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4 Full 3D Model – Solid Source Conductor

4 Full 3D Model – Solid Source Conductor

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J. Roupec et al.

With the new fully 3D geometry, a new mesh was created. Discretization was

done using 986,000 nodal points and 732,000 tetrahedral elements. Element

SOLID117 was used. Source of magnetic field (source conductor) was set to a

solid and defined by the zero potential (ground) and by the current on the both

terminations of coil conductor. Proportionally to the lower number of turns (5)

towards the real coil (118), it was necessary to adjust the amperage from 3.36 to

79 A. Figure 7 shows the distribution and size of magnetic flux density throughout

the fully 3D model with the current 3.36 A.



Table 1 compares the individual FE models with the measurement results according to the number of elements, solution time and maximal magnetic flux density.

3D axisymmetric models are marked as stranded and solid with the corresponding

entering of the magnetic field source. All analyses show a higher magnetic flux

density than what was actually measured. Magnetic flux density in the table is the

maximum from the entire course of path. Models with setting of the magnetic

field using current density (Stranded and 2D models) are the closest to the measured values. The fully 3D model could be more accurate if the mesh was finer. But

it was not possible due to the use of available PC.

Table 1 Compared the results of FEM analysis and experiment

Fig. 8 Courses of magnetic flux density – FEM analysis (red); measurement (blue)

Problems of FEM Analysis of Magnetic(Circuit


Figure 8 shows the measured flux density course and results of the analysis of

model Stranded under the one edge of magnetic circuit. The courses are to some

extent equal.



According to Table 1, stranded FE model was evaluated as the most accurate.

However, the 2D model is also very close to the measurement results and solution

time is significantly shorter. Regarding to the possibility of assigning a various

magnetic field source, it can be concluded that the most accurate results are

achieved through precise definition of current density. In the process of designing

of MR node, it is suitable for fast proposal of solution to use a 2D model in classic

ANSYS. Also freely available software FEMM uses the same approach to solving

and assignment of the magnetic field source. On the other side, for the final geometry optimization of MR node, it is preferred to use the ANSYS Workbench.

This environment allows performing a sensitivity analysis of dimensions. Parametric input of any dimension of magnetic circuit using a table allows determining its

effect on the resulting flux density. Thus more efficient circuit can be designed.

Sensitivity analysis can be also used to define the tolerance of the individual dimensions. If the geometry of the magnetic circuit exhibits axis symmetry, it is

suitable, in terms of accuracy of solution, to model a circuit as 3D axisymmetric

and specify the magnetic field source as Stranded coil. Otherwise, it is necessary

to select the 3D model. In any case, the solution time can be greatly decreased by

the choice of a direct solver. It has, however, limitations in the number of elements, depending on the size of the memory of computer station.

Acknowledgments. This work was developed with the support of the grants ED0002/01/01,

GAČR 13-31834P and CZ.1.07/2.3.00/30.0039.


[1] Mei, D., Kong, T., Shih, A.J., Chen, Z.: Magnetorheological fluid-controlled boring

bar for chatter suppression. J. Mater. Process. Tech. 209(4), 1861–1870 (2009)

[2] Cong, M., Dai, P., Shi, H.: A Study on Wafer-Handling Robot with Coaxial TwinShaft Magnetic Fluid Seals. In: Xie, M., Xiong, Y., Xiong, C., Liu, H., Hu, Z. (eds.)

ICIRA 2009. LNCS, vol. 5928, pp. 1123–1137. Springer, Heidelberg (2009)

[3] Lozada, J., Roselier, S., Periquet, F., Boutillon, X., Hafez, M.: Mechatronic Systems,

Applications – ch. 12, pp. 187–212. InTech, India (2010)

[4] Yatchev, I., Ilieva, N., Hinov, K.: 3D Finite Element Modelling of a Permanent Magnet Linear Actuator. Serb. J. Electr. Eng. 5(1), 99–108 (2008)

[5] Ciocanel, C., Nguyen, T., Elahinia, M.: Design and modeling of a mixed mode magnetorheological (MR) fluid mount. In: Proc. SPIE, vol. 6928, p. 10 (2008)

FEM Model of Induction Machine’s Air Gap

Force Distribution

J. Sobra and V. Kindl

University of West Bohemia in Pilsen, Faculty of Electrical Engineering, Univerzitni 26,

306 14, Plzen, Czech Republic


Abstract. This paper deals with the forces acting in the air gap of an induction

machine. The theoretical force distribution around the air gap is described. That is

performed by the variable permeance of the magnetic circuit. Different permeance

of both, the stator and the rotor slots and teeth is respected. An analytical calculation of Lorentz force acting on the rotor bars is presented. The 2D FEM model of

squirrel cage induction machine is used for a calculation of the Maxwell force

distribution in the air gap. That is realized by computing forces acting on the stator

and the rotor teeth. The method used for the calculation is Maxwell Stress Tensor.



The air gap force distribution [1, 2, 3] has a significant influence on the induction

machines operation. That influence can be positive (making the torque) or negative as well [1]. For example, the forces acting in the air gap can excite the motor

frame or the stator core vibrations [4, 5, 6]. There is also possibility of unbalanced

magnetic pull, in case of eccentric or bent rotor.

The induction machine’s air gap magnetic field is affected by many factors.

These factors concern especially the slot harmonics caused by the stator and

the rotor slotting and the harmonics of the magnetomotive force (MMF) of both

windings [1].

A number of papers dealing with the air gap field calculation have been presented. Heller, Hamata [1] and Heller, Jokl [7] have calculated the air gap flux

density as the product of permeance and the MMF. That calculation has considered

MMF harmonics, rotor angular velocity, time and both; stator and rotor slotting.

However, the FEM model is valid for conditions defined below. For this reason, the equations presented in [1] and [7] are slightly simplified in this paper.


Flux Density in the Air Gap

The permeance value of the induction machine’s magnetic circuit varies around

the air gap circumference periodically. That is caused by different permeability in

T. Březina and R. Jabloński (eds.), Mechatronics 2013,

DOI: 10.1007/978-3-319-02294-9_39, © Springer International Publishing Switzerland 2014



J. Sobra and V. Kindl

the stator and the rotor slots and teeth. Due to permeability, flux density in the air

gap changes as well and it can be computed as a product of the MMF and permeance. In this calculation, the MMF harmonics, rotor angular velocity and stator

radian frequency are neglected.

For a symmetrical three-phase stator winding the MMF fundamental is

obtained by

F1 ( x) = Ap sin ( px )



Ap - maximum value of working wave, p - number of pole pairs and

x - radian space location along the inner bore diameter of the stator.

Provided fixed position between the rotor and the stator; the air gap permeance

including both the rotor and the stator slotting is given by

Λ ( x) = c0 + c1' cos ( Q1 x ) + c1" cos ( Q2 x )

c0 =




δ kc1kc 2

c1' =



β s

δ kc 2  δ

  bs 

 F1  

  ts 

c1" =



β r

δ kc1  δ

  br 

 F1  

  tr 

Q1 , Q2 - number of stator/rotor slots, kc1 , kc 2 - Carter coefficient of stator/rotor winding, δ - air gap length, bs , br - width of stator/rotor slot opening,


 b (b )   b (b ) 

ts , tr - stator/rotor slot pitch and β  s r  , F1  s r  - coefficients given

 δ   ts (tr ) 

by characteristics in [7].

Finally, the flux density in the air gap caused by MMF fundamental and both

stator and rotor slotting is obtained by

B( x) = F ( x)Λ ( x) = Ap c0 sin ( px )


Ap c1' sin ( ( p − Q1 ) x ) + sin ( ( p + Q1 ) x ) 



− Ap c1" sin ( ( p − Q2 ) x ) + sin ( ( p + Q2 ) x ) 



FEM Model of Induction Machine’s Air Gap Force Distribution



Lorentz Force Calculation

Based on the previous calculation, an analytical examination of Lorentz part of the

force can be performed. The rotor current waveform is given by

I = I m cos ( Q2 nξ + ϕ ) + i sin ( Q2 nξ + ϕ ) 





Q2 p

I m - rotor current amplitude, Q2n - rotor bar number, ϕ - phase shift


When the rotor current waveform is known, the Lorentz forces acting on the rotor bars can be determined [8]. In the Fig. 1, the Lorentz force distribution in the

air gap and the force values acting on the rotor bars are shown. The values in the

Fig. 1 correspond with the modeled machine.

It is obvious that the Lorentz force is negligible in comparison with the Maxwell one (Fig. 3 and Fig. 4). Considering the shape of the stator slots and the rotor

bars, an exact analytical solution of the Maxwell force is impossible to derive. In

the case of double squirrel cage especially. By this reason FE analysis is very

useful way to determine the Maxwell force.

Fig. 1 Lorentz force in the air gap and force acting on the rotor bars



J. Sobra and V. Kindl

Model Description

For an accurate calculation of the air gap force distribution for specific machine

geometry, the 2D FEM model of 4-pole, 11kW SIEMENS 1LA7 163-4AA10

induction machine is presented. The motor’s power plate can be found in the Table 1. The model is valid for a steady nominal state and for fixed position between

the rotor and the stator. Change of the rotor rotation angle for a new calculation is

possible. The motor has 48 slots on the stator and 36 slots on the rotor. Geometry

of the one motor’s pole pitch is shown in the Fig. 2.

Table 1 Modeled motor’s power plate

parameter name






Voltage Δ / Y



Current Δ /Y






Number of poles



cos φ



Fig. 2 Model geometry


Air Gap Force Distribution

Forces acting in the air gap are calculated in the nodes of high permeance parts

of the magnetic circuit, which are surrounded by the air. For the calculation,

FEM Model of Induction Machine’s Air Gap Force Distribution


Maxwell Stress Tensor method is used. That method is commonly used for a force

calculation on the borderline of two materials with different permeability. For a

2D analysis of forces acting on the ferromagnetic material – air borderline, total

force can be expressed by [9, 10]

 2 1 2

B − B

1  x 2

Fm =


μ0 S 

Bx By



   nx 

    dS

1 2   ny 


By − B 


 

Bx By


Fm - total force acting on the object, which surface is S , μ0 - permeability of air, Bx , By - flux density components in the Cartesian coordinate system,


B - absolute value of flux density vector, nx , n y - components of the normal

unit vector of the surface.

Directly on that borderline, relatively high flux density evaluation error can occur. By this reason, the air gap force is evaluated in the center of the air gap [11].

In the following figures, the force distribution in the modeled motor is presented. Forces acting on the stator (Fig. 3) and the rotor (Fig. 4) teeth are shown

there. The forces are transformed to the cylindrical coordinate system. The fact

that the stator forces act against the rotor ones is obvious.

Fig. 3 Radial and tangential force components acting on the stator teeth


J. Sobra and V. Kindl

Fig. 4 Radial and tangential forces acting on the rotor teeth



The air gap field of induction machine for fixed position between the rotor and the

stator is described in this paper. An analytical calculation of Lorentz force and a

graphical representation of the Maxwell force distribution via FEM model are

carried out.

Comparing Lorentz and Maxwell force, disregard of the Lorentz force can be

concluded. The dominant force in the air gap is the Maxwell one. The FE analysis

results can be used as an input values for a coupled electrical – mechanical problem [12]. The presented model is valid for simplified conditions than during operation occurs. The way to include these conditions and non-standard operational

states modeling (eccentric rotor for example) are the subject of further research.

Acknowledgments. This paper was written with SGS-2012-071 project support.


[1] Heller, B., Hamata, V.: Additional fields, forces and losses in the induction machine.

NCSAV, Praha (1961)

[2] Jimoh, A.A., Findlay, R.D.: Parasitic torques in saturated induction motors. IEEE

Transactions on Energy Conversion 3(1), 157–163 (1988)

[3] Golebiowski, L., Mazur, D.: The effect of strong parasitic synchronous and asynchronous torques in induction machine with rotor eccentricity. In: 10th Mediterranean Electrotechnical Conference, MELECON 2000, May 29-31, vol. 3, pp. 982–985 (2000)

FEM Model of Induction Machine’s Air Gap Force Distribution


[4] Nau, S.L.: The influence of the skewed rotor slots on the magnetic noise of threephase induction motors. In: 1997 Eighth International Conference on Electrical Machines and Drives (Conf. Publ. No. 444), September 1-3, pp. 396–399 (1997)

[5] Zhu, H., Zhou, G., Chen, J., Liu, H.: Analysis and Study of Skewed Slot Tooth Distance on Low Electromagnetic Noise of Three-Phase Induction Motor with Squirrel

Cage Rotor. In: 2012 Sixth International Conference on Electromagnetic Field Problems and Applications (ICEF), June 19-21, pp. 1–4 (2012)

[6] Onodera, S., Yamasawa, K.: Electromagnetic vibration analysis of a squirrel-cage induction motor. IEEE Transactions on Magnetics 29(6), 2410–2412 (1993)

[7] Heller, B., Jokl, A.L.: Tangential Forces in Squirrel-Cage Induction Motors. IEEE

Transactions on Power Apparatus and Systems PAS-88(4), 484–492 (1969)

[8] Griffiths, D.J.: Introduction to electrodynamics, 3rd edn. Prentice-Hall, Upper Saddle

River (1999) ISBN 0-13-805326-X

[9] Mayer, D.: Aplikovany elektromagnetismus, KOPP, Ceske Budejovice (2012) ISBN


[10] Promberger, M.: Anwendung von Matrizen und Tensoren in der theoretischen Elektrotechnik, pp. 126–128. Akad.-Verlag (1960)

[11] Dombrowsky, W.W., Khanin, M.D., Kuchinska, Z.M.: Common software for electromagnetic and heat field analysis of electrical machines including the force calculation. Advances in Engineering Software 22(3), 147–152 (1995)

[12] Lee, J.-H., Lee, Y.-H., Kim, D.-H., Lee, K.-S., Park, I.-H.: Dynamic vibration analysis of switched reluctance motor using magnetic charge force density and mechanical

analysis. IEEE Transactions on Applied Superconductivity 12(1), 1511–1514 (2002)

Current-Voltage Characteristics and IR

Imaging of Organic Light-Emitting Diodes

G. Koziol, J. Gromek, A. Arazna, K. Janeczek, K. Futera, and W. Steplewski

Tele and Radio Research Institute, Ratuszowa 11, 03-450 Warsaw, Poland


Abstract. In this paper, a study of current-voltage characteristics and temperature

distribution in the polymer organic light-emitting diodes are presented and discussed. The fabricated diodes consisted of ITO coated glass, PEDOT:PSS as

a hole injection layer, one of eight different examined light-emitting compounds

as an emissive layer, and aluminium cathode. The spectrum of light emitted by the

fabricated OLEDs was also measured. Based on the results the most efficient.



Organic Light Emitting Diodes (OLEDs) hold great promise for future use

as a new generation of solid state light sources. In contrast to point source LED

luminaries, OLEDs are dispersive light sources. Some of the many advantages are

that OLEDs are “green” without hazardous material such as mercury, potentially

energy efficient, and emit low intensity uniform light from an extremely thin flat

surface [1].

There are two basic types of OLED systems: low molecular weight OLEDs and

polymer OLEDs. Small molecule OLEDs are made via evaporation of materials

under high vacuum. This method is so far mostly used for OLED lighting panels

manufacturing. Polymer OLEDs are made of long chains of repeating structures

and deposited from a solution. This solution processing bears the advantage

of mass reproduction by e. g. gravure printing.

Today‘s OLEDs performance is already reaching market requirements for less

demanding lighting applications, such as signage and signaling. Especially in monochrome colors, red and green, OLEDs perform already very well. The efficacies

of 130 lm/W in green has already been achieved [2-7].

Worldwide research is ongoing to create high-brightness, highly efficient and

long living OLEDs, especially manufactured using solution processable emitting

layer. Tele- and Radio Research Institute has also undertaken studies on this area.

In this paper, the electric response of the devices was evaluated based on the current-voltage characteristics. The evaluation of a working temperature of OLED

operating under a changing DC voltage level were done used IR camera. The degradation at the cathode surface were evaluated through SEM (Scanning Electron

T. Březina and R. Jabloński (eds.), Mechatronics 2013,

DOI: 10.1007/978-3-319-02294-9_40, © Springer International Publishing Switzerland 2014



G. Koziol et al.

Microscope). Based on the results demonstrators of OLEDs with the most efficient

emission compound (achieved so far), were produced and evaluated.



OLED devices were manufactured on the glass slides (the dimension of 25 x 25 x

1.1 mm) coated with ITO (film thickness of 15 - 30 nm, and sheet resistance of 70

- 100 Ω/□). In order to improve the hole injection, a highly conductive and transparent organic layer of Poly(3,4-ethylenedioxythiophene): poly(styrenesulfonate)

(PEDOT:PSS) was used. Both glass substrates and HIL material (2% water

solution) were purchased from Sigma-Aldrich Chemical.

Single-layer organic-light-emitting devices were fabricated by spin coating

of polymeric solutions of emissive materials from American Dye Source: Poly[2methoxy-5-(2-ethylhexyloxy)-1,4-phenylene-vinylene] – end capped with DMP

(ADS1), Poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylene-vinylene] – end





Poly[2-methoxy-5-(3,7dimethyloctyloxy)-1,4-phenylene-vinylene] – end capped with DMP (ADS3),

Poly[2-(5-cyano-5-methylhexyloxy)-1,4-phenylene] – end capped with DMP

(ADS4), Poly[(9,9-dioctylfluorenyl-2,7-diyl)-co-(1,4-benzo-{2,1’,3}-thiadiazole)]

10% benzothiadiazole (y) (ADS5), Poly[(9,9-dihexylfluorenyl-2,7-diyl)-alt-co-(2methoxy-5-{2-ethylhexyloxy}-1,4-phenylene)]



Poly[{9,9dioctylfluorenyl-2,7-diyl}-co-{1,4-(2,5-dimethoxy)benzene}] (ADS8). All these

emissive materials (EML) were dissolved in xylene (concentration 5 mg/ml).

The ITO coated glass substrates were first ultrasonically cleaned in acetone,

and ethanol, for 5 minutes each. Such ITO treatment was considered as an effective method of ITO treatment for organic light-emitting devices in our previous

work [8]. Next, the substrates were dried with compressed air and then on a hot

plate PZ-28-2 (Harry Gestigkeit) in 80°C for 10 min. Then, two PEDOT:PSS

layers were deposited on ITO with a modular spin processor WS-650-23NPP

(Laurell Technologies Corporation) set to speed of 7500 rpm, acceleration of 6000

rpm/s and process time of 6 s. After deposition of each layer the sample was dried

on a hot plate in 80°C for 10 min. EML layers were also spin coated with following settings: speed of 5500 rpm, acceleration of 4000 rpm/s and process time of

6s. Each layer was dried on a hot plate in 80C for 3 min. In the last step, the aluminum cathode was evaporated from aluminum slug (99.999% trace metals basis)

at a base pressure of ∼10-3 mbar (Type Q150T ES, Quorum Technologies). All

tested OLED devices were prepared in ambient conditions.

The structure of tested devices was ITO/PET/PEDOT:PSS 2x/ EM (ADS1-8)

3x/Al (100 nm). The device active area was 1 cm2.

Current-voltage (I-V) characteristics of the prepared OLEDs were measured

using a Hameg Instruments Company HMP 2020 Power Supply SourceMeter

under ambient atmosphere at room temperature. The results given here represent

the average of three measurements carried out for fresh manufactured devices

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