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Influence of geometry and wave shape on magnetic amorphous material
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 290–291 (2005) 1520–1523 www.elsevier.com/locate/jmmm
Influence of geometry and wave shape on magnetic amorphous material A.J. Mosesa,, J. Leichta, D. Foxb a
Wolfson Centre for Magnetics Technology, School of Engineering, Cardiff University, P.O. Box 925, Newport Road, CF24 0YF, UK b Cogent Power Ltd., Newport, UK Available online 22 December 2004
Abstract The magnetic performance of 0.03 mm thick Co-based and 0.026 mm thick Fe-based amorphous ribbon in toroidal and strip form was measured under sine and pulse width modulation (PWM) waveform conditions. The measured loss, at 100 Hz fundamental frequency and a peak flux density of 91% of the saturation of each material, was separated into classical eddy current, hysteresis and anomalous loss components and the effect of geometry and waveform on these loss components was analysed. The results in general show a dimensional and waveform dependence which is not so great as in electrical steels. r 2004 Elsevier B.V. All rights reserved. PACS: 85.79.w; 70.50.y; 07.55.w; 70.60.Es Keywords: Magnetic loss; Pulse width modulation; Eddy current—loss; Hysteresis loss
Previous investigation [1,2] concludes that the magnetic properties of strip wound electrical steel cores are affected by their geometry, particularly the inner (ID) and the outer diameter (OD), the strip width (SW) and the build-up (BU) thickness of the toroid. The aspect ratio (AR ¼ SW/BU) and the winding ratio (WR ¼ ID/ SW) are defined in order to describe the effects of SW, BU and diameters on the magnetic performance of wound toroids. In general, the magnetic performance of the strip wound electrical steel toroids improves by increasing the aspect ratio. For example, the specific total loss measured in a sample of grain oriented 3% silicon steel with an aspect ratio of 1.7 was 22% lower than in a sample of the same material with an aspect ratio of 0.5 [1]. Corresponding author. Tel.: +44 29 2087 6854; fax: +44 29 20 876729. E-mail address: [email protected] (A.J. Moses).
Cobalt-based amorphous toroidal wound core with constant ID (25.5 mm), OD (37.5 mm) and BU thickness (6 mm), and with SW varying from 3.2 to 10 mm, were tested using a Power Loss Measurement System [3] over a fundamental frequency range from 100 Hz to 100 kHz under sinusoidally varying flux density and from 100 Hz to 1 kHz under pulse width a modulation (PWM) waveform excitation with a modulation index of 1.0 and frequency ratios of 7 and 15. For sine wave excitation, during the loss measurement the percentage of harmonics of the voltage induced in the secondary winding was kept lower than 3% to guarantee a form factor of 1:11 1%:The percentage total harmonic distortion (THD%) of the PWM waveform was kept within 3% of the calculated value of 57%. Table 1 shows the dimensions, winding factors and the aspect ratios of the cobalt-based amorphous toroidal wound cores investigated. Three samples of each size were measured and in all cases the standard deviation
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2004.11.565
ARTICLE IN PRESS A.J. Moses et al. / Journal of Magnetism and Magnetic Materials 290–291 (2005) 1520–1523
was around 3%. The measurements were repeated at least three time at 0.5 T peak flux density and the difference between each repeatability test was within 1%. The graphs presented are based on the results obtained from the samples with the higher winding ratios due to the effect of this parameter on the magnetising current. Fig. 1 shows that the specific total loss varies only a little with aspect ratio (AR) under sine wave excitation at 0.5 T peak flux density and fundamental frequency ranging from 1 to 100 kHz. The variation in each case Table 1 Dimensions and winding ratio of test samples Sample
OD (mm)
ID (mm)
SW (mm)
AR
WF
A1-A3 B1-B3 C1-C3 D1-D3 E1-E3
37.5 37.5 37.5 37.5 37.5
25.5 25.5 25.5 25.5 25.5
3.2 5.0 6.3 8.4 10.0
0.53 0.83 1.05 1.40 1.67
90–92% 85–87% 83–85% 69–72% 87–88%
Symbols are defined in the text.
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cannot be obviously linked with aspect ratio; the maximum difference between any size cores at a given frequency is 13% but there is no apparent trend relating loss frequency and geometry. This does not follow the same trend as in electrical steel previously measured at 50 Hz [1]. Of course the magnetic properties of the cobalt-based amorphous material used in this investigation are very different from those of electrical steel, particularly lower loss, higher permeability, higher resistivity, very low coercivity (0.3 A/m) and a rectangular hysteresis loop. The total power loss was measured under PWM waveform excitation and compared with the results obtained under sine wave conditions. This relates to a typical application of Co-based amorphous wound cores in magnetic amplifiers commonly used as high speed on/ off switches in switched-mode power suppliers. Fig. 2 shows the variation of specific total loss in sample A1 with fundamental frequency under sine and PWM waveform excitation at 0.55 T peak flux density. At 1.0 kHz, the specific total loss under PWM conditions was about 16% higher than under sinusoidal excitation. For the PWM waveforms the THD% decreases with the
Fig. 1. Variation of specific total loss with aspect ratio (AR) under sinusoidal magnetisation conditions at 0.5 T and frequencies of 1, 10 and 100 kHz in samples A1, B2, C2, D3 and E1.
ARTICLE IN PRESS 1522
A.J. Moses et al. / Journal of Magnetism and Magnetic Materials 290–291 (2005) 1520–1523
increase of the modulation index (ma), which in linear modulation conditions has a maximum value of unity (i.e. map1). In this investigation measurements on the cobalt-based material were carried out only at unity modulation index. If lower modulation indices were used, the ratio between power loss under PWM and sine waveform would increase. The specific total loss was separated into hysteresis, classical eddy current and anomalous loss components under sinusoidal and PWM magnetisation conditions. The hysteresis loss was measured using a D.C. permeameter. Classical eddy current loss Pe (W/kg) under sine wave excitation was calculated from Eq. (1), and under PWM conditions it was calculated from Eq.
Fig. 2. Variation of specific total loss in sample A1 (37.5 25.5 3.2 mm) with fundamental frequency under sine and PWM waveform excitation at 0.55 T peak flux density.
(2) [4], where the conductivity of the material (s) is 741,000 (O m)1, the thickness (d) is 3.0E05 m, and the ^ density (D) is 7700 kg/m3. BðTÞ and f (Hz) in Eq. (1) are the peak flux density (T) and the fundamental frequency (Hz), respectively. Erms, A and N2 in Eq. (2) are the root mean square value of the voltage induced (V) in the secondary winding, the cross section area and the number of secondary turns, respectively. The anomalous loss, for both types of excitation, was obtained by subtracting the hysteresis and classical eddy current loss from the total value. Pe ¼
2 sd 2 dB 2 p2 sd 2 B^ f 2 ¼ 12D dt 6 D
(1)
Pe ¼
sd 2 dB 2 sd 2 E rms 2 ¼ : 12D dt 12D N 2 A
(2)
Fig. 3 shows the variation of hysteresis loss, classical eddy current loss and anomalous loss with AR under sinusoidal flux conditions at 0.55 T peak flux density and 1 kHz fundamental frequency. Fig. 3 also shows the ratio of the individual components under PWM and sine waveform excitation. The hysteresis loss under sinusoidal flux for the AR of 1.67 was 8% higher (measurement uncertainty 2%) than for the AR of 0.53. This is not influenced by winding stress variations because the sample was previously annealed and therefore it must be due to the effect of geometry on internal flux distribution. The classical eddy current loss under PWM conditions was around 33% higher than the eddy current loss under sinusoidal excitation. For both
Fig. 3. Variations of hysteresis loss (Ph), classical eddy current (Pe), anomalous loss (Pa), and ratios of loss component under PWM and sine conditions with aspect ratio at 0.55 T peak flux density and 1 kHz fundamental frequency.
ARTICLE IN PRESS A.J. Moses et al. / Journal of Magnetism and Magnetic Materials 290–291 (2005) 1520–1523
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total loss under PWM conditions was, respectively, 11% and 7% higher than under sinusoidal excitation at 1.4 T. The main reason for this difference between PWM and sine conditions is the increase in the eddy current loss, which depends on the harmonic component in the flux density waveform. For a THD of 57%, (PWM, m ¼ 1) and 68% (PWM, m ¼ 0:8), the classical eddy current loss was, respectively, 49% and 89% higher than under sine waveform conditions. In conclusion, as anticipated the losses in the materials were very waveform dependent but, unlike electrical steel, only a little variation due to geometry was found for the range of samples investigated. Fig. 4. Variation of specific total loss in iron-based amorphous Epstein strip samples varying with peak flux density under sine and PWM (modulation index 1.0 and 0.8) waveform excitation at 50 Hz fundamental frequency.
waveforms the eddy current loss does not vary with the AR, hence indicating that this loss component does not depend on material geometry. Iron-based amorphous Epstein strips were measured under sine and PWM (modulation index 0.8 and 1.0, frequency ratio 15) magnetising conditions at 50 Hz fundamental frequency. Fig. 4 shows the variation of total loss with the peak flux density under sine and PWM excitations. For modulation index 0.8 and 1.0, the
The authors are grateful to EPSRC for financial support under Grant no. GR/R82869.
References [1] A.J. Moses, P.C.Y. Ling, Physica Scripta 40 (1989) 249. [2] W. Grimmond, A.J. Moses, P. Ling, IEEE Trans. on Magnetics 25 (1989) 2686. [3] P. Anderson, J. Leicht, A.J. Moses, UK Magnetic Society Seminar, Warwick, 2000. [4] A.J. Moses, J. Leicht, Report Series of the Physikalisch– Technische Bundesanstalt Braunschweig, PTB-E-81, (2003), pp. 181.
Journal of Magnetism and Magnetic Materials 290–291 (2005) 1520–1523 www.elsevier.com/locate/jmmm
Influence of geometry and wave shape on magnetic amorphous material A.J. Mosesa,, J. Leichta, D. Foxb a
Wolfson Centre for Magnetics Technology, School of Engineering, Cardiff University, P.O. Box 925, Newport Road, CF24 0YF, UK b Cogent Power Ltd., Newport, UK Available online 22 December 2004
Abstract The magnetic performance of 0.03 mm thick Co-based and 0.026 mm thick Fe-based amorphous ribbon in toroidal and strip form was measured under sine and pulse width modulation (PWM) waveform conditions. The measured loss, at 100 Hz fundamental frequency and a peak flux density of 91% of the saturation of each material, was separated into classical eddy current, hysteresis and anomalous loss components and the effect of geometry and waveform on these loss components was analysed. The results in general show a dimensional and waveform dependence which is not so great as in electrical steels. r 2004 Elsevier B.V. All rights reserved. PACS: 85.79.w; 70.50.y; 07.55.w; 70.60.Es Keywords: Magnetic loss; Pulse width modulation; Eddy current—loss; Hysteresis loss
Previous investigation [1,2] concludes that the magnetic properties of strip wound electrical steel cores are affected by their geometry, particularly the inner (ID) and the outer diameter (OD), the strip width (SW) and the build-up (BU) thickness of the toroid. The aspect ratio (AR ¼ SW/BU) and the winding ratio (WR ¼ ID/ SW) are defined in order to describe the effects of SW, BU and diameters on the magnetic performance of wound toroids. In general, the magnetic performance of the strip wound electrical steel toroids improves by increasing the aspect ratio. For example, the specific total loss measured in a sample of grain oriented 3% silicon steel with an aspect ratio of 1.7 was 22% lower than in a sample of the same material with an aspect ratio of 0.5 [1]. Corresponding author. Tel.: +44 29 2087 6854; fax: +44 29 20 876729. E-mail address: [email protected] (A.J. Moses).
Cobalt-based amorphous toroidal wound core with constant ID (25.5 mm), OD (37.5 mm) and BU thickness (6 mm), and with SW varying from 3.2 to 10 mm, were tested using a Power Loss Measurement System [3] over a fundamental frequency range from 100 Hz to 100 kHz under sinusoidally varying flux density and from 100 Hz to 1 kHz under pulse width a modulation (PWM) waveform excitation with a modulation index of 1.0 and frequency ratios of 7 and 15. For sine wave excitation, during the loss measurement the percentage of harmonics of the voltage induced in the secondary winding was kept lower than 3% to guarantee a form factor of 1:11 1%:The percentage total harmonic distortion (THD%) of the PWM waveform was kept within 3% of the calculated value of 57%. Table 1 shows the dimensions, winding factors and the aspect ratios of the cobalt-based amorphous toroidal wound cores investigated. Three samples of each size were measured and in all cases the standard deviation
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2004.11.565
ARTICLE IN PRESS A.J. Moses et al. / Journal of Magnetism and Magnetic Materials 290–291 (2005) 1520–1523
was around 3%. The measurements were repeated at least three time at 0.5 T peak flux density and the difference between each repeatability test was within 1%. The graphs presented are based on the results obtained from the samples with the higher winding ratios due to the effect of this parameter on the magnetising current. Fig. 1 shows that the specific total loss varies only a little with aspect ratio (AR) under sine wave excitation at 0.5 T peak flux density and fundamental frequency ranging from 1 to 100 kHz. The variation in each case Table 1 Dimensions and winding ratio of test samples Sample
OD (mm)
ID (mm)
SW (mm)
AR
WF
A1-A3 B1-B3 C1-C3 D1-D3 E1-E3
37.5 37.5 37.5 37.5 37.5
25.5 25.5 25.5 25.5 25.5
3.2 5.0 6.3 8.4 10.0
0.53 0.83 1.05 1.40 1.67
90–92% 85–87% 83–85% 69–72% 87–88%
Symbols are defined in the text.
1521
cannot be obviously linked with aspect ratio; the maximum difference between any size cores at a given frequency is 13% but there is no apparent trend relating loss frequency and geometry. This does not follow the same trend as in electrical steel previously measured at 50 Hz [1]. Of course the magnetic properties of the cobalt-based amorphous material used in this investigation are very different from those of electrical steel, particularly lower loss, higher permeability, higher resistivity, very low coercivity (0.3 A/m) and a rectangular hysteresis loop. The total power loss was measured under PWM waveform excitation and compared with the results obtained under sine wave conditions. This relates to a typical application of Co-based amorphous wound cores in magnetic amplifiers commonly used as high speed on/ off switches in switched-mode power suppliers. Fig. 2 shows the variation of specific total loss in sample A1 with fundamental frequency under sine and PWM waveform excitation at 0.55 T peak flux density. At 1.0 kHz, the specific total loss under PWM conditions was about 16% higher than under sinusoidal excitation. For the PWM waveforms the THD% decreases with the
Fig. 1. Variation of specific total loss with aspect ratio (AR) under sinusoidal magnetisation conditions at 0.5 T and frequencies of 1, 10 and 100 kHz in samples A1, B2, C2, D3 and E1.
ARTICLE IN PRESS 1522
A.J. Moses et al. / Journal of Magnetism and Magnetic Materials 290–291 (2005) 1520–1523
increase of the modulation index (ma), which in linear modulation conditions has a maximum value of unity (i.e. map1). In this investigation measurements on the cobalt-based material were carried out only at unity modulation index. If lower modulation indices were used, the ratio between power loss under PWM and sine waveform would increase. The specific total loss was separated into hysteresis, classical eddy current and anomalous loss components under sinusoidal and PWM magnetisation conditions. The hysteresis loss was measured using a D.C. permeameter. Classical eddy current loss Pe (W/kg) under sine wave excitation was calculated from Eq. (1), and under PWM conditions it was calculated from Eq.
Fig. 2. Variation of specific total loss in sample A1 (37.5 25.5 3.2 mm) with fundamental frequency under sine and PWM waveform excitation at 0.55 T peak flux density.
(2) [4], where the conductivity of the material (s) is 741,000 (O m)1, the thickness (d) is 3.0E05 m, and the ^ density (D) is 7700 kg/m3. BðTÞ and f (Hz) in Eq. (1) are the peak flux density (T) and the fundamental frequency (Hz), respectively. Erms, A and N2 in Eq. (2) are the root mean square value of the voltage induced (V) in the secondary winding, the cross section area and the number of secondary turns, respectively. The anomalous loss, for both types of excitation, was obtained by subtracting the hysteresis and classical eddy current loss from the total value. Pe ¼
2 sd 2 dB 2 p2 sd 2 B^ f 2 ¼ 12D dt 6 D
(1)
Pe ¼
sd 2 dB 2 sd 2 E rms 2 ¼ : 12D dt 12D N 2 A
(2)
Fig. 3 shows the variation of hysteresis loss, classical eddy current loss and anomalous loss with AR under sinusoidal flux conditions at 0.55 T peak flux density and 1 kHz fundamental frequency. Fig. 3 also shows the ratio of the individual components under PWM and sine waveform excitation. The hysteresis loss under sinusoidal flux for the AR of 1.67 was 8% higher (measurement uncertainty 2%) than for the AR of 0.53. This is not influenced by winding stress variations because the sample was previously annealed and therefore it must be due to the effect of geometry on internal flux distribution. The classical eddy current loss under PWM conditions was around 33% higher than the eddy current loss under sinusoidal excitation. For both
Fig. 3. Variations of hysteresis loss (Ph), classical eddy current (Pe), anomalous loss (Pa), and ratios of loss component under PWM and sine conditions with aspect ratio at 0.55 T peak flux density and 1 kHz fundamental frequency.
ARTICLE IN PRESS A.J. Moses et al. / Journal of Magnetism and Magnetic Materials 290–291 (2005) 1520–1523
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total loss under PWM conditions was, respectively, 11% and 7% higher than under sinusoidal excitation at 1.4 T. The main reason for this difference between PWM and sine conditions is the increase in the eddy current loss, which depends on the harmonic component in the flux density waveform. For a THD of 57%, (PWM, m ¼ 1) and 68% (PWM, m ¼ 0:8), the classical eddy current loss was, respectively, 49% and 89% higher than under sine waveform conditions. In conclusion, as anticipated the losses in the materials were very waveform dependent but, unlike electrical steel, only a little variation due to geometry was found for the range of samples investigated. Fig. 4. Variation of specific total loss in iron-based amorphous Epstein strip samples varying with peak flux density under sine and PWM (modulation index 1.0 and 0.8) waveform excitation at 50 Hz fundamental frequency.
waveforms the eddy current loss does not vary with the AR, hence indicating that this loss component does not depend on material geometry. Iron-based amorphous Epstein strips were measured under sine and PWM (modulation index 0.8 and 1.0, frequency ratio 15) magnetising conditions at 50 Hz fundamental frequency. Fig. 4 shows the variation of total loss with the peak flux density under sine and PWM excitations. For modulation index 0.8 and 1.0, the
The authors are grateful to EPSRC for financial support under Grant no. GR/R82869.
References [1] A.J. Moses, P.C.Y. Ling, Physica Scripta 40 (1989) 249. [2] W. Grimmond, A.J. Moses, P. Ling, IEEE Trans. on Magnetics 25 (1989) 2686. [3] P. Anderson, J. Leicht, A.J. Moses, UK Magnetic Society Seminar, Warwick, 2000. [4] A.J. Moses, J. Leicht, Report Series of the Physikalisch– Technische Bundesanstalt Braunschweig, PTB-E-81, (2003), pp. 181.