Scientific Journal of Riga Technical University
Power and Electrical Engineering
2010
_________________________________________________________________________________________________________________________ Volume 27
Analysis of a Permanent - Magnet Brushless DC
Motor with Fixed Dimensions
Uldis Brakanskis, Riga Technical University, Janis Dirba, Riga Technical University,
Ludmila Kukjane, Riga Technical University, Viesturs Drava, Riga Technical University
Abstract. The purpose of this paper is to describe the analysis often considered as a synchronous machine operating in
of a permanent – magnet brushless DC motor with fixed outer specific modes [6] - [7]. In this case the analysis is relatively
diameter and active zone length. The influence of air gap,
simpler and more visual.
material of permanent magnets and their size on the magnetic
flux density of the machine and magnetic flux is analyzed. The
work presents the calculations of two programs, the comparison II. ANALYSIS OF THE OBJECT UNDER INVESTIGATION
of the results and the most suitable combination of factors that This paper considers the calculations of outer – rotor PM
has been found. BLDC motor for the case when the motor parameters
Keywords: brushless DC motors, flux density, magnetic flux, indicated in the Table I are set.
outer – rotor motor, permanent – magnet, synchronous machine. TABLE I
FIXED PARAMETERS OF THE MOTOR UNDER INVESTIGATION
I. INTRODUCTION Number of poles 4
Brushless DC (BLDC) motors are constantly getting wider Outer diameter of the rotor yoke 61 mm
application in adjustable electric drives especially in the cases Inner diameter of the rotor yoke 53 mm
of changing load. Their basic advantages in comparison with
Length of the active zone 100 mm
AC and DC collector motors are longer service life, higher
Rotation frequency in the rated mode 13000 min-1
level of safety and higher dimensioning and power indices [1]
- [2].
Among BLDC motors widely used today the core place is The influence of some factors on the magnetic flux of the
occupied with the motors with permanent magnet excitation. machine and flux density distribution in the parts of magnetic
In their embodiment these motors can have an inner as well as circuit is investigated. In this case the motor is considered
outer rotor [3] – [4]. from the theory of synchronous machines point of view.
Lack of high - quality and relatively cheap magnets resulted The following parameters influencing the value of magnetic
in delay of permanent – magnet brushless DC motors (PM flux density and magnetic field are assumed as those initial
BLDC) utilization during the last years. The situation started variables:
positive changes in 1950s when aluminium - nickel based
permanent magnets were introduced into production with • permanent – magnet angle α;
energy up to 60 kJ/m3. Especially sharp development of the • permanent – magnet residual flux density Br;
electric machines with permanent magnets has been • permanent – magnet relative permeability µr;
considered in 1970s when the production of new materials on • permanent – magnet thickness h;
the basis of samarium cobalt and other rare elements was • air gap length δ.
settled with energy about 360 kJ/m3, residual flux density
higher than 1.2 T and coercive force higher than 900 kA/m. Thus there are 5 initial factors not dependent each on other.
Besides the magnets on the rare elements base in the Preliminary for the reviewing of the investigation range the
construction of brushless DC motors the metal ceramic values of the variables are limited as it is demonstrated in
magnets on the basis of barium and strontium ferrites are Table II.
applied. The main advantage of these magnets is in their TABLE II
simple production and relatively low expenses [5]. LIMITS OF VARIABLES CHANGING
Scientists from many countries investigate the brushless DC Variable factor min. value max. value
motors by means of different approaches: considering them
α, el. deg 108 158
from the DC classic or automatic regulation theory point of
Br, T 0.4 1.2
view, using as a basis main principles of the theory of
machines control, theory of synchronous machines control or µr 1.2 3.6
describing the operation of brushless motor within δ, mm 0.4 0.8
uninterrupted transient process together with semiconductor h, mm 2 3.6
switch with the help of system of differential equations. Each Each of the mentioned factors is assigned with 5 fixed
of these approaches has its advantages and disadvantages, values (Table III).
however during the last time the brushless motors are being
77
Scientific Journal of Riga Technical University
Power and Electrical Engineering
2010
_________________________________________________________________________________________________________________________ Volume 27
TABLE III Table IV represents the results of the calculated magnetic
FIXED VALUES OF THE FACTORS flux density in air gap, maximum magnetic flux density in
1 2 3 4 5 teeth and in the yoke as well as magnetic flux density of the
α, el. deg 158 146 133 121 108 outer rotor yoke under the condition of no - load.
Br, T 0.4 0.6 0.8 1 1.2
µr 1.2 1.8 2.4 3 3.6
δ, mm 0.4 0.5 0.6 0.7 0.8
h, mm 3.6 3.2 2.8 2.4 2
δ
h
According to the methodology of the experiments rational
planning [8] 25 possible experiments are investigated only, α
instead of 55 = 3125. Table IV represents the combinations of
factors and the results of these combinations examining as
well.
Realization of the experiments within a wide range gives an
opportunity to define preliminary results of the calculations.
A virtual training program for designing of the synchronous
machines with permanent magnets is applied for the
acceleration of the experiments examination process, Emetor
[9]. Fig. 1. The geometry of PM BLDC motor [9]
The geometry of one of the virtual experiments is
demonstrated in Fig.1.
TABLE IV
RESULTS OF THE CALCULATION OF THE VARIANTS
α, el.deg Br, T µr δ, mm h, mm B δ, T Ba.t, T Ba.y, T Br.y, T D, mm τ, mm Φ,Wb
1 158 0.4 3 0.6 2.8 0.319 0.85 0.875 1.05 47.8 37.54 0.000762
2 158 0.6 1.2 0.7 2.4 0.587 1.576 1.527 1.947 46.8 36.76 0.001374
3 158 0.8 3.6 0.4 2 0.6 1.682 1.433 2.077 48.2 37.86 0.001446
4 158 1 1.8 0.8 3.2 0.919 2.367 2.784 2.924 45 35.34 0.002068
5 158 1.2 2.4 0.5 3.6 1.201 3.121 3.761 3.855 44.8 35.19 0.00269
6 146 0.4 1.2 0.5 2 0.392 1.032 0.894 1.274 48 37.70 0.000941
7 146 0.6 3.6 0.6 3.6 0.482 1.181 1.459 1.459 44.6 35.03 0.001075
8 146 0.8 1.8 0.7 3.2 0.745 1.835 2.108 2.266 45.2 35.50 0.001684
9 146 1 2.4 0.4 2.4 0.465 0.987 1.875 1.218 47.4 37.23 0.001102
10 146 1.2 3 0.8 2.8 0.824 2.051 2.202 2.533 45.8 35.97 0.001887
11 133 0.4 3.6 0.8 2.4 0.22 0.53 0.523 0.654 46.6 36.60 0.000513
12 133 0.6 1.8 0.5 2.8 0.561 1.355 1.366 1.673 46.4 36.44 0.001302
13 133 0.8 2.4 0.6 3.6 0.712 1.652 2.041 2.041 44.6 35.03 0.001588
14 133 1 3 0.7 2.8 0.699 1.665 1.75 2.056 46 36.13 0.001608
15 133 1.2 1.2 0.4 3.2 1.305 3.123 3.353 3.856 45.8 35.97 0.002988
16 121 0.4 1.8 0.4 3.6 0.397 0.897 1.055 1.107 45 35.34 0.000893
17 121 0.6 2.4 0.8 3.2 0.44 0.98 1.153 1.211 45 35.34 0.00099
18 121 0.8 3 0.5 2.8 0.605 1.405 1.417 1.736 46.4 36.44 0.001404
19 121 1 1.2 0.6 2 0.854 2.029 1.79 2.506 47.8 37.54 0.002041
20 121 1.2 3.6 0.7 2.4 0.673 1.564 1.515 1.932 46.8 36.76 0.001575
21 108 0.4 2.4 0.7 3.2 0.286 0.617 0.709 0.762 45.2 35.50 0.000646
22 108 0.6 3 0.4 2.8 0.454 1.021 1.009 1.261 46.6 36.60 0.001058
23 108 0.8 1.2 0.8 2.4 0.623 1.375 1.359 1.699 46.6 36.60 0.001452
24 108 1 3.6 0.5 3.6 0.726 1.568 1.89 1.937 44.8 35.19 0.001626
25 108 1.2 1.8 0.6 2 0.837 1.911 1.686 2.360 47.8 37.54 0.002
78
Scientific Journal of Riga Technical University
Power and Electrical Engineering
2010
_________________________________________________________________________________________________________________________ Volume 27
The magnetic flux within the air gap is calculated according
to the expression:
2
Φ= ⋅ Bδ τ L ,
π
πD
where τ = - pole division, m; Bδ - magnetic flux
4
density in the air gap, T; D – outer diameter of the yoke, m;
L – length of the active zone of the motor, m.
The restrictions for the selection of factor combination are
accepted like: magnetic flux density in the air gap should not
exceed 1 Т, magnetic flux density in teeth and yoke is B ≤
1.65 Т, in the yoke of outer rotor – В ≤ 2 Т. The painted
spaces in the Table IV are those values of the magnetic flux
density that exceed the limitations indicated above. For the
further testing, choose the most appropriate combination of
factors that corresponds to the 23rd variant, where the
magnetic flux of the first harmonic is Φ = 0.001452Wb.
The repeated test is made for the results improvement
varying the factors within the range values α = 108 (el.deg.),
Br = 0.8 (T), µr = 1.2, δ = 0.8 (mm) and h = 2.4 (mm).
The more appropriate factor combination has been found
after the repeated test: α = 123 (el.deg.), Br = 0.7 (T), µr = 1.1, Fig. 2. Distribution of the magnetic field of brushless DC motor without
saturation under no - load condition
δ = 0.5 (mm) and h = 2.5 (mm). The results of this
combination examined with the help of program Emetor are For calculation of magnetic field taking into account the
given in Table V. saturation of the material the saturation curve of 2411 grade
TABLE V
steel is assigned.
EMETOR RESULT
Table VII represents the results of magnetic field
calculation with material saturation under no - load condition.
B δ, T Ba.t, T Ba.y, T Br.y, T D, mm Φ,Wb
The distribution of the magnetic field of brushless DC motor
0.679 1.605 1.525 1.983 47 0.001596 with saturation is given in Fig.3.
TABLE VII
It should be mentioned that the program under RESULT OBTAINED IN QUICKFIELD TAKING SATURATION INTO ACCOUNT
consideration does not take into account saturation of the
Program B δ, T Φ, Wb
ferromagnetic material in the motor.
For the further examining of the selected variant with QuickField 0.553 0.0013
saturation of the material under no - load condition and with
the load program QuickField is applied. It allows solution of The calculation results with saturation obtained in
plane and axis symmetric tasks with the use of final elements QuickField program differs from that obtained in Emetor for
method. 19%.
First of all the calculation results of both programs Emetor Under the loaded condition calculated magnetic field (Table
and QuickField without saturation of the material under no - VIII), the magnetic flux of the first harmonic is practically
load condition are compared. The results are in Table VI. unchanged. It could be concluded that the influence of
TABLE VI
armature reaction in the present construction is insignificant.
EMETOR RESULT IN COMPARISON WITH QUICKFIELD TABLE VIII
Programs Bδ, T Φ,Wb RESULT OBTAINED IN QUICKFIELD UNDER LOADED CONDITION
Emetor 0.679 0.001596 Program Bδ, T Φ,Wb
QuickField 0.597 0.001403 QuickField 0.554 0.001302
The results indicate that the magnetic flux of the first The distribution of the magnetic field of brushless DC
harmonic, received in QuickField, is 12% less than the value motor under loaded condition is demonstrated in Fig. 4.
received in the Emetor.
The distribution of the magnetic field of brushless DC
motor without saturation is given in Fig.2.
79
Scientific Journal of Riga Technical University
Power and Electrical Engineering
2010
_________________________________________________________________________________________________________________________ Volume 27
0,001400
Ф, 0,001300
Φ=f(α)
Wb
0,001200
0,001100
100 120 140 160 180
α, el.deg
Fig. 5. Changing of magnetic flux according to the permanent magnet angle.
III. CONCLUSION
Program Emetor is convenient for the preliminary
examining and selection of the correspondent variant,
however, it should be taken into consideration that the values
of flux density and the magnetic flux calculated by this
program are considerably overstated.
To obtain more precise results of the analysis it is
Fig. 3. Distribution of the magnetic field of brushless DC motor with
reasonable to apply the programs of magnetic field
saturation under no-load condition. calculations that take into account saturation of magnetic
circuit of the machine, for example QuickField.
During the planning of the calculation with the set outer
rotor diameter, his inner diameter should not be fixed.
REFERENCES
[1] P. Yedamale, “Brushless DC (BLDC) Motor Fundamentals (AN885),”
Microchip Tecnology Inc., 2003. [Online]. Available:
http://www.jimfranklin.info/microchipdatasheets/00885a.pdf.
[Accessed: Sep. 6, 2010].
[2] P. P. Acarley and J. F. Watson, “Review of Position – Sensorless
Operation of Brushless Permanent – Magnet Machines,” IEEE Trans.
Ind. Electron. Vol. 53, № 2, pp. 352 – 362, Apr. 2006.
[3] И. Н. Радимов, В. В. Рымша, Ч.Т.Т. Хыонг и З. П. Процина, “Выбор
геометрии вентильного двигателя с постоянными магнитами,”
Електротехніка і електромеханіка, № 5, c.26-28, 2008.
[4] Xose M. Lopez – Fernandez, J. Gyselinck and R. Silveira – Correa.,
“Finite element analysis of an outer - rotor permanent - magnet brushless
DC motor for light traction,” The International Journal for Computation
and Mathematics in Electronic Engineering, vol. 25, no. 3, pp. 705-712,
2006.
[5] J. Dirba, N. Levins un V. Pugačevs, Vēja enerģijas elektromehāniskie
parveidotaji, Rīga: RTU izdevniecība, 2006.
[6] J. Dirba, Sinhrono mašīnu speciālie režīmi, Rīga: RTU izdevniecība,
1997.
[7] И.Е. Овчинников, Вентильные электрические двигатели и привод
на их основе, СПб.: КОРОНА – Век, 2006..
Fig. 4. Distribution of the magnetic field of brushless DC motor under loaded [8] М. М. Протодьяконов и Р. И. Тедер, Методика рационального
condition. планирования экспериментов, Москва: Издательство «НАУКА»,
1973.
The applied methodology of the magnetic field calculation [9] KTH Royal Institute of Technology, Emetor. [Online]. Available:
http://emetor.org. [Accessed: Sep.7, 2010].
in program QuickField taking into account the saturation of
the material could be used for the analysis of some factors Uldis Brakanskis - lecturer, RTU, mobile phone: +371 25972802, E-mail:
influence on the magnetic flux of the first harmonic, for brakansk@inbox.lv;
example that of the permanent magnet angle. As an example
Janis Dirba – professor, RTU, phone: +371 67089926, E-mail:
Fig. 5 represents magnetic flux changing according to the dirba@eef.rtu.lv;
permanent magnet angle keeping values of other factors
unchangeable. Ludmila Kukjane – Mg. stud., RTU, mobile phone: +371 22425753, E-mail:
ludmilakukjane@inbox.lv;
It is obvious from graph Φ = f(α), that the magnetic flux of
the first harmonic achieves its peak value (Φ = 0.00131 Wb) at Viesturs Drava – Mg. stud., RTU, mobile phone +371 29266556, E-mail:
α = 133 el. deg. drviesturs@inbox.lv.
80
