MECHANICAL HYSTERESIS IN MATERIALS USED
IN SUPERCONDUCTING ELECTRICAL MACHINES
R. Adams, V. Coveney
To cite this version:
R. Adams, V. Coveney. MECHANICAL HYSTERESIS IN MATERIALS USED IN SUPERCONDUCTING ELECTRICAL MACHINES. Journal de Physique Colloques, 1983, 44 (C9),
pp.C9-291-C9-296. <10.1051/jphyscol:1983940>. <jpa-00223387>
HAL Id: jpa-00223387
https://hal.archives-ouvertes.fr/jpa-00223387
Submitted on 1 Jan 1983
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
JOURNAL DE PHYSIQUE
Colloque C9, supplement au n°12, Tome 44, decembre 1983
page C9-291
MECHANICAL HYSTERESIS IN MATERIALS USED IN SUPERCONDUCTING ELECTRICAL
MACHINES
R.D. Adams and V.A. Coveney
University of Bristol,
Bristol BS8 1TR, U.K.
Dept. of Mechanical Engineering,
Queen's
Building,
Resunfe -- Nous presentons
Resunfe
présentons iici
o i lles
e s rrésultats
e s u l t a t s pour
pour quelques
quelques materiaux
matériaux qui
qui seront
seront
u t i l i s e s dans
utilisas
dans lles
e s machines 'électriques
e^lectriques supraconductrices
supraconductrices (cryogênerateurs).
(cryogenerateurs).
Abstract -- W
Abstract
Wee present
present damping rresults
e s u l t s for
for aa v
variety
a r i e t y of
of m
materials
a t e r i a l s which will
will
be used in
in superconducting eelectrical
l e c t r i c a l machines (cryoalternators).
(cryoalternators).
I - INTRODUCTION
There are several practical applications for which knowledge of the dynamic
behaviour of materials at temperatures near and below 20 K is important. These
applications include liquid hydrogen technology and superconductor applications.
At present, most of the liquid hydrogen applications are in the area of rocket
propulsion although there are tentative plans for hydrogen powered aircraft.
Superconductor applications include NMR, particle accelerators, plasma confinement
and nuclear fusion, and superconducting AC generators. The purpose of this work
was to study the materials used in superconducting AC generators so that losses due
to mechanical hysteresis can be established reliably.
The problem is the inverse of that which is usually encountered in engineering.
Here, the interest is in low energy dissipation since the problem is not that of
resonance, but rather of heat generation within the AC generator which can result
in the conductors losing their superconducting properties. While much is known of
the damping properties of constructional materials at room temperature, less is
known of these properties at very low temperatures, and even less when cyclic
stresses of engineering significance are considered. The objective of this work is
to obtain results for several structural materials, such as copper, superconducting
alloys, stainless steel and glass fibre reinforced plastics. The unit of damping
used here is the specific damping capacity, IJJ, defined as ty = bJJ/U where U is the
maximum energy stored per cycle, and At/ is the energy dissipated.
Some predictions will be made for the power dissipation per unit volume of material
assuming a cyclic strain amplitude of 10 4 and a frequency of 50 Hz.
II - EXPERIMENTAL PROGRAMME
The specimen was in the form of a free-free beam and was driven in its first
flexural mode of vibration by a coil/magnet pair. The damping and natural frequency
were recorded automatically as the temperature changed over the range from M-K to
293 K. A programmed microcomputer was used to control the frequency and amplitude
of the excitation via a digital frequency synthesiser and a digital voltmeter. The
microcompter controlled up to twenty information channels, so that readings were
also taken of temperature as well as calculating the damping values. In this way,
a print-out was given of damping and natural frequency at different cyclic stress
amplitudes over a range of temperatures.
The specimen consists of a beam in bending and it is known that there is a linear
variation of stress across the section in addition to the lengthwise variation in
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983940
C9-292
JOURNAL DE PHYSIQUE
bending moment. However, t h i s can be accounted f o r by measuring t h e v a r i a t i o n
of damping with displacement amplitude and then using a f u n c t i o n of t h e form
t o g e t h e r with t h e v a r i a t i o n of s t r e s s , o, with p o s i t i o n i n t h e specimen.
technique is f u l l y described i n r e f e r e n c e s 1 and 2 .
This
-4
could be a t t a i n e d i n t h e apparatus
Cyclic s t r a i n s of t h e order of 10
%
used and t h i s was necessary i n o r d e r t o cover t h e range of amplitudes l i k e l y t o
be achieved i n c r y o a l t e r n a t o r s .
I11 RESULTS AND DISCUSSION
Annealed cryogenic grade copper
We were r a t h e r s u r p r i s e d a t first a t f i n d i n g a Bordoni peak i n annealed copper
( s e e Fig. l ) , a s t h i s r e s u l t appeared t o c o n t r a d i c t work published by N i b l e t t
& Wilks ( 3 ) who found a ~ d r d o n peak
i
only f o r cold-worked copper. In o r d e r t o
check t h a t t h e v i b r a t i o n t e s t i n g had not cold-worked t h e copper, t h e Vickers
hardness (KV10 = 5052) of a specimen t h a t had been t e s t e d a t l o w temperature was
compared with a s i m i l a r , u n t e s t e d annealed specimen,
Temperature
Fig. 1 V a r i a t i o n of s p e c i f i c damping c a p a c i t y , 6, with temperature f o r copper,
two Nb T i superconductors, a composite c a b l e and GlOCR g l a s s c l o t h i n
eP oxy
and with another s i m i l a r u n t e s t e d annealed specimen which had subsequently been
extended c o l d by 1.4% (HV10 = 56+2). These hardness t e s t s i n d i c a t e d t h a t t h e
e x t e n s i o n , whereas
amount of cold-work introduced by t e s t i n g was e q u i v a l e n t <1%
t h e curve of damping a g a i n s t temperature c l o s e l y ressembled N i b l e t t and Wilks'
curves f o r >2%. I t i s now b e l i e v e d t h a t t h e Bordoni peak occurs f o r annealed
when t h e a p p l i e d c y c l i c s t r e s s i s s u f f i specimens i n very pure f . c . c . metals
c i e n t l y high ( 4 , 5 ) .
Superconducting a l l o y s
S e v e r a l superconducting a l l o y s were t e s t e d , both i n t h e pure form and f a b r i c a t e d
a s f i l a m e n t s i n a copper m a t r i x . There was a s t r o n g maximum i n damping (I) 2 1.9%)
i n t h e as-received NbTi and a s s o c i a t e d with t h i s damping peak was a minumum i n
If changes i n l e n g t h can
resonant frequency and, t h e r e f o r e , i n Youns modulus.
be n e g l e c t e d , a t t h e minimum t h e modulus i s 3% below t h e room temperature v a l u e .
I n a d d i t i o n , t h e r e is a secondary damping peak (I) 2 0.95%) a t 25K. A f t e r 300%
cold work, t h e major damping peak has diminished t o approximately t h e same l e v e l
a s t h e secondary peak, which h a s been much l e s s e f f e c t e d .
Not s u r p r i s i n g l y , t h e behaviour of t h e Cu/NbTi composite ( t y p e A61) r e f l e c t s t h a t
of both t h e copper and t h e NbTi. A s f o r copper, t h e Bordoni peak is t h e dominant
f e a t u r e a t 70K (I) = 2.6%). But it should be noted t h a t t h i s peak i s s t r o n g e r t h a n
t h e ("law of mixtures") combination of r e s u l t s f o r copper and NbTi. I t appears
t h a t t h e r e i s a r e s i d u a l e f f e c t of cold-work on t h e copper i n s p i t e of t h e anneali n g a t 350 C t o one hour a f t e r each draw.
Glass f i b r e r e i n f o r c e d p l a s t i c s
R e s u l t s a r e given here f o r t y p e GlOCR GRP composite which i s a cryogenic grade
m a t e r i a l made from g l a s s c l o t h i n a n epoxy matrix. It can be seen from Fig. 1
t h a t t h e r e is a l a r g e damping peak (6 = 6.6%) a t 240K. There was a l s o a l a r g e
i n c r e a s e i n Young's modulus (about 20%) a s t h e temperature was decreased from
30GK t o 4K.
It i s believed t h a t t h e main damping peaks i n t h e epoxies a r e due t o (main chain)
segmental motion and it is t h i s behaviour t h a t g i v e s epoxies t h e i r r e l a t i v e l y high
damping c h a r a c t e r i s t i c s near room temperature; a t low temperatures t h e y t a k e on a
different (glassy) character.
Since GlOCR u s e s a solid-type epoxy r e s i n t h e manufacturers were unable t o manuf a c t u r e a s u i t a b l e p i e c e o f r e a c t e d r e s i n f o r our t e s t s . However, a specimen made
from a s i m i l a r epoxy (Ciba MY750) gave a damping peak of I) = 20% a t 210K, confirming t h a t t h e peak i n t h e GlOCR m a t e r i a l was matrix dominated.
Stainless s t e e l s
Three s t a i n l e s s s t e e l s o f t h e AISI 316 family were t e s t e d . These a r e candidate
m a t e r i a l s f o r t h e r o t o r of a c r y o a l t e r n a t o r and comprise t h e bulk of m a t e r i a l .
A l l of t h e s e m a t e r i a l s gave very much lower damping v a l u e s ( s e e Fig. 2) than t h e
copper, superconductors and GRP, t h e lowest being 316 LN. The anomalies i n t h e
r e s u l t s f o r 316 LN were r e p e a t a b l e , b u t not e x p l a i n a b l e .
A l l t h e s t a i n l e s s s t e e l s t e s t e d showed a p p a r e n t l y anomalous behaviour i n Young's
modulus below a c e r t a i n temperature (40-70K).
This t y p e of anomalous behaviour
( 6 ) and
has been r e p o r t e d ( a t very much h i g h e r f r e q u e n c i e s ) by Ledbetter
Ledbetter ( 7 ) , who have suggested t h a t it was due t o magnetic t r a n s i t i o n s ( 6 ) and
probably s p i n - g l a s s t r a n s i t i o n s ( 8 ) . However, it h a s a l s o been suggested t h a t t h e
anomalies might be due t o p a r t i a l A u s t e n i t i c - M a r t e n s i t i c t r a n s i t i o n s , which could
have important i m p l i c a t i o n s f o r t h e use of t h e s e s t e e l s . A simple experiment has
been c a r r i e d out by u s which involved comparing t h e inductance of a c o r e l e s s c o i l
and a s i m i l a r c o i l with EN58B (304) s t e e l specimen a s t h e c o r e . The two c o i l s
which formed two limbs of an out of balance, 2kHz a . c . bridge were taken through
st
JOURNAL DE PHYSIQUE
Temperature
K
Fig. 2
Variation of s p e c i f i c damping c a p a c i t y , $, w i t h temperature f o r t h r e e
stainless steels
t h e temperature range 4K - 300K. There was some p o s s i b l e i n d i c a t i o n of "anomalous"
magnetic behaviour ( i e : r e v e r s a l i n dL/dT) a t and below l o O K , whereas t h e anomaly
i n e l a s t i c modulus occurred a t and below 70K. The magnitude of t h e anomaly i n
inductance was not c o n s i s t e n t with an A u s t e n i t i c t o M a r t e n s i t i c t r a n s i t i o n of more
than I%,and was t h e r e f o r e u n l i k e l y t o have caused t h e l a r g e modulus anomaly
observed.
It should be pointed out t h a t both we and Ledbetter measure E from t h e v e l o c i t y of
sound ( ~ / p ) +and t h e dimensions of t h e specimen. I f t h e dimensions show some
anomalous v a r i a t i o n w i t h temperature, then it is d i f f i c u l t by dynamic t e s t s t o
s e p a r a t e t h e two parameters.
Additional work on t h e expansion of m a t e r i a l s ( e s p e c i a l l y s t a i n l e s s s t e e l s ) i n t h e
range 4 - 300K is t h e r e f o r e being c a r r i e d out using a very s e n s i t i v e d i l a t o m e t e r .
The purpose of t h i s work is t o s e e i f t h e r e a r e any anomalies i n expansion which can
be r e l a t e d t o t h e anomalies i n r e s o n a n t frequency.
Energy d i s s i p a t i o n
To convert t h e values of damping i n t o energy d i s s i p a t i o n , we use t h e equation:
AU
where
and
=
$j'EE2lJ,
f = frequency of v i b r a t i o n ,
E = Young's modulus
E = s t r a i n amplitude.
-4
Using v a l u e s of f = 50hz and E = 10
f o r a temperature of 4K.
, we
a r r i v e a t t h e values given i n Table 1
Table 1 Energy d i s s i p a t i o n i n c r y o a l t e r n a t o r m a t e r i a l s
3
(Watts/m )
Material
All
Cryogenic grade copper
>350
NbTi a s received
103
NbTi cold worked 300%
A61 superconductor
88
-200
GlOCR GRP
20
316 annealed
33
316 LN annealed
17
316 High C
17
It is c l e a r from t h e s e r e s u l t s t h a t t h e superconductor is a s i g n i f i c a n t source
of energy d i s s i p a t i o n , owing t o t h e high damping of both t h e NbTi and t h e copper.
Under c y c l i c c o n d i t i o n s of l o a d i n g , it i s t h e r e f o r e e s s e n t i a l t h a t t h e h e a t gene r a t e d be conducted away e f f i c i e n t l y .
IV
CONCLUSIONS
Damping r e s u l t s have been given f o r a v a r i e t y of c r y o a l t e r n a t o r m a t e r i a l s . Under
t h e c y c l i c loading c o n d i t i o n s which may be experienced i n p r a c t i c e , t h e h i g h e s t
energy d i s s i p a t i o n w i l l occur i n t h e superconductors and t h e s e must t h e r e f o r e be
adequately cooled.
V
REFERENCES
1. Adams R.D.&
J. Phys. D: Appl. Phys,
Bacon D.G.C.,
2.
Guild F.J.& Adams R.D.,
3.
N i b l e t t D.H.
4.
N i b l e t t D .H.,
5.
Stadelmann P. & Benoit W . ,
6.
Ledbetter H.M.,
J . Phys. E: S c i . I n s t r . ,
& Wilks J . , P h i l . Mag.,
2,
6,
(1973), 27.
14,(1981),
355.
(1957), 1427.
P r i v a t e communication.
Weston W.F.
S c r i p t a Metallurgica,
& Naimon E.R.,
11,(1977),
J . Appl. Phys.,
645.
5, (1975),
3855.
C9-296
7.
L e d b e t t e r H.M.,
8.
C o l l i n g s E.W.
JOURNAL DE PHYSIQUE
J . Appl. Phys.,
& L e d b e t t e r H.M.,
52,
(19811, 1587.
Physics L e t t e r s ,
c,
(1979),
53.