[ ] These are the motor parameters that are needed: Motor voltage constant. J total (lb-in-sec^2)

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Steven Tucker
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1 MEASURING MOOR PARAMEERS Fil: Motor paramtrs hs ar th motor paramtrs that ar ndd: Motor voltag constant (volts-sc/rad Motor torqu constant (lb-in/amp Motor rsistanc R a (ohms Motor inductanc L a (Hnris Motor inrtia m (lb-in-sc^ Load inrtia lctd to th motor armatur shaft load (lb-in-sc^ otal inrtia m + load total (lb-in-sc^ Not that th abov valus ar statd for a singl winding with dc motors, and ar th phas valus for a BLDC motor. Brushlss dc motors (BLDC ar 3 phas synchronous motors usd in a configuration to b tratd as dc drivs. MOOR RESISANCE For th winding rsistanc us an ohmmtr. For a dc motor masur th rsistanc btwn th armatur wirs. If it is a WYE connctd BLDC motor, th rsistanc is th lin-to-lin rsistanc. hus divid th rsistanc (l-l by to gt th phas rsistanc. MOOR VOLAGE CONSAN o masur th of th motor, put th motor shaft in a lath and rotat th shaft at som spd [rpm such as 1000rpm. With a dc motor, us a dc voltmtr to masur th armatur voltag. h is thn th voltag you rad dividd by th spd in rad/sc. Convrt rpm to rad/sc asrv π radians min rad min rv 60sc sc Volts [ v Volts[ v or spd [ rad / sc spd rpm [ With a BLDC motor us an ac voltmtr to masur th voltag btwn any wirs of th 3 motor wirs and thn convrt th lin-to-lin voltag to th phas voltag valu by dividing th lin-to-lin voltag by ( phas ( lin to lin 1.73 MOOR ORQUE CONSAN (for a BLDC MOOR h motor torqu constant ( can b computd from th voltag constant ( as- 1

and ar th phas valus for a BLDC motor. Brushlss dc motors (BLDC ar 3 phas synchronous motors usd in a configuration to b tratd as dc drivs. MOOR RESISANCE For th winding rsistanc us an ohmmtr.

2 lb in volts ( l amp rpm l h drivation for th abov quation is- Equat Elctrical Powr to Mchanical Powr convrtd to Watts π 3 E I N whr: lb-in I Amps E Volts rms(lin-to-lin N rpm Rarranging trms and simplifying: E N I E Voltsrms Whr : Back mf cons tant, N rpm lb in orqu cons tan t, I A ( l l Convrting rpm to rad/sc- v rv 60 sc v 60 v( l l 9.55 rv min rad rad π π min sc sc hus [ v sc/ rad lb in v( l l 15.3 amp rad sc

1.356 60 1 whr: lb-in I Amps E Volts rms(lin-to-lin N rpm Rarranging trms and simplifying: E 0.

3 MOOR ORQUE CONSAN t (for a DC MOOR E I π N E I N E N I hor : lb in amp V RPM MOOR INERIA m Motor rotor inrtia can b masurd by making an primnt. h inrtia can b calculatd from th quation- rad Acclrati on torqu[ lb in Inrtia[ lb in sc^ acclration sc^ Also (rarranging trms accl torqu Inrtia [ lb in sc^ acclration DC MOORS o do this tst it is ncssary to masur th acclration of th motor rotor and th acclration torqu of th motor rotor. hs two paramtrs ar dscribd as follows: ACCELERAION his paramtr is dtrmind by putting a stp in currnt into th motor winding to bring th motor up to ratd spd. h motor will acclrat ponntially. h acclration is a masur of th rat of chang of vlocity ovr a priod of tim. o mak this tst, a dc tachomtr should b connctd to th motor shaft. h output of th tachomtr should b connctd to a stripchart rcordr. Whn a stp input in currnt is applid to th motor winding, th chart rcordr will plot th rat of chang of th motor shaft vlocity as a function of th tachomtr output voltag. h tachomtr calibration can b usd to convrt volts to rpm. h acclration is thor th chang in vlocity for th linar part of th ponntial curv dividd by th tim lapsd for th dtctd rat of chang in vlocity. h rsulting calculation of th acclration must hav th dimnsions changd to b in units of rad/sc^. ORQUE- An ammtr must b insrtd in sris with th motor input winding. Whn th stp in input currnt is applid to th motor input, th maimum valu of currnt 3

ncssary to masur th acclration of th motor rotor and th acclration torqu of th motor rotor.

4 should b notd. his currnt must b convrtd to torqu. h torqu is qual to th maimum valu of currnt obsrvd multiplid by th motor torqu constant. orqu [lbin amps[a [lb-in/a. h inrtia is thn th acclration torqu dividd by th acclration as statd abov. BLDC MOORS- h tsts dscribd thus far must b modifid for a bldc motor. A bldc motor must b tstd with its srvo amplifir. h stp input will b a stp in dc voltag to th srvo amplifir input. h voltag stp should b larg nough to caus th motor to rach ratd spd. With bldc motors it is not possibl to masur th high frquncy phas currnt in a WYE connctd motor. hus som othr procdur must b usd to masur th currnt or torqu and vlocity. Commrcial bldc srvo amplifirs hav two dc output tst points. On output is a dc voltag proportional to vlocity with a givn calibration. h voltag can b dirctly connctd to a strip chart as dscribd prviously to masur th motor acclration, A scond tst output provids a dc voltag proportional to torqu or a prcntag of ratd torqu. his calibratd voltag can also b rcordd with a stripchart rcordr to obsrv its maimum valu for a stp voltag input to th srvo amplifir. h inrtia can thus b calculatd as don prviously. MOOR INDUCANCE L o masur th motor inductanc us a low voltag ac sourc to th motor winding. For a dc motor, apply th ac voltag to th armatur winding. For a BLDC motor apply th ac voltag to on pair of th thr wirs. In both cass masur th voltag and th currnt. Rmmbr that th BLDC motor is usually connctd in WYE. hus th radings will b lin-to-lin. You want th phas valus for th voltag, so divid th voltag by. h impdanc of th BLDC motor phas winding is thn- [ volts [ amps phas voltag Im pdanc [ ohms lin currnt h impdanc racc tan c + rsis tan c [ ohms Rac tan c [ var s impdanc rsis tan c Solv for th ractanc from this quation. Not that th phas rsistanc was masurd prviously. h inductanc can than b calculatd from- h rac tan c [var s π frquncy induc tan c h frquncy is probably going to b from th ac sourc at 60 Hz. hus- rac tan c Induc tan c[ hnris π frquncy [ var s [ hz

h stp input will b a stp in dc voltag to th srvo amplifir input. h voltag stp should b larg nough to caus th motor to rach ratd spd.

5 MERIC CONVERSIONS If mtric valus ar usd, units convrsions ar includd h quation to calculat inrtia for round objcts (such as th motor shaft is- SHAFS,PULLEYS,GEARS D[in LGH[in [lb-in-s DDiamtr MERIC D[cm LGH[cm [g-m h quation to calculat th inrtia of round hollow shafts is- HOLLOW SHAF-GEAR OR PULLEY [D 1 D LGH [in [lb-in-sc D [in MERIC [D 1 D LGH [cm [G-M D [cm MECHANICAL IME CONSAN tm With th motor constants known, you can thn calculat th mchanical tim constant- t m RL L ( L L * 1.73 [ sc Rl l * 0.86 total ( L L at motor * 5

077 10-6 [g-m h quation to calculat th inrtia of round hollow shafts is- HOLLOW SHAF-GEAR OR PULLEY [D 1 D LGH [in 7.

6 Not that w us th phas valus instad of lin-to-lin valus. Us half th rsistanc lin-to-lin and add som rsistanc for th wiring from th amplifir to th motor. Usually a factor of 1.35 tims th phas valu of th rsistanc is a good approimation. h quation to calculat th lctd inrtia of a lad scrw is- MERIC LEAD SCREW 3 D[ cm L[ cm [ g / cm [ g M N D[cm L[ cm N [ g M 3 D[in L[in 0.8[lb/in [ lb in sc N 16 6 in D[in L[in N -5 [Lb - in - sc h quation to calculat th lctd inrtia of a rack driv is- RAC DRIVE 6

35 tims th phas valu of th rsistanc is a good approimation.

7 Llad in/rv [ lbs W sc 386 L[in [rv [rv [π rad lb - in - sc 386(π lb in sc (π in W[lb L [lb - in - s π W[lbs L [lb-in-sc MERIC W[g L mm rv rv π rad cm 10mm g cm (0π Wt[g cm L (0π M (100cm [ g M W[g mm L rv mm 6 W[g L rv [g - M 7

00006569 [lb-in-sc MERIC W[g L mm rv rv π rad cm 10mm g cm (0π Wt[g

by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia

by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia Studnt Nots Cost Volum Profit Analysis by John Donald, Lcturr, School of Accounting, Economics and Financ, Dakin Univrsity, Australia As mntiond in th last st of Studnt Nots, th ability to catgoris costs