bartoszek engineering 1 review of the stress analysis of the miniboone horn mh1 larry bartoszek,...

BARTOSZEK ENGINEERING

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Review of the Stress Analysis of the MiniBooNE

Horn MH1

Larry Bartoszek, P.E.

1/20/00



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Overview 1

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 MIL-SPEC 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

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 max=13 ksi (89.6 MPa)

» Atlas of Fatigue Curves max=17 ksi (117.1 MPa)

» Fatigue Design of Al… max=16 ksi (110.2 MPa)

» Metals Handbook (N=5*108) max=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

Graph from Atlas of Fatigue Curves

ASM data showing effect of notches on fatigue strength


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Welding influences fatigue:» Welded and unwelded specimens are

tested

Welding reduces fatigue strength by ~1/2 » see graph on next slide

Graph from Atlas of Fatigue Curves

ASM data showing effect

of welding


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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 -1R1– R = -1 alternating stress) max=16 ksi– R = 0 Smin=0) max=24 ksi, (1.5X at R=-1)– R = .5 max=37 ksi, (2.3X at R=-1)

» These values are for N=107 cycles, 50% confidence Stress ratio is a variable modifier to maximum

stress. Whole stress cycle must be known.

This is the page from the MIL-SPEC 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.

MIL-SPEC Data Showing Effect of R


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Moisture reduces fatigue strength» For R = -1, smooth specimens, ambient

temperature:– N=108 cycles in river water, max= 6 ksi

– N=107 cycles in sea water, max~ 6 ksi Hard to interpret this data point

– N=5*107 cycles in air, max= 17 ksi

» See data source on next slide» Note curve of fatigue crack growth rate in

humid air, second slide

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 corrosion fatigue strength of many

Al alloys

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.

ASM data on effect of moisture on fatigue crack

growth rate


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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.

Stress/ Cycle Confidence Contours (97.5%, 94.9%, 75%, 50%, 25%)

Seq : Smax*(1-R) 0̂.63

Nf

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

1.0E+08

1.0E+09

0 10 20 30 40 50 60 70

R M Laszewski 22 September 1999

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.

From this graph we concluded that the equivalent stress for >97.5% confidence at 2e8 cycles was 10 ksi.

Confidence Curves on Equivalent Stress data

plot


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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, max = 6 ksi» At R = -1, N = 5*108 in air, max = 14 ksi» 6 ksi/14 ksi = .43

Moisture effect could be .43 max 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)

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


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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

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.

Stress intensity caused by high temperature + magnetic force loads on horn end cap

Stress units above are Pascals.


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Conclusions from magnetic + thermal analysis

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

Scalc/Smax vs Element Number, (No combined stress, assuming welding everywhere)

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0 200 400 600 800 1000 1200 1400 1600 1800

Element Number

Sc

alc/S

ma

x

Summary graph for uncombined principal normal stresses


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Combined Stress Results

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

Scalc/Sallow vs Element Number

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

0 500 1000 1500 2000

Element Number

Sca

lc/S

allo

w

Summary graph for combined stress data


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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.

bartoszek engineering 1 review of the stress analysis of the miniboone horn mh1 larry bartoszek,...

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