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Frictional heating of magnet structural materials at cryogenic temperatures
Frictional heating of magnet structural materials at cryogenic temperatures A. Iwabuchi and K. Komuro Department of Mechanical Engineering, Iwate University, 4-3-5 Ueda, Morioka 020, Japan
Received 13 February 1991; revised 17 June 1991 One of the causes of quench in a superconducting magnet is frictional heat. The properties of the frictional force and the frictional heat of magnet structural materials were investigated at 4.2 K in liquid helium. The relationship between temperature rise, measured with a thermocouple, and frictional heat has been discussed. The coefficient of friction varied with the change in frictional variables such as normal load, sliding distance and surface roughness, even for the same material combination. When slip was repeated, a heat pulse occurred due to alternate stick and slip during sliding, and a peak in the temperature rise appeared, corresponding to the heat pulse. The temperature rise was insensitive to the small change in frictional heat in the pulse. The first peak in the temperature rise, which was associated with the temperature rise due to friction in the magnet, was not related to the frictional heat, Fv, directly but to a function of Fv 3/4, where F is the frictional force and v the sliding velocity.
Keywords: superconducting magnets; quench; friction
One of the problems to be solved in the development of a large-scale superconducting magnet for a nuclear fusion reactor is how to prevent coil quench. The way to avoid quench is to prevent the nucleation of the normal zone, or to prevent its propagation. At the final stage of magnet design, during which the material, the cooling method, the shape and dimensions of each element, etc. are determined, a precise estimation of the heat from the various heat sources will be completed in order to avoid the quench. One of the mechanical disturbances causing quench is the frictional heating at the contact points in a magnet due to micro-slips ~. From the point of view of the heat calculation of a magnet 2, it is absolutely necessary to prepare data on the frictional heat of the specific material combination, not its coefficient of friction. At present, information about the sliding parameters, such as real contact area, the stress condition at that area, actual sliding velocity and sliding distance in the magnet, are limited, although the actual sliding event and the sliding point in a magnet can be detected using an acoustic emission (AE) technique 3. In addition, attempts have been made to measure the rigidities of the contact surfaces and the wound coil, and the misalignment of wound wires, which ~govern the ease of the slip movement in a magnet ~. To evaluate the frictional heat for a quench, not only should the factors affecting the slip event be obtained in an actual magnet, but, in parallel, the fundamental frictional data should also be obtained in laboratory tests on candidate materials. 0011 - 2275/91/110969-06 © 1991 Butterworth-Heinemann
For the precise heat calculation, it is essential to estimate the frictional heat. In the heat calculation the units of heat are usually W m -3 (Reference 2). It is significant that the frictional heat is not produced uniformly over the apparent contact area. As the frictional heat and the temperature rise occur locally at the real contact points in the apparent contact area, the estimation of the local temperature is important. Therefore, measurement of the temperature rise has been performed using simplified friction test apparatus to make an appropriate model for the heat calculation 5. The objective of this paper is to examine the fundamental properties of the coefficient of friction, frictional heat and the temperature rise due to friction of the structural materials of a superconducting magnet in laboratory tests.
Experimental details The experimental apparatus used in this work was the fretting wear testing machine at cryogenic temperatures described in previous work 5'6. Details of the apparatus are described in Reference 6. Oscillating linear slip motion was exerted on a moving specimen clamped by two fixed specimens. The moving cylindrical specimen, which had a spherical tip, was SUS316L stainless steel. The fixed fiat specimens were made of SUS316L, polyimide, CFRP and GFRP. The SUS316L specimens were turned, polished and buffed to give a surface roughness,
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Cryogenics 1991 Vol 31 November
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Frictional heating: A. Iwabuchi and K. Komuro Table 1
Specimen materials and their Vickers microhardness and peak-to-valley surface roughness
Material
Composition
Hv (MPa)at 293 K
Rmax (#m)
SUS316L CFRP(s) CFRP(r) GFRP Polyimide PTFE
18Cr - 1 5Ni - 1Mn - 3 M e - C - Fe Graphite fibre epoxy (cloth) Graphite fibre epoxy (cloth) Glass fibre epoxy (Arisawa EL850) ( D u P o n t - T o r a y , Kapton 50OH)
3210 140 166 368 -
0.05 4.23 96.1 O.61 0.3 1.1
Rm,x, of 0.05/zm. The polyimide film and CFRP and GFRP plates were cut to size and glued using epoxy t o the SUS316L flat specimen. The surfaces of these specimens were as received. There are two kinds of surfaces on the CFRP specimens, with different surface roughness. Table 1 lists the characteristics of the specimens. In order to measure the temperature rise of the specimen due to the frictional heating, a thermocouple ( A u - 0 . 0 7 at% Fe versus Chromel, each with a diameter of 75 #m) was inserted into the moving metal specimen ~ 0 . 4 mm below the contacting surface. The appropriate details are noted in Reference 5. A schematic diagram of the specimen arrangement is shown in Figure 1. Experiments were conducted under conditions of normal loading from 10 to 60 N, with sliding distances from 50 to 650/~m, in liquid helium at 4.2 K. The sliding velocity was varied by driving the pulley of an eccentric device manually. Frictional force and relative displacement (sliding distance) were measured using strain gauges attached to the elastic ring and plate spring, respectively. Frictional force, displacement and temperature rise were recorded by a digital recorder, the sampling time of which was set from 100 to 200/~s, depending on the sliding velocity. Based on the data of displacement versus time, actual sliding velocity was calculated, while the instantaneous frictional heat (frictional power) was calculated as the product of the sliding velocity and frictional force.
Experimental results and discussion Properties of coefficient of friction
Figure 2 shows the range of the coefficient of friction for various material combinations at various mechanical conditions, which includes data obtained in previous papers 5-7. It is important to mention that the coefficient of friction is not constant for the specific material combination, but varies depending on the experimental conditions. Therefore, the actual sliding conditions in a magnet should be known to estimate the frictional heating. Typical examples of the dependence of the coefficient of friction on mechanical factors are shown as follows. Figure 3 reveals the relationship between coefficient of friction and normal load for the S U S 3 1 6 L - C F R P combination, where the coefficient of friction was derived from the peak-to-peak frictional force in one cycle (see Figure 7). The coefficient of friction decreased with an increase in the normal load, and the coefficient of friction for the smooth CFRP is higher than that for rough CFRP at light loads. However, the difference in the coefficient of friction between two different surface roughness types disappears at 60 N. No clear effect of the sliding velocity is observed in the figure.
SUS316L-SUS316L
4.0 0
//
Cu-Cu JN1-JN1
0
0
JN2-JN2
/cu
04
0z5
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0
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PI-Cu
0
0
Epoxy-SUS316L
O.
Epoxy-Cu
0
0
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o (smooth)
o
CFRP-SUS316L
o
o ( rough )
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0
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?!,, /
o 0
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o
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0
I
0.2
I
I
0.4
I
I
0.6
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i
0.8
I
[
//
10
Coefficient of friction CoLd
Figure 1
970
junction
Schematic diagram of specimen assembly
Cryogenics
1991
V o l 31 N o v e m b e r
Figure 2 Range of coefficient of friction for different combinations at 4.2 K in liquid helium
Frictional heating: A. Iwabuchi and K. Komuro 0.6 0.5
SUS316L-CFRP o •
0.5
V (mm/s)0.28
c" O
z~ •
[] •
Smooth Rough
c-
.o
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SUS316L-CFRP o 5N • 40N z~ 1ON • 60N [] 20N O
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._u 0.2
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lb
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Figure 3 C o e f f i c i e n t SUS31 6L - C F R P
of
friction
6'0
Figure 4 Coefficient SUS31 6L - CFRP(s)
, N versus
normal
load
1130 2()0 3C)0 4C)0 5C)0 6()0 Slip distance , )Jm of friction
sliding
versus
7()0
distance
for
for
The decrease in the coefficient of friction with increase in normal load can be explained by the elastic contact. IAccording to Hertzian contact between a sphere and a plate, the contact area is proportional to the twothirds power of magnitude of load. Then, the coefficient of friction is inversely proportional to the one-third power of magnitude of load '. When Hertzian mean contact pressure exceeds the hardness of the material, full plastic contact takes place 8. The contact pressure ~s calculated using available data for materials, and it is 115 MPa at a normal load of 60 N, which is almost the same as the hardness of CFRP in Table 1. As a result, plastic contact occurs for both rough and smooth surfaces at 60 N, and it can be said that the effect of surface roughness disappears in such plastic contact. The fact that the smooth surface shows higher friction at light loads is explained as follows: the smooth surface against smooth sphere makes a single contact point, and the contact area is proportional to the two-thirds power of magnitude in the elastic contact region, as noted above. On the other hand, the rough surface makes multi-contact points, and the total contact area is proportional to a higher power of magnitude than that for the single contact point s . The contact area thus becomes less for the rough surface than for the smooth surface and, therefore, the coefficient of friction is smaller for the rough surface. In the case of the fiat-to-fiat contact configuration, the criterion for plastic contact is that the plastic contact takes place when the parameter referred as to the 'plasticity index', which is a function of the surface roughness, the tip radius of surface asperities, the hardness and the Young's modulus, exceeds unity 9. For an actual coil, the nominal cramping stress between conductor and spacer is designed in the range 1 0 - 5 0 MPa. It is difficult to determine clearly whether the contact is elastic or plastic under such a condition. However, it appears that the contact is basically elastic because the stress level is not as high as the hardness of the spacer materials shown in Table 1, though the higher asperities on the rough surfaces deform plastically.
Figure 4 exhibits the effect of sliding distance on the coefficient of friction. The coefficient of friction generally increases with the sliding distance. In this case the increase in the coefficient of friction is caused by the increase in the frictional force with the sliding distance, as shown in Figure 5. At the small sliding distance of 100 #m (Figure 5a), the static friction is greater than the kinetic friction. The static friction does not depend on the sliding distance. At the large sliding distance of 550 #m, the friction reaches a maximum at the end of sliding (Figure 5c). The hysteresis curves of sliding distance and frictional force for five material combinations are shown in Figure 6. It can be seen that the features of the curves are not the same, and that, even if the coefficient of friction is the same, the frictional work, i.e. the area of the hysteresis curve, is not the same. The change in the hysteresis curve has been discussed elsewhere 1°. Properties of frictional heating and temperature rise
Figure 7 illustrates an example of the changes in frictional force, displacement, velocity, frictional heat, Q, and temperature rise against time for the S U S 3 1 6 L CFRP(s) combination. From the displacement curve it is
[ 100,urn (a) 100,um
(b) 400~Jm
(c) 550jum
Figure 5 Hysteresis curves of frictional force and sliding distance for different sliding distances at 3.1 4 m m s - ~ for SUS31 6 L - CFRP(s)
Cryogenics 1991 Vol 31 November
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Frictional heating: A. Iwabuchi and K. Komuro stick
I::
sti~ slips.tic~,slip .J..~ip
i i
200k_ r: ~
r ', / Ill
• ol -200
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SUS316L-Polyimde
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-
\
_
/"
..
rq
f
-,0[
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~,~
t._/
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Hysteresis curves for five combinations at 20 N, and 550/~m
s -1
6 4 2 0
o
obvious that sliding is not continuous, and slip and stick appear alternately in a half-cycle. Frictional force is not constant, but peaks at the beginning of the slip, i.e. the static friction, then increases again with sliding. The velocity reaches a maximum at the middle of the slip period. Two heat pulses occur in each cycle, corresponding to two slip events per cycle. The first heat pulse is rather small because of the acceleration process; the heat increases with time due to the increase in velocity over one pulse, and a large fluctuation occurs in the latter half of the pulse, depending on the changes in both the frictional force and the velocity. This tendency in the frictional heat is also observed for four other different material combinations. A distinct sharp peak appears for S U S 3 1 6 L - SUS316L and SUS316L-polyimide. In accordance with the frictional heat, the peak of the temperature rise appears twice a cycle; the peak increases and becomes saturated at and after the fourth peak. The increase in the temperature is caused by the frictional heat during the slip and the decrease is caused by cooling by liquid helium during the stick. The saturated temperature is attributed to the heat balance between the heating and the cooling. It has been emphasized that the 'micro-slip', the sliding distance of which is 10/zm or less, is important for the magnet ~'~. The fluctuation of the sliding velocity and frictional force is caused by this micro-slip, which is referred to as 'stick-slip' behaviour during sliding. Compared with the fluctuation of the frictional heat, the temperature rise is rather smooth. Therefore, it can be said that the small fluctuation derived from the stick-slip behaviour does not significantly affect the temperature rise in the substrate. The frictional heat caused by the micro-slip is much smaller than that caused by the gross slip or macro-slip. Figure 8 shows the relationship between the mean frictional heat, Qav, which is the mean height of all the pulses shown in Figure 7, and the normal load for the SUS316L-CFRP(s) combination. The mean frictional heat increases linearly with the normal load. It is also dependent on sliding velocity: the higher the sliding
972
\ll
SUS316L-CFRP(S)
200~um
Figure 6 9.57 m m
i] ''
z0o
SUS316L-CFRP(R)
\
'
'
L
;4
Cryogenics 1991 Vol 31 November
I
00
100
200
300
400
500
Time, ms Figure 7 Changes in displacement, frictional force, velocity, fricheat, Q, and temperature rise versus time for SUS31 6L - CFRP(s)
tional
velocity, the greater the frictional heat. The sliding velocity in this case is the nominal sliding velocity obtained from 2 x (slip amplitude)/one cyclic period. Figure 9 shows the relationship between the coefficient of friction and the mean frictional heat of the pulses, aav, at a normal load of 20 N and a sliding velocity of 9.57 mm s -~ for five combinations. It is apparent that the relationship between them is almost linear. From this result, the frictional heat can be evaluated, to a first approximation, from the coefficient of friction of the materials under the same conditions. xlO-2 SUS316L-CFRP(S) 3
.2
• 9.57mm/s
•
~
s
~
/
~
~
~
0 1
0 Figure 8
10
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50
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Effect of sliding velocity on the relationship between mean frictional heat of all heat pulses, Oav, and normal load
Frictional heating: A. Iwabuchi and K. Komuro x104
3
>
o SUS316L z~ Polyimide o GFRP • CFRP(S) • CFRP(R)
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SUS316L-CFRP(S)
V=9.5?mm/s
°°/
o 3.14mm/s
1.5 •
"2
~
1.0
1
E Q;
0.5
• 9.57minis
0
o
o'.1
0'.2
o13
0'.4
o
Figure 9 Relationship between mean frictional heat, Qav, and coefficient of friction
The increase in temperature peak with repeated sliding is illustrated in Figure 10 against the frictional heat pulse for the SUS316L-CFRP(s) combination, where the heat pulse, qav, is obtained as the average height of the corresponding heat pulse shown in Figure 7. The temperature increases and then saturates at 2.7 K at and after the fourth peak, where the mean frictional heat also saturates at ~ 23 mW. The saturation of the frictional heat means that the repeated sliding is in the steady state. When the sliding velocity is low at 3.14 mm s -l, the temperature rise is low because of the lower frictional heat, in spite of the same value of frictional work. When considering sliding in the magnet, the slip event between the conductor and the spacer is not cyclic. Therefore, the first temperature peak caused by the first slip in this work is important. The relationships between the first peak of the temperature rise and the average frictional heat, q,v, of the first pulse at different normal loads were obtained for the SUS316L-CFRP(s) combination. Although the temperature rise increases with the frictional heat for sliding velocities of 3.14 and 9.57 mm s -1, the temperature rise at 9.57 mm s -1 is lower than that at 3.14 mm s -1 in the lower frictional heat region. This result means that the actual temperature rise is not directly related to the frictional heat, Fv, or to the sliding velocity, v. After some calculation, we find that the temperature rise against the mean value of a function of Fv 3/4 in the first heat pulse
~
o 3.14mm/s • 9.57minis
"I " 2
/= "-/~/
P=20N
z/
2
I
I
i
I
1
2 qav,
W
i
L
3
xlO-2
Figure 10 Temperature rise v e r s u s mean frictional heat of a corresponding heat pulse, qav, for SUS316L-CFRPIs)
4
6 Fv 3/4
8 ,
10 12 N(m/s)314
1/. xl0-3
Figure 11 Relationship between the first temperature rise and the mean value of F v 3t4 of the first heat pulse for SUS31 6L - CFRP(s)
gives a good relationship, irrespective of sliding velocity, as shown in Figure 11. The velocity of the slip plays a significant part in determining the temperature rise occurring with frictional heat, as noted above. Therefore, what governs the velocity should be stated. It has been determined that the sliding velocity relates linearly to the loading rate of the tangential force in the range 5 - 1 0 3 N s -1 in the present work. This means that if the excitation rate of the magnet is rapid, the induced sliding velocity becomes fast, and the resultant frictional heat and temperature rise become large. Finally, the relation between the fundamental friction test carried out in this work and the actual conductor sliding friction in a magnet is discussed. In this work the contact geometry is a sphere-to-fiat configuration, while the actual contact geometry between a conducting wire and spacer in a magnet is apparently the fiat-to-fiat configuration. These two configurations are quite different. However, in spite of the apparent flat-to-fiat contact, microscopically the real contact occurs at higher asperities on the surfaces. Contact between such asperities resembles sphere-to-fiat contact. Therefore, the approach described in this paper is adequate for obtaining the fundamental frictional data. In the heat calculation, it was assumed that the heat disturbance was a rectangular pulse and that it was generated uniformly over a certain contact area 2. It is important to recognize that the frictional heat is generated at the real contact junctions locally distributed over the apparent contact area. For a rough estimation of the real contact area under plastic contact, it is assumed that the nominal contact pressure is 10 MPa, the apparent contact area between spacer and conductor is 400 mm 2 and the hardness of GFRP is 368 MPa. The real contact area, Ar, is obtained by the following equation
ar
/
0
o
i
0
Coefficient of friction
SUS316L- CFRP (S)
•
=
P/H
= paa/H
(1)
where: P is the normal load applied on the apparent contact area, Aa; H is the hardness; and p is the nominal pressure. If we put the above values into Equation (1), the real contact area is 10.9 mm 2. The ratio of the real contact area to the apparent contact area is
Cryogenics 1991 Vol 31 November
973
Frictional heating: A. Iwabuchi and K. Komuro 0.027. This means that only 2.7% of the apparent contact area can bear the normal load in plastic contact. Measurement of the temperature rise during sliding has been attempted by Kensley et al. 12 and Takao et al. 13, who inserted the thermocouple between two-fiat surfaces. In these cases the temperature rise measured did not reflect the real temperature rise at the interface. It is uncertain as to whether the tip of the thermocouple junction is located in the real contact area. It is reasonable to analyse the frictional heat and temperature rise using the frictional data obtained in the present work. For the next stage, therefore, the calculation method should be developed for interactions between the actual contact points on the surface using frictional data for a single point contact, because the fiat surface consists of many real contact points. Of course, if the contact spots are distributed uniformly over the apparent contact area, it can be assumed that the frictional heat is generated uniformly over the contact area. This is possible because the spaces between contact spots are uniform and the thermal conductivity and thermal diffusivity of OHFC copper, used as the stabilizer in the conductor, are rather high. However, if a misalignment of the wound wire in a coil occurs, the contact spots can be expected to be distributed irregularly in the contact area and the generated frictional heat concentrates at certain localized places in the apparent contact area, as noted above. Consequently, the frictional data concerning the interaction of the contact points can be applied to the heat calculation of the magnet.
Conclusion The properties of the friction and the frictional heat of magnet materials were investigated at 4.2 K in liquid helium. The following conclusions are drawn. 1 The coefficient of friction is not constant for a given material combination; it depends on mechanical conditions such as normal load or sliding distance. Therefore, the actual sliding condition in the magnet should be obtained to estimate the frictional heat precisely. 2 If the sliding condition is the same, the frictional heat is related to normal load and the coefficient of friction linearly. 3 When the slip event is repeated, the frictional heating appears in the form of a pulse. The frictional heat fluctuates in a pulse according to the variation of the frictional force and velocity due to the micro-slip.
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Cryogenics 1991 Vol 31 November
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5
The temperature rise has peaks according to the frictional heat pulses, and the temperature peak increases with repetition of the heat pulse. However, the temperature rise is insensitive to the fluctuation in heating during a single pulse. The first temperature peak is not directly related to the frictional heat, but is related to a function of
El,' 3/4.
Acknowledgements
The authors wish to thank Professor H. Takahashi at Tohoku University for his guidance and discussion in this work. The authors also wish to thank K. Hosokawa and K. Saita for their experimental assistance. This work was supported by the research grant aid of the Ministry of Education, Japan (Nos 01050022 and 02650106).
References 1 Iwasa, Y. Cryogenics (1985) 25 304 2 Okada, T., Aihara, T., Kim, J.K. and Kuroda, K. J Cryog Eng Jpn (1990) 25 323 3 Mito, T., Yamamoto, J., Motojima, O., Takahata, K., Takeo, M., Tuda, Y., Obiki, T. and Iiyoshi, A. Excitationtests of the first superconductinghelical coil as R&D programof large helicaldevice Proc MT-11 ElsevierApplied Science, LondonUK (1989) 783 4 Shindou, Y. Shoji, T., Nakajima, M., Nakajima, H., Sugimoto, M., Yoshida, K. and Tsuji, H. The estimationof the coil rigidity of a superconductingmagnetProc 44th Meeting on Cryogenics and Superconductivity Cryogenic Association of Japan, Tokyo, Japan
(1990) 225 5 Iwabuchi, A. and Honda, T. Temperature rise due to frictional
sliding of SUS316Lvs SUS316Land SUS316Lvs Polyimideat 4 K Proc MT-11 ElsevierApplied Science, London, UK (1989) 686 6 Iwabuchi, A., Honda, T. and Tani, J. Cryogenics (1989) 29 124 7 lwabuchi, A. and Yoshida, K. Frictionalpropertiesof JN1 and JN2 at cryogenic temperatures Proc 44th Meeting on Cryogenics and Superconductivity Cryogenic Association of Japan, Tokyo Japan
(1990) 78 8 Bowden, F.P. and Tabor, D. Friction and Lubrication Clarendon Press, Oxford, UK (1986) 10 9 Moore, D.F. Principles and Applications of Tribology Pergamon Press, London, UK (1975) 37 10 Iwabuchi, A. and Honda, T. J Jpn Soc Tribol (1991) 36(9) (in Japanese) 11 Maeda, H., Tsnkamoto, O. and Iwasa, Y. Cryogenics (1982) 22 287 12 Kensley,R.S., Maeda, H. and Iwasa, Y. Cryogenics (1981)21 479 13 Takao, T., Honjo, S. and Tsukamoto, O. Techniqueto reduce disturbance energy due to frictional conductor motion in superconducting magnet Proc MT-11 ElsevierApplied Science, London, UK (1989) 1108
Received 13 February 1991; revised 17 June 1991 One of the causes of quench in a superconducting magnet is frictional heat. The properties of the frictional force and the frictional heat of magnet structural materials were investigated at 4.2 K in liquid helium. The relationship between temperature rise, measured with a thermocouple, and frictional heat has been discussed. The coefficient of friction varied with the change in frictional variables such as normal load, sliding distance and surface roughness, even for the same material combination. When slip was repeated, a heat pulse occurred due to alternate stick and slip during sliding, and a peak in the temperature rise appeared, corresponding to the heat pulse. The temperature rise was insensitive to the small change in frictional heat in the pulse. The first peak in the temperature rise, which was associated with the temperature rise due to friction in the magnet, was not related to the frictional heat, Fv, directly but to a function of Fv 3/4, where F is the frictional force and v the sliding velocity.
Keywords: superconducting magnets; quench; friction
One of the problems to be solved in the development of a large-scale superconducting magnet for a nuclear fusion reactor is how to prevent coil quench. The way to avoid quench is to prevent the nucleation of the normal zone, or to prevent its propagation. At the final stage of magnet design, during which the material, the cooling method, the shape and dimensions of each element, etc. are determined, a precise estimation of the heat from the various heat sources will be completed in order to avoid the quench. One of the mechanical disturbances causing quench is the frictional heating at the contact points in a magnet due to micro-slips ~. From the point of view of the heat calculation of a magnet 2, it is absolutely necessary to prepare data on the frictional heat of the specific material combination, not its coefficient of friction. At present, information about the sliding parameters, such as real contact area, the stress condition at that area, actual sliding velocity and sliding distance in the magnet, are limited, although the actual sliding event and the sliding point in a magnet can be detected using an acoustic emission (AE) technique 3. In addition, attempts have been made to measure the rigidities of the contact surfaces and the wound coil, and the misalignment of wound wires, which ~govern the ease of the slip movement in a magnet ~. To evaluate the frictional heat for a quench, not only should the factors affecting the slip event be obtained in an actual magnet, but, in parallel, the fundamental frictional data should also be obtained in laboratory tests on candidate materials. 0011 - 2275/91/110969-06 © 1991 Butterworth-Heinemann
For the precise heat calculation, it is essential to estimate the frictional heat. In the heat calculation the units of heat are usually W m -3 (Reference 2). It is significant that the frictional heat is not produced uniformly over the apparent contact area. As the frictional heat and the temperature rise occur locally at the real contact points in the apparent contact area, the estimation of the local temperature is important. Therefore, measurement of the temperature rise has been performed using simplified friction test apparatus to make an appropriate model for the heat calculation 5. The objective of this paper is to examine the fundamental properties of the coefficient of friction, frictional heat and the temperature rise due to friction of the structural materials of a superconducting magnet in laboratory tests.
Experimental details The experimental apparatus used in this work was the fretting wear testing machine at cryogenic temperatures described in previous work 5'6. Details of the apparatus are described in Reference 6. Oscillating linear slip motion was exerted on a moving specimen clamped by two fixed specimens. The moving cylindrical specimen, which had a spherical tip, was SUS316L stainless steel. The fixed fiat specimens were made of SUS316L, polyimide, CFRP and GFRP. The SUS316L specimens were turned, polished and buffed to give a surface roughness,
Ltd
Cryogenics 1991 Vol 31 November
969
Frictional heating: A. Iwabuchi and K. Komuro Table 1
Specimen materials and their Vickers microhardness and peak-to-valley surface roughness
Material
Composition
Hv (MPa)at 293 K
Rmax (#m)
SUS316L CFRP(s) CFRP(r) GFRP Polyimide PTFE
18Cr - 1 5Ni - 1Mn - 3 M e - C - Fe Graphite fibre epoxy (cloth) Graphite fibre epoxy (cloth) Glass fibre epoxy (Arisawa EL850) ( D u P o n t - T o r a y , Kapton 50OH)
3210 140 166 368 -
0.05 4.23 96.1 O.61 0.3 1.1
Rm,x, of 0.05/zm. The polyimide film and CFRP and GFRP plates were cut to size and glued using epoxy t o the SUS316L flat specimen. The surfaces of these specimens were as received. There are two kinds of surfaces on the CFRP specimens, with different surface roughness. Table 1 lists the characteristics of the specimens. In order to measure the temperature rise of the specimen due to the frictional heating, a thermocouple ( A u - 0 . 0 7 at% Fe versus Chromel, each with a diameter of 75 #m) was inserted into the moving metal specimen ~ 0 . 4 mm below the contacting surface. The appropriate details are noted in Reference 5. A schematic diagram of the specimen arrangement is shown in Figure 1. Experiments were conducted under conditions of normal loading from 10 to 60 N, with sliding distances from 50 to 650/~m, in liquid helium at 4.2 K. The sliding velocity was varied by driving the pulley of an eccentric device manually. Frictional force and relative displacement (sliding distance) were measured using strain gauges attached to the elastic ring and plate spring, respectively. Frictional force, displacement and temperature rise were recorded by a digital recorder, the sampling time of which was set from 100 to 200/~s, depending on the sliding velocity. Based on the data of displacement versus time, actual sliding velocity was calculated, while the instantaneous frictional heat (frictional power) was calculated as the product of the sliding velocity and frictional force.
Experimental results and discussion Properties of coefficient of friction
Figure 2 shows the range of the coefficient of friction for various material combinations at various mechanical conditions, which includes data obtained in previous papers 5-7. It is important to mention that the coefficient of friction is not constant for the specific material combination, but varies depending on the experimental conditions. Therefore, the actual sliding conditions in a magnet should be known to estimate the frictional heating. Typical examples of the dependence of the coefficient of friction on mechanical factors are shown as follows. Figure 3 reveals the relationship between coefficient of friction and normal load for the S U S 3 1 6 L - C F R P combination, where the coefficient of friction was derived from the peak-to-peak frictional force in one cycle (see Figure 7). The coefficient of friction decreased with an increase in the normal load, and the coefficient of friction for the smooth CFRP is higher than that for rough CFRP at light loads. However, the difference in the coefficient of friction between two different surface roughness types disappears at 60 N. No clear effect of the sliding velocity is observed in the figure.
SUS316L-SUS316L
4.0 0
//
Cu-Cu JN1-JN1
0
0
JN2-JN2
/cu
04
0z5
PI -SUS316L
0
0
PI-Cu
0
0
Epoxy-SUS316L
O.
Epoxy-Cu
0
0
PTFE-SUS316L
0
O~O
o (smooth)
o
CFRP-SUS316L
o
o ( rough )
GFRP-SUS316L
0
GFRP-JN1
?!,, /
o 0
GFRP-JN2
o
o-.o I
0
I
0.2
I
I
0.4
I
I
0.6
I
i
0.8
I
[
//
10
Coefficient of friction CoLd
Figure 1
970
junction
Schematic diagram of specimen assembly
Cryogenics
1991
V o l 31 N o v e m b e r
Figure 2 Range of coefficient of friction for different combinations at 4.2 K in liquid helium
Frictional heating: A. Iwabuchi and K. Komuro 0.6 0.5
SUS316L-CFRP o •
0.5
V (mm/s)0.28
c" O
z~ •
[] •
Smooth Rough
c-
.o
334 9.57
U
0.4
SUS316L-CFRP o 5N • 40N z~ 1ON • 60N [] 20N O
I O
o.4
o
0.3
o
Z~
¢-
o 0.3
0.2
._~
o
._u 0.2
0.1
__•
.I.
o ~.)
0.1
o
0
lb
2'0
3'0 Load
Figure 3 C o e f f i c i e n t SUS31 6L - C F R P
of
friction
6'0
Figure 4 Coefficient SUS31 6L - CFRP(s)
, N versus
normal
load
1130 2()0 3C)0 4C)0 5C)0 6()0 Slip distance , )Jm of friction
sliding
versus
7()0
distance
for
for
The decrease in the coefficient of friction with increase in normal load can be explained by the elastic contact. IAccording to Hertzian contact between a sphere and a plate, the contact area is proportional to the twothirds power of magnitude of load. Then, the coefficient of friction is inversely proportional to the one-third power of magnitude of load '. When Hertzian mean contact pressure exceeds the hardness of the material, full plastic contact takes place 8. The contact pressure ~s calculated using available data for materials, and it is 115 MPa at a normal load of 60 N, which is almost the same as the hardness of CFRP in Table 1. As a result, plastic contact occurs for both rough and smooth surfaces at 60 N, and it can be said that the effect of surface roughness disappears in such plastic contact. The fact that the smooth surface shows higher friction at light loads is explained as follows: the smooth surface against smooth sphere makes a single contact point, and the contact area is proportional to the two-thirds power of magnitude in the elastic contact region, as noted above. On the other hand, the rough surface makes multi-contact points, and the total contact area is proportional to a higher power of magnitude than that for the single contact point s . The contact area thus becomes less for the rough surface than for the smooth surface and, therefore, the coefficient of friction is smaller for the rough surface. In the case of the fiat-to-fiat contact configuration, the criterion for plastic contact is that the plastic contact takes place when the parameter referred as to the 'plasticity index', which is a function of the surface roughness, the tip radius of surface asperities, the hardness and the Young's modulus, exceeds unity 9. For an actual coil, the nominal cramping stress between conductor and spacer is designed in the range 1 0 - 5 0 MPa. It is difficult to determine clearly whether the contact is elastic or plastic under such a condition. However, it appears that the contact is basically elastic because the stress level is not as high as the hardness of the spacer materials shown in Table 1, though the higher asperities on the rough surfaces deform plastically.
Figure 4 exhibits the effect of sliding distance on the coefficient of friction. The coefficient of friction generally increases with the sliding distance. In this case the increase in the coefficient of friction is caused by the increase in the frictional force with the sliding distance, as shown in Figure 5. At the small sliding distance of 100 #m (Figure 5a), the static friction is greater than the kinetic friction. The static friction does not depend on the sliding distance. At the large sliding distance of 550 #m, the friction reaches a maximum at the end of sliding (Figure 5c). The hysteresis curves of sliding distance and frictional force for five material combinations are shown in Figure 6. It can be seen that the features of the curves are not the same, and that, even if the coefficient of friction is the same, the frictional work, i.e. the area of the hysteresis curve, is not the same. The change in the hysteresis curve has been discussed elsewhere 1°. Properties of frictional heating and temperature rise
Figure 7 illustrates an example of the changes in frictional force, displacement, velocity, frictional heat, Q, and temperature rise against time for the S U S 3 1 6 L CFRP(s) combination. From the displacement curve it is
[ 100,urn (a) 100,um
(b) 400~Jm
(c) 550jum
Figure 5 Hysteresis curves of frictional force and sliding distance for different sliding distances at 3.1 4 m m s - ~ for SUS31 6 L - CFRP(s)
Cryogenics 1991 Vol 31 November
971
Frictional heating: A. Iwabuchi and K. Komuro stick
I::
sti~ slips.tic~,slip .J..~ip
i i
200k_ r: ~
r ', / Ill
• ol -200
~,_~oo
SUS316L-SUS316L
SUS316L-Polyimde
II I
-
\
_
/"
..
rq
f
-,0[
qJ
10P
~,~
t._/
5US316L-GFRP
Hysteresis curves for five combinations at 20 N, and 550/~m
s -1
6 4 2 0
o
obvious that sliding is not continuous, and slip and stick appear alternately in a half-cycle. Frictional force is not constant, but peaks at the beginning of the slip, i.e. the static friction, then increases again with sliding. The velocity reaches a maximum at the middle of the slip period. Two heat pulses occur in each cycle, corresponding to two slip events per cycle. The first heat pulse is rather small because of the acceleration process; the heat increases with time due to the increase in velocity over one pulse, and a large fluctuation occurs in the latter half of the pulse, depending on the changes in both the frictional force and the velocity. This tendency in the frictional heat is also observed for four other different material combinations. A distinct sharp peak appears for S U S 3 1 6 L - SUS316L and SUS316L-polyimide. In accordance with the frictional heat, the peak of the temperature rise appears twice a cycle; the peak increases and becomes saturated at and after the fourth peak. The increase in the temperature is caused by the frictional heat during the slip and the decrease is caused by cooling by liquid helium during the stick. The saturated temperature is attributed to the heat balance between the heating and the cooling. It has been emphasized that the 'micro-slip', the sliding distance of which is 10/zm or less, is important for the magnet ~'~. The fluctuation of the sliding velocity and frictional force is caused by this micro-slip, which is referred to as 'stick-slip' behaviour during sliding. Compared with the fluctuation of the frictional heat, the temperature rise is rather smooth. Therefore, it can be said that the small fluctuation derived from the stick-slip behaviour does not significantly affect the temperature rise in the substrate. The frictional heat caused by the micro-slip is much smaller than that caused by the gross slip or macro-slip. Figure 8 shows the relationship between the mean frictional heat, Qav, which is the mean height of all the pulses shown in Figure 7, and the normal load for the SUS316L-CFRP(s) combination. The mean frictional heat increases linearly with the normal load. It is also dependent on sliding velocity: the higher the sliding
972
\ll
SUS316L-CFRP(S)
200~um
Figure 6 9.57 m m
i] ''
z0o
SUS316L-CFRP(R)
\
'
'
L
;4
Cryogenics 1991 Vol 31 November
I
00
100
200
300
400
500
Time, ms Figure 7 Changes in displacement, frictional force, velocity, fricheat, Q, and temperature rise versus time for SUS31 6L - CFRP(s)
tional
velocity, the greater the frictional heat. The sliding velocity in this case is the nominal sliding velocity obtained from 2 x (slip amplitude)/one cyclic period. Figure 9 shows the relationship between the coefficient of friction and the mean frictional heat of the pulses, aav, at a normal load of 20 N and a sliding velocity of 9.57 mm s -~ for five combinations. It is apparent that the relationship between them is almost linear. From this result, the frictional heat can be evaluated, to a first approximation, from the coefficient of friction of the materials under the same conditions. xlO-2 SUS316L-CFRP(S) 3
.2
• 9.57mm/s
•
~
s
~
/
~
~
~
0 1
0 Figure 8
10
2'0 3? 4? Load , N
50
6'0
Effect of sliding velocity on the relationship between mean frictional heat of all heat pulses, Oav, and normal load
Frictional heating: A. Iwabuchi and K. Komuro x104
3
>
o SUS316L z~ Polyimide o GFRP • CFRP(S) • CFRP(R)
P=20N
SUS316L-CFRP(S)
V=9.5?mm/s
°°/
o 3.14mm/s
1.5 •
"2
~
1.0
1
E Q;
0.5
• 9.57minis
0
o
o'.1
0'.2
o13
0'.4
o
Figure 9 Relationship between mean frictional heat, Qav, and coefficient of friction
The increase in temperature peak with repeated sliding is illustrated in Figure 10 against the frictional heat pulse for the SUS316L-CFRP(s) combination, where the heat pulse, qav, is obtained as the average height of the corresponding heat pulse shown in Figure 7. The temperature increases and then saturates at 2.7 K at and after the fourth peak, where the mean frictional heat also saturates at ~ 23 mW. The saturation of the frictional heat means that the repeated sliding is in the steady state. When the sliding velocity is low at 3.14 mm s -l, the temperature rise is low because of the lower frictional heat, in spite of the same value of frictional work. When considering sliding in the magnet, the slip event between the conductor and the spacer is not cyclic. Therefore, the first temperature peak caused by the first slip in this work is important. The relationships between the first peak of the temperature rise and the average frictional heat, q,v, of the first pulse at different normal loads were obtained for the SUS316L-CFRP(s) combination. Although the temperature rise increases with the frictional heat for sliding velocities of 3.14 and 9.57 mm s -1, the temperature rise at 9.57 mm s -1 is lower than that at 3.14 mm s -1 in the lower frictional heat region. This result means that the actual temperature rise is not directly related to the frictional heat, Fv, or to the sliding velocity, v. After some calculation, we find that the temperature rise against the mean value of a function of Fv 3/4 in the first heat pulse
~
o 3.14mm/s • 9.57minis
"I " 2
/= "-/~/
P=20N
z/
2
I
I
i
I
1
2 qav,
W
i
L
3
xlO-2
Figure 10 Temperature rise v e r s u s mean frictional heat of a corresponding heat pulse, qav, for SUS316L-CFRPIs)
4
6 Fv 3/4
8 ,
10 12 N(m/s)314
1/. xl0-3
Figure 11 Relationship between the first temperature rise and the mean value of F v 3t4 of the first heat pulse for SUS31 6L - CFRP(s)
gives a good relationship, irrespective of sliding velocity, as shown in Figure 11. The velocity of the slip plays a significant part in determining the temperature rise occurring with frictional heat, as noted above. Therefore, what governs the velocity should be stated. It has been determined that the sliding velocity relates linearly to the loading rate of the tangential force in the range 5 - 1 0 3 N s -1 in the present work. This means that if the excitation rate of the magnet is rapid, the induced sliding velocity becomes fast, and the resultant frictional heat and temperature rise become large. Finally, the relation between the fundamental friction test carried out in this work and the actual conductor sliding friction in a magnet is discussed. In this work the contact geometry is a sphere-to-fiat configuration, while the actual contact geometry between a conducting wire and spacer in a magnet is apparently the fiat-to-fiat configuration. These two configurations are quite different. However, in spite of the apparent flat-to-fiat contact, microscopically the real contact occurs at higher asperities on the surfaces. Contact between such asperities resembles sphere-to-fiat contact. Therefore, the approach described in this paper is adequate for obtaining the fundamental frictional data. In the heat calculation, it was assumed that the heat disturbance was a rectangular pulse and that it was generated uniformly over a certain contact area 2. It is important to recognize that the frictional heat is generated at the real contact junctions locally distributed over the apparent contact area. For a rough estimation of the real contact area under plastic contact, it is assumed that the nominal contact pressure is 10 MPa, the apparent contact area between spacer and conductor is 400 mm 2 and the hardness of GFRP is 368 MPa. The real contact area, Ar, is obtained by the following equation
ar
/
0
o
i
0
Coefficient of friction
SUS316L- CFRP (S)
•
=
P/H
= paa/H
(1)
where: P is the normal load applied on the apparent contact area, Aa; H is the hardness; and p is the nominal pressure. If we put the above values into Equation (1), the real contact area is 10.9 mm 2. The ratio of the real contact area to the apparent contact area is
Cryogenics 1991 Vol 31 November
973
Frictional heating: A. Iwabuchi and K. Komuro 0.027. This means that only 2.7% of the apparent contact area can bear the normal load in plastic contact. Measurement of the temperature rise during sliding has been attempted by Kensley et al. 12 and Takao et al. 13, who inserted the thermocouple between two-fiat surfaces. In these cases the temperature rise measured did not reflect the real temperature rise at the interface. It is uncertain as to whether the tip of the thermocouple junction is located in the real contact area. It is reasonable to analyse the frictional heat and temperature rise using the frictional data obtained in the present work. For the next stage, therefore, the calculation method should be developed for interactions between the actual contact points on the surface using frictional data for a single point contact, because the fiat surface consists of many real contact points. Of course, if the contact spots are distributed uniformly over the apparent contact area, it can be assumed that the frictional heat is generated uniformly over the contact area. This is possible because the spaces between contact spots are uniform and the thermal conductivity and thermal diffusivity of OHFC copper, used as the stabilizer in the conductor, are rather high. However, if a misalignment of the wound wire in a coil occurs, the contact spots can be expected to be distributed irregularly in the contact area and the generated frictional heat concentrates at certain localized places in the apparent contact area, as noted above. Consequently, the frictional data concerning the interaction of the contact points can be applied to the heat calculation of the magnet.
Conclusion The properties of the friction and the frictional heat of magnet materials were investigated at 4.2 K in liquid helium. The following conclusions are drawn. 1 The coefficient of friction is not constant for a given material combination; it depends on mechanical conditions such as normal load or sliding distance. Therefore, the actual sliding condition in the magnet should be obtained to estimate the frictional heat precisely. 2 If the sliding condition is the same, the frictional heat is related to normal load and the coefficient of friction linearly. 3 When the slip event is repeated, the frictional heating appears in the form of a pulse. The frictional heat fluctuates in a pulse according to the variation of the frictional force and velocity due to the micro-slip.
974
Cryogenics 1991 Vol 31 November
4
5
The temperature rise has peaks according to the frictional heat pulses, and the temperature peak increases with repetition of the heat pulse. However, the temperature rise is insensitive to the fluctuation in heating during a single pulse. The first temperature peak is not directly related to the frictional heat, but is related to a function of
El,' 3/4.
Acknowledgements
The authors wish to thank Professor H. Takahashi at Tohoku University for his guidance and discussion in this work. The authors also wish to thank K. Hosokawa and K. Saita for their experimental assistance. This work was supported by the research grant aid of the Ministry of Education, Japan (Nos 01050022 and 02650106).
References 1 Iwasa, Y. Cryogenics (1985) 25 304 2 Okada, T., Aihara, T., Kim, J.K. and Kuroda, K. J Cryog Eng Jpn (1990) 25 323 3 Mito, T., Yamamoto, J., Motojima, O., Takahata, K., Takeo, M., Tuda, Y., Obiki, T. and Iiyoshi, A. Excitationtests of the first superconductinghelical coil as R&D programof large helicaldevice Proc MT-11 ElsevierApplied Science, LondonUK (1989) 783 4 Shindou, Y. Shoji, T., Nakajima, M., Nakajima, H., Sugimoto, M., Yoshida, K. and Tsuji, H. The estimationof the coil rigidity of a superconductingmagnetProc 44th Meeting on Cryogenics and Superconductivity Cryogenic Association of Japan, Tokyo, Japan
(1990) 225 5 Iwabuchi, A. and Honda, T. Temperature rise due to frictional
sliding of SUS316Lvs SUS316Land SUS316Lvs Polyimideat 4 K Proc MT-11 ElsevierApplied Science, London, UK (1989) 686 6 Iwabuchi, A., Honda, T. and Tani, J. Cryogenics (1989) 29 124 7 lwabuchi, A. and Yoshida, K. Frictionalpropertiesof JN1 and JN2 at cryogenic temperatures Proc 44th Meeting on Cryogenics and Superconductivity Cryogenic Association of Japan, Tokyo Japan
(1990) 78 8 Bowden, F.P. and Tabor, D. Friction and Lubrication Clarendon Press, Oxford, UK (1986) 10 9 Moore, D.F. Principles and Applications of Tribology Pergamon Press, London, UK (1975) 37 10 Iwabuchi, A. and Honda, T. J Jpn Soc Tribol (1991) 36(9) (in Japanese) 11 Maeda, H., Tsnkamoto, O. and Iwasa, Y. Cryogenics (1982) 22 287 12 Kensley,R.S., Maeda, H. and Iwasa, Y. Cryogenics (1981)21 479 13 Takao, T., Honjo, S. and Tsukamoto, O. Techniqueto reduce disturbance energy due to frictional conductor motion in superconducting magnet Proc MT-11 ElsevierApplied Science, London, UK (1989) 1108