particularities of construction and design of permanent magnets
Post on 14-Apr-2018
216 Views
Preview:
TRANSCRIPT
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
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 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
http://slidepdf.com/reader/full/particularities-of-construction-and-design-of-permanent-magnets 2/6
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
7/27/2019 Particularities of Construction and Design of Permanent Magnets
http://slidepdf.com/reader/full/particularities-of-construction-and-design-of-permanent-magnets 3/6
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
7/27/2019 Particularities of Construction and Design of Permanent Magnets
http://slidepdf.com/reader/full/particularities-of-construction-and-design-of-permanent-magnets 4/6
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
http://slidepdf.com/reader/full/particularities-of-construction-and-design-of-permanent-magnets 5/6
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
7/27/2019 Particularities of Construction and Design of Permanent Magnets
http://slidepdf.com/reader/full/particularities-of-construction-and-design-of-permanent-magnets 6/6
[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
top related