A study on the integration of contactless energy transfer in the end teeth of a PM synchronous linear motor

A study on the integration of contactless energy transfer in the

end teeth of a PM synchronous linear motor

Citation for published version (APA):

Krop, D. C. J., Lomonova, E. A., Jansen, J. W., & Paulides, J. J. H. (2009). A study on the integration of contactless energy transfer in the end teeth of a PM synchronous linear motor. Journal of Applied Physics, 105(7), 07F115-1/3. [07F115]. https://doi.org/10.1063/1.3074785

DOI:

10.1063/1.3074785 Document status and date: Published: 01/01/2009

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A study on the integration of contactless energy transfer in the end teeth

of a PM synchronous linear motor

D. C. J. Krop,a兲 E. A. Lomonova, J. W. Jansen, and J. J. H. Paulides

Department of Electrical Engineering, Eindhoven University of Technology, Den Dolech 2, 5612 AZ Eindhoven, The Netherlands

共Presented 14 November 2008; received 13 October 2008; accepted 11 December 2008; published online 16 March 2009兲

Linear motors find their utilization in an increasing number of industrial applications. Permanent magnet linear synchronous motors共PMLSMs兲 are favorable in many applications due to their servo characteristics, robustness, and high force density. The major disadvantage of moving coil type PMLSMs is the cable slab that energizes the coils from the fixed world to the moving parts of the machine. These cable slabs introduce extra wear and dynamical distortions. Moreover, in precision application the cable slab is supported by additional linear drives. These disadvantages can be eliminated if the coils could be powered wirelessly. In this paper two topologies are proposed that are capable of transferring 1 kW of power at most. The transformer part of the CET is characterized by means of two dimensional finite element analysis, and the influence of using additional capacitors to boost the output power is examined. Furthermore, an analysis of the core losses is conducted. Conclusions are drawn from the results. © 2009 American Institute of Physics. 关DOI:10.1063/1.3074785兴

I. PROBLEM DESCRIPTION

Currently, contactless energy transfer共CET兲 is only in-tegrated in slotless actuators.1For slotted machines CET can be obtained via high frequency sliding transformers2 mounted separately along the mover of the PMLSM. Re-cently a linear motor that acts as both transformer and motor was presented by Fujii and Mizuma,3 but here the machine can work as either motor or transformer and cannot operate in both modes simultaneously. With the integration of the contactless energy transfer 共CET兲 into a slotted permanent magnet linear synchronous motor共PMLSM兲, certain parts of the machine will have a double functionality, i.e., simulta-neously being a component from an actuator point of view as well as being a component from CET point of view, e.g., the core material of a moving high frequency transformer. It is inevitable that both functions will interfere with each other. From a motor perspective no additional parasitic force com-ponents should be introduced due to the CET and also the magnetic coupling of the CET should be position indepen-dent. Therefore, during the design of such a machine the appropriate physical phenomena have to be monitored atten-tively to ensure good decoupling between both functions. The frequency of the magnetic field used for CET has to be significantly higher than the frequency of the one that is normally present in the machine for motor operation. First, this originates from the fact that the space for the transfer is limited and the extra mass added to the PMSLM is prefer-ably kept as low as possible. The higher frequency allows less core material to be used for the CET. Second, the extra magnetic field might introduce an additional undesirable force component共vibration兲 that acts on the mover. By using a high frequency the vibration component will be filtered out by the mass of the mover. Using high frequency magnetic

fields the eddy current and hysteresis losses in the machine will also increase. So to have an acceptable trade-off be-tween losses, good electromagnetic coupling, and low para-sitic forces, appropriate soft magnetic material has to be cho-sen. For high frequency applications ferrites possess the best properties, but they are generally not applicable in permanent magnet application due to their low saturation level. The opposite applies for soft magnetic steel due to its high elec-trical conductivity. Laminating the steel decreases the eddy current losses and still ensure good coupling.

II. TOPOLOGIES

Apart from the phenomena mentioned in the previous paragraph, also a good geometrical shape of the system plays a dominant role. To keep cross coupling of magnetic fields between operations low, the CET is integrated as a single phase transformer with airgap in the end teeth of the machine as shown in Fig.1. First, the magnetic flux density in the end teeth is in general lower than in the regular teeth of the machine because there are no coils to directly magnetize them. Figure2shows the flux density distribution in the end tooth and a phase tooth at a position where the flux density in the end tooth is maximal. Simulations showed that the width of the end teeth can be increased without compromising the

a兲_{Electronic mail: d.c.j.krop@tue.nl.} FIG. 1. Topology of the CET integrated in an end tooth of a PMLSM with_{a cross-cut.} JOURNAL OF APPLIED PHYSICS 105, 07F115共2009兲

0021-8979/2009/105共7兲/07F115/3/$25.00 105, 07F115-1 © 2009 American Institute of Physics

cogging force profile of the machine if it is extended with an integer multiple of the pole pitch. Second, the flux flow of the CET in the end teeth is chosen to be perpendicular to the flux flow of the motor to diminish again cross coupling ef-fects. The elongated primary winding of the transformer is located under the Halbach magnet array. The quasi-Halbach array is used to focus the magnetic field in the air-gap. The magnet array is mounted onto a nonmagnetic plate. This is necessary since the use of soft magnetic material would shortcut the flux path of the primary core. The core secondary coils are attached to the end tooth.

Figure3depicts a configuration where the transformer is completely integrated in the back iron of the machine. The plane of drawing is perpendicular to the direction of move-ment. There are two quasi-Halbach magnet arrays and two mover parts. The secondary core moves in between the two magnet arrays and the secondary coil is in between the two mover parts. The primary coils have the same length as the total length of the PMLSM. The CET flux path is relatively short and is scalable with the depth of the machine.

In each case of the presented topologies, the CET con-sists of single phase transformers, whereas the motor has three phases. This means that additional power conversion electronics on the mover part of the machine is necessary.

III. SIMULATIONS

The transformer part of the topologies is analyzed and characterized by means of a two dimensional finite element analysis steady state ac solver. Figure4 shows the flux line distributions of the first and second topologies. The depth of the first model is 8 mm, which is equal to the width of an end tooth. The second topology has the same flux line

distribu-tion but the depth is increased with the length of the pole pitch. The depth of the third model, as shown in Fig. 5, is equal to the mover length 共120 mm兲. For sinusoidal time variation of the magnetic field, the frequency is given by

f = Vrms

␲NAcBˆ

冑

, 共1兲

where Vrms is the primary rms voltage, N is the number of

primary turns, Acis the cross section of the core, and Bˆ is the

peak value of the flux density. By extending the width of the end teeth in topology 1 from 8 to 20 mm, topology 2 is obtained. Now, Ac increases and the frequency and thus

losses decrease. From Figs.4and5it can be seen that there is a relatively high leakage inductance due to the airgaps in the transformer. The leakage inductances can be compen-sated for without increasing the primary voltage by the use of a capacitor on the primary side in series with the

trans-FIG. 2.共Color online兲 Flux density distribution in an end tooth and a phase tooth for a position where the flux density in the end tooth is maximal.

FIG. 3. Topology for the CET integrated in the back iron of a PMLSM.

FIG. 4. Flux line distributions of topology 1 with a depth of 8 mm and topology 2 with a depth of 20 mm.

FIG. 5. Flux line distribution of topology 3 with a depth of 120 mm.

07F115-2 Krop et al. J. Appl. Phys. 105, 07F115共2009兲

former. The LC combination is tuned to the frequency of the magnetic field,

f = 1

2␲

冑

where L_␴ is the leakage inductance.

The lamination direction of the secondary cores is per-pendicular to the regular lamination direction of the mover to decrease the losses due to the high frequency magnetic field. The total losses in the volume V can be calculated by means of Bertotti’s formula:4

冕冕冕

再

冕

冋

冉

冊

冉

冊

册

冎

where khand keare coefficients given by the manufacturer of

the steel, kf is the stacking factor共0.9兲, T is the period,␴is

the conductivity of the steel, and d is the thickness of the lamination. The thickness of the lamination d = 0.1 mm and the conductivity␴= 1.92 MS. The power transfer per trans-former as a function the load with and without capacitor for

each topology is plotted in Fig.6. An overview of important characteristics of the transformer for each topology is given in Table I. Since topologies 1 and 2 have a transformer in each end tooth, the total power to be transferred per trans-former is 500 W.

IV. CONCLUSION

From the obtained results it can be concluded that the presented topologies are able to transfer 1 kW of power wire-lessly from the static part of the PMLSM to the moving part. It is also shown that the use of a resonant capacitor boosts the power transfer. Topology 1 requires no changes in the geometrical structure of the mover but the lamination direc-tion of the end tooth. However, due to the small volume of the end teeth, the frequency has to be sufficiently high to be able to transfer the required amount of power. Inevitably this also leads to the highest core losses. Using the same prin-ciple as topology 1 but extending the end tooth gives topol-ogy 2, which allows lowering of the frequency and thus losses without compromising the cogging profile of the PMLSM. An increase in efficiency of 33% is obtained com-pared to topology 1. Topology 3 has the lowest core losses since the cross section is the largest and the frequency is relatively low. However, due to the large slit in which the secondary coil is placed, the force density of this topology is poor.

1_{J. de Boeij, E. A. Lomonova, and A. J. A. Vandenput,IEEE Trans. Magn.}

44, 1118共2008兲.

2_{J. Lastowiecki and P. Staszewski, IEEE Trans. Ind. Electron. 53, 1943} 共2006兲.

3_{N. Fujii and T. Mizuma, IEEE IAS ’08, 2008共unpublished兲.}

4_{J. J. H. Paulides, G. W. Jewell, and D. Howe,IEEE Trans. Magn.40, 2041} 共2004兲.

TABLE I. Overview of important transformer characteristics.

Topology Nprim Nsec

Vp 共V兲 Ac 共mm2_兲 f 共Hz兲 Ploss 共W兲 B 共T兲 L_␴ 共mH兲 1 500 250 250 40 2500 22 0.9 2.5 2 500 250 250 160 1000 14 0.9 6.7 3 250 500 500 360 1000 11 0.9 54.9 1000 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000 1100 Load R [ Ω] P out [W] topology 1, no C topology 2, no C topology 3, no C topology 1, with C topology 2, with C topology 3, with C

FIG. 6. Output power per transformer for three topologies with and without resonant capacitor.

07F115-3 Krop et al. J. Appl. Phys. 105, 07F115共2009兲