Proiect la Finite Element Method Magnetics si Proiectarea Optimala a Masinilor PROIECTAREA MASINII SINCRONE CU MAGNETI PERMANENTI Tema de proiectare

Universitatea “Politehnica”din TimişoaraFacultatea de Electrotehnică şi Electroenergetică

An I Master

Proiect la Finite Element Method Magnetics siProiectarea Optimala a Masinilor

PROIECTAREA MASINII SINCRONE CU MAGNETIPERMANENTI

Coordonator ştiinţific: Student:Conf. Dr. Ing. Lucian Tutelea

Dan-Claudiu Marcu

2009

Tema de proiectare

Să se proiecteze o maşină sincronă cu magneţi permanenţi, având puterea nominală de18.5 kW şi numărul de poli egal cu 4. Proiectarea ei va fi optimizată folosindu-se algoritmul Hooke Jeeves.

Cu ajutorul programului FEMM 4.2 se va realiza modelul maşinii şi cu metoda elementului finit se va face o analiză a modelului maşinii din care se vor evidenţia :

- Pulsaţiile de cuplu la curent zero (cogging torque).

- Cuplul funcţie de poziţie la curentul nominal.

- Pulsaţiile de cuplu în sarcină la curentul nominal.

- Cuplul funcţie de curent la un unghi dat.

- Inducţia.

- Pierderile.

Fisierul de iesire – pmm_ hgout.m – calculeaza parametri ce se folosesc pentru proiectare in FEMM 4.2

% Electrical rated parameters Pn=18.500000; % W - rated power fn=50.000000; % Hz - rated frequency Vfn=220.000000; % V - dc voltage Iq=31.046625; % A - rms value Pcu=346.676473; % W - Rated copper loss

Pfe=239.287245; % W - Rated iron loss Pmec=92.500000; % W - Mechanical loss (given in input file) etan=0.964624; % W - Rated efficiency

% Constructive dimensions sDo=267.000000; % mm - Stator outer diameter sDi=183.000000; % mm - Stator inner diameter sh4=0.500000; % mm - Stator tooth pole tip height- fig.3.1sh3=0.334169; % mm - Stator wedge place height - fig.3.1shOA=18.172003; % mm - overall slot height - fig.3.1shy=23.827997; % mm - Stator yoke width swp=5.474068; % mm - Stator tooth width hag=2.700000; % mm - Air-gap height hpm=5.600000; % mm - PM heightlcpertau=1.677677; % mm - Core stack lengthsh1=16.687834; % mm - Stator coil height sW1=8.886275; % mm - Stator slot width (root)sW2=6.698718; % mm - Stator coil width (top)sMs=5.000000; % mm - Stator slot mouth R1=92.334169; % mm - Radius of tooth head N1=64.000000; % Turns per coil rDo=177.600000; %mm - Rotor outer diameter rDi=125.000000; %mm - Rotor inner diameter

% WeightsWeightIronUsed=124.695066; % kg - Stator core mass WeightStCu=10.496782; % kg - total cooper mass WeightPM=4.223674; % kg - total PM mass WeightRtIron=17.968461; % kg - Rotor mass WeightMot=72.881075; % kg -Motor total mass

% Costscu_c=104.967821 % USD Copper costlam_c=623.475329 % USD Lamination costPM_c=211.183681 % USD PM costrotIron_c=89.842306 % USD PM costpmw_c=364.405377 % USD passive material costi_cost=1393.874515 % USD initial cost

energy_c=1017.695576 % USD energy loss costt_cost=2411.570092 % USD total cost

% -------------------------------------------------------------------------------

%This outputs was produced using the next data asinput:%Data InPn=18.5; % KW - rated powerfn=50; % Hz - base speedVfn=220; % V - phase voltage

%Primary Dimensionpoles=4; % number of polesnphase=3; % number of phaseParallelPaths=1; % parallel current path

%Optimization variable limitationselsp_min=15; %kA/m Minimum Specificate electric load Bagsp_min=0.45; %T Minimum Specificate magneticinductin in air gap sBt_min=1; %T Mimnimum Specificate magnetic inductin in stator ToothsBy_min=0.9; %T Minimum magnetic induction in stator yokerBy_min=0.9; %T Minimum magnetic induction in rotor yokeJs_min=3; %a/mm^2 Minimum stator current densitylcpertau_min=0.5; %mm Minimum value of Core stack lengthq1_min=2; % number of stator slots per pole per phasesMs_min=1; %mm Minimum value of Stator open widthsh4_min=0.5; %mm Minimum value of Stator tooth pole tip height

cSpan_min=0.66; % Coil openalpm_min=0.5; % acoperirea polara magnet permanent

elsp_max=30; %kA/m Maximum Specificate electric load Bagsp_max=0.75; %T Maximum Specificate magnetic inductin in air gapsBt_max=2; %T Maximum Specificate magnetic inductin in stator ToothsBy_max=1.9; %T Maximum magnetic induction in stator yoke rBy_max=2.1; %T Maximum magnetic induction in rotor yoke Js_max=8; %a/mm^2 Maximum stator current densitylcpertau_max=3; %mm Maximum value of Core stack lengthq1_max=4; % number of stator slots per pole per phasesMs_max=5; %mm Maximum value of Stator open widthsh4_max=2; %mm Maximum value of Stator tooth pole tip heightcSpan_max=1; % Coil openalpm_max=1; % acoperirea polara magnet permanent

%Minimum variationdXmin=[0.2 0.01 0.05 0.02 0.02 0.1 0.1 1 0.2 0.1 0.05 0.01];

%Extra constrain%eta_min=0.92; % minimum efficiency n1_pu=1; % tipically speed kn1=0.9; % probability of the typical speed

%Secondary data prescriptinlayers=2;%layers=1;

%Technological dimensionsetaSpec=0.8; %RandamentulcosPhiSpec=0.95; %Factorul de puterehag_min=0.5;

sAlpha=22.5;% degrees - wedge angleslotInsulThick = 0.15; % Thickness of slot insulationslotClosureThick = 0.5; % Thickness of slot closure (wedge)lf1=8; % mm - right part of overhang coilssSlotFill=0.4; % slot filling factorsf=0.97; % - stacking factornce=1; % number of elementary conductorsdlpm=2; %mm PM over-lengthKso=1;kl=1.8; % over load factor

%Geometric minimum dimensionsrDo_min=8; % mmrDi_min=8; % mm - Minimum shaft diametersTeethAlpha_min=0;sh3_min=0; % mmshOA_min=4; % mmsh1_min=4; % mm - Minimum stator coil height sW3_min=2; % mm%sSlotWindingArea_min=10;

dk66_65; % Magnetic material data for statorVAC677; % Permanent magnet

%Objective function coefficientscu_pr=10; %USD/kg copper pricelam_pr=5; %USD/kg lamination pricePM_pr=50; %USD/kg PM pricerotIron_pr=5; %USD/kg - shaft iron priceenergy_pr=0.1; %USD/kWh energy pricepmw_pr=5; %USD/kg passive material pricehpy=1500; %h hour per yearny=10; %years of usekct=1; %over temperature penalty cost coefficient

% Other specificationTw1=105; % deg. C - stator winding temperatureTpm=100; % deg. C - rotor PM temperature

Tw_max=155; %deg.C - maximum winding temperatureTamb=50; %deg.C - temperature of cooling fluidalpha_t=14.2; %W/m^2*deg. thermal transmission coefficientkff=3; %increasing factor of cooling surfacekpfe=1.45; % iron losses factor (the iron loss are larger due field non-uniformity)Pmec=5*Pn; %assumed mechanical losses in WPem_n=1000*Pn+Pmec; % W - rated electromechanically powerrun_mode='o'; % Run mode: 'o' - optimization, 'e' - performances evaluationoutput_file='pmm1_hgout.m'; % Name of the output filet_file='pmm_hg.txt'; % Name of the table output filetrace_file='pmm_hg1'; % Name of the trace file for optimization

Algoritmul de calcul al coordonatelor punctelor necesare desenarii MASINII SINCRONE in FEM

Date de intrare:

Toate aceste date se iau din fisierul Output File (pmm_hgout.m), dupa ce inainte au fostintroduse datele personale in fisierul Input File (pmm1.m) si salvate, iar apoi s-a apasatbutonul Calculate. (mai putin cele la care se specifica clarde unde se iau)

Iq=31.046625; % A - rms value

sDo=267.000000; % mm - Stator outer diameter

sDi=183.000000; % mm - Stator inner diameter

sh4=0.500000; % mm - Stator tooth pole tip height- fig.3.1

sh3=0.334169; % mm - Stator wedge place height - fig.3.1

shOA=18.172003; % mm - overall slot height - fig.3.1

hpm=5.600000; % mm - PM height

sW1=8.886275; % mm - Stator slot width (root)

sW2=6.698718; % mm - Stator coil width (top)

sMs=5.000000; % mm - Stator slot mouth

N1=64.000000; % Turns per coil

rDo=177.600000; %mm - Rotor outer diameter

rDi=125.000000; %mm - Rotor inner diameter

q1=4 - Se ia din Fig. 13 ''Slot per pol per phase'' valorea ultimului pas (de pe axa y).

m1=3 - Este numarul de faze.

p=2 - Este numarul de perechi de poli (numarul de poli este 2p)

kpm=0.75 - Se ia din Fig. 12 ''PM width to pole pitch" valorea ultimului pas (de pe axa y - este cea cu punct rosu).

j=5.22 Se ia din Fig. 11 ''Curent density" valorea ultimuluipas (de pe axa y).

Calcule

Nc=2p*m1*q1 => Nc=48

αs=π/Nc => αs=0.065

αpm=π*kpm/2p => αpm=0.588

Swcu=Iq/j => Swcu=5.947

Dw=(4Swcu/π)1/2 => Dw =2.752

Sb=N1/2p*q1 => Sb =4

I=Iq*21/2 => I=43.77

Calcularea coordonatelor pentru punctele necesare desenarii statorului :

x1=sDi*sin(αs)/2 => x1=5.94

y1=sDi*cos(αs)/2 => y1=91.306

x2=sMs/2 => x2=2.5

y2=[(sDi/2)2 - (sMs/2)2 ]1/2 => y2=91.465

x3=sMs/2 => x3=2.5

y3=[(sDi/2)2 - (sMs/2)2 ]1/2 + sh4 => y3=91.965

x4=sW2/2 => x4=3.34

y4=[(sDi/2)2 - (sMs/2)2 ]1/2 + sh4 + sh3 => y4=92.299

x5=sW1/2 => x5=4.443

y5=sDi/2 + shOA => y5=109.67

x6=0

y6= sDi/2 + shOA => y6=109.67

x7=0

y7=sDo/2 => y7=133.5

x8=sDo*sin(αs)/2 => x8=8.671

y8= sDo*cos(αs)/2 => y8=133.218

Calcularea coordonatelor pentru punctele necesare desenarii rotorului :

x11=(rDo/2-hpm)*sin(αpm) => x11=46.15

y11=(rDo/2-hpm)*cos(αpm) => y11=69.226

x12=rDo/2*sin(αpm) => x12=49.257

y12= rDo/2*cos(αpm) => y12=73.886

x13=-[(rDo/2-hpm)*sin(αpm)] => x13=-46.15

y13=(rDo/2-hpm)*cos(αpm) => y13=69.226

x14= -rDo/2*sin(αpm) => x14=-49.257

y14= rDo/2*cos(αpm) => y14=73.886

x15=rDi/2 => x15=62.5

y15=0

x16=-rDi/2 => x16=-62.5

y16=0

Unghiurile pentru arcurile de cerc :

αs1=180/Nc => αs1=3.75 – intre punctele P8 si P7

αs2= αs1-asin(2*x2/sDi) => αs2=2.185 – intre punctele P1 si P2

αpm1=360*kpm/2p => αpm1=67.5 – intre punctele P11 si P12, respectiv P12 si P14

αpm2=90- αpm1 => αpm2=22.5 – pentru completarea rotorului

αs3=2* αs1 => αs3=7.5 – unghiul de copiere pentru stator

αr=180 – intre punctele P15 si P16

Modelul masinii in FEMM 4.2

Fig. 1 – Modelul masinii sincrone cu magnetipermanenti

Fig. 2 – Reteaua de calcul a masinii (mesh)

Fig. 3 – Campul magnetic al masinii la curentnominal

Fig. 4 – Campul magnetic al masinii nealimentate

Tabelul 1 – masina nealimentata Θ [⁰] M [Nm] IA

[A]ΨA

[Wb]IB

[A] ΨB [Wb] IC

[A] ΨC [Wb]

0 0.001497 0 0.0016

80 0-

0.001973

0 0.000292

2.5 0.008185

0 0.001794

0 -0.00189

0 0.000097

4

5-

0.009298

0 0.001892 0

-0.00179

10

-0.00009

9

7.5 0.001234 0 0.0019

75 0-

0.001684

0-

0.000293

10 0.008345 0 0.0020

40 0-

0.001562

0-

0.000481

15 0.001165 0 0.0021

25 0-

0.001291

0-

0.000830

20-

0.007872

0 0.002136 0

-0.00099

30

-0.00114

7

25 0.007726 0 0.0020

92 0-

0.000659

0-

0.001432

30 0.001399 0 0.0019

71 0-

0.000293

0-

0.001685

35-

0.008891

0 0.001793 0 0.00010

0 0-

0.001889

40 0.006937 0 0.0015

60 0 0.000482 0

-0.00204

2

45 0.000962 0 0.0012

93 0 0.000830 0

-0.00212

2

Tabelul 2 – masina alimentata la curent nominal

Θ [⁰] M [Nm] IA

[A]ΨA

[Wb]IB

[A] ΨB [Wb] IC

[A] ΨC [Wb]

0 0.017721

35.85

0.002256

-17.92

-0.002583

-17.92

-0.000948

2.5 0.020833

35.85

0.002347

-17.92

0.002552

-17.92

-0.001134

5 0.004859

35.85

0.002426

-17.92

-0.002510

-17.92

-0.001313

7.5 0.01085

35.85

0.002493

-17.92

-0.002447

-17.92

-0.001477

10 0.013258

35.85

0.002547

-17.92

-0.002381

-17.92

-0.001632

15 0.004468

35.85

0.002615

-17.92

-0.002219

-17.92

-0.001900

20 -0.0064

35.85

0.002630

-17.9

-0.0020

-17.9

-0.0021

34 2 18 2 20

25-

0.000293

35.85

0.002590

-17.92

-0.001773

-17.92

-0.002304

30-

0.008531

35.85

0.002495

-17.92

-0.001475

-17.92

-0.002447

35-

0.021845

35.85

0.002350

-17.92

-0.001128

-17.92

-0.002553

40-

0.012441

35.85

0.002163

-17.92

-0.000753

-17.92

-0.002601

45-

0.017966

35.85

0.001966

-17.92

-0.000354

-17.92

-0.002589

Fig 5. – B(H)

Fig. 6 - Pierderi