Measurement of internal forces in superconducting accelerator magnets with strain gauge transducers Page: 3 of 7
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.. :: r"merts are :.-t'd at operating temperature nen
thC cor:esnoing resistances and coelicients at --4.2"K are
use(:.
For the numerical example a typical measurement made
during a magnet test is used. In this case the magnet tem-
perature :s --3.8'K and a current of 7000 A is present which
correspon1s to a central Held of --7 Tesia.
Th- yanrm resms ance, in onms for the active and two
compensa::g gauges are
1:.,,, - 350 3173
P- = 349.2203 and 349.2299
The reference resistances for the active and two compensating
gauges at 4.2' K are:
Rc2 = 349.7893
R, = 348.9909 and 348.9898
The beam calibration least squares fit calibration constants at
4.2*K are'
A2 = 165.92
B2 = 3.5218 x 106
C2 = 3.5626 x 108
Thus, the total resistance change for the active gauge is .5285
ohms from its initial unstrained state at 4.2'K and the corre-
sponding change in the average of the two compensating gauges
was .2347 ohms due to the combined effect of the tempera-
ture change from 4.2'K to that of the operating temperature
and the effect of the magnetic field. The resistance change
of the active gauge caused by the mechanical strain only is
therefore .2938 ohms. The mechanical strain resistance ratio,
RR = .2938/349.7893 or 84.0 x 10-5. Substituting this value
in the least square fit equation for coil stress gives a value of
3376 psi for the coil stress under these conditions. The rela-
tive error in the stress measurement can be estimated if it is
assumed that the accuracy of the resistance measurement is
i.005 ohms which is consistent with the previously mentioned
accuracy of the resistance measurement system. The relative
error in the stress measurement would be as follows:
Since the individual resistance measurements are uncorrolated,
then the variance in resistance ratio is
ARR = _ R,
where R, are the five individual measurements to determine
RR and AR; = AR is the uncertainty in the measurements.
Performing the indicated partial differentiation,fAR \2. /' Ra \2
4 1- since 0
4 I RR) R 2 /Using Rae = 350 and AR = .005:
ARR = (28 x 10-6)2
The variance in stress, from the equation for the least squares
fit of the calibration data is
r s l 2 2
As2 = B2+2C2RR)ARR]
with B2 = 3.5 x 106, C2 = 3.5 x 108, the accuracy of the
calculated coil stress is 114 psi.\tcra rencnts of Thermal Stres C
Stress Change with Magnet Current
Thermal Stress Changes in SSC Magnets
Measurement of the thermal contraction in the azimuthal
direction for SSC molded coils indicate that the thermal shrink-
age from 300 K to 4.2 K is about the same as that of aluminum,
i.e., -.004 in/in. The coils are assembled and compressed in
stainless steel collars having a thermal contraction of -.003
in/in for the same temperature range. Thus, there would be
a loss in compressive stress in the coils during cooldown. The
thermal stress change also depends on complex mechanical fac-
tors affecting the assembly of the collared coils in the yoke such
as the fit of the collared coil assembly in the foke and the in-
teraction of the thermal contraction of the helium containment
shell as the magnet cools down. Such assembly dependent ef-
fects are not readily calculable and thus, the beam type trans-
ducers provide a method of measuring the polar stress of the
coils as the magnet reaches operating temperature.
Several such measurements have been made on SSC model
magnets and some examples are given in the following table:
Table 1: SSC Model Magnets. Thermal Stress
Loss to Operating Temperature (Inner Coils,
Polar Stress, psi).
Operating
Magnet Ambient Temperature Delta
Designation Stress Stress Stress
DSS-006 8760 6660 2100
DSS-006R 7140 5100 2040
DSS-010 11850 4930 6920
DSS-011 9940 5530 4410
DSS-012 9550 4790 4760
DD-Ol0 6060 3500 2560
DD-012 7010 5400 1610Coil Polar Stress
Change with Magnet Current
The SSC magnets operate at high current (-7000 A) and
high field (-6.6 Tesla). The inner coils see the highest field
and are thus subjected to large Lorentz forces which tend to
move the conductors away from the poles. If the coils are not
held in compression against the poles under these conditions
the magnet could quench or suffer a loss of field quality. Thus,
it is important to ascertain that the coils are always compres-
sively stressed during magnet excitation in order to verify the
adequacy of the design and determine the available operating
margin. Again, the beam type transducers have been used for
this purpose. An example of this variation in stress is given
with some recent test results obtained from the 1.8 meter SSC
model magnet DSS012. Figure 9 shows that the average zero
current stress in the inner coils at the pole is about 4500 psi
and drops about 2300 psi at 6500 amps. It is noted that the
slope of the curves is not decreasing at the high current lev-
els indicating that there is ample reserve coil stress to prevent
unloading at the poles.
Measurement of Macnet End Forces
Measurements of magnet end forces are made with post
type compression transducers approximately 1.38 inches long
by .38 inches square with strain gauges mounted on opposite
sides as shown in Figure 10. The aspect ratio of this bar is
such that the gauges are mounted a sufficient distance away
from the edges so that they see a uniform strain field free from
edge effects. The two gauges on the opposite sides of the bar2 /R 2 RR- a / R- \2\
a~a = 4+
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Goodzeit, C. L.; Anerella, M. D. & Ganetis, G. L. Measurement of internal forces in superconducting accelerator magnets with strain gauge transducers, article, January 1, 1988; Upton, New York. (https://digital.library.unt.edu/ark:/67531/metadc1111161/m1/3/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.