__________________________________________
* Brno University of Technology.
Ramia DEEB*
Marcel JANDA*
Zbynek MAKKI*
COMPARISON OF 2D AND 3D FEM ANALYSIS OF THE MAGNETIC FIELD IN A PM SERVO MOTOR
Nowadays, the applications of the electrical machines with permanent magnets become very common, because of the outstanding properties of these devices in comparison with the induction machines. PM machines do not indicate electrical losses with the field excitation, which means increasing of their efficiency. This is a very important factor considering the urgent need of the energy conservation. Although, numerical methods for a field computation are time consuming, they provide accurate results without making any simplification of the geometry. The paper presents a comparison of 2D and 3D magnetic analysis of a PM servo motor. The analyzed servo motor is designed with a surface magnet rotor and produced by the VUES Brno company. The applied PM material is of rare earth type NdFeB. This material is characterized by a very high energy product. 2D model of this servo motor is created using AutoCAD program. The 2D magnetic analysis is computed using FEMM (finite element method magnetics). The 3D magnetic analysis is computed using a modern technique in the field of magnetic analysis of electrical machines. 3D model of the servo motor is generated using RMxprt program. The 3D magnetic analysis of the generated 3D model is computed using Maxwell 3D program. The program Maxwell 3D generates fine mesh automatically with a high accuracy. The distribution of the magnetic field inside the servo motor is computed for the case of the nominal current in both of 2D and 3D magnetic analysis. The distribution of the magnetic flux density according to the air gap length is presented too. The FEM (finite element method) is used for both 2D and 3D magnetic analysis of this servo motor.
1. INTRODUCTION
Many researches focused on the magnetic analysis of machines with permanent magnets using numerical methods for many purposes. The analytical method is widely used in calculations of synchronous reactances of salient pole synchronous machines with electromagnetic excitation. Rotors of PM synchronous machines have more complicated structures; that makes prediction of the magnetic field distribution in their air gaps more difficult. In small PM synchronous motors with
complicated structure, it is necessary to obtain an accurate distribution of the magnetic field. This distribution is very helpful for a correct estimation of the form factors of the rotor and stator magnetic flux densities. The FEM makes it possible to find the d and q axis synchronous reactances and mutual (armature reaction) reactances by computing the corresponding inductances [1].
In the paper [2], a general analytical solution of magnetic field in slotted surface-mounted PM machines is presented. A new analytical solution based on 2-D analysis in polar coordinates and suitable for radial/parallel magnetization, internal/external rotor topologies is developed. The radial and tangential flux density is obtained by using the Fourier’s series and the method of separating variables. The cogging torque characteristic is deduced by calculating the Maxwell tensors. Other researches focused on the magnetic analysis using modern softwares such as ANSYS [3, 4]. The distribution of magnetic field inside PM synchronous motor was analyzed and calculated. The no-load and load electromagnetic field in this motor was obtained. When the PM synchronous motor was loaded, direct axis and quadrature axis armature reaction magnetic field were obtained. Furthermore, back EMF of PM synchronous motor was figured out with two different approaches and the calculation results were compared and analyzed. By back-dealing model of ANSYS, the pictures of magnetic flux density (B) and magnetic vector potential (A) were gained. Back EMF is a critical parameter of PM synchronous motor.
The numerical techniques, such as FEM, provide accurate enough solutions either for two or for three dimensional field problems in complex geometries, which in turn could be used to predict device performance with a good precision.
But these techniques require a detailed definition of the geometry and boundary conditions to be solved, assuming that an initial design of the studied object already exists. Consequently, the computer-based field analysis may be employed as an effective tool for simulating the performance characteristics of the device. It should be pointed out, that computational FE results can be obtained both for the steady-state and transient operating conditions; in the first case the magnetostatic FEM is used, while in the second case the time-harmonic or time-stepping FEM is applied [5].
In this paper, the magnetic field of PM servo motor M 718 is computed in both 2D and 3D dimensions. The FEM is used for both 2D and 3D magnetic analysis of this servo motor.
2. MODEL DESCRIPTIONS
The mathematical model of the permanent magnet synchronous motor (PMSM) can be described as [5]:
) 2 (
3
d q q d m em
r m d q q q
r m q d d
d
i i P T
dt P ri d u
dt P ri d u
(1)
where: r is the synchronous rotational speed, Tem is the electromagnetic torque, uq
is the q-axis voltage, ud is the d-axis voltage, iq is the q-axis current, id is the d-axis current, Pm is the number of pole pairs, q is the q-axis flux linkage, d is the d- axis current flux linkage.
q and d are both currents and rotor’s position functions. They can be written as:
) , , (
) , , (
q d q q
q d d d
i i
i i
(2)
The nonlinear influence caused by the magnet saturation can be expressed as:
s s
s
s
R i p
U
(3)When the nonlinear influence caused by the magnet saturation is ignored, Eq. 2 can be depicted linearly with iq and id, then Eq. 1 can be written as:
) ) (
2( 3
q d q d q f em
q q r d d d d
f r d d r q q q q
i i L L i T
i L dt P
L di ri u
P i L dt P
L di ri u
(4)
where Ld is the d-axis inductor, Lq is the q-axis inductor.
If id is could be equalled to zero using the feedback linear scheme, and the PMSM model is simplified as:
q f em
q d r m d
f r m q q q q
i T
i L P u
dt P L di ri u
2
3
(5)
for PMSM, f is constant, and according to Eq. 5, the electromagnetic torque can be controlled by controlling iq.
3. PROPERTIES OF THE ANALYZED PM SERVO MOTOR M 718
PM servo motor M 718 is produced by VUES Brno company. The nominal values of this motor are:Voltage Vn 280 V
Current In 11.56 A
Torque Mn 16.5 Nm
Rotational speed nN 3000 rpm
Output power PN 5174 W
PM servo motor M 718 is presented in Fig. 1.
Fig. 1. PM servo motor M 718 [6]
The outline of PM servo motor M 718 is presented in Fig. 2.
Fig. 2. Outline of PM servo motor M 718 [6]
NdFeB permanent magnet material is applied to the servo motor M 718. The magnets are mounted on the surface of the rotor. This magnet material is
characterized by high remanence Br, high coercivity Hc, very high energy product (B∙H)max, and very high strength.
The specifications of the PM servo motor M 718 is presented in Table 1.
Table 1. Specification of the PM servo motor M 718
Number of pole pairs 2p 6
Number of slots Ns 18
Stator inner radius [mm] Rs 31.5
Air gap length [mm] g 0.7
Magnet thickness [mm] hm 3.5 Remanence of magnet [T] Br 1110 Coercivity of magnet [kA/m] Hc 850 Relative permeability of magnet µr 1.1
4. 2D ANALYSIS OF THE MAGNETIC FIELD
OF SERVO MOTOR M 718
2D model of PM servo motor M 718 is created using AutoCAD program, and presented in Fig. 3.
Fig. 3. 2D model of PM servo motor M 718
2D magnetic analysis of the servo motor M 718 is computed using FEMM program. The magnetic analysis is computed in the case of nominal current In applied to the three phase armature winding. FEMM is a freeware software which
generates free mesh using simple algorithm. The generated mesh is presented as follows:
Fig. 4. Mesh inside PM servo motor M 718
For higher accuracy, fine mesh should be generated in the air gap between stator and rotor as presented in Fig. 5.
Fig. 5. Mesh in the air gap between stator and rotor
The distribution of the magnetic flux density and the magnetic flux lines are presented as follows:
Fig. 6. Distribution of the magnetic flux lines inside PM servo motor M 718
Fig. 7. Distribution of the magnetic flux density inside PM servo motor M 718
Figs. 6 and 7 present the distribution of the magnetic flux lines and magnetic flux density in the analyzed motor, respectively. The values of the magnetic flux density are between 0.09-1.75 T. The distribution of the magnetic flux density in the air gap between stator and rotor is presented in Fig. 8.
0 20 40 60 80 100
0.0 0.2 0.4 0.6 0.8 1.0
Magnetic flux density [T]
Length of the air gap [mm]
Bavg = 0.678
Fig. 8. Circumferential distribution of the magnetic flux density in the air gap center
5. 3D ANALYSIS OF THE MAGNETIC FIELD OF SERVO MOTOR M 718
3D magnetic analysis of the servo motor M 718 is computed using Maxwell 3D program. The magnetic analysis is computed in the case of nominal current In is applied to the armature winding. 3D model of the analyzed motor is generated using RMxpert program. The generated model is presented as follows:
Fig. 9. Generated 3D model of PM servo motor M718
ANSOFT software generates an adaptive mesh using improved algorithms. The generated mesh of the 3D analysis is presented as follows:
Fig. 10. Generated mesh in the servo motor parts (stator, rotor, PMs)
Mesh is presented clearly in some parts of servo motor as follows:
Fig. 11. Mesh in one magnet
Fig. 12. Mesh in the cross section of the servo motor
The distribution of the magnetic flux density in different parts of the servo motor is presented as follows:
Fig. 13. Distribution of magnetic flux density along cross section of stator
It can be noticed from Fig. 13 the magnetic field produced by the winding in stator. The magnetic flux density of the winding field is about 3.1 T. Permanent magnets can keep their magnetic field stable under a proper application after they are magnetized, because of their high coercivity. They can produce a magnetic field in the air gap without dissipation of the electric power. The distribution of the magnetic flux density in the permanent magnets mounted on the rotor of the servo motor M 718 is presented as follows:
Fig. 14. Distribution of magnetic flux density in the PMs
According to the Fig. 14, the applied permanent magnets produce a magnetic field with maximum magnetic flux density about 1.4 T. The polarization of the applied magnets is presented in the following figure.
Fig. 15. Distribution of the magnetic vector of the permanent magnets
A cross section of the PM servo motor M 718 is created to show the magnetic flux density distribution more clearly inside the servo motor.
Fig. 16. Magnetic flux density distribution along a cross section of the servo motor
Fig. 16 presents the distribution of the magnetic flux density inside the PM servo motor M 718 for the 3D analysis. The interaction between the magnetic field produced by the stator winding and the magnetic field produced by the permanent magnets can be shown clearly. The magnetic flux density values are between 0.0049-3.1 T. The distribution of the magnetic flux density in the air gap for 3D analysis is presented as follows.
0 20 40 60 80 100 Distance [mm]
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Mag_B [tesla]
XY Plot 1 ANSOFT
Curve Info avg
Mag_B
Setup2 : LastAdaptive 0.7201
Fig. 17. Circumferential distribution of the magnetic flux density in the air gap center
Fig. 17 presents the magnetic flux density according to the air gap length. The average value is about 0.7201 T.
6. CONCLUSION
In this paper, the magnetic field distribution in the surface mounted permanent magnet servo motor has been computed according to the FEM for both two and three dimensions. The 2D analysis of the magnetic field is computed using FEMM program. This freeware software can be used only for two dimensional static analysis. The 3D magnetic analysis is computed using commercial ANSOFT Maxwell program, which uses an adaptive mesh and can be used for different static and transient analysis for both 2D and 3D applications.
According to the performed analysis of the given M718 PM servo motor , the average values of the magnetic flux density component in the air gap for the 2D analysis is about 0.678 T (Fig. 8), while this value for the 3D analysis is about 0.7201 T (Fig. 17).
The permanent magnets applied to this servo motor are of the rare earth NdFeB type. These magnets have high coercive force. They produce a magnetic field of about B = 1.4 T (Fig. 14).
According to the results above, the 3D analysis results have higher accuracy in comparison with the 2D analysis.
The 3D analysis is time consuming, but it is applied with no simplifications to the servo motor geometry, which is considered as a positive point of the numerical methods applications.
A
CKNOWLEDGEMENTAuthors gratefully acknowledge financial support under project No.
CZ.1.05/2.1.00/01.0014 funded by European Regional Development Fund and project No.
FEKT S-11-9 funded by the Ministry of Education of the Czech Republic.
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