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 otor-driv 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 otor-driv 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 (otor-driv) 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 opn-loop 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 ll-digitl 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 5-phs 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-, icro-stp) 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 ovr-hting. Thr r ny diffrnt typs of drivs dsignd to ccoplish this tsk (L/R, uni-polr, i-polr, 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 opn-loop 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 0-50% 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 closd-loop. In th following discussion, w will rfrring to srvos s th ny fors of lctric otors nd plifirs (p) usd s closd-loop 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 srvo-syst. 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: d-tun. 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 opn-loop 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? Worst-cs 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 Flow-Chrt Ecpt otor 4. Clcult Non-Inrtil Forcs Grvity? Friction? Pr-Lods? Push-Pull? 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 non-inrtil forcs, torqus Forcs, torqus du to grvity? Torqus du to othr trnl forcs? Friction? Pr-lods? 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 Doul-chck your ssuptions Rdo your clcultions Tripl-chck 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 - in-s - α ngulr cclrtion rt rd-s - rd-s - g grvity ccl constnt s in-s - J ss ont of inrti for... kg- l-in J B...Blt rflctd to otor or or J C...Coupling g-c oz-in J G...Gr tc. or J L...Lod in-l-s J L...Lod rflctd to otor or...otor in-oz-s 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 (rd-sc -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 (rd-sc -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) (rd-s - ) 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 in-l T,c, or d...during ccl, constnt, or dcl or T CL...Constnt t Lod in-oz 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 in-s -1 ω O initil ngulr/rottionl vlocity rd-s -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 in-l T PS Pk Torqu t Stll (zro spd) or T PR Pk Torqu t Rtd Spd in-oz 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) rd-s -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 Countr-lnc vrticl lods if possil Brk on vrticl lods Linr ring spd liit Pully inrtis Blt/chin inrti Countr-lnc 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 Ac-scrw w/rss nut ~ Stl on Stl ~0.58 Bll Bushings <.001 Aluinu ~.66 ~0.096 Ac-scrw w/plstic nut ~ Stl. On Stl. (grsd) ~0.15 Linr Brings <.001 Brss ~8.30 ~0.300 Bll-scrw ~ Aluinu on Stl ~0.45 Dov-Til Slids ~0.++ Bronz ~8.17 ~0.95 Prlodd Bll-Scrw ~ 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 (otor-driv 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 otor-driv systs ing considrd. For vill torqu, us th otor-driv torqu vs. spd prfornc curvs whnvr possil!! 1) T Pk (Rquird) = T TOTAL = T + T c : Totl Rquird Torqu (N or in-l) = Acclrtion Torqu (N or in-l) + Constnt Torqus (N or in-l). T = J Totl * α : Acclrtion Torqu (N or in-l) = Torqu Inrti (kg- or in-l-s ) * Acclrtion Rt (rdins-sc - ) 1. J Totl = otor inrti plus chnis inrtis rflctd to otor (s foruls on Pg 4). α = ω /t * π : Angulr Acclrtion (rdins-sc - ) = (or chng in) Spd/ccl ti (rps/sc) * unit convrsion (π rd/rv). T C = Torqu du to ll othr non-inrtil forcs such s grvity, friction, prlods, tool, nd othr push-pull 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 closd-loop 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 (~0-50%) Stll Torqu Lin Rlistic Oprting Torqu Lin 0 1 H Stpprs: Stppr otor-driv systs r usd vry succssfully in ny offic nd industril utotion pplictions. Proprly pplid thy r typiclly th ost cost-ffctiv solution to Srt otion ppliction. If thir chrctristics r is-undrstood nd thy r is-pplid, 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 5-10% of holding torqu T H t ω H (typiclly <3000 rp). Thus, whn slcting stppr otor-driv 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 ovr-ly 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 zro-spd 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 ovr-phsizd 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 Nwton-tr ft-l (or in-l) foot-pound Work (nrgy) W (E) J Joul ft-l (or in-l) foot-pound Powr P W Wtt hp (or W) horspowr Voltg, EF V V Volt V Volt Rsistnc R Ω ohs Ω ohs Inrti J kg- kilogr-tr in-l-s (+othrs) inch-pound-scond 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. in-s -1 inch pr scond cclrtion -s - tr pr sc. in-s - inch pr scond vlocity (ngulr) ω rd-s -1 rd pr scond rd-s -1 rd pr scond vlocity (rottionl) ω rp rv pr inut rp rv pr inut ccl (ngulr) α rd-s - rd pr scond rd-s - 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 in-s - ) * 386 in-s - Torqu (ccl) T = J * α 1 N = 1 kg- * 1 rd-s - 1 in-l = 1 in-l-s * 1 rd-s - 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 in-l =.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 ft-l-s -1 = W or P = T * ω 1 W = 1 N * 1 rd-s -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 = in-l/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 (in-l/a) Srvo otor Forul Currnt Drw I = T * K -1 t 1 A = 1 N * (N/A) -1 1 A = 1 in-l * (in-l/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- in-l=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 in-s - ρ ss dnsity of tril g-c -3 l-in -3 / g Gnrl Forul: ss: = Wight / grvity (y dfinition, 1 N = 1 kg--s - ) (kg) = W (9.81 N) / g (9.81 -s - ) (l) = (lf-s /386 in) = W (lf) / g (386 in-s - ) (s lvl) Wight: W = Volu * dnsity (t s lvl) W (N) = V (c 3 ) * ρ (g-c -3 ) * (.001 kg/g * s - ) W (l) = V (in 3 ) * ρ (l-in -3 /g) * (386 in-s - ) Wight: W = * grvity (t s lvl) W (N) = (.10 kg) * g (9.81 -s - ) W (l) = (l/386 in-s - ) * g (386 in-s - ) Coon Unit Convrsions Lngth 1 in = in =.54 c = in = 5,400 µ (icrons) 1 µ = * 10-6 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 in-s - = 3.1 ft-s - = s - Torqu 1 in-l = 16 in-oz =.113 N 1 ft-l = 1 in-l = N 1 ft-l =.138 kg- 1 in-oz = N Inrti 1 l-in =.93*10-4 kg- 1 in-l-s = kg- 1 oz-in = 1.83*10-5 kg- 1 in-oz-s = 7.06*10-3 kg- 1 l-ft = 4.1*10 - kg- 1 ft-l-s = kg- 1 kg-c = 10-4 kg- Rottion 1 rv = 360 dg 1 rv = π rdins 1 rv = 1,600 rc-in 1 rv = 1.96*10 6 rc-sc Enrgy 1 in-l =.113 N =.113 J 1 BTU = 1055 J 1 BTU = 5 cloris Powr 1 hp ~ 746 W = 746 J-s -1 1 hp = 550 ft-l-s -1 1 hp ~ 550 ft-l-rp 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 10-1 cnti c 10 - illi 10-3 icro µ 10-6 nno n 10-9 pico ρ 10-1 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... in-l-s (ss inrti) = l-in /(386in/s ) Not: rdins r unitlss vlus! Hint: convrt to SI units nd ll will co out corrctly!