ns=1500/60 %synchronous speed in rps f=50 p=2*f/ns % no.of poles rating=2.5 %input('enter the kW rating of IM, 2.5kW') %choosing values of magnetic and electrical loadings from the standards %according to the machine specifications required. The machine is designed %to have good performance alongwith lesser cost Bav=.44 %input('value of magnetic loading') ac=21000 %input('value of electric loading') %taking winding factor as 0.955 Kw=0.955; Co=11*0.955*Bav*ac*1e-3 %output cofficient %given efficiency=0.85 and pf(at full load)=0.83 Q=rating/(0.85*0.83) % input kVA rating D2L=Q/(Co*ns) % as Q=Co*D2L*ns % For a cheap design ratio L/t(pole length to pole face length) should be b/w 1.5 to % take L/t=1.5 ...so L/(pi*D/4), %where, D=inner Dia of stator % L=length of pole or core % t=pole face length % L/D=1.18; D=(D2L/1.18)^(1/3) L=1.18*D Li=L*0.9 %stackins factor=0.9 t=L/1.5 %STATOR DESIGN----WINDING %Machine is designed to start with star-delta starter and operate as delta Es=400 %stator voltage per phase phim=Bav*t*L % Flux per pole Ts=floor(Es/(4.44*f*phim*Kw)) %as Es=4.44*f*phim*Kw*Ts, stator turns/phase qs=3 ; %slot/pole/phase Ss=qs*p*3 %stator slots=qs*no. of poles*no. of phases % as there are many slots, thus slot harmonics and tooth pulsation is reduced yss=3.14*D*1e3/Ss % Stator slot pitch = pi*D/(stator slots) %stator slot pitch is allowable as we are using semi-closed slots Zss=floor(6*Ts/Ss) % Total Stator conductors/slot % Now we are using single layer MUSH winding. As single layer thus the no. % of stator coils =1/2(stator slots). % We are not using double layer winding as then the slot area would be % large and as the slot pitch is very small thus mechanical strength of the % stator tooth will be poor Cs=Ss/p % Coil span % as the coil span is odd (9), thus no need of shorting the coil and we % will use it as it is, angle_of_chording=0 Kp=cos(angle_of_chording/2) %pitch factor %slot pitch=180/9=20deg Kd=sin(pi/6)/(3*sin(10*pi/180)) Kws=Kd*Kp % stator winding factor % CONDUCTOR SIZE Is=Q*1e3/(3*Es) %stator current per phase Isl=sqrt(3)*Is % Taking current density as 4 A/mm2 asc=Is/4 % area of stator conductor in mm2 dsc=sqrt(4*asc/pi) % nearest standard diameter= 0.95mm ascn=pi*((0.95)^2)/4 % new area of stator conductor used cds=Is/ascn % current density in stator cond. %using medium covering the Dia of enamelled conductor is 1.041 mm % SLOT DIMENSIONS %taking a space factor of 0.4 As=round(Zss*ascn/0.4) % area of each slot % maximun allowable flux density is 1.7 Wb/mm2, so minimum tooth width to % keep flux density within limits Wtsmin=phim*1e3/(1.7*Cs*Li) %min width in mm %tooth of width 6mm is chosen. lip=1mm, wedge=3mm swts=pi*(D*1e3+2*4)/24-6 % slot width of the portion near to rotor; 2*4 for % wedge and lip for dimetrically opposite slots %slot width top of stator %slot width at bottom= pi*(D+8+2*h)/24-6= 9.1+(pi*h/12) ; h=height of slot % area of conductor portion =.5*(slot width at bottom+slot width at top)*h % equating we get h=11.1 swbs=9.1+(pi*h/12) %slot width at bottom of stator dss=h+4 %depth of slot Lmts=2*L+2.3*t+0.24 % length of mean turn % STATOR TEETH Bst=phim/(Cs*6*1e-3*Li) % flux density in stator teeth % flux density is coming out very small, thus we can increase the magnetic % loading ; taking Bst=0.8 Wb/m2 %STATOR CORE flux_in_stator_core=phim/2 Acs=flux_in_stator_core/0.8 %Area of stator core dcs=round(Acs/Li*1e3) %depth of stator core Bsc=(Acs/Li)/dcs*0.8*1e3 % flux density in core Do=round(D*1e3+2*dss+2*dcs) % outsise dia of stator lamination % ROTOR DESIGN lg=0.2+2*sqrt(L*D) % air gap length % as flux density is very less so we can use large air gap so that overload % capacity of motor increases %taking lg=0.4 Dr=D*1e3-2*0.4 % ROTOR SLOTS %no. of rotor slots=one pole pair less than stator poles Sr=Ss-2 ysr=pi*Dr/Sr % rotor slot pitch at air gap %ROTOR BARS Ib=2*3*Kws*Ts*Is*0.83/Sr %bar current % taking bar current density=6A/mm2 ab=Ib/6 % area of rotor bar % standard size= 7mm*4mm with area=27.1mm2 Wsr=4+0.3 %width of rotor slot dsr=7+1+1+0.15+0.15 % depth of rotor slot swbr=pi*(Dr-2*dsr)/Sr Brt=phim*p/(Sr*Li*(swbr-Wsr)*1e-3) % extending bars 15mm and extra 10mm due to skewing Lb=L*1e3+2*15+10 % length of bar in mm rb=0.021*Lb*1e-3/27.1 % resistance of each bar ohmlossB=Sr*(Ib^2)*rb % total copper losses in bars % END RINGS Ier=Sr*Ib/(pi*4) % end ring current % taking current density in end ring=7 A/mm2 ae=Ier/7 %area % using a ring of 10*7mm de=10 % depth of ring te=7 %thickness of ring % so area of each end ring=70 mm2 Doer=Dr-2*dsr % outer dia of ring Dier=Doer-2*de % inner dia of ring Dme=(Doer+Dier)/2 % mean dia re=0.021*pi*Dme*1e-3/70 ohmlossER=2*(Ier^2)*re % copper loss in end ring ohmlossTR=ohmlossB+ohmlossER %total copper loss in rotor % (rotor copper loss/rotor output)=s/(1-s) s=ohmlossTR/(rating*1e3+ohmlossTR) % full load slip % ROTOR CORE %depth of rotor core is same as stator core dcr=dcs Di=Dr-2*dsr-2*dcr % inner dia of rotor lamination % NO LOAD CURRENT % MAGNETIZING CURRENT % i) AIR GAP Wos=2 % stator slot opening ratios=Wos/0.4 %(slot opening/gap length) % for this value of ratio the carter's coffecient for semi closed slots % is Kcss=0.6 Kgss=yss/(yss-Kcss*Wos) % gap contraction factor for stator slots Wor=1.5 % rotor slot opening ratior=Wor/0.4 % for this value of ratio the carter's coffecient for semi closed slots % is Kcsr=0.5 Kgsr=ysr/(ysr-Kcsr*Wor) % gap contraction factor for rotor slots Kgs=Kgss*Kgsr % gap contraction factor for slots %as there are no ducts so Kgd=1 for them Kg=Kgs*1 % overall gap contraction factor Ag=pi*D*L/4 %area of air gap per pole Bg60=1.36*Bav lge=lg*Kg % effective air gap length ATg=800000*Bg60*lg*1e-3*Kg %Ampere turns required for air gap % ii) STATOR TEETH Ast=(Ss/p)*6*1e-3*Li % tooth width=6mm; are aof stator teeeth /pole Bst60=1.36*Bst % flux density of stator teeth % corresponding to this value of B ampere turns/meter required are ATst=300 mmfst=ATst*dss*1e-3 % iii) STATOR CORE Asc=Li*dcs*1e-3 % area of stator core lcs=pi*(D+2*dss*1e-3+dcs*1e-3)/(3*pi) % length of magnetic path through stator core % corresponding to this value of B ampere turns/meter required are ATsc=200 mmfsc=ATsc*lcs % iv) ROTOR TEETH Wtr13=pi*(Dr-4*dsr/3)/Sr-Wsr % width of rotor teeth at 1/3 height from % narrow end Atr=Sr/4*Wtr13*1e-3*Li Btr60=Brt*1.36*0.85 % width of rotor teeth at 1/3 height(0.85 for 1/3 hgt) % corresponding to this value of B ampere turns/meter required are ATrt=700 mmfrt=ATrt*dsr*1e-3 % v) ROTOR CORE Acr=dcr*Li % rotor core area % corresponding to this value of B(Bsc) ampere turns/meter required are ATrc=200 lcr=pi*Di*1e-3/(3*p) mmfrc=ATrc*lcr AT60=ATg+mmfst+mmfsc+mmfrt+mmfrc % total mmf required Im=0.427*p*AT60/(Kws*Ts) % LOSSES % Iron Loss in stator teeth Vst=Ast*p*dss*1e-3 % volume of stator teeth WTst=Vst*7.6*1e3 % weight of teeth Bmst=pi*Bst/2 % maximum B at stator teeth % for this value of Bmst, specific iron loss=5.5W/kg ironlossST=5.5*WTst % stator teeth % Iron Loss in stator core Vsc=(D+2*dss*1e-3)*pi*L*dcs*1e-3 WTsc=Vsc*7.6*1e3 % corresponding to the flux density=Bsc, specific iron loss=2.8 W/kg ironlossSC=2.8*WTsc % iron loss in stator core ironlossTS=2*(ironlossST+ironlossSC) % normally total loss is taken twice % the calculated value % FRICTION & WINDAGE LOSS % with use of ball bearing FW losses are about 1.5% of output FWloss=1.5*rating*1e3/100 NLloss=ironlossTS+FWloss % total no load losses Inll=NLloss/(3*Es) % loss component of no load current per phase Io=sqrt(Im^2+Inll^2) no_load_current_as_percentage_of_full_load_currrent=Io/Is*100 no_load_pf=Inll/Io phio=(acos(no_load_pf))*180/pi %SHORT CIRCUIT CURRENT %Leakage Reactance %stator slot leakage Pss=4*3.14*(10^-7)*((2*h/(3*(swts+swbs)))+(2*3/(swbs+2))+(1/2)) %specific slot permeance for a tapered slot %(considering h2 also to be occupied by conductors) %rotor slot leakage Psr=(4*3.14*10^-7)*((7/(3*6.8))+(2*1/(6.8+1.5)+(1/1.5))) %4*3.14*10^-7*((h1/3*Ws)+(h2/Ws)+(2*h3/(Ws+W0))+(h4/W0)) %specific slot permeance for a parallel sided slot Psr1=Psr*Kws^2*Ss/(1^2*Sr) %referred to stator side Ps=Pss+Psr1 %total specific slot permeance xs=8*3.14*f*Ts^2*L*(Ps/(p*3)) %q=3 %overhang leakage %coil span / pole pitch =1 so corresponding Ks=1 LoPo=4*3.14*10^-7*1*t^2/(3.14*yss) x0=8*3.14*f*Ts^2*(LoPo/(p*3)) %overhang leakage reactance %Zigzag leakage Xm=Es/Im %magnetizing reactance qr=Sr/(p*3) xz=(5*Xm/(6*3^2))*(1/3^2+1/qr^2) %zigzag leakage reactance per phase %the differential leakage reactance can be ignored in case of squirrel %cage induction motors Xs=xs+x0+xz %total leakage reactance per phase referred to stator %Resistance rs=0.021*Ts*Lmts/ascn ohmlossS=3*Is^2*rs ohmlossTRpp=ohmlossTR/3 rr1=(ohmlossTRpp)/((Is*0.83)^2) Rs=rs+rr1 %total resistance referred to stator %Impedeance Zs=(Xs^2+Rs^2)^0.5 %total impedance of the rotor at standstill Isc=Es/Zs %short circuited current per phase scpf=Rs/Zs %short circuit power factor phase_angle_of_short_circuit_current=(acos(scpf))*180/pi %Losses and efficiency total_loss_at_full_load=ohmlossS+ohmlossTR+ironlossTS+FWloss %total_loss_at_full_load=total_stator_copper_loss+total_rotor_copper_loss+ % total_iron_loss+friction_and_windage_loss input_at_full_load=rating*1e3+total_loss_at_full_load %output_at_full_load+total_loss_at_full_load efficiency_at_full_load=rating*1e3*100/input_at_full_load
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