Particularities of construction and design of permanent magnets synchronous motors for driving electric bicycles 1) SILVIA-MARIA DIGĂ2) NICOLAE DIGĂ3) 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) Universityof 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, ArgeșROMANIA 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 7.0that were run (results are synthesized as a spreadshee t) for two constructive variants (Variant Iand Variant II) characterized by 48 = sIZslots and 54 = sIIZslots respectively, chosen because the existing constructive solution characterized of 51 = real s Zslots is the middle of interval between sIZand sIIZ. It is estimated that the real constructive variant characteristics are between those for the two variants comparatively analyzed. Thus were resulted some specific aspectsof 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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Particularities of Construction and Design of Permanent Magnets
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7/27/2019 Particularities of Construction and Design of Permanent Magnets
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
7/27/2019 Particularities of Construction and Design of Permanent Magnets
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
7/27/2019 Particularities of Construction and Design of Permanent Magnets