A method of simulation and modeling outer rotor permanent magnet brushless DC (ORPMBLDC) motor under dynamicconditions using finite element method by FEMM 4.2 software package is presented. In the proposed simulation, the torquedeveloped at various positions of the rotor, under a complete cycle of excitation of the stator, is analysed. A novel method ofsinusoidal excitation is proposed to enhance the overall torque development of ORPMBLDC motor.
1. Introduction
The impressive improvement in power electronic switchingdevices, integrated circuits, developments and refinementsin permanent-magnetic materials, and manufacturing tech-nology have led to the development of brushless permanent-magnet motors that offer significant improvements in pow-er density, efficiency, and noise reduction [1]. Brushlesspermanent-magnet motors are especially demanded in cleanand explosive environments such as aeronautics, robotics,food and chemical industries, electric vehicles, medicalinstruments, and computer peripherals [2–4]. PM D.C.brushless motors use direct feedback of the rotor angularposition so that the input armature current can be switched,among the motor phases, in exact synchronism with therotor motion. This concept is known as self-controlledsynchronization or electronic commutation. The electronicinverter and position sensors are equivalent to the mechani-cal commutator in D.C. motors [4].
There are several reasons for the overwhelming preva-lence of motors having inner rotors [3]. These reasonsinclude the ease of heat removal, because the windings areon the outside, and the containment of the rotating element.In some applications, these attributes are not as importantas the benefits gained from having an outer rotor andinner stator. Motors having this construction are sometimes
called inside-out motors. Outer rotor motors appear mostcommonly as spindle motors for hard disk drives and asthe drive motor for ventilation fans, water pumps, power-assisted steering such as those used to cool CPUs andcomputer cases. In these applications, the motor becomesan integrated part of a larger structure. Although individualmagnets can be used in outer rotor motors, it is commonto use a single-bonded magnet ring inside a rotor. Since thestator teeth point outward, this motor is relatively easy towind. For a given outer radius, an outer rotor motor has amuch larger air gap radius than that of an inner rotor motor.As a result, higher torque is achievable, provided the ohmiclosses of the stator windings can be dissipated [5–7].
The finite element method (FEM) has proved to be par-ticularly flexible, reliable, and effective in the analysis andsynthesis of power-frequency electromagnetic and electro-mechanical devices. Even in the hands of non-specialists,modern FEM packages are user friendly and allow for cal-culating the electromagnetic field distribution and integralparameters without detailed knowledge of applied mathe-matics. The FEM can analyze PM circuits of any shape andmaterial. There is no need to calculate reluctances, leakagefactors, or the operating point on the recoil line. The PMdemagnetization curve is input into the finite element pro-gram which can calculate the variation of the magnetic fluxdensity throughout the PM system. An important advantage
2 Modelling and Simulation in Engineering
of finite element analysis over the analytical approach to PMmotors is the inherent ability to calculate accurately armaturereaction effects, inductances and the electromagnetic torquevariation with rotor position (cogging torque) [5, 8–10].In electrical machine problems four methods of calculatingforces or torques are used: the Maxwell stress tensor, thecoenergy method, the Lorentz force equation, and the rateof change of field energy method. The most appropriatemethod is usually problem dependent, although the mostfrequently used is the Maxwell stress tensor method [11].
FEMM package is an open source, simple, accurate,and low computational cost freeware product, popular inscience and engineering. Several applications in areas suchas Electromagnetics, Materials Science, Industry, Medicine,Experimental and Particle Physics, Robotics, Astronomy, andSpace Engineering can be found. The software is reasonablyfast and accurate, user friendly, and freely distributed. Thelast seems to be its main advantage concerning its educa-tional value. Its capability to meet as a complementary toolthe needs of teaching electromagnetic in higher educationwill be explored and evaluated [12].
In the proposed model FEMM 4.2 software packagehas been used to investigate the excitation currents to thedifferent phases of stator windings and corresponding torquedeveloped to enhance the torque produced by ORPMBLDCMotors.
2. Mathematical Modeling
The most frequently used methods are the Maxwell stresstensor; the use of the Maxwell stress tensor is simple froma computational perspective, since it requires only the localflux density distribution along specific line or contour. Usingthe definition of Maxwell stress tensor, the electromagneticforces can be determined on the basis of the magnetic fluxdensity, that is:
the total force:
�F =∫∫[
1μ0
�B(�B · �n
)− 1
2μ0
B2�n]ds, (1)
the normal force:
Fn = 12μ0
∫ [B2−n B2
t
]dl, (2)
the tangential force:
Ft = Liμ0
∫Bn Bt dl, (3)
where �n, Li, l, Bn, and Bt are the normal vector to thesurface S, stack length, integration contour, radial (normal)component to the magnetic flux density and tangentialcomponent of the magnetic flux density, respectively.
The torque �T = �r × �F in connection with (3) is
T = Li2μ0
∮rBn Bt dl, (4)
where r is the radius of the circumference which lies in the airgap. since a finite grid is being used, the previous equationscan be written for element i. The torque shown below incylindrical coordinates is a sum of torques for each elementi, that is:
T = Liμ0
∑r2∫ θi+1
θiBri Bθi dθ. (5)
The accuracy of this method is markedly dependenton the model discretization and on the selection of theintegration line or contour. The Maxwell stress tensor lineintegration necessitates a precise solution in the air gap,demanding a fine discretization of the model in the air gapsince the flux density is not continuous at the nodes andacross boundaries of first-order elements [13].
3. Modeling of ORPMBLDC Motor by FEMM
Finite element method magnetic (FEMM 4.2) is the softwarepackage has been used to model the ORPMBLDC motor.FEMM 4.2 is a suite of programs for solving low frequencyelectromagnetic problems on two-dimensional planar andaxisymmetric domains. The program currently addresses lin-ear/nonlinear magnetostatic problems, linear/nonlinear timeharmonic magnetic problems, linear electrostatic problems,and steady-state heat flow problems.
FEMM 4.2 is divided into three parts: Interactive shell(femm.exe). This program is a multiple document interfacepreprocessor and a post-processor for the various typesof problems solved by FEMM4.2. It contains a CAD-likeinterface for laying out the geometry of the problem to besolved and for defining material properties and boundaryconditions. AutoCAD DXF files can be imported to facilitatethe analysis of existing geometries [12]. Field solutions canbe displayed in the form of contour and density plots. Theprogram also allows the user to inspect the field at arbitrarypoints, as well as evaluate a number of different integralsand plot various quantities of interest along user-definedcontours triangle.exe. Triangle breaks down the solutionregion into a large number of triangles, a vital part of thefinite element process. Each solver takes a set of data files thatdescribe problem and solve the relevant partial differentialequations to obtain values for the desired field throughoutthe solution domain. The Lua scripting language is integratedinto the interactive shell. Unlike previous versions of FEMM(i.e., v3.4 and lower), only one instance of Lua is running atany one time. This single instance of Lua can both build andanalyze geometry and evaluate the postprocessing results,simplifying the creation of various sorts of “batch” runs. Inaddition, all edit boxes in the user interface are parsed byLua, allowing equations or mathematical expressions to beentered into any edit box in lieu of a numerical value. Inany edit box in FEMM 4.2, a selected piece of text can beevaluated by Lua via a selection on the right mouse buttonmenu.
The motor with specifications given in Table 1 is modeledby FEMM package Version 4.2. Here the permanent magnetsof outer rotor material property are chosen as ALNICO 8 and
Modelling and Simulation in Engineering 3
Figure 1: Motor model.
Figure 2: Fem meshed 2D model.
Table 1: Motor specifications.
Outer rotor radius 15 mm
Stator radius 14 mm
Air gap .2 mm
Rotor pole 8
Stator slots 12
stator with silicon core iron. Material properties chosen forvarious components are detailed in Table 2. The developedORPMBLDC motor model has been shown in Figure 1;stator windings are excited by three phases, namely A, B, andC. electromagnetic properties of the three phase windings.
The motor has been modeled with 5894 nodes and11419elements by 2D planar 1 mm depth which is shown in
Figure 3: Flux plot.
Table 2: Material properties.
Rotor
Alnico 8 linear B-H relationship
Relative μx = 6.678
Relative μy = 6.678
Coercivity Hc, A/m = 109300
Electrical conductivity σ , ms/m= 2.25
Air
Linear B-H relationship
Relative μx = 1
Relative μy = 1
Stator
Silicon core iron
Nonlinear B-H relationship
Electrical conductivity σ , ms/m= 4
Stator slots
Copper
Number of turns used= 100
Relative μx = 1
Relative μy = 1
Linear B-H relationship
Figure 2. Flux lines established, and flux density distributionfor the given excitation in three phases is shown in Figures 3and 4, respectively. Here stator and rotor have been modeledby using magnetic materials using silicon core iron andALNICO, respectively, and these materials’ B-H characteris-tics have been shown in Figures 5 and 6.
4. Lua Scripting Implementation
The Lua extension language has been used to add script-ing/batch processing facilities to FEMM. The interactive shell
can run Lua scripts through the Open Lua Script selectionon the Files menu, or Lua commands can be entered indirectly to the Lua Console Window. Lua is a complete, open-source scripting language. Source code for Lua, in additionto detailed documentation about programming in Lua, canbe obtained from the Lua homepage at http://www.lua.org.Because the scripting files are text, they can be edited withany text editor (e.g., notepad). As of this writing, the latestrelease of Lua is version 5.0. However, the version of Luaincorporated into FEMM is Lua 4.0. In addition to thestandard Lua command set described, a number of FEMM-specific functions have been added for manipulating files inboth the pre- and postprocessor.
5. Results and Discussions
The developed motor model is discretised into 5894 nodesand 11419 elements by using FEMM 4.2 software pack-age. The three-phase stator windings are excited by phasecurrents A, B, and C by varying the phase angles from 0◦
to 360◦ with interval of 5, that is, totally 73 iterations foreach rotor position. The corresponding torque values areinvestigated. This procedure is repeated for rotor angles from0◦ to 90◦ with an increment of 2.5◦. Torque for various phaseangles from 0◦ to 360◦ with interval of 10 (for simplicity)for rotor at starting position at 00◦, 45◦, and 87.5◦ andFigures 7, 8, and 9, respectively. For each rotor position peaktorque value is determined, and in total 36 rotor positionsare studied for one quadrant. As the motor model is beingaxisymmetry, investigations are carried out for one quadrant.A plot between peak torque values and rotor angles hasbeen obtained as in Figure 10. It is observed from the plotthe torque developed by the ORPMBLDC motor can beimproved to approach the ideal torque by designing theswitching circuit to the motor drive to supply the phase
Modelling and Simulation in Engineering 5
0.02
0.015
0.01
0.005
0
−0.005
−0.01
−0.015
Torq
ue
(N-m
)
Phase angle (deg)
0 100 200 300 40000 100 200 300
Figure 7: Rotor angle-00◦: phase angle versus torque.
0.02
0.015
0.01
0.005
0
−0.005
−0.01
−0.015
Torq
ue
(N-m
)
Phase angle (deg)
0 100 200 300 40000 100 200 300
Figure 8: Rotor angle-45◦: phase angle versus torque.
current to develop the maximum torque for particularrotor positions. The average torque developed will be themaximum for the particular machine and hence the outputpower. The efficiency of the motor will be maximum at anyload.
6. Conclusions
FEMM package is useful software to solve any electromag-netic problems. It is concluded that from the FEMM outputthe motor can be driven at its peak torque at any rotorposition to drive the load connected by switching the exci-tation supply to the phase windings at phase angle for peaktorque. This will lead to the maximum average torque for anyload and maximum efficiency. It is possible nowadays withthe impressive improvement in power electronic switchingdevices and integrated circuits.
00
100 200 300 400
Phase angle (deg)−0.09
−0.08
−0.07
−0.06
−0.05
−0.04
−0.03
−0.02
−0.01
Torq
ue
(N-m
)
Figure 9: Rotor angle-87.5◦: phase angle versus torque.
0 10 20 30 40 50 60 70 80
Rotor angle (deg)
Peak
torq
ue
(Nm
)
0.1
0.08
0.06
0.04
0.02
0
−0.02
−0.04
−0.06
−0.08
−0.1
Figure 10: Rotor angle versus peak torque.
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6 Modelling and Simulation in Engineering
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