Transcript Review of the Design of the MiniBooNE Horn

Review of the Modal Analysis
of the MiniBooNE Horn MH1
Larry Bartoszek, P.E.
1/25/00
BARTOSZEK ENGINEERING
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Overview 1

The pulsing of the MiniBooNE horn sends a
power spectrum of vibrations into the horn’s
mechanical structure.
» Pulse is 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 concern is that the frequencies
propagating in the horn might match the
natural frequencies of the structure and
induce mechanical resonances that
overstress the horn.
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Analysis Outline: Vibration

Two step analysis:
1. Calculate relative amplitudes of
frequencies in the pulse spectrum by
Fourier analysis
2. FEA modal analysis of horn to get natural
frequencies and normal modes

With this information we can see the
implications for horn design.
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Comparison of NuMI and MiniBooNE
pulse spectra

The pulse width determines the dominant driving
frequencies
» Numi pulse width = 5*10-3 sec
» MiniBooNE pulse width = 1.43*10-4 sec
» NUMI has a calculated natural frequency for the inner
conductor of 358 Hz in the 3 spider support design


The Fourier analysis of the NUMI pulse structure
shows no significant frequency components above
200 Hz.
They should not have a resonance problem with
their inner conductor.
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Chart of all the Fourier Coefficient Amplitudes of the NuMI pulse spectrum
NUMI Fou rier Analysis: An, Bn, Cn, Phin [T = 2 sec, Delta = 5 E-3 sec]
0.004
0.003
Relative Amp litu d e
0.002
0.001
0
-0.001
p h ase x E-3
-0.002
-0.003
-0.004
0
200
400
600
Frequ en cy (H z)
800
1000
1200
MiniBooNE Fourier Analysis

We have a different situation:
» Significant frequency components out to >5 KHz
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Graph of Relative Amplitude of Fourier Coefficient Cn vs. Frequency
MiniBooNE Fou rier Analysis: SQRT(An^ 2+Bn^ 2) [T = 1/ 15 sec, Delta = 0.143
E-3 sec]
1.00E-04
9.00E-05
8.00E-05
Relative Amp litu d e Cn
7.00E-05
6.00E-05
5.00E-05
4.00E-05
3.00E-05
2.00E-05
1.00E-05
0.00E+00
0.00
5000.00
10000.00
15000.00
20000.00
Frequ en cy (H z)
25000.00
30000.00
35000.00
Refinement to the MiniBooNE
Fourier Analysis

The previous analyses repeated the
1/15th second repetitions forever and did
not include the time off.
» During Run II and MiniBooNe running we
will be running up to 8 MiniBooNE Booster
cycles under a Main Injector stacking cycle
which is 22 Booster cycles long (1.467 sec)
for an average rep rate of 5.45 Hz.
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Combining wave forms together to get the pulse structure
These wave forms were
multiplied together to get the
time structure of the pulse train.
The Booster rep rate was
truncated to 66 msec (instead of
its actual 66.6) for simplicity.
This shifts the fine structure
plot power clusters (shown on
slide 11) slightly away from 15
Hz multiples but the real
numbers are centered on 15 Hz
multiples.
Si = Ci*Pi*Ti
Details of the sub-structure of the
Fourier spectrum

Within the envelopes shown above, the
Fourier spectrum has discrete lines because
the current pulse structure is periodic with a
super-period of 1.467 sec.
» The line spacing in the Fourier spectrum is 0.68
Hz (1/1.467 sec).

There is significant power in the spectrum in
clusters separated by 15 Hz.
» The 1/2 width of the power clusters is 22/8 * 0.68
Hz=1.9 Hz.
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Plot of the fine structure of the Fourier Spectrum
Frequency, Hz
Implications of the sub-structure
of the spectrum


The natural frequency of the inner conductor
should not be close to a multiple of 15 Hz.
If the Q of the horn structure is low enough,
details of the spectrum sub-structure may not
matter because many frequencies around a
given natural frequency could excite
resonance
» Low Q would mean lower amplitude than in a high
Q system, but more frequencies can excite the
system
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MiniBooNE Design Concerns

If we have a natural frequency of the inner
conductor under the available driving
components, the inner conductor may
resonate, causing ringing between pulses
» The number of rings between pulses will be limited
by the available damping.
» Ringing effect may increase the number of cycles,
affecting the fatigue life
» Ringing stresses should be a smaller component
than primary thermal and magnetic stresses (if Q
is low enough to eliminate serious resonances,) so
cycle life of the horn may not be significantly
affected.
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FEA Modal Analysis Results
The next slide shows the finite element
model of horn MH1.
 The following slide shows the first four
mode shapes for horn MH1 without any
spiders on the inner conductor.

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Finite Element model of Horn, half symmetric
First Four Normal Modes of Horn with No Spiders
The Influence of Spiders


“Spiders” are attachments between the
inner and outer conductor to help stabilize
the inner conductor and stiffen it.
We created an FEA model of the horn with
three spiders.
»
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One spider is modeled as three thin stiff beams
connecting the IC and OC, radially oriented and
equally spaced around inner conductor in 120
intervals.
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Reasons to add spiders

There are two reasons to have spiders:
1. Increase the column buckling strength of
the inner conductor
» Differential thermal expansion of the inner
conductor with respect to the outer puts the IC in
compression.
» The temperature rise of MH1 is not great enough
to warrant this reason to have spiders
2. Stiffen the IC to raise its natural frequency.
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Disadvantages of Spiders

The main disadvantage of spiders is
that they represent material that can
lower the yield of the horn by multiple
scattering losses.
» The perfect horn has no material in the
way of the particles being focused.

They also add components to the horn
that may fail, affecting system reliability.
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First Four Normal Modes of Horn with 3 Spiders
Potential Problems with Analysis

The stiffness of the spiders modeled is probably not
similar to the stiffness of the spider conceptual design
we are developing
» The design is not far enough along yet to estimate stiffness.

Some of the mode shapes look like they rely on local
deformations in the OC or IC that are probably not
physically realistic.
» This is made obvious in the animations of the mode shapes.

Changing element types shifts frequencies
» It’s hard to know the accuracy of the analysis
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Conclusions from Fourier
Analysis and Modal FEA
1.
2.
We have significant frequency components
out to about 5 KHz, spaced very closely in
frequency.
Adding three spiders raises the fundamental
natural frequency of the inner conductor
from ~77 Hz to ~206 Hz

3.
Fundamental of no-spider horn is uncomfortably close
to a multiple of 15 Hz.
Spiders are not going to raise the natural
frequency beyond the range of the pulse
spectrum.

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Do they do anything useful to justify the loss in yield?
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Further considerations



The thermal and magnetic axisymmetric
analysis of the horn indicated that the middle
of the end cap sees ~60% of its allowable
stress from the inner conductor pushing on it.
All of the mode shapes show inflections of the
curvature of the end cap when the inner
conductor vibrates away from the beam axis.
These inflections will increase the stress level
in the end cap.
» Is this effect significant enough to want to limit it?
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Two questions about inner
conductor vibrations:
1.
2.
What is the additional stress imposed on the
end cap from inner conductor vibrations?
Can spiders limit the additional stress on the
end cap from inner conductor bending?
» We can’t calculate the amplitude of the
oscillations because we don’t know the Q of the
horn structure.
» We think Q is low because of Al construction.
» We can estimate the incremental increase in
stress in the end cap just from static stress
analysis
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Next Finite Element Model

The half symmetric model of the horn was rerun as a static stress analysis with the spiders
removed.
» We knew that the static deflection of the IC without
spiders just from gravity was .002 inches.

The inner conductor was displaced by .020
inches from the beam axis and we looked at
end cap stresses.
» We neglected the influence of inertia and assumed
the static stress from this amplitude of deflection
matched stress from dynamic deflections
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FEA model of IC displacement
End Cap Stress from IC Displacement
Maximum
equivalent stress in
end cap is 2.33MPa
= 338 psi
Summary of results:



Maximum axisymmetric stress intensity in end
cap from thermal and magnetic forces is 3.84
ksi (26.5 MPa).
Maximum incremental stress from .020 inch
offset of IC is .338 ksi (2.33 MPa)
Allowable stress at center of end cap
(corrected for moisture and R) = 6.63 ksi
» Without offset:
Scalc/Sallow = .58
» With offset:
Scalc/Sallow = .63
» % Increase in ratio = 8.6%
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Conclusions 1:

The incremental stress increase due to a .020
inch offset is still well under the 97.5%
confidence stress allowable at 2e8 cycles
» The curve of stress increase vs displacement is
probably not linear and we should run a series of
larger offsets

Looking at the mode shapes with spiders, it is
not clear that they are effective
» There is still an inflection in the end cap with
spiders
» The amplitude of the oscillations is probably less
with spiders than without
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Conclusions 2:



We are designing a spider and putting ports
on the outer conductor to allow them to be
installed.
We plan to make displacement and frequency
measurements on the horn without spiders
during testing to determine if amplitudes are
large enough to want to install spiders
We then plan to make more measurements to
determine if the spiders are effective.
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