On measurement and modelling of 2D magnetization and magnetostriction of SiFe sheets Anders ...

229 Pages·1999·1.99 MB·English

On measurement and modelling of 2D magnetization and
magnetostriction of SiFe sheets
Anders Lundgren
Royal Institute of Technology
Electric Power Engineering
Stockholm 1999
Anders Lundgren On measurement and modelling of 2D magnetization and magnetostriction of SiFe sheets
TRITA-EEA-9901
ISSN 1100-1593
Department of Electric Power Engineering
Royal Institute of Technology
SE-100 44 Stockholm
SWEDEN
On measurement and modelling of 2D magnetization and
magnetostriction of SiFe sheets
Anders Lundgren
Royal Institute of Technology
Electric Power Engineering
Stockholm 1999
Akademiskavhandlingsommedtillst(cid:23)andavKunglTekniskaH(cid:127)ogskolanframla(cid:127)gges
till o(cid:11)entlig granskning f(cid:127)or avla(cid:127)ggande av teknisk doktorsexamen m(cid:23)andagen den
21 juni 1999 kl 14.00i Kollegiesalen, Administrationsbyggnaden, Kungl Tekniska
H(cid:127)ogskolan, Valhallav(cid:127)agen 79, Stockholm.
TRITA-EEA-9901
ISSN 1100-1593
cAnders Lundgren, 1999
(cid:13)
KTH Reprocentral, Stockholm 1999
Abstract
The development and technological aspects of a 2D magnetization and magne-
tostriction measurement setup are documented and described. Local magnetic in-
tensity and (cid:13)ux density are measured with Rogowskiand material encircling coils.
In-plane strain is measured with a homodyne laser interferometer. Measured and
processed time-domain signals, hysteresis plots and signature data such as loss are
presentedbyane(cid:14)cientandcommunicativeinterface. Measurementsonquadratic
siliconironsheetsamplesareincluded. Materialtypestestedonthesetuparewith
non-oriented and oriented textures. Possible excitations include uniaxial alternat-
ingmagnetic(cid:12)eldintherollingandtransversedirectionsbetween10and300Hzat
least. Rotational excitations are possible at least for the non-oriented and conven-
tional grain-orientedtypes. The value of the setup lies in the possibility of using it
for routine measurements on samples.
The interplay between mathematical modelling and physical experimenting is de-
scribed. Investigationsby algebraicandnumericalmethods aredone to(cid:12)nd a pos-
sible way to parameterize material behaviour and include this behaviour in (cid:12)nite
element programs. On the basis of a proposed one-dimensional nonlinear model,
algorithms are devised to compute magnetostrictive responses to uniaxially alter-
nating magnetic (cid:12)elds. An experimental FEM program to calculate strain (cid:12)elds
frominhomogeneousmagnetizationisdeveloped. Itsuseforinvestigationofsample
behaviour during the operation of the setup is shown. The value of the proposed
modelling methodology lies in the study of possibilities of loweringthe production
of magnetostrictive vibration in transformer,motor and generatorcores.
IEEE index terms: Magnetostriction, silicon steel, magnetic cores, strain, inter-
ferometry, magnetic anisotropy, magnetic (cid:12)elds, magnetic measurements, magne-
toelasticity, nonlinear magnetics, power transformers, power distribution acoustic
noise, (cid:12)nite element methods.
TRITA-EEA-9901
ISSN 1100-1593
Acknowledgements
I would like to thank the members of the reference committee, Jan Anger (ABB
Transformers), Thomas Edstro(cid:127)m (ABB Corporate Research) and Birger Nilsson
(ABBCorporateResearch)andElektraprogrammemanagerStenBergman(Elforsk
AB) for their work in supporting this project.
On the department side I owe thanks to the project manager G(cid:127)oran Engdahl for
energizingtheproject,applying forfunding andproofreading. Headofdepartment
RolandErikssonisthankedforemployingmeandforadministeringthe(cid:12)nancesand
agreements. I especially wish to thank former research associate Anders Bergqvist
for many stimulating discussions and collaborations. I thank Olle Br(cid:127)annvall, Go(cid:127)te
Bergh and Yngve Eriksson for making parts to the experimental setup and trans-
porting it. I send greetings to friendly department colleagues Eckart Nipp, Niklas
Magnusson, Fredrik Stillesj(cid:127)o, Mats Kvarngren and Anders Helgesson.
I (cid:12)nally express heartily thanks to my girlfriend Cecilia H(cid:127)aggmark for her encour-
agement, proofreading and general support.
Anders Lundgren
i
Contents
1 Introduction 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation and goals . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Credits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4.1 Magnetic hysteresis models . . . . . . . . . . . . . . . . . . . 5
1.4.2 Magnetostriction . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.3 Stress dependence . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.4 Measurement methods . . . . . . . . . . . . . . . . . . . . . . 12
1.4.5 Numerics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.6 Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Measurement system 17
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Purposes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Drawing and design system . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Data acquisition programs . . . . . . . . . . . . . . . . . . . . . . . . 21
ii
2.5 Magnetic circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.6 Excitation frequency limits . . . . . . . . . . . . . . . . . . . . . . . 23
2.7 Voltage or current sti(cid:11) ampli(cid:12)er . . . . . . . . . . . . . . . . . . . . 28
2.8 B-coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.9 Calibration of the H-coil . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.10 Measurement table . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.10.1 Support placement . . . . . . . . . . . . . . . . . . . . . . . . 33
2.10.2 Optic component placement . . . . . . . . . . . . . . . . . . . 33
2.11 Vibration of material . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.12 Digital control issues . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.13 Strain measurement by interferometry . . . . . . . . . . . . . . . . . 36
2.14 Stress in(cid:13)uence, frame e(cid:11)ect . . . . . . . . . . . . . . . . . . . . . . . 37
2.15 Yoke design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.16 Magnetic sensor design . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.17 Temperature drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.18 Signal conditioning and Nyquist limit . . . . . . . . . . . . . . . . . 39
2.19 Signal bu(cid:11)ering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.20 Measurement coil misalignments . . . . . . . . . . . . . . . . . . . . 43
2.21 Using the measurement system . . . . . . . . . . . . . . . . . . . . . 43
2.21.1 Magnetic measurements . . . . . . . . . . . . . . . . . . . . . 43
2.21.2 Peak (cid:13)ux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.21.3 Measurement procedure . . . . . . . . . . . . . . . . . . . . . 44
3 Interferometer 46
iii
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 Homodyne interferometry . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 Heterodyne interferometry . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4 Interferometer alignment . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5 Doppler e(cid:11)ect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.6 Motion of measurement table . . . . . . . . . . . . . . . . . . . . . . 52
3.7 Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.8 The acousto-opticmodulator . . . . . . . . . . . . . . . . . . . . . . 60
3.9 Beam splitters and prisms . . . . . . . . . . . . . . . . . . . . . . . . 62
3.10 Interference (cid:12)lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.11 Photodiode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.12 Demodulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.13 Interferometer type . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.14 Re(cid:13)ector placements and properties . . . . . . . . . . . . . . . . . . 65
4 Strain analysis 68
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.2 De(cid:12)nitions of observables . . . . . . . . . . . . . . . . . . . . . . . . 68
4.2.1 2D strain measurement analysis. . . . . . . . . . . . . . . . . 73
4.2.2 Deformation of volume elements . . . . . . . . . . . . . . . . 76
4.3 Stress and 3D elastic material relations. . . . . . . . . . . . . . . . . 77
4.4 2D elastic material modelling . . . . . . . . . . . . . . . . . . . . . . 80
4.4.1 Magnetostriction components and constitutive relations . . . 80
4.4.2 Elasticity and compliance matrices . . . . . . . . . . . . . . . 85
iv