibl for any damags arising from th us of ths nots in any fashion. Calculus concpts drivativs Concpts involving
More information5.80 SmallMolecule Spectroscopy and Dynamics
MIT OpnCoursWar http://ocw.mit.du 5.80 SmallMolcul Spctroscopy and Dynamics Fall 008 For information about citing ths matrials or our Trms of Us, visit: http://ocw.mit.du/trms. Lctur # 3 Supplmnt Contnts
More informationSUMMER 17 EXAMINATION
(ISO/IEC  75 Crtifid) SUMMER 7 EXAMINATION Modl wr jct Cod: Important Instructions to aminrs: ) Th answrs should b amind by ky words and not as wordtoword as givn in th modl answr schm. ) Th modl answr
More informationMTH 505: Number Theory Spring 2017
MTH 505: Numer Theory Spring 207 Homework 2 Drew Armstrong The Froenius Coin Prolem. Consider the eqution x ` y c where,, c, x, y re nturl numers. We cn think of $ nd $ s two denomintions of coins nd $c
More information, each of which is a tree, and whose roots r 1. , respectively, are children of r. Data Structures & File Management
nrl tr T is init st o on or mor nos suh tht thr is on sint no r, ll th root o T, n th rminin nos r prtition into n isjoint susts T, T,, T n, h o whih is tr, n whos roots r, r,, r n, rsptivly, r hilrn o
More information1 General boundary conditions in diffusion
Gnral boundary conditions in diffusion Πρόβλημα 4.8 : Δίνεται μονοδιάτατη πλάκα πάχους, που το ένα άκρο της κρατιέται ε θερμοκραία T t και το άλλο ε θερμοκραία T 2 t. Αν η αρχική θερμοκραία της πλάκας
More informationV={A,B,C,D,E} E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)}
Introution Computr Sin & Enginring 423/823 Dsign n Anlysis of Algorithms Ltur 03 Elmntry Grph Algorithms (Chptr 22) Stphn Sott (Apt from Vinohnrn N. Vriym) I Grphs r strt t typs tht r pplil to numrous
More informationIntegration by Parts
Intgration by Parts Intgration by parts is a tchniqu primarily for valuating intgrals whos intgrand is th product of two functions whr substitution dosn t work. For ampl, sin d or d. Th rul is: u ( ) v'(
More informationChapter 6: Polarization and Crystal Optics
Chaptr 6: Polarization and Crystal Optics * P61. Cascadd Wav Rtardrs. Show that two cascadd quartrwav rtardrs with paralll fast axs ar quivalnt to a halfwav rtardr. What is th rsult if th fast axs ar
More informationThus, because if either [G : H] or [H : K] is infinite, then [G : K] is infinite, then [G : K] = [G : H][H : K] for all infinite cases.
Homwork 5 M 373K Solutions Mark Lindbrg and Travis Schdlr 1. Prov that th ring Z/mZ (for m 0) is a fild if and only if m is prim. ( ) Proof by Contrapositiv: Hr, thr ar thr cass for m not prim. m 0: Whn
More informationCOORDINATION OF FAST NUMERICAL RELAYS AND CURRENT TRANSFORMERS OVERDIMENSIONING FACTORS AND INFLUENCING PARAMETERS
COORDINATION OF FAST NUMERICAL RELAYS AND CURRENT TRANSFORMERS OVERDIMENSIONING FACTORS AND INFLUENCING PARAMETERS Stig Holst ABB Automation Products Swdn Bapuji S Palki ABB Utilitis India This papr rports
More informationThis chapter will show you. What you should already know. 1 Write down the value of each of the following. a 5 2
1 Direct vrition 2 Inverse vrition This chpter will show you how to solve prolems where two vriles re connected y reltionship tht vries in direct or inverse proportion Direct proportion Inverse proportion
More informationINTRODUCTION TO AUTOMATIC CONTROLS INDEX LAPLACE TRANSFORMS
adjoint...6 block diagram...4 clod loop ytm... 5, 0 E()...6 (t)...6 rror tady tat tracking...6 tracking...6...6 gloary... 0 impul function...3 input...5 invr Laplac tranform, INTRODUCTION TO AUTOMATIC
More informationUniversity of Washington Department of Chemistry Chemistry 453 Winter Quarter 2010 Homework Assignment 4; Due at 5p.m. on 2/01/10
University of Wshington Deprtment of Chemistry Chemistry 45 Winter Qurter Homework Assignment 4; Due t 5p.m. on // We lerned tht the Hmiltonin for the quntized hrmonic oscilltor is ˆ d κ H. You cn obtin
More informationSP490/SP491. Full Duplex RS485 Transceivers. Now Available in Lead Free Packaging
SP490/SP491 Full uplx RS485 Transcivrs FTURS +5V Only Low Powr icmos rivr/rcivr nal (SP491) RS485 and RS422 rivrs/rcivrs Pin Compatil with LTC490 and SN75179 (SP490) Pin Compatil with LTC491 and SN75180
More information