When current flows through the armature, the magnetic fields create a torque. Torque = T =. K T i a

Transcription

1 D Motor Bic he D pernent-gnet otor i odeled reitor ( ) in erie with n inductnce ( ) nd voltge ource tht depend on the ngulr velocity of the otor oltge generted inide the rture K ω (ω i ngulr velocity) K oltge contnt When current flow through the rture, the gnetic field crete torque orque K i K orque contnt ec N heoreticlly, K K hi torque goe to overcoing friction nd ccelerting the otor (nd ttchent) orque: K I ( ) d θ d d t dt θ he friction coe in two vrietie, one tht defend on ngulr velocity: icou dping friction nd one tht doen't oulob Friction ( N ) hi one i jut contnt he oent of inerti ply the e roll in rottionl yte tht doe in liner yte Moent of inerti of the pinning prt of the otor nd wht it' ttched to kg wht' left fter friction loe orque d dt ω ut like: F M N ec otor terinl rture \ ngulr ccelertion rture reitnce v ( t) i ( t) rture inductnce otor Bck EMF (voltge generted due to pinning) K ω K d / dt θ icou dping friction ( N ec) terinl oulob Friction ( N ) / Moent of inerti kg θ ngle ( ) d dt θ ω ngulr peed ec d θ d d t dt ω ngulr ccelertion ec Procedure & Ue the HP 344 DM to eure the rture reitnce t 5 to different hft poition nd tke the verge: R Ω 787 Ω Note: let ech reding ettle before you record it p EE 35 D Motor Lb

2 Ue the HP LR eter in lb (et to Hz) to eure the rture reitnce t 5 to different hft poition nd tke the verge: L H 3834 H Note if you reove the tet fixture be ure to bind thee pot together: K & K Uing the bucket O' bolt nd the otor rck, couple the ll otor to the big one tht you re chrcterizing nd ecure the both to the rck Ue rubber coupler between the two otor nd don't puh the tightly gint ech other Leve plenty of lop nd ply Hook the power p to the ll otor (red nd blck terinl) Hook up the encoder on the big otor o you cn ee the ngulr velocity on the coputer Hook volteter up to the big otor terinl urn on the power p Mke the ll otor turn the big one nd eure the generted voltge t everl different peed When you red the ngulr velocity on the coputer you y notice tht it bounce between two vlue tht re ignificntly different thi i n rtifct of how the peed i coputed nd I will try to get it chnged In the entie ke entl verge of the two reding nd record tht vlue Meureent 55 ω g 7 ec g lp lope ω g, g lp 5 oltge genertion contnt K lp K 5 ec ec gi Enter your dt into tlb by hnd nd plot it Liner regreion: lp ω gi You cn ue "polyfit (x,y,)" to find the lope nd y-intercept of the bet-fit tright line through your dt nd "polyvl" to plot it on top of your eured dt he function below do the e for e in Mthcd Generted voltge (volt) int 6 4 int intercept ω g, g int 6 Intercept i cloe to zero, it hould be 3 4 We don't hve good wy to eure torque o we'll ue tht the torque contnt i the equl to the genertion contnt, it theoreticlly hould be K K K 5 ω gi ngulr elocity (/ec) N 48 ozf in opre to the pec for thi otor: K p note: ozf oz force p3 EE 35 D Motor Lb K rp K 5 K 5 N ec greeent i perfect

3 & he next tet will conit of free-running the otor t everl different peed When the otor hft i diconnected fro ll lod, ny torque it develop i diipted friction, o thi i good wy to find tht friction urn off the power p nd decouple the ll otor fro the big otor Setup the HP 344 DM to red current nd hook the 5 terinl of the HP E363 power upply through the eter to the big otor Let the otor free-run with vriou input voltge Meureent i 5 53 in 55 9 I 5 fr ω 73 fr 37 ec in i unneeded orque: fri I fri K fr ll thi torque ut be lot to friction N Liner regreion lp lope ω fr, fr lp 76 5 N icou dping lp 76 5 N ec ontnt (oulob) friction int 4 N fri lp ω fri int ω fri ec 4 3 int intercept ω fr, fr int 37 N icou dping only odel If I try to force the friction to ll be vicou dping nd ue eureent ner the center: 8 N 37 ec ω fri ngulr elocity (/ec) Now turn down the voltge to bout 7, then lowly continue turning down the voltge until the otor top turning t thi voltge nd current the otor torque jut blnce the coulob friction Meureent: tll 4 I tll 3 lculted fro : I tll I tll 36 tll I tll tll 364 K opre to the tedy-tte error fro lb 3, criticlly dped curve: gin: k p 66 tll tll deg k p k p p4 EE 35 D Motor Lb ctul tedy-tte error in the lt lb: 5 copre well

4 , the Moent of Inerti o get the Motor' oent of inerti (with coupler) we'll go bck to the very iple otor trnfer function ued in the firt lb: ω( ) K k ( ) K R B R K K lo et up the equipent you did in the firt lb B R K K τ τ B R K K Ue 5 tep input nd tke dt to get curve iilr to wht you did in the firt lb ccurtely eure nd record the tep voltge (the 5), don't jut depend on wht the lider y Move thi dt into Mtlb nd ke plot like the one below You'll need to get the tie contnt of the big curve fro thi plot If you cn do tht fro the coputer creen then you don't need to print the plot Don't include the firt prt of the curve in the tie contnt, ee below ngulr elocity (/ec) % finl vlue < τ > tie () Meureent: τ 5 ec τ ec τ B R K K kg opre to the pec for thi otor: 88 3 ozf in ec 64 5 kg p5 EE 35 D Motor Lb Not too cloe on thi one, I wonder bout thi eureent nd bout the pec You'll get chnce to twek thi vlue lter

5 Full odel of D pernent-gnet otor It' tie to develop the full odel of D pernent-gnet otor, including ll the preter tht we've jut found You don't hve to enter thi in your notebook, jut try to follow long I dded in the contnt in one direction becue in the tep repone the otor i lwy running in only one direction In generl i uch ore coplex to include rture 787 Ω rture reitnce v 5 ( ) 5 i I ( ) 3834 H rture inductnce Bck EMF (voltge generted due to pinning) K θ( ) 76 5 N ec 37 N icou dping fctor oulob Friction Moent of inerti: N ec θ ngle in in θ ngulr peed in in/ec θ ngulr ccelertion in in/ec orque: ( ) θ( ) B ( θ( ) ) K I ( ) K ( ) K θ( ) R θ( ) B ( θ( ) ) K ( ) K θ( ) R θ( ) B ( θ( ) ) R K ( ) K θ( ) θ( ) R 3 θ( ) L θ( ) R θ( ) L L K ( ) K K θ( ) θ( ) R 3 θ( ) L θ( ) R θ( ) L L K K θ( ) K ( ) R 3 L R L K K θ( ) ( ) K L K L θ( ) ( ) L 3 R B R K K L 3 R B R K K K ω( ) ( ) L R B R K K L L R B R K K p6 EE 35 D Motor Lb

6 K L ω( ) ( ) B K K B R K K Find the pole: B R K K 4 B R K K 666 ec 4 B R K K 87 ec K v K v k k B k k k Del with the prt due to oulob friction: k k L k 3 L k 3 k k k k 3 k 3 k 3 k 3 ω( t) k k 3 k k 3 k e t k k 3 k e t p7 EE 35 D Motor Lb

7 Plot nd opre Now, you hve to do the following to plot your theoreticl curve on the e plot your eured dt Enter your preter: 787 Ω henry K 5 ec K K 76 5 N ec 4 N kg lculte the following (nd ke it utotic, o you cn ply with the nuber bove nd ee the effect on the plot): R R B K K ec 4 B R K K 87 ec K v k k k 3 ω( t) k k 3 k k 3 k e t k k 3 k e t You don't hve to dd thi junk to your plot: k k 3 fin fin 33 ec f f 6 dely( t ) fin e t, 5 tc 63 fin dot( t) if( ω( t) < tc, tc, ) t f iple delyed exponentil ngulr elocity (/ec) Your plot hould lo include your eured dt p8 EE 35 D Motor Lb tie ()