Transcript Review of the Design of the MiniBooNE Horn

Review of the Stress Analysis of
the MiniBooNE Horn MH1
Larry Bartoszek, P.E.
1/20/00
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Overview 1
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The MiniBooNE horn carries 170 kiloamps of
current in a pulse 143 microseconds long.
The pulse repeats 10 times in a row, 1/15 sec
between each pulse, then the horn is off until
2 seconds from the first pulse in train.
The horn is stressed by differential thermal
expansion and magnetic forces. We need to
design it to survive 200 million cycles with
>95% confidence.
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Overview 2

Motivation for design lifetime:
» The horn will eventually become very radioactive
and require a complicated handling procedure in
the event of a replacement. We don’t want to
make many of these objects.
» We can’t afford to make many horns.


The major design issue is fatigue.
Every component around the horn needs to
survive 200 million pulses to get overall
system reliability.
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Analysis Outline 1: Fatigue theory

Discussion of fatigue in Al 6061-T6
» Presentation of data sources
» Discussion of effects that modify maximum
stress in fatigue
» Discussion of scatter in the maximum
stress data in fatigue
» Discussion of multiaxial stress in fatigue
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Analysis Outline 2: Allowable stress

Determination of allowable stress in
fatigue
» Perform a statistical analysis on the MILSPEC data to get confidence curves for a
sample set of fatigue tests.
» This yields a starting point for maximum
stress that needs to be corrected for
environmental factors.
» The allowable is then compared with the
calculated stress from the FEA results.
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Analysis Outline 3: Calculated Stress


Description of the finite element model
FEA results on MH1 and the calculated
stresses
»
»
»
»
»
Assumptions
Thermal analysis
Magnetic force analysis
Combined forces transient analysis
Results for stress ratio R and maximum calculated
stress in horn
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Sources of Fatigue Data for
AL 6061-T6 used in analysis
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
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MIL-SPEC Handbook #5, Metallic Materials
and Elements for Aerospace Vehicles
ASM Metals Handbook Desk Edition
ASM Handbook Vol. 19, Fatigue and Fracture
“Aluminum and Aluminum Alloys”, pub. by
ASM
“Atlas of Fatigue Curves”, pub. by ASM
“Fatigue Design of Aluminum Components
and Structures”, Sharp, Nordmark and
Menzemer
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How well do sources agree?

For unwelded, smooth specimens, R=-1, room
temperature, in air, N=5*107
»
»
»
»

MIL-SPEC
smax=13 ksi (89.6 MPa)
Atlas of Fatigue Curves
smax=17 ksi (117.1 MPa)
Fatigue Design of Al…
smax=16 ksi (110.2 MPa)
Metals Handbook (N=5*108)smax=14 ksi (96.5 MPa)
These numbers represent 50% probability of
failure at 5*107 cycles.
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Effects that lower fatigue strength, 1

Geometry influences fatigue:
» Tests are done on “smooth” specimens and
“notched” specimens
» Smooth specimens have no discontinuities in
shape
» Notched specimens have a standard shaped
discontinuity to create a stress riser in the material

Notches reduce fatigue strength by ~1/2
» see graph on next slide
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ASM data showing effect of notches on fatigue strength
Graph from Atlas of Fatigue Curves
Effects that lower fatigue strength, 2

Welding influences fatigue:
» Welded and unwelded specimens are
tested

Welding reduces fatigue strength by
~1/2
» see graph on next slide
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ASM data
showing effect of
welding
Graph from Atlas of Fatigue Curves
Effects that lower fatigue strength, 3

The stress ratio influences fatigue strength:
» Stress Ratio, R, is defined as the ratio of the
minimum to maximum stress.
– Tension is positive, compression is negative
» R=Smin/Smax varies from -1R1
– R = -1 alternating stress) smax=16 ksi
– R = 0 Smin=0)
smax=24 ksi, (1.5X at R=1)
– R = .5 
smax=37 ksi, (2.3X at R=1)
» These values are for N=107 cycles, 50%
confidence
Stress ratio is a variable modifier to maximum
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stress.
Whole
stress
cycle
must
be
known.
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MIL-SPEC Data Showing Effect of R
This is the page from the MILSPEC handbook that was used
for the statistical analysis of the
scatter in fatigue test data.
The analytical model assumes
that all test data regardless of
R can be plotted as a straight
line on a log-log plot after all
the data points are corrected
for R.
The biggest problem with this
data presentation style is that
the trend lines represent 50%
confidence at a given life and
we need >95% confidence of
ability to reach 200 x 106
cycles.
Effects that lower fatigue strength, 4

Moisture reduces fatigue strength
» For R = -1, smooth specimens, ambient
temperature:
– N=108 cycles in river water,
– N=107 cycles in sea water,

smax= 6 ksi
smax~ 6 ksi
Hard to interpret this data point
– N=5*107 cycles in air,
smax= 17 ksi
» See data source on next slide
» Note curve of fatigue crack growth rate in
humid air, second slide
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ASM data on corrosion fatigue
strength of many Al alloys
Graph from “Atlas of
Fatigue Curves” showing
that the corrosion fatigue
strength of aluminum
alloys is almost constant
across all commercially
available alloys,
independent of yield
strength.
Data from this graph was
used to determine the
moisture correction factor.
ASM data on effect of moisture
on fatigue crack growth rate
Graph from “Atlas of Fatigue
Curves”
This graph is for a different
alloy than we are using, but
the assumption is that
moisture probably increases
the fatigue crack growth rate
for 6061 also.
It was considered prudent to
correct the maximum stress
for moisture based on this
curve and the preceding
one.
Discussion of scatter in the
maximum stress data in fatigue

The MIL-SPEC data is a population of 55 test
specimens that shows the extent of scatter in
the test results.
» Trend lines in the original graph indicate 50%
chance of part failure at the given stress and life.
» The source gave a method of plotting all the points
on the same curve when corrected for R.

We used statistical analysis to create
confidence curves on this sample set.
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Confidence Curves on
Equivalent Stress data plot
Stress/ Cycle Confidence Contours (97.5%, 94.9%, 75%, 50%, 25%)
This graph plots all
of the MIL-SPEC
data points
corrected for R by
the equation at
bottom. The y axis
is number of cycles
to failure, the x
axis is equivalent
stress in ksi.
1.0E+09
1.0E+08
Nf
1.0E+07
1.0E+06
1.0E+05
1.0E+04
1.0E+03
0
10
20
30
40
50
60
Seq : Sm ax*(1-R)^0.63
R M Laszew ski 22 September 1999
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From this graph
we concluded
that the
equivalent stress
for >97.5%
confidence at 2e8
cycles was 10 ksi.
Discussion of multiaxial stress in
fatigue

Maximum stress in fatigue is always
presented as result of uniaxial stress tests
» Horn stresses are multiaxial.

We assumed that we could sensibly compare
the uniaxial stress allowable with calculated
multiaxial combined stresses
» FEA provided stress intensities and principal
normal stresses that were converted to combined
stress
» See next slide for combined stress expression
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Expression for combined stress

Maximum Distortion Energy Theory
provides an expression for comparing
combined principal normal triaxial
stresses to yield stress in uniaxial
tension
» We assumed this expression was valid
comparing combined stress with uniaxial
fatigue maximum stress limit
» Sallow (S1-S2)2+(S2-S3)2+(S3-S1)2]/2}.5
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Allowable Stress Determination 1

Allowable stress starts as the equivalent
stress for 97.5% confidence that material will
not fail in 2e8 cycles
» Seq = 10 ksi (68.9 MPa)

Allowable stress is then corrected by
multiplicative factors, as described in
Shigley’s “Mechanical Engineering Design”
» Sallow = Seq*fR*fmoisture*fweld
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Calculation of stress ratio correction
factor:

First correction is for R,stress ratio
» We determined that the minimum stress was
thermal stress alone after the horn cooled
between pulses just before the next pulse.
» Maximum stress happened at time in cycle when
magnetic forces and temperature were peaked
simultaneously
» R was calculated by taking the ratio in every horn
element in the FEA of the maximum principal
normal stresses at these two points in time
– Results not significantly different for ratios of combined
stress
– Smax = Seq/(1-R).63 therefore: fR = 1 /(1-R).63
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Finding the moisture correction factor:

Determining the fatigue strength moisture
correction factor:
» At R = -1, N = 108 in river water, smax = 6 ksi
» At R = -1, N = 5*108 in air, smax = 14 ksi
» 6 ksi/14 ksi = .43

Moisture effect could be .43 smax in air
» We used this number, and assumed that all of
the aluminum was exposed to moisture
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Other Correction Factors

From data above,
» Welding correction factor, fweld = .5
» Welding correction factor only applied to welded
areas

We assumed that there were no notches
anywhere.
» This is fair for the inner conductor
» Stresses are so low on the outer conductor that it
doesn’t matter

We did not include a size correction to go
from sample size to horn size.
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Description of the finite element
model

We created a 2D axisymmetric model of the
horn and first did a transient thermal analysis
» We assumed 3000 W/m2-K convective heat
transfer coefficient all along the inner conductor
only
» The only heat transfer from the outer conductor
was by conduction to inner
» The skin depth of the current was explicitly
modeled (all heat was generated within 1.7mm of
surface of conductors)
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Plot of temperature of smallest radius of inner conductor vs time
High Temperature profile in cross-section
The beam axis in the
model is a vertical line
(not shown) just to the
left of the shape in the
figure
Conclusions from thermal analysis



Temperature difference between hot end of
pulse and cool end are not that different.
Heating of the inner conductor elongates it
and pushes end cap along beam axis, putting
itself in compression and the end cap in
bending
There are only two areas of the horn that see
significant stress
» Middle of the end cap
» Welded region immediately upstream of end cap
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Magnetic Force FEA
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Magnetic forces were modeled in the 2D
axisymmetric model as element pressures
using an analytical expression for the
pressure as a function of radius in the horn.
This model was verified by a 3D 10 sector
model of the horn.
We needed to model the magnetic forces in
the 2D model to be able to combine thermal
and magnetic stress effects.
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Stress intensity caused by high temperature + magnetic force loads on horn end cap
Stress units above
are Pascals.
Conclusions from magnetic +
thermal analysis
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The magnetic field creates a pressure normal
to the surface the current is flowing through
The magnetic field pressure is non-linear and
maximum at small radii.
Stress ratio in the welded neck is ~ -.16 (low
temperature thermal stress is small
compression)
Stress ratio in the end cap varies from -.3
near beam axis to .5 at middle
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Results of Finite Element Analysis

The following plot is a graph of the ratio of
calculated principal normal stress to
allowable stress for every element in the horn
axisymmetric model
» Stresses have not been combined in this graph
» Values are maximum of S1 and S3 only

Allowable stress has been derated for
moisture and welding everywhere
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Summary graph for uncombined principal normal stresses
Scalc/Smax vs Elem ent Num ber, (No com bined stress, assum ing
w elding everyw here)
1.000
0.900
0.800
Scalc/Smax
0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000
0
200
400
600
800
1000
Elem ent Num ber
1200
1400
1600
1800
Combined Stress Results
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The following graph presents the same results, but
the principal normal stresses have been combined by
the equation shown above
Allowable stress corrected for moisture everywhere,
but welding only where appropriate in horn
The places where the ratio is >1 are welded areas
that we have since thickened as a result of this
analysis
Any stress value over 20% of allowable is in the inner
conductor smallest radius tube section
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Summary graph for combined stress data
Scalc/Sallow vs Element Number
1.400
1.200
Scalc/Sallow
1.000
0.800
0.600
0.400
0.200
0.000
0
500
1000
Element Number
1500
2000
Conclusion

After correcting the thickness of the
welded region upstream of the end cap,
the graphs indicate that the stress level
everywhere in the horn during pulsing is
below the maximum set by the 97.5%
confidence level that the material will
not fail in 2e8 cycles.
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