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Power losses of Finemet using nonsinusoidal waveforms
Journal of Magnetism and Magnetic Materials 203 (1999) 298}300
Power losses of Finemet using nonsinusoidal waveforms D. Ramin*, W. Riehemann Institut fu( r Werkstowkunde und Werkstowtechnik, TU Clausthal, Agricolastr. 6, D-38678 Clausthal-Zellerfeld, Germany
Abstract Though many practical applications preferably take advantage of nonsinusoidal induction waveforms the characterisation of soft magnetic materials is performed under sinusoidal induction waveforms. Therefore, it would be useful if results from magnetic measurements could be transformed to be valid for applications using di!erent waveforms. This also enables to compare results obtained from measurements where sinusoidal waveforms could not be realised and thus makes them independent of the measuring device used. The dynamic hysteresis loops of di!erently prepared Finemet ribbons were measured with a computer controlled device at di!erent frequencies and polarisations using sinusoidal and triangular waveforms of the magnetic "eld which leads to induction waveforms varying with frequency, amplitude of polarisation, waveform of the magnetising "eld and preparation of specimen material. The samples measured were strips of Fe Si Cu Nb B nanocrystallised at 5803C for 1 h. Di!erent types of samples were used which includes specimens surface treated prior to heat treatment in order to achieve domain re"nement. A one to one functional dependency between power loss, frequency, and k-factor was found that enables the comparison of power losses for di!erent induction signals characterised by their form factor as it is already known for grain oriented silicon steel sheets. This dependency is valid for all types of specimen investigated regardless of their di!erent magnetic properties. 1999 Elsevier Science B.V. All rights reserved. Keywords: Power losses; Form factor; Finemet; Frequency dependence
1. Introduction
2. Experimental
The power losses of soft magnetic materials are usually measured under sinusoidal induction waveforms at test frequencies of 50 or 60 Hz. However, many practical applications preferably take advantage of nonsinusoidal induction waveforms. Therefore, it would be useful if results from magnetic measurements could be converted to be valid for applications using di!erent waveforms. The aim of this paper is to show that this can be done for Finemet [1] as it was already achieved for grain oriented silicon iron steel applying the form factor k of the induced signal [2].
Strips 110 mm long and 3 mm wide were cut out of amorphous Fe Cu Nb Si B tapes (14.9 mm wide with thicknesses of 21 and 17 lm). Some of the specimens were surface treated prior to nanocrystallisation using a XeCl-Excimer laser. The surface treated and plain strips were both annealed in evacuated quartz tubes at 5803C for 1 h followed by quenching in a water bath at room temperature. The magnetic properties were measured in the frequency range between 3.2 Hz and 20 kHz at polarisations from 0.6 to 1 T with a computerised digital hysteresis recorder which is described in more detail elsewhere [3]. A magnetising "eld with sinusoidal or triangular waveform leads to induction waveforms (J dJ/dt) caused by the change of the specimen's magnetisation varying with frequency and amplitude of polarisation J . The waveforms of the digitally recorded induced voltages ; (t ) (i"121024, t: time) were charG G
* Corresponding author. Fax.: #49-5323-723-148. E-mail address: [email protected] (D. Ramin)
0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 2 5 8 - 9
D. Ramin, W. Riehemann / Journal of Magnetism and Magnetic Materials 203 (1999) 298}300
acterised by the form factor k numerically calculated over the signal period ¹: ((1/¹)2;(t) dt ( ; G G . k"
(1/¹)2";(t)"dt "; " G G
(1)
The form factor of the induced signal varies from k"1.04 up to 2.5 depending on the waveform of the magnetising "eld, the frequency, and the maximum polarisation.
299
3. Results Plotting the energy density P/f of Finemet versus the frequency for di!erent waveforms the losses increase with frequency. At a given frequency the losses with the larger corresponding form factor will be higher (Fig. 1). If the same data are plotted versus the frequency multiplied by the square of the form factor of each measurement both curves match each other within the error of measurement as shown in Fig. 2. Fitting the power of k to
Fig. 1. Total loss per cycle vs. frequency f on a logarithmic scale of untreated Finemet (heat treatment: 5803C for 1 h, maximum magnetisation J "0.9 T) using sinusoidal and triangular waveform.
Fig. 2. Total loss per cycle of the same sample and polarisation as shown in Fig. 1 vs. frequency f multiplied by the square of the form factors of each measurement.
300
D. Ramin, W. Riehemann / Journal of Magnetism and Magnetic Materials 203 (1999) 298}300
Fig. 3. Anomaly factor g determined from measured losses vs. frequency f k on a logarithmic scale of both axis. Surface treated Finemet (heat treatment: 5803C for 1 h, maximum magnetisation J "0.9 T).
the best match some specimens give slightly higher values. The dependency of the losses on the form factor can be analysed in more detail by separation of the losses. The frequency-dependent loss P( f ) can be divided into the frequency-independent hysteresis loss P which was esti mated by extrapolation of the power loss P( fP0) and the frequency-dependent dynamic loss P ( f ). P ( f ) can be expressed by the classical losses P ( f ) and the anomaly factor g( f ). P( f )"P #P ( f ), (2) P ( f )"g( f )P ( f ), (3) P ( f )"(2kdJ f )/(3o), (4) where d is the ribbon's thickness, J the amplitude of polarisation, f the frequency and o the electrical resistivity. The classical part P ( f ) of the dynamic losses P depends on f k of the induced signal. Because g de pends also on f it must be a function of k too. This is veri"ed by plotting the anomaly factor versus f k (Fig. 3). The same holds true for the excess "eld H if plotted analogously.
4. Conclusions If the form factor k is known, a one to one dependence of the power losses on the frequency multiplied by the
square of the form factor was found which is independent on the waveform used. Analogous results were obtained for the anomaly factor and the excess "eld. This behaviour is independent of the frequency dependence of the magnetic properties as observed for di!erently treated specimen of the Finemet material. Utilising these results the magnetic properties at sinusoidal waveform can be computed from measured results obtained for di!erent waveforms and thus are independent on the measuring device used.
Acknowledgements This work was supported by the Deutsche Forschungsgemeinschaft. The authors wish to thank G. Herzer and Dr. H.R. Hilzinger, Vakuumschmelze, Hanau for providing us with amorphous Fe Cu Nb Si B tapes.
References [1] T. Iuchi, S. Yamaguchi, T. Ichiyama, M. Nakamura, T. Ichimoto, K. Kuroki, J. Appl. Phys. 53 (1982) 2410. [2] B. Weidenfeller, W. Riehemann, Proceedings of ISEM.8, Braunschweig, 1997. [3] M. Pott-Langemeyer, W. Riehemann, W. Heye, An. Fis. B 86 (1990) 232.
Power losses of Finemet using nonsinusoidal waveforms D. Ramin*, W. Riehemann Institut fu( r Werkstowkunde und Werkstowtechnik, TU Clausthal, Agricolastr. 6, D-38678 Clausthal-Zellerfeld, Germany
Abstract Though many practical applications preferably take advantage of nonsinusoidal induction waveforms the characterisation of soft magnetic materials is performed under sinusoidal induction waveforms. Therefore, it would be useful if results from magnetic measurements could be transformed to be valid for applications using di!erent waveforms. This also enables to compare results obtained from measurements where sinusoidal waveforms could not be realised and thus makes them independent of the measuring device used. The dynamic hysteresis loops of di!erently prepared Finemet ribbons were measured with a computer controlled device at di!erent frequencies and polarisations using sinusoidal and triangular waveforms of the magnetic "eld which leads to induction waveforms varying with frequency, amplitude of polarisation, waveform of the magnetising "eld and preparation of specimen material. The samples measured were strips of Fe Si Cu Nb B nanocrystallised at 5803C for 1 h. Di!erent types of samples were used which includes specimens surface treated prior to heat treatment in order to achieve domain re"nement. A one to one functional dependency between power loss, frequency, and k-factor was found that enables the comparison of power losses for di!erent induction signals characterised by their form factor as it is already known for grain oriented silicon steel sheets. This dependency is valid for all types of specimen investigated regardless of their di!erent magnetic properties. 1999 Elsevier Science B.V. All rights reserved. Keywords: Power losses; Form factor; Finemet; Frequency dependence
1. Introduction
2. Experimental
The power losses of soft magnetic materials are usually measured under sinusoidal induction waveforms at test frequencies of 50 or 60 Hz. However, many practical applications preferably take advantage of nonsinusoidal induction waveforms. Therefore, it would be useful if results from magnetic measurements could be converted to be valid for applications using di!erent waveforms. The aim of this paper is to show that this can be done for Finemet [1] as it was already achieved for grain oriented silicon iron steel applying the form factor k of the induced signal [2].
Strips 110 mm long and 3 mm wide were cut out of amorphous Fe Cu Nb Si B tapes (14.9 mm wide with thicknesses of 21 and 17 lm). Some of the specimens were surface treated prior to nanocrystallisation using a XeCl-Excimer laser. The surface treated and plain strips were both annealed in evacuated quartz tubes at 5803C for 1 h followed by quenching in a water bath at room temperature. The magnetic properties were measured in the frequency range between 3.2 Hz and 20 kHz at polarisations from 0.6 to 1 T with a computerised digital hysteresis recorder which is described in more detail elsewhere [3]. A magnetising "eld with sinusoidal or triangular waveform leads to induction waveforms (J dJ/dt) caused by the change of the specimen's magnetisation varying with frequency and amplitude of polarisation J . The waveforms of the digitally recorded induced voltages ; (t ) (i"121024, t: time) were charG G
* Corresponding author. Fax.: #49-5323-723-148. E-mail address: [email protected] (D. Ramin)
0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 2 5 8 - 9
D. Ramin, W. Riehemann / Journal of Magnetism and Magnetic Materials 203 (1999) 298}300
acterised by the form factor k numerically calculated over the signal period ¹: ((1/¹)2;(t) dt ( ; G G . k"
(1/¹)2";(t)"dt "; " G G
(1)
The form factor of the induced signal varies from k"1.04 up to 2.5 depending on the waveform of the magnetising "eld, the frequency, and the maximum polarisation.
299
3. Results Plotting the energy density P/f of Finemet versus the frequency for di!erent waveforms the losses increase with frequency. At a given frequency the losses with the larger corresponding form factor will be higher (Fig. 1). If the same data are plotted versus the frequency multiplied by the square of the form factor of each measurement both curves match each other within the error of measurement as shown in Fig. 2. Fitting the power of k to
Fig. 1. Total loss per cycle vs. frequency f on a logarithmic scale of untreated Finemet (heat treatment: 5803C for 1 h, maximum magnetisation J "0.9 T) using sinusoidal and triangular waveform.
Fig. 2. Total loss per cycle of the same sample and polarisation as shown in Fig. 1 vs. frequency f multiplied by the square of the form factors of each measurement.
300
D. Ramin, W. Riehemann / Journal of Magnetism and Magnetic Materials 203 (1999) 298}300
Fig. 3. Anomaly factor g determined from measured losses vs. frequency f k on a logarithmic scale of both axis. Surface treated Finemet (heat treatment: 5803C for 1 h, maximum magnetisation J "0.9 T).
the best match some specimens give slightly higher values. The dependency of the losses on the form factor can be analysed in more detail by separation of the losses. The frequency-dependent loss P( f ) can be divided into the frequency-independent hysteresis loss P which was esti mated by extrapolation of the power loss P( fP0) and the frequency-dependent dynamic loss P ( f ). P ( f ) can be expressed by the classical losses P ( f ) and the anomaly factor g( f ). P( f )"P #P ( f ), (2) P ( f )"g( f )P ( f ), (3) P ( f )"(2kdJ f )/(3o), (4) where d is the ribbon's thickness, J the amplitude of polarisation, f the frequency and o the electrical resistivity. The classical part P ( f ) of the dynamic losses P depends on f k of the induced signal. Because g de pends also on f it must be a function of k too. This is veri"ed by plotting the anomaly factor versus f k (Fig. 3). The same holds true for the excess "eld H if plotted analogously.
4. Conclusions If the form factor k is known, a one to one dependence of the power losses on the frequency multiplied by the
square of the form factor was found which is independent on the waveform used. Analogous results were obtained for the anomaly factor and the excess "eld. This behaviour is independent of the frequency dependence of the magnetic properties as observed for di!erently treated specimen of the Finemet material. Utilising these results the magnetic properties at sinusoidal waveform can be computed from measured results obtained for di!erent waveforms and thus are independent on the measuring device used.
Acknowledgements This work was supported by the Deutsche Forschungsgemeinschaft. The authors wish to thank G. Herzer and Dr. H.R. Hilzinger, Vakuumschmelze, Hanau for providing us with amorphous Fe Cu Nb Si B tapes.
References [1] T. Iuchi, S. Yamaguchi, T. Ichiyama, M. Nakamura, T. Ichimoto, K. Kuroki, J. Appl. Phys. 53 (1982) 2410. [2] B. Weidenfeller, W. Riehemann, Proceedings of ISEM.8, Braunschweig, 1997. [3] M. Pott-Langemeyer, W. Riehemann, W. Heye, An. Fis. B 86 (1990) 232.