particularities of construction and design of permanent magnets

6
Particularities of construction and design of permanent magnets synchronous motors for driving electric bicycles 1) SILVIA-MARIA DIGĂ 2) NICOLAE DIGĂ 3) CONSTANTIN STOICA 1) Department of Electrical, Energetic and Aerospace Engineering 2) Doctoral School of Electrical Engineering 3) Department of Electronics, Computers and Electrical Engineering 1) University of Craiova 2) POLYTECHNIC University of Bucharest 3) University of Pitești 1) 107, Decebal Boulevard, Craiova, 200440 2) 313, Splaiul Independenţei, 060042 Bucharest 3) 1, Str. Târgul din Vale, 110040 Pite ști, Argeș ROMANIA  sdiga2002@yahoo .fr nicolae.diga@yahoo .ro costelstoica67@yahoo. com  Abstract: - In this paper, the authors present some specific aspects of construction and calculation of permanen t magnets synchronous motors used in electric bicycles driving. Thus was developed a complete calculation algorithm, which was then translated into a computing main program developed in the Mathcad programming environment. The facilities offered by this computing program's own conception, have allowed the developme nt of a comparative analysis of two computation variants of interpolation which can get details about the constructive solution of the motor on which the experiments and numerical modelling were performed. Key-Words: - electric bicycles driving, permanent magnets synchronous motors, design and construction, dedicated programs. 1 Introduction For a type of motor there may be several design methods because the design data from which it starts can be different, imposed by the practical use of that motor, the differences consisting less in relations contained and more in their sequence [10]. Complete methodology for the calculation of permanent magnets synchronous motor for driving a bicycle, was designed by the authors, by sequentially and structured in several stages [5], [7], [8], [11]: I. Calculation of main dimensions II. Stator winding calculation III. Calculation of rotor magnetic circuit (Variant a - Starting cage, Variant b - No starting cage) IV. Magnetic characteristics V. Elements calculation of the equivalent circuit of the magnetic circuit VI. Determination of operation characteristics. Own calculation algorithm of this methodology was implemented in computer programs developed in the programming environment  Mathcad Version 7.0 that were run (results are synthesized as a spreadshee t) for two constructive variants (Variant I  and Variant II ) characterized by 48 = sI  Z slots and 54 = sII  Z slots respectively, chosen because the existing constructive solution characterized of 51 = real s  Z slots is the middle of interval between sI  Z and sII  Z . It is estimated that the real constructive variant characteristics are between those for the two variants comparatively analyzed. Thus were resulted some specific aspects of the design calculation of this type of permanent magnets synchronous motors for driving a bicycle, which are summarized in the following subsections. 2 Description of the machine on which the experiments and numerical modelling were performed Machine on which the experiments and numerical models were performed is represented by a low power motor P 2N =500 W, with 46 magnetic poles and 51 stator slots, which has nominal line voltage U N1 =36 V. This permanent magnets synchronous motor made with technology ”brushless” comes mounted in wheel centre (tire) (20”, 26” or 28”') and is part of the kit Tucano (Spain) with which is equipped the electric bike in the endowment of the University of Pitești where there were also performed all experimen ts. The motor (motor stator and rotor) studied can be seen in Fig. 1. Recent Researches in Electric Power and Energy Systems ISBN: 978-960-474-328-5 75

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Page 1: Particularities of Construction and Design of Permanent Magnets

7/27/2019 Particularities of Construction and Design of Permanent Magnets

http://slidepdf.com/reader/full/particularities-of-construction-and-design-of-permanent-magnets 1/6

Particularities of construction and design of permanent magnets

synchronous motors for driving electric bicycles

1)SILVIA-MARIA DIGĂ

2)NICOLAE DIGĂ

3)CONSTANTIN STOICA

1)Department of Electrical, Energetic and Aerospace Engineering

2)Doctoral School of Electrical

Engineering3)

Department of Electronics, Computers and Electrical Engineering

1)University of Craiova

2)POLYTECHNIC University of Bucharest

3)University of Pitești

1)107, Decebal Boulevard, Craiova, 200440

2)313, Splaiul Independenţei, 060042 Bucharest

3)1, Str. Târgul din Vale, 110040 Pitești, Argeș

ROMANIA

[email protected] [email protected] [email protected]

Abstract: - In this paper, the authors present some specific aspects of construction and calculation of permanent

magnets synchronous motors used in electric bicycles driving. Thus was developed a complete calculation

algorithm, which was then translated into a computing main program developed in the Mathcad programming

environment. The facilities offered by this computing program's own conception, have allowed the

development of a comparative analysis of two computation variants of interpolation which can get details aboutthe constructive solution of the motor on which the experiments and numerical modelling were performed.

Key-Words: - electric bicycles driving, permanent magnets synchronous motors, design and construction,

dedicated programs.

1 IntroductionFor a type of motor there may be several design

methods because the design data from which it startscan be different, imposed by the practical use of that

motor, the differences consisting less in relationscontained and more in their sequence [10].

Complete methodology for the calculation of permanent magnets synchronous motor for driving a

bicycle, was designed by the authors, bysequentially and structured in several stages [5], [7],

[8], [11]:

I. Calculation of main dimensionsII. Stator winding calculation

III. Calculation of rotor magnetic circuit (Variant a -Starting cage, Variant b - No starting cage)

IV. Magnetic characteristicsV. Elements calculation of the equivalent circuit of

the magnetic circuit

VI. Determination of operation characteristics.Own calculation algorithm of this methodology

was implemented in computer programs developedin the programming environment Mathcad Version

7.0 that were run (results are synthesized as a

spreadsheet) for two constructive variants (Variant I

and Variant II ) characterized by 48=sI Z slots and

54=sII Z slots respectively, chosen because the

existing constructive solution characterized of

51=reals Z slots is the middle of interval between

sI Z and sII Z . It is estimated that the real constructive

variant characteristics are between those for the two

variants comparatively analyzed.Thus were resulted some specific aspects of the

design calculation of this type of permanentmagnets synchronous motors for driving a bicycle,which are summarized in the following subsections.

2 Description of the machine on which

the experiments and numerical

modelling were performedMachine on which the experiments and numericalmodels were performed is represented by a low

power motor P2N=500 W, with 46 magnetic polesand 51 stator slots, which has nominal line voltage

UN1=36 V. This permanent magnets synchronousmotor made with technology ”brushless” comesmounted in wheel centre (tire) (20”, 26” or 28”') and

is part of the kit Tucano (Spain) with which is

equipped the electric bike in the endowment of theUniversity of Pitești where there were also

performed all experiments.

The motor (motor stator and rotor) studied can beseen in Fig. 1.

Recent Researches in Electric Power and Energy Systems

ISBN: 978-960-474-328-5 75

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2.1 Defining geometric parameters of the

machineIn Table 1 and Table 2 are provided the principaldimensions of the machine.

Table 1Stator dimensions

Parameter Value

Stator diameter(seen from the centre of

symmetry of the motor )

mm Ds 199=

Shaft diameter mm Dax 40=

Stator core length mm23.529=sl

Number of stator slots 51=reals Z

Slot height mmh realacs 14=

Slot width mmb realacs 5.5=

Isthmus width mmb reala 201 =

Isthmus height mmhistm 5.0=

Average width of thetooth

mmb realamed zs 6=

Table 2Rotor dimensions

Parameter Value

External diameter of the

rotor

(seen from the centre of symmetry of the motor )

mm D exterior r 2,222=

(Internal diameter of therotor)

(seen from the centre of

symmetry of the motor )

mm D erior r 2.204int =

External diameter of the

permanent magnet(seen from the centre of

mm D exterior m 2,204=

symmetry of the motor )

Internal diameter of the

permanent magnet

(seen from the centre of

symmetry of the motor )

mm D erior m 201int =

Rotor core length mmll mr 24==

Number of permanentmagnets 46=m N

Permanent magnetlength

mmlm 24=

Permanent magnet

widthmmbm 13=

Permanent magnetheight

mmhm 5,2=

2.2 Physical properties of materials used for

making the motorThe physical properties of the material used for

making permanent magnets are given in Table 3 andthe magnetization curve of the material used in the

construction of stator electrical sheets is given in

Fig. 2. The rotor core is made of robust steel.

Table 3Magnet parameters

Name magnet R1 sintered

Remanent induction (to

200)

Br-

200C

Br=0,7 T

Coercive magnetic field

strength (to 200)

Hc-

200C

Hc=480000

A/m

Relative permeability(coefficient of return)

rev µ 05,1=rev µ

Maximum magnetic

energy per unit volumeof magnetic material

(BH)max (BH)max=96000

J·m-3

Fig. 1. Permanent magnets synchronous motor

studied

Fig. 2. Magnetization curve of the stator

electric sheets material

Hot rolled electrical steel sheet, low and medium alloyed

(0.5 mm nominal thickness)

0

0.5

1

1.5

2

2.5

3

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

H [ A/cm ]

B [ T

]

Recent Researches in Electric Power and Energy Systems

ISBN: 978-960-474-328-5 76

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2.3 Stator winding of the machineThe parameters characterizing the studied machineare given in Table 4 and its image is given in Fig. 3.

Table 4

Winding parameters

Windingtype

1=d y

slot

Winding in two layers,with short step with

two slots

Phasesnumber1m 31

=m phases

Poles

number

p2 162 = p

poles

182 = p

poles

Slotsnumber per

pole andphase

q 1=q slot

Number of coilings per

coil

bw 17=bw coilings

The fillingfactor of the

slot

uck 75.0=uck

d -axis

synchronous

inductivity

d L

mH3.0656

mH2.7031

=<

<=

II primd

d I primd

L

L L

q-axis

synchronous

inductivity

q L

mH7.9327

mH7.7219

=<

<=

II q

q I q

L

L L

Inductivity

(mean)

2

q primd

s

L L

L

+

=

mH L

LmH L

II s

s I s

4991.5

2125.5

=<

<=

Inductivity

of one phaseσ L L

L

s

f

+

=

mH L

LmH L

II f

f I f

6781.6

1859.6

=<

<=

Statorwinding

phaseresistance

R

Ω=

<<Ω=

0.7427

0.7182

II

I

R

R R

Conductordiameter

over

insulation

primizd mmd primiz 4,1=

3 Specific aspects of design

calculationA first aspect is to identify by calculation the type of

used permanent magnet . For this have been used

two methods: indirect and direct method. The existence of several types of magnetic

materials, with magnetic characteristics verydifferent from one type to another in terms of the

values of the remanent induction ( Br ) and coercivemagnetic field strength ( H c) has a major influence

on the construction of the rotor magnetic circuit at

brushless motors. Thus, the use of one or anothertype of permanent magnets influences not only

quantitatively certain dimensions of the rotor, but

can change structural the rotor, the constructivesolution of its [3], [9].

From the analysis presented in [2] it can be seen

that the two methods of calculating the necessarypermanent magnet are complementary, especially if

are not known the construction details for aparticular motor of this type.

The results obtained by applying the twomethods are comparable; the resulting calculation

error is significantly less in the case of the directmethod. But it must be taken into account in

interpreting these results and the inherent existenceof certain objectives errors of measurement.

Also it was verified that for this type of sintered

R1 permanent magnet, low residual induction

(Br=0,7 T) and high coercive magnetic field strength

(Hc=480 kA/m) to have the desired air gap inductionis needed a constructive solution of the

concentration of produced magnetic flux, and eachof the 46=m N magnets will be large cross-section

2312mmS m = and of small height mmhm 5,2= .

The second aspect to be highlighted is

argumentation of the choice of constructive variant

of rotor magnetic circuit (we chose Variant b -Without starting cage because its presence leads to

magnetic saturation of rotor yoke - the exactcalculation being content of [1]).

The third aspect was represented by

recalculation (adjustment) of the magnetic

characteristics and operating characteristics, as

well as all stages of calculation of designmethodology taking into account continuously of

measured values of the types and sizes parameters

of machine.The fourth aspect relates to the need to draw up a

balance sheet analysis of the electric motor , usingcomplete mathematical model (BEMOS) for the

nominal regime (highlighting the opportunity to

extend this analysis to varying motor load (no load

Fig. 3. Motor winding

Recent Researches in Electric Power and Energy Systems

ISBN: 978-960-474-328-5 77

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regime, a certain load for which will be measured I ,cosφ)).

This type of analysis enables the identification of share of different types of losses on which one canact to decrease of their in order to optimize the

studied motor.

3.1 Determination of operating

characteristicsWere graphically represented using programs

developed in the Mathcad 7.0 programming

environment all motor operating characteristics.

Thus from these graphical representations

showed that the rated power N P2 is obtained at a

certain internal angle

N δ ( W P I N 5002 = ( )0541.60= I N δ ;

W P II N 5.5022 = ( )0784.63= II N δ ).

The nominal efficiency and nominal power

factor are obtained by drawing curves ( )21 P f =η ,

( )22cos P f =ϕ and determining on the curves the

points corresponding to nominal power N P2 or

directly by customizing the expressions in [1] for

the internal angle N δ

( 0.786= I N η 0.811cos = I N ϕ ; 0.7813= II N η

0.819cos = II N ϕ ).

Also still directly by customizing the expressions

of [1], for the internal angle N δ are obtained the

nominal current and nominal torque developed by

the motor

( ( )A7.2624= I fN I ( )mN13.0465 ⋅= I sN M ;

( )A7.2716= II fN I ( )mN14.7485 ⋅= II sN M ).

8.253027

3.69918

I_I δ_grd( )

I_II δ_grd( )

1900 δ_grd

0 25 50 75 100 125 150 175 2002

3

4

5

6

7

8

910

delta [grd]

I_ I [ A ] , I_ I I [ A ]

Fig. 4. Absorbed current variation I f by the

internal angle δ

781.903627

68.3389

P1_I δ_grd( )

P1_II δ_grd( )

1900 δ_grd

0 25 50 75 100 125 150 175 2000

250

500

750

1000

delta (grd)

P 1_

I , P 1_

I I [ W ]

Fig. 5. Variation of the absorbed power P1 by theinternal angle δ

624.296736

11.827107

P2_I δ_grd( )

P2_II δ_grd( )

1900 δ_grd

0 25 50 75 100 125 150 175 2000

200

400

600

800

delta [grd]

P 2_

I , P 2_

I I [ W ]

Fig. 6. Variation of the useful power developed

by motor P2 by internal angle δ

ηI δ_grd( )

ηII δ_grd( )

δ_grd

0 25 50 75 100 125 150 175 2000

0.25

0.5

0.75

1

delta [grd]

e t a I , e t a I I

Fig. 7. Efficiency variation η by the internal angle

δ

0.877235

0.134522

FPI δ_grd( )

FPII δ_grd( )

1900 δ_grd

0 25 50 75 100 125 150 175 2000

0.25

0.5

0.75

1

delta [grd]

c o s f i I , c o s f i I I

Fig. 8. Power factor variation cosφ by the internal

angle δ

17.152683

0.338822

MsI δ_grd( )

MsII δ_grd( )

1900 δ_grd

0 25 50 75 100 125 150 175 2000

2.5

5

7.5

10

12.5

15

17.5

20

delta [grd]

M s I , M s I I [ N m ]

Fig. 9. Variation of the torque developed by the

motor M s by the internal angle δ

Recent Researches in Electric Power and Energy Systems

ISBN: 978-960-474-328-5 78

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3.2 Motor electrical balance drawn up with

complete mathematical model (BEMOS) for

the nominal regime

Table 5

Balance componentsVariant I Variant II

( )0541.60= I N δ

W P I N 52.6091 =

( )0976.60

5.92

=

⇔=

I N

I Js W P

δ

W P I Fe 3538.6=

W P I s 5.3=

W P I vmec 5903.0=+

W P I N 5002 =

( )0784.63= II N δ

W P II N 76.6041 =

( )0415.63

75.88

=

⇔=

II N

II Js W P

δ

W P II Fe 404.6=

W P I s 0238.3=

W P II vmec 4664.0=+

W P II N 5.5022 =

It notes that determined points respect the laws

of variation of different characteristics of the motorbut they are not exactly on the curves represented in

the figures. These points were determined using

Mathcad 7.0 option for determining the coordinates

of a point on the graph [6].

Graphical representations were made of theactive power balance diagrams for the nominal

regime, both in absolute and in percentage valuesfor the two constructive variants (Variant I , Variant

II ) alone [1] and compared to the same system of

coordinate axes (Fig. 10).By analyzing these diagrams of active power

balance can be identified different categories of losses to which it may act to decrease them in order

to optimize the studied motor.

It will extend this comparative electric balancedrawn up with the complete mathematical model

(BEMOS) for different degrees of load (no load

regime, a certain load for which will measure I ,cosφ).

It will be considered in further researches and thesimplified mathematical model (BEMOS-1) which

permits determination of losses and useful power if

known a minimal set of input data, evaluating thecalculation error that occurs when using it to whenusing complete mathematical model BEMOS.

4 ConclusionIt can be concluded that such an approach to the

design calculation of such an electric machine isnecessary to be supplemented necessarily with

modelling and numerical simulation, for witch the

authors used further the customized software Flux9.3 [4], [12].

It was thus found that the magnetic stresses fall

within the maximum allowable limits being evenbelow the values resulted for the two variants of

calculation.

References:

[1] N. Digă, Design and 2D numerical modelling of permanent magnet synchronous motor, for

driving a bicycle, Research Report no. 1, Electrical Engineering Doctoral School,

Polytechnic University of Bucharest, June 20,

2013 (in Romanian).[2] N. Digă, Specific Aspects of Designing A

Permanent Magnet Synchronous Motor for

Driving A Bicycle, International Scientific

Session of Students, Constanta, May 31-June 2,

2013 (in English).

P_I_II_percentages

0

012

3456

7891011

12130

20

40

60

80

100

Fig. 10. Percentage electrical balance of motorpowers [%] to nominal regime, Var. I, Var. II.

0, 1 - II N I N PP 11 , - puterea activă nominală

absorbită de la rețea;

2, 3 - II Js I Js PP , - pierderile Joule nominale în

înf ășurarea statorică;

4, 5- II Fe I Fe PP , - pierderile în fier nominale;

6, 7 - II s I s PP , - pierderile suplimentare

nominale;

8, 9 - II vmec I vmec PP++

, - pierderile mecanice

pfrecare

Fig. 10. Percentage electrical balance of motor

active powers [%] to nominal regime, Var. I,

Var. II.

0, 1 - II N I N PP 11 , - nominal active power

absorbed from the network;

2, 3 - II Js I Js PP , - nominal Joule losses in the

stator winding;

4, 5- II Fe I Fe PP , - nominal iron losses;6, 7 - II s I s PP , - nominal additional losses;

8, 9 - II vmec I vmec PP++

, - nominal mechanical

losses through friction and own ventilation;

10, 11 - II N I N PP 22 , - nominal output power

developed by the motor shaft available;

12, 13 - II I R R , - residue closing balance.

Recent Researches in Electric Power and Energy Systems

ISBN: 978-960-474-328-5 79

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[3] I. F. Soran, Electric drive systems, Matrix RomPublishing House, Bucharest, 2010 (in

Romanian).[4] Cedrat Group Flux 10: User’ guide, June 2009

(in English).

[5] C. Ghiţă, A.-I. Chirilă, I.-D. Deaconu, D.-I.

Ilina, Wind turbine permanent synchronous

generator magnetic field study, Proceedings ICREPQ’07 , no. 247, 2007 (in English).

[6] V. Ivanov, Mathcad and MATLAB

Applications, Universitaria Craiova Publishing

House, Craiova, 2007 (in Romanian).

[7] C. Ghiță, Electromechanical converters. Vol. II. The Synchronous Machine and DC

Machine, ICPE Publishing House, Bucharest,

1999 (in Romanian).[8] I. Cioc, C. Nică, The design of electrical

machines, Didactic and Pedagogical R.A.Publishing House, Bucharest, 1994 (in

Romanian).

[9] R. Măgureanu, N. Vasile, Brushless

synchronous servomotors, Technical

Publishing House, Bucharest, 1990 (inRomanian).

[10] R. Măgureanu, N. Vasile, Permanent magnet

synchronous motors and variable reluctance,

Technical Publishing House, Bucharest, 1982

(in Romanian).[11] D. F. Lăzăroiu, S. Șlaiher, Low power

electrical machines, Technical PublishingHouse, Bucharest, 1973 (in Romanian).

[12] S. M. Digă, C. Stoica, N. Digă and M.

Brojboiu, Considerations on 2D numericalmodelling of permanent magnet synchronous

motors for driving electric bicycles, The Fourth

International Symposium on Electrical and

Electronics Engineering - ISEEE 2013, 11-13

October 2013, Galați, Romania, in press (inEnglish).

Recent Researches in Electric Power and Energy Systems

ISBN: 978-960-474-328-5 80