International Journal of Innovative Research in Advanced Engineering (IJIRAE)
Issue 1, Volume 1 (JANUARY 2012)
ISSN: 2349-2163
www.ijirae.com
PERFORMANCE ANALYSIS OF USING EXTERIOR
ROTOR PERMANENT MAGNET BRUSHLESS DC
(ERPMBLDC) MOTOR
K.Uma devi1, R.Satish kumar2 & Dr.M.Y.Sanavullah3
1
2
Assistant Professor,EEE Department, Sengunthar Engineering College,Tiruchengode,India
Assistant Professor,EEE Department, Sengunthar Engineering College,Tiruchengode,India
3
Professor,EEE Department,V.M.K.V. Engineering College,Salem, India
Abstract — Magnetic flux pattern and magnetization curve of Exterior (Outer) Rotor Permanent Magnet Brushless DC
(ERPMBLDC) Motor are obtained using an advanced numerical method called Finite Element Method. The method is
much suited for dealing with the complicated internal structure of the machine and non linear magnetic characteristics.
Finite Element Magnetic software Version 4.2 (FEMM) is applied to two dimensional structure of the machine. The result
of the computation are plotted to produce flux and torque patterns in the ORPMBLDC domain. The open circuit
characteristics obtained agree with the conventional curve.
Keywords- : Exterior rotor brushless Permanent Magnet DC Motor (ORPMBLDC), Finite Element Method (FEM),
Magnetic Vector Potential and torque.
I .INTRODUCTION
The permanent magnet brushless motor can be classified upon to the back-EMF waveform, where it can be operated in either
brushless AC (BLAC) or brushless DC (BLDC) modes. Usually the BLAC motors have a sinusoidal back-EMF waveform
and BLDC motors have a trapezoidal back-EMF. In modern electrical machines industry productions the brushless direct
current (BLDC) motors are rapidly gaining popularity. Brushless permanent-magnet motors are low cost and simple drive
requirements especially demanded in clean and explosive environments such as aeronautics, robotics, food and chemical
industries, electric vehicles, medical instruments, and computer peripherals. Thus there has been an enormous interest in the
analysis and design of brushless permanent-magnet motors in order to make them more efficient and more robust [1-15].
Analysis and prediction of Exterior Rotor Permanent Magnet Brushless DC (ERPMBLDC) Motor magnetic field
pattern and characteristics are difficult due to irregular geometry and non-linear magnetic materials associated with this
motor .In order to obtain accurately the performance of this machine at its design stage, the magnetic field distribution of the
internal structure and performance characteristics are necessary. Different methods have been deployed over the years to
handle this task. These are the Finite Difference Method (FDM), Boundary Element Method (BEM) and the Finite Element
Method (FEM). However the FEM is increasingly being used by designers due to its ability to handle the complex internal
structure and non-linear materials present in the machine structure.
In practice, magnetic saturation has made the characteristics of these machines to be non-linear as such require
accurate method of modeling and computation. Consequently the machines calculations are based on approximation that
typifies the operating point. Inaccuracies resulting from these approximations make it necessary to employ high precision
analytical tool – the finite element method.
The proposed methodology is to compute the flux pattern in eight poles, Exterior Rotor Permanent Magnet Brushless DC
Motor and obtain magnetization curve and magnetic flux density in the air gap.
A. Statement of Problem: The basic problem of the electromagnetic field computation that resulted in the magnetic field
distribution / mapping in the Outer Rotor Permanent Magnet Brushless DC Motor cross section machine is modeled by the
two dimensional Poisson Equation as follows:
1
1
+
= − − − − − − (1)
+
=−
− − − − − (2)(2)
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© 2012, IJIRAE- All Rights Reserved
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International Journal of Innovative Research in Advanced Engineering (IJIRAE)
Issue 1, Volume 1 (JANUARY 2012)
ISSN: 2349-2163
www.ijirae.com
Where:
µ0 = Permeability of free space
µr= Relative Permeability
µ = Absolute permeability = µ 0 µr
Az = Magnetic vector potential normal to the section of the motor
Jz = current density vector normal to the section
However, vector magnetic potential is of great value when solving two-dimensional problems containing current carrying
areas. This equation is reformulated by variational calculus, in the finite element method, and first-order triangular elements
are used to discretize the field region, resulting in a set of linear algebraic equations. These linear simultaneous equations are
solved using Newton-Raphson technique to obtain the magnetic vector potential.
II.MATHEMATICAL FORMULATION
Finite Element Method is used to solve electromagnetic field problems using variational calculus of Poisson’s type from
basic magnetostatic Maxwell equations. The equations relate magnetic vector potential A, magnetic flux density B and
magnetic field intensity H to obtain the Poisson’s equation.
A.Maxwell’sequation ; Finite Element Method Magnetics (FEMM) 4.2 is a suite of programs used to solve low frequency
electromagnetic problems on two dimensional planar and axi-symmetric domains [1]. An electromagnetic problem generally
needs a lot of calculations for finding out various parameters associated with it. FEMM 4.2 simplifies this problem by
reducing the calculations needed to find out parameters like flux density (B) and field intensity (H) by using Maxwell's
equations.
Maxwell's equations are a set of differential equations used to describe the properties of electric and magnetic fields.
FEMM uses two of these four equations. They are:
Ampere's law
The governing equation of the magnetic field is represented by Maxwell’s equation in the form of a magnetic vector
potential as
∇×
= +
− − − − − (3)
Initially it is assumed no displacement of D=0
∇×
= − − − − − (4)
From Gauss law for magnetism
∇ ∙ = 0 − − − − −(5)
where B is magnetic flux density
The quantities B and H can be related as follows
=
− − − − − (6)
where µ is magnetic permeability
For non-linear materials, the permeability is a function of B:
=
− − − − − (7)
( )
The Magnetic Flux density can also be expressed in terms of magnetic vector potential (A) as
= ∇ × − − − − − (8)
where A is magnetic vector potential
A current in the z direction produces A only, and x and y component of B. A is then related to the flux circulating in the x, y
plane, per unit length in the z direction: it has the units of Webers per meter length. Thus for two-dimensional field, A can be
treated as a scalar quantity. The magnetic flux flowing in a conducting iron core carrying current has its permeability greater
than that of copper conductor of o permeability. Solving for the magnetic vector potential A, the component of the magnetic
flux density are obtained by finding the derivatives and
as shown below
Re write the equation (8)
=
−
− − − − − (9)
With current density Jz only, and hence Az only, and no variation of these quantities in the z direction,
,
− − − − − (10)
Rewrite the equation 4 and Jx and Jy=0 do not exist
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International Journal of Innovative Research in Advanced Engineering (IJIRAE)
Issue 1, Volume 1 (JANUARY 2012)
ISSN: 2349-2163
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Therefore only
=
−
− − − − − (11)
Using equation (6) and substituting equation (10) into the above equation gives,
1
1
+
=−
And so for fixed µ
+
=−
which is Poisson’s Equation. Along these equations FEMM also uses a series of equations related to electric field
distribution, electric field intensity (E) and electric flux density (D) in particular, are used to solve time-harmonic magnetic
problems and electrostatic problems.
III.SHAPE FUNCTION AND DISCRETIZATION
A similar two-dimensional derivation may be made for axisymmetric problems, In either case, the device being
analyzed must be subdivided (Or) discretized into triangles or quadrilaterals called elements. Each element has at least three
vertices called nodes or grid points. The number of nodes corresponding to each element depends on the shape of the element
and also on the type of function used to model the potential within the element. This function is called the shape function and
can be of any order depending on the desired complexity. Usually linear or second-order shape functions .
IV. EXTERIOR ROTOR PERMANENT MAGNET BRUSHLESS DC (ORPMBLDC) MOTOR
Exterior rotor brushless DC motors differ from typical brushless DC motors in that the rotor is situated outside,
instead of inside. The external rotor configuration also has lower total weight and cost. The former also has advantages such
as ease of installation and cooling. Therefore the external rotor construction is more suitable to be applied in wind power
systems. For most of the comparisons, the low speed constructions are superior to the high speed constructions, which mean
that multi-pole PM generators are preferred in the application of small, gearless, low speed.
V. ERPMBLDC MOTOR FIELD COMPUTATION AND SOLUTION
Finite Element Method Magnetics (FEMM) is a software package for solving electromagnetic problems using FEM. The
program addresses 2D planar axisymmetric linear and nonlinear harmonic low frequency magnetic and magneto static
problems and linear electrostatic problems. It is a simple, accurate, and low computational cost open source product, popular
in science, engineering, and education [9].
Finite Element Method Magnetics (FEMM) is a suite of programs for solving low frequency electromagnetic
problem on figure (1) two-dimensional planar and axi-symmetric domain. The procedure for implementing this numerical
computation of magnetic field problems is by using the finite element method which is divided into three main steps:
A. Pre-Processing
In the analysis of the electrical machines, the problems are
almost always nonlinear due to the presence of ferromagnetic materials. Good designs will typically operate at or near the
saturation point. The magnetic permeability or reluctivity is nonhomogenous and will be a function of the local magnetic
fields which are unknown at the start of the problem. The most popular method of dealing with nonlinear problems in
magnetic is the Newton–Raphson method Newton–Raphson procedure is applied to linearize the nonlinear system equations
[3]. The nonlinear magnetic field finite element analysis (FEA) can provide accurate results.[4]. The finite element method
use quicker and easier for the de signer. It offers well-known topologies of rotor, stator, winding, and methods of analysis
[10].
This processor is used for drawing the problems geometry, defining materials and defining boundary conditions. The
derivation of the finite element model of this ERPMBLDC Motor under consideration involves defining conduction
materials, electromagnetic materials and their properties and boundary conditions and eventually resulted in mesh generation.
The ERPMBLDC Motor is made up of two sections, the rotor and stator. The materials properties and boundary conditions
are input into various defined region/section of the computation space. These values are used for computation within the
defined boundary of the region. Mesh generation for the FEM should be simple, robust, and rotor mesh should be allowed to
rotate easily.
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International Journal of Innovative Research in Advanced Engineering (IJIRAE)
Issue 1, Volume 1 (JANUARY 2012)
Rotor angle00(Degree)
PHASE ANGLE
Rotor angle 45(Degree)
TORQUE
Rotor angle - Rotor angle 60(Degree) 87.5(Degree)
PHASE ANGLE
TORQUE
0
0.002135
5.00455
90.08189
-0.011
180.1638
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PHASE ANGLE
TORQUE
PHASE ANGLE
TORQUE
0.000873
10.0091
0.014308
30.0273
-0.0735279
50.0455
-0.00804
95.08644
0.007653
90.08189
-0.0746
0.001999
105.0955
-0.01071
160.1456
-0.00626
145.1319
-0.05908
270.2457
0.015113
185.1683
0.003046
265.2411
-0.00545
230.2093
-0.03615
330.3003
0.008626
250.2275
0.014239
315.2866
0.005404
300.273
-0.04505
360.3276
0.002102
355.323
0.003123
350.3185
0.012039
350.3185
-0.06232
Table 1.Rotor Angle 000,450,600 and 87.50 Phase Angle Vs Torque
In this approach, the FEM mesh of the cross section of the BLDC motor is divided into two parts: the stator and the
rotor, with each including a part of the air gap. The figure (2) is part of pre-processing that shows a typical representation of
mesh generation in motor computation space generated by FEMM. This entire
ERPMBLDC Motor solution region defined by materials, circuit properties and boundary conditions is broken down
into 11419 triangular elements and 5894 nodes before mathematical computation is carried out to obtain magnetic field
distribution with the cross section of the motor.
Fig. 1. Section of
Computational Space.
Fig. 2. Generated Mesh in the
ORPMBLDC Motor
Computation Space.
B. Processing
Solving the problem by the relevant Maxwell’s equations and obtaining the field distribution in the analyzed domain
of the geometry for the ORPMBLDC Motor at arbitrary chosen excitations and loading conditions.
C. Post Processing
This section of FEMM is used to view the solutions generated by FEMM solver. This is the process of calculating
and presenting a ERPMBLDC Motor flux pattern and deducing some results as well as parameters from the analyzed model.
The finite element analysis and allows for fast parameterization to scrutinize the manipulate of the number of segments on the
magnetic flux density distribution[12]. Figure (3) is the flux pattern obtained from the computations ,Figure (4) Distribution
of the magnetic flux vector , Figure (5) Air gap absolute magnetic flux density variation and Figure (6) Magnetization curve
in ORPMBLDC Motor. Finite Element Method Magnetic solver that takes a set of data that describe the problem from the
region and solves relevant Maxwell’s equations to obtain field values which are translated to field distribution in the analyzed
domain for this machine. In order to obtain the desired result Finite Element Method Magnetic will then be run at arbitrary
condition which is determine by value of the excitation.
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International Journal of Innovative Research in Advanced Engineering (IJIRAE)
Issue 1, Volume 1 (JANUARY 2012)
Fig. 3. Magnetic Flux
Pattern by Finite Element
Magnetic Method
Fig. 5. Air gap absolute
magnetic flux density
ISSN: 2349-2163
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Fig. 4, Distribution of the magnetic
flux vector
Fig. 6. Magnetization
curve
VI. MODELLING OF THE ERPMBLDC MOTOR
A. Geometrical Data
1. Air Gap length: 0.2cm
2. Stator Slots: 12 slots
3. Outer rotor radius: 15mm
4. Stator radius: 14mm
5. Rotor pole: 8
B. Material properties
The materials for this machine modeling can be user defined or can be obtained from FEMM material library.
1. Rotor: Alnico 8
2. Stator: Silicon Core Iron
3. Stator core: Copper
VII. LUA SCRIPTING IMPLEMENTATION
The Lua extension language has been used to add scripting/batch processing facilities to FEMM. The Interactive Shell can
run Lua scripts through the Open Lua Script selection on the Files menu, or Lua commands can be entered in directly to the
Lua Console Window. Lua is a complete, open-source scripting language. Source code for Lua, in addition to detailed
documentation about programming in Lua, can be obtained from the Lua homepage at http://www.lua.org. Because the
scripting files are text, they can be edited with any text editor (e.g. notepad). As of this writing, the latest release of Lua is
version 5.0. However, the version of Lua incorporated into FEMM is Lua 4.0. In addition to the standard Lua command set
described in, a number of FEMM-specific functions have been added for manipulating files in both the pre- and postprocessor[16].
VIII. RESULTS AND DISCUSSIONS
The developed motor model is discredited into 5894 nodes and 11419 elements by using FEMM 4.2 software package. The
three phase stator windings are excited by phase currents A, B and C by varying the phase angles from 00-3600 with interval
of 5 i.e. totally 73 iterations for each rotor position. The corresponding torque values are investigated.
____________________________________________________________________________________________________
© 2012, IJIRAE- All Rights Reserved
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International Journal of Innovative Research in Advanced Engineering (IJIRAE)
Issue 1, Volume 1 (JANUARY 2012)
ISSN: 2349-2163
www.ijirae.com
This procedure is repeated for rotor angles from 00- 900 with an increment of 2.50. Torque for various phase angles from
0 -3600 with interval of 10 (for simplicity) for rotor at starting position at 000,450,600, and 87.50 has been depicted in table 1
and figures 7, 8,9,10 and 11 respectively. For each rotor position peak torque value is determined and in total 36 rotor
positions are studied for one quadrant. As the motor model is being axisymmetry investigations are carried out for one
quadrant. From the study phase angle at which the torque is maximum is identified and tabulated for various rotor positions
in table 2. A plot between peak torque values and rotor angles has been obtained as in figure 12. It is observed from the plot
the torque developed by the ERPMBLDC motor can be improved to approach the ideal torque by designing the switching
circuit to the motor drive to supply the phase current to develop the maximum torque for particular rotor positions. The
average torque developed will be the maximum for the particular rotor position.
0
Fig,. 7. Rotor angle-87.50
Phase Angle Vs Torque
Fig. 9. Rotor angle-600
Phase Angle Vs Torque
Fig. 11. Rotor angle-000
Phase Angle Vs Torque
Rotor Angle
in Degree
0
10
20
30
40
50
60
Fig. 8. Rotor angle-77.50
Phase Angle Vs Torque
Fig. 10. Rotor angle-450
Phase Angle Vs Torque
Fig. 12. Rotor angle Vs peak
torque
step-000.dxf
Phase angle
in Degree
270.246
Torque
in N-M
0.01511
Step-100
Step-200
Step-300
Step-400
Step-500
Step-600
345.314
70.0637
150.136
230.209
310.282
30.0273
-0.0088
0.03771
0.01509
-0.0088
0.03771
0.01512
File Name
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International Journal of Innovative Research in Advanced Engineering (IJIRAE)
Issue 1, Volume 1 (JANUARY 2012)
70
80
87.5
Step-700
Step-800
Step-875
110.1
190.173
245.223
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-0.0088
0.03766
-0.0356
Table 2: Rotor angle Vs peak torque
IX.CONCLUSION
Computational procedure for finite element method and its application to solve magnetic field problems in
ERPMBLDC Motor is presented. The Poisson’s equation, which govern the approximating function and functional
minimization by using first order triangular finite elements. The result obtained shows two dimensional magnetic field model
of ERPMBLDC Motor which include absolute and normal magnetic flux component in the air gap; magnetic field
distribution and peak torque in a cross section of the ERPMBLDC Motor and its magnetization curve. The magnetization
curve plotted correspond with the conventional curve obtained from typical ERPMBLDC Motor. Therefore FEM is an
excellent tool for electromagnetic field mapping, which one could obtain electrical machine variables easily, quickly and
accurately as compared to other method. Another advantage of FEM is also its ability to deal with complicated geometries
such as the magnetic circuit of ERPMBLDC Motor.
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
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