Beam Structured Tubes and Tube Support Elimination Using Finite
Element Method (FEM)
by
Murat Yazici
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN SCIENCE
Approved:
_________________________________________
Professor Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
DECEMBER 2012
7
CONTENTS
CONTENTS ...................................................................................................................... 2
LIST OF FIGURES ........................................................................................................... 3
LIST OF TABLES ............................................................................................................. 5
LIST OF SYMBOLS ......................................................................................................... 6
ABSTRACT ...................................................................................................................... 7
1. Introduction.................................................................................................................... 8
1.1
Background ........................................................................................................ 8
1.2
Beam Types ...................................................................................................... 10
2. Methodology ................................................................................................................ 11
2.1
Description of High Cycle Fatigue (HCF) Stress ............................................ 11
2.2
Description of Natural Frequency .................................................................... 11
2.3
Sample Tubes ................................................................................................... 12
2.4
Analysis Conditions ......................................................................................... 15
3. Analysis Results........................................................................................................... 16
4. Conclusions.................................................................................................................. 42
4.1
Summary of Results ......................................................................................... 42
2
LIST OF FIGURES
Figure 1: Typical Tube Support Hardware’s .................................................................... 8
Figure 2: Different Beam Types on Tube ......................................................................... 9
Figure 3: Different Beam Types on Tube ....................................................................... 10
Figure 4: Explanation of Natural Frequency .................................................................. 11
Figure 5: Straight Tube with Three Clamps ................................................................... 12
Figure 6: Straight Tube with Two Clamps (One Clamp Removed) ............................... 13
Figure 7: Tube with Bend and Three Clamps ................................................................. 13
Figure 8: Tube with Bend and Two Clamps (One Clamp Removed) ............................ 14
Figure 9: Straight Tube with Three Clamps (No Beam) ................................................ 16
Figure 10: Straight Tube with Two Clamps (One Clamp Removed/No Beam)............. 17
Figure 11: Straight Tube and Two Clamps with Square Shape Beam ............................ 18
Figure 12: Straight Tube and Two Clamps with I Shape Beam ...................................... 19
Figure 13: Straight Tube and Two Clamps with Circular Shape Beam .......................... 20
Figure 14: Straight Tube and Two Clamps with Rectangular Shape Beam .................... 21
Figure 15: Straight Tube and Two Clamps with Circular Shape Beam with T.H. .......... 22
Figure 16: Straight Tube and Two Clamps with T Shape Beam ..................................... 23
Figure 17: Straight Tube and Two Clamps with Square Shape Beam with T.H ............. 24
Figure 18: Straight Tube and Two Clamps with U Shape Beam .................................... 25
Figure 19: Straight Tube and Two Clamps with Rectangular Shape Beam with T.H..... 26
Figure 20: Straight Tube and Two Clamps with Z Shape Beam ..................................... 27
Figure 21: Straight Tube and Two Clamps with L Shape Beam ..................................... 28
Figure 22: Tube with Bend and Three Clamps (No Beam) ............................................. 29
Figure 23: Tube with Bend and Two Clamps (One Clamp Removed/No Beam) ........... 30
Figure 24: Tube with Bend, Two Clamps and Square Shape Beam ............................... 31
Figure 25: Tube with Bend, Two Clamps and I Shape Beam ......................................... 32
Figure 26: Tube with Bend, Two Clamps and Circular Shape Beam ............................. 33
Figure 27: Tube with Bend, Two Clamps and Rectangular Shape Beam ....................... 34
Figure 28: Tube with Bend, Two Clamps and Circular Shape Beam with T.H .............. 35
Figure 29: Tube with Bend, Two Clamps and T Shape Beam ........................................ 36
3
LIST OF FIGURES
Figure 30: Tube with Bend, Two Clamps and Square Shape Beam with T.H ................ 37
Figure 31: Tube with Bend, Two Clamps and U Shape Beam ........................................ 38
Figure 32: Tube with Bend, Two Clamps and Rectangular Shape Beam with T.H ........ 39
Figure 33: Tube with Bend, Two Clamps and Z Shape Beam ........................................ 40
Figure 34: Tube with Bend, Two Clamps and L Shape Beam ........................................ 41
4
LIST OF TABLES
Table 1: Tube Specifications / Material Properties ........................................................ 15
Table 2: Analysis Assumptions ...................................................................................... 15
Table 3: Tube Sample 1 .................................................................................................. 16
Table 4: Tube Sample 1a ................................................................................................ 17
Table 5: Tube Sample 1b ................................................................................................ 18
Table 6: Tube Sample 1c ................................................................................................ 19
Table 7: Tube Sample 1d ................................................................................................ 20
Table 8: Tube Sample 1e ................................................................................................ 21
Table 9: Tube Sample 1f................................................................................................. 22
Table 10: Tube Sample 1i ................................................................................................ 23
Table 11: Tube Sample 1j ................................................................................................ 24
Table 12: Tube Sample 1k ............................................................................................... 25
Table 13: Tube Sample 1l ................................................................................................ 26
Table 14: Tube Sample 1m .............................................................................................. 27
Table 15: Tube Sample 1n ............................................................................................... 28
Table 16: Tube Sample 2 ................................................................................................. 29
Table 17: Tube Sample 2a ............................................................................................... 30
Table 18: Tube Sample 2b ............................................................................................... 31
Table 19: Tube Sample 2c ............................................................................................... 32
Table 20: Tube Sample 2d ............................................................................................... 33
Table 21: Tube Sample 2e ............................................................................................... 34
Table 22: Tube Sample 2f................................................................................................ 35
Table 23: Tube Sample 2i ................................................................................................ 36
Table 24: Tube Sample 2j ................................................................................................ 37
Table 25: Tube Sample 2k ............................................................................................... 38
Table 26: Tube Sample 2l ............................................................................................... 39
Table 27: Tube Sample 2m ............................................................................................. 40
Table 28: Tube Sample 2n .............................................................................................. 41
Table 29: HCF/Natural Frequency Results..................................................................... 42
5
LIST OF SYMBOLS
f
Natural Frequency (Hz)
k
Beam Stiffness (Pounds/In)
m
Mass (Pound)
D
Tube Diameter (In)
w
Tube Wall Thickness (In)
L
Tube Length (In)
T
Temperature (°F)
N
Number of Modes
g
Vibration Input (G)
Q
Damping Factor
σ
High Cycle Stress (ksi)
6
ABSTRACT
Tube support hardware is commonly used in the Aerospace industry to maintain tube
vibratory stress within acceptable limits. Block clamps, saddle clamps, and P clamps are
some of the commonly used tube support hardware in Aerospace industry. Since cost
and weight factors are two most significant factors, elimination of tube support hardware
brings many benefits. Those benefits are low cost, lighter weight, fewer parts in the bill
of material (BOM), and less complexity at install level. Using fewer tube support
hardware presents a challenge to structural integrity of the part while lowering the cost
and weight. The biggest structural challenges are High Cycle Fatigue (HCF) stress and
lower natural frequency modes in case of using fewer tube supports. This paper
conducted a study with using welded beam along the tube while eliminating tube support
hardware at Ansys software. The eleven different types of welded beams tested with two
different tube routings. Analyses were able to display the results of High Cycle Stress
(HCF) and Natural Frequency behaviors for different beam types.
7
1.Introduction
1.1 Background
Weight and cost factors are critical parameters in aerospace industry. It is important to
have lightweight but structurally sound tube installs. An average tube install comes with
two brackets, two clamps and six bolts. The only way to reduce weight in a tube install is
the elimination of support hardware. The elimination of clamps will also cancel out
brackets and bolts and it will come with weight and cost reduction, less hardware, and
reduced labor cost for assembly. Having less tube support hardware brings potential
problem of higher High Cycle Fatigue (HCF) stress and lower Natural Frequency within
the operating range. The purpose of this study is to perform HCF/Modal analysis to
replace tube supports with different type of beams to understand, whether adding a beam
helps to reduce HCF stress and increase natural frequency modes. Figure 1 shows a
representation of commonly used tube support hardware.
Figure 1: Typical Tube Support Hardware’s [1]
High Cycle Fatigue (HCF) is the single largest cause of component failure in
modern military gas turbine engines. There are several distinctly different sources of
HCF damage in turbine engines, which can be generally classified as follows:
• Aerodynamic excitation - caused by engine flow path pressure perturbations,
affecting primarily blades and vanes.
• Mechanical vibration - caused by rotor imbalance which affects external
components, plumbing, and static structures; and rub, affecting blade tips and gas path
seals.
• Airfoil flutter - caused by aeromechanical instability, affecting blades
8
• Acoustic fatigue - affecting mostly sheet metal components in the combustor,
nozzle and augmentor.
Modal analysis identifies the natural frequencies of a vibration structure. The
frequencies are important since a structure may resonate catastrophically under
fluctuating loads. Modal analysis produces natural frequencies and associated stresses
and these can be used to determine the structural worthiness of the component. Figure 2
shows schematically safe and unsafe domains of operation of a component subject to
HFC conditions. The fundamental tenet is that operation within the allowable region will
not result in HCF failure. If the resultant vibratory stresses stay below the material
capability line, the component will survive.
Figure 2: Relation between Vibratory Stress and Steady Stress [2]
9
1.2 Beam Types
The purpose of creating different beam types is to find optimized beam shape while
maintaining low stress at out of operating modes with eliminating support hardware. It
will be accomplished by analyzing different beam shapes in the Ansys software. Two
different tube routing and 11 different beam shapes will be tested for High Cycle Fatigue
(HCF) stress and Natural Frequency comparison as shown in Figure 3.
Figure 3: Different Beam Types on Tube
10
2. Methodology
2.1 Description of High Cycle Fatigue (HCF) Stress
High-cycle fatigue involves a large number of cycles (N>10^5 cycles) and an elastically
applied stress. High-cycle fatigue tests are usually carried out for 10^7 cycles and
sometimes 5 X10^8 cycles for nonferrous metals. Although the applied stress is low
enough to be elastic, plastic deformation can take place at the crack tip. [3]
2.2 Description of Natural Frequency
Natural frequency is the frequency at which a system naturally vibrates once it has been
set into motion. In other words, natural frequency is the number of times a system will
oscillate (move back and forth) between its original position and its displaced position, if
there is no outside interference. For example, consider a simple beam fixed at one end
and having a mass attached to its free end, as shown in Figure 3. If the beam tip is pulled
downward, then released, the beam will oscillate at its natural frequency. [4]
Figure 4: Explanation of Natural Frequency
If the tip mass (m) weighs much more than the beam to which it is attached, the natural
frequency can be calculated using the simple formula:
 1  k
f 

 2  m
Where k is the beam stiffness in pounds/inch.
11
2.3 Sample Tubes
This project used to find out response of the tube system with having minimal amount of
support while adding different shape of beams to tubes. In order to increase accuracy of
the results, two different tubes routing will be used. Baseline tubes will have three
support points and HCF / Modal analysis will be performed. In the next set of analysis,
one clamp will be removed, and HCF / Modal analysis will be performed again. These
results will be baseline point for comparison against tubes with different beams. As last,
sets of structural analysis will be performed for the tubes with different beam shapes.
Figure 4 shows a representation of a straight tube with three support points and it will be
the baseline for structural analysis of straight routing.
Figure 5: Straight Tube with Three Clamps
12
Figure 5 shows a representation of a straight tube with two support points. In this case
one clamp eliminated as part of project to understand structural behaviors of the tube.
Figure 6: Straight Tube with Two Clamps (One Clamp Removed)
Figure 6 shows a representation of a tube with bend and there support points. It will be
the baseline for structural analysis of bend tube.
Figure 7: Tube with Bend and Three Clamps
13
Figure 6 shows a representation of a tube with bend and two support points. In this case
one clamp eliminated as part of project to understand structural behaviors of the tube.
Figure 8: Tube with Bend and Two Clamps (One Clamp Removed)
14
2.4 Analysis Conditions
Analysis will be performed in Ansys software for industry standard AMS4928 titanium
material tube. Required outputs are High Cycle Fatigue (HCF) stress and Natural
Frequency. Tube specifications, material properties and analysis assumptions can be
seen at Table1 and Table2.
Tube Specifications
Diameter
0.375"
Wall Thickness
0.028"
Material
Titanium
Length
46"
Clamp Spacing
11.5"
Material Properties
Material
AMS4928
Density lb/in3
0.16
Metallurgical Condition
1,300 °F anneal
Tensile Strength, ksi
135
0.2% Yield Strength, ksi
125
Elongation, %
15
Reduction in Area, %
30
Typical Hardness
36 HRC
Table 1: Tube Specifications / Material Properties
Analysis Assumptions
Analysis Software
Ansys (Version12.1)
Fluid
Air
Temperature (T)
70 °F
Pressure (P)
0 Psi
Vibration Input (g)
10G
Q Factor
20
Number of Modes (N)
6
Table 2: Analysis Assumptions
15
3. Analysis Results
Sample 1: Straight Tube with 3 Clamps
The first analysis has been done for the straight tube with three clamps. First set of
analysis results will be the baseline result for upcoming iterations. As result of analysis,
HCF stress is 4.24 ksi and first mode of Natural Frequency is 262 Hz as shown in Figure
8 and Table 3.
Figure 9: Straight Tube with Three Clamps (No Beam)
Mode (Hz)
1
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
262
268
286
297
350
365
4.24
Table 3: Tube Sample 1
16
Sample 1a: Straight Tube with 2 Clamps (One Clamp Removed)
Second analysis has been done for the straight tube with two clamps. In this analysis,
one clamp removed and HCF increased from 4.24 ksi from 10.57 ksi as expected.
Natural Frequency decreased from 262 Hz to 107 Hz for first mode as shown in Figure
10 and Table 4. Result of analysis showed that tube support is very critical for HCF
stress and Natural Frequency.
Figure 10: Straight Tube with Two Clamps (One Clamp Removed/No Beam)
Mode (Hz)
1a
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
107
109
282
296
356
376
10.57
Table 4: Tube Sample 1a
17
Sample 1b: Straight Tube with 2 Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and square shape beam added to straight tube.
Respect baseline (Sample 1a) results, HCF stress increased from 10.57 ksi to 13.80 ksi
and Natural Frequency decreased from 107 Hz to 262 Hz for first mode as shown in
Figure 11 and Table 5. It is clear that adding square shape of beam did not help to
decrease HCF stress and it is not a valid option for replacement of clamp hardware.
Figure 11: Straight Tube and Two Clamps with Square Shape Beam
Mode (Hz)
1b
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
93
128
246
311
322
388
13.80
Table 5: Tube Sample 1b
18
Sample 1c: Straight Tube with 2 Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and I beam added to straight tube. Respect baseline
(Sample 1a) results, HCF stress increased from 10.57 ksi to 16.24 ksi and Natural
Frequency decreased from 107 Hz to 86 Hz for first mode. as shown in Figure 12 and
Table 6. It is clear that adding I beam did not help to decrease HCF stress and it is not a
valid option for replacement of clamp hardware.
Figure 12: Straight Tube and Two Clamps with I Shape Beam
Mode (Hz)
1c
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
86
139
225
285
324
355
16.24
Table 6: Tube Sample 1c
19
Sample 1d: Straight Tube with 2 Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and circular shape beam added to straight tube.
Respect baseline (Sample 1a) results, HCF stress increased from 10.57 ksi to 13.16 ksi
and Natural Frequency decreased from 107 Hz to 96 Hz for first mode as shown in
Figure 13 and Table 7. It is clear that adding circular beam did not help to decrease HCF
stress and it is not a valid option for replacement of clamp hardware.
Figure 13: Straight Tube and Two Clamps with Circular Shape Beam
Mode (Hz)
1d
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
96
127
252
319
323
398
13.16
Table 7: Tube Sample 1d
20
Sample 1e: Straight Tube with 2 Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and rectangular shape beam added to straight tube.
Respect baseline (Sample 1a) results, HCF stress increased from 10.57 ksi to 16.99 ksi
and Natural Frequency decreased from 107 Hz to 84 Hz for first mode as shown in
Figure 14 and Table 8. It is clear that adding rectangular shape beam did not help to
decrease HCF stress and it is not a valid option for replacement of clamp hardware.
Figure 14: Straight Tube and Two Clamps with Rectangular Shape Beam
Mode (Hz)
1e
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
84
140
221
279
325
348
16.99
Table 8: Tube Sample 1e
21
Sample 1f: Straight Tube with 2 Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and circular shape beam with through hole added to
straight tube. Respect baseline (Sample 1a) results, HCF stress increased from 10.57 ksi
to 12.00 ksi and Natural Frequency decreased from 107 Hz to 100 Hz for first mode as
shown in Figure 15 and Table 9. It is clear that adding circular shape beam with through
hole did not help to decrease HCF stress and it is not a valid option for replacement of
clamp hardware.
Figure 15: Straight Tube and Two Clamps with Circular Shape Beam with Through Hole
Mode (Hz)
1f
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
100
133
262
332
336
416
12.00
Table 9: Tube Sample 1f
22
Sample 1i: Straight Tube with 2 Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and T shape beam added to straight tube. Respect
baseline (Sample 1a) results, HCF stress increased from 10.57 ksi to 11.78 ksi and
Natural Frequency decreased from 107 Hz to 101 Hz for first mode as shown in Figure
16 and Table 10. It is clear that adding T shape beam did not help to decrease HCF stress
and it is not a valid option for replacement of clamp hardware.
Figure 16: Straight Tube and Two Clamps with T Shape Beam
Mode (Hz)
1i
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
101
122
267
321
337
401
11.78
Table 10: Tube Sample 1i
23
Sample 1j: Straight Tube with 2 Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and I square beam with through hole added to
straight tube. Respect baseline (Sample 1a) results, HCF stress increased from 10.57 ksi
to 12.60 ksi and Natural Frequency decreased from 107 Hz to 98 Hz for first mode as
shown in Figure 17 and Table 11. It is clear that adding square shape beam with through
hole did not help to decrease HCF stress and it is not a valid option for replacement of
clamp hardware.
Figure 17: Straight Tube and Two Clamps with Square Shape Beam with Through Hole
Mode (Hz)
1j
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
98
125
257
324
326
407
12.60
Table 11: Tube Sample 1j
24
Sample 1k: Straight Tube with 2 Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and U shape beam added to straight tube. Respect
baseline (Sample 1a) results, HCF stress increased from 10.57 ksi to 11.55 ksi and
Natural Frequency decreased from 107 Hz to 102 Hz for first mode as shown in Figure
18 and Table 12. It is clear that adding U shape beam did not help to decrease HCF
stress and it is not a valid option for replacement of clamp hardware.
Figure 18: Straight Tube and Two Clamps with U Shape Beam
Mode (Hz)
1k
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
102
119
269
317
340
396
11.55
Table 12: Tube Sample 1k
25
Sample 1l: Straight Tube with 2 Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and rectangular shape beam with through hole
added to straight tube. Respect baseline (Sample 1a) results, HCF stress increased from
10.57 ksi to 11.86 ksi and Natural Frequency decreased from 107 Hz to 101 Hz for first
mode as shown in Figure 19 and Table 13. It is clear that adding rectangular shape beam
with through hole did not help to decrease HCF stress and it is not a valid option for
replacement of clamp hardware.
Figure 19: Straight Tube and Two Clamps with Rectangular Shape Beam with Through
Hole
Mode (Hz)
1l
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
101
125
264
323
334
406
11.86
Table 13: Tube Sample 1l
26
Sample 1m: Straight Tube with 2 Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and Z shape beam added to straight tube. Respect
baseline (Sample 1a) results, HCF stress increased from 10.57 ksi to 12.19 ksi and
Natural Frequency decreased from 107 Hz to 100 Hz for first mode as shown in Figure
20 and Table 14. It is clear that adding Z shape beam did not help to decrease HCF stress
and it is not a valid option for replacement of clamp hardware.
Figure 20: Straight Tube and Two Clamps with Z Shape Beam
Mode (Hz)
1m
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
100
124
262
323
332
405
12.19
Table 14: Tube Sample 1m
27
Sample 1n: Straight Tube with 2 Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and L shape beam added to straight tube. Respect
baseline (Sample 1a) results, HCF stress increased from 10.57 ksi to 11.72 ksi and
Natural Frequency decreased from 107 Hz to 101 Hz for first mode as shown in Figure
21 and Table 15. It is clear that adding L shape beam did not help to decrease HCF stress
and it is not a valid option for replacement of clamp hardware.
Figure 21: Straight Tube and Two Clamps with L Shape Beam
Mode (Hz)
1n
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
101
123
267
323
338
404
11.72
Table 15: Tube Sample 1n
28
Sample 2: Tube with Bend and Three Clamps
In this test case, analysis has been done for the bend tube with three clamps. Reason of
having two different tube routing is to increase accuracy of analysis. First set of analysis
results will be the baseline result for upcoming iterations. As result of analysis, HCF
stress is 4.09 ksi and first mode of Natural Frequency is 258 Hz as shown in Figure 22
and Table 16.
Figure 22: Tube with Bend and Three Clamps (No Beam)
Mode (Hz)
2
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
258
261
269
279
356
374
4.09
Table 16: Tube Sample 2
29
Sample 2a: Tube with Bend and Two Clamps (One Clamp Removed)
Second analysis has been done for the bend tube with two clamps. In this analysis, one
clamp removed and HCF increased from 4.09 ksi to 11.37 ksi as expected. Natural
Frequency decreased from 258 Hz to 80 Hz for first mode as shown in Figure 23 and
Table 17. Result of analysis showed that tube support is very critical for HCF stress and
Natural Frequency.
Figure 23: Tube with Bend and Two Clamps (One Clamp Removed/No Beam)
Mode (Hz)
2a
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
80
209
254
265
354
370
11.37
Table 17: Tube Sample 2a
30
Sample 2b: Tube with Bend and Two Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and square shape beam added to bend tube. Respect
baseline (Sample 2a) results, HCF stress increased from 11.37 ksi to 14.61 ksi and
Natural Frequency decreased from 80 Hz to 71 Hz for first mode as shown in Figure 24
and Table 18. It is clear that adding square shape of beam did not help to decrease HCF
stress and it is not a valid option for replacement of clamp hardware.
Figure 24: Tube with Bend, Two Clamps and Square Shape Beam
Mode (Hz)
2b
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
71
195
233
259
321
329
14.61
Table 18: Tube Sample 2b
31
Sample 2c: Tube with Bend and Two Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and I beam added to bend tube. Respect baseline
(Sample 2a) results, HCF stress increased from 11.37 ksi to 14.04 ksi and Natural
Frequency decreased from 80 Hz to 73 Hz for first mode as shown in Figure 25 and
Table 19. It is clear that adding I beam did not help to decrease HCF stress and it is not a
valid option for replacement of clamp hardware.
Figure 25: Tube with Bend, Two Clamps and I Shape Beam
Mode (Hz)
2c
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
73
198
242
262
330
342
14.04
Table 19: Tube Sample 2c
32
Sample 2d: Tube with Bend and Two Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and circular shape beam added to bend tube.
Respect baseline (Sample 2a) results, HCF stress increased from 11.37 ksi to 14.47 ksi
and Natural Frequency decreased from 80 Hz to 70 Hz for first mode as shown in Figure
26 and Table 20. It is clear that adding circular shape beam did not help to decrease HCF
stress and it is not a valid option for replacement of clamp hardware.
Figure 26: Tube with Bend, Two Clamps and Circular Shape Beam
Mode (Hz)
2d
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
70
193
230
259
316
325
14.47
Table 20: Tube Sample 2d
33
Sample 2e: Tube with Bend and Two Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and rectangular shape beam added to bend tube.
Respect baseline (Sample 2a) results, HCF stress increased from 11.37 ksi to 17.64 ksi
and Natural Frequency decreased from 80 Hz to 65 Hz for first mode as shown in Figure
27 and Table 21. It is clear that adding rectangular shape beam did not help to decrease
HCF stress and it is not a valid option for replacement of clamp hardware.
Figure 27: Tube with Bend, Two Clamps and Rectangular Shape Beam
Mode (Hz)
2e
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
65
182
211
254
286
296
17.64
Table 21: Tube Sample 2e
34
Sample 2f: Tube with Bend and Two Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and circular shape beam with through hole added to
bend tube. Respect baseline (Sample 2a) results, HCF stress increased from 11.37 ksi to
12.59 ksi and Natural Frequency decreased from 80 Hz to 76 Hz for first mode as shown
in Figure 28 and Table 22. It is clear that adding circular shape beam with through hole
did not help to decrease HCF stress and it is not a valid option for replacement of clamp
hardware.
Figure 28: Tube with Bend, Two Clamps and Circular Shape Beam with Through Hole
Mode (Hz)
2f
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
76
204
248
270
341
351
12.59
Table 22: Tube Sample 2f
35
Sample 2i: Tube with Bend and Two Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and T shape beam added to bend tube. Respect
baseline (Sample 2a) results, HCF stress increased from 11.37 ksi to 13.60 ksi and
Natural Frequency decreased from 80 Hz to 74 Hz for first mode as shown in Figure 29
and Table 23. It is clear that adding T shape beam did not help to decrease HCF stress
and it is not a valid option for replacement of clamp hardware.
Figure 29: Tube with Bend, Two Clamps and T Shape Beam
Mode (Hz)
2i
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
74
202
243
272
333
344
13.60
Table 23: Tube Sample 2i
36
Sample 2j: Tube with Bend and Two Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and square shape beam with through hole added to
bend tube. Respect baseline (Sample 2a) results, HCF stress increased from 11.37 ksi to
13.39 ksi and Natural Frequency decreased from 80 Hz to 74 Hz for first mode as shown
in Figure 30 and Table 24. It is clear that adding square shape beam with through hole
did not help to decrease HCF stress and it is not a valid option for replacement of clamp
hardware.
Figure 30: Tube with Bend, Two Clamps and Square Shape Beam with Through Hole
Mode (Hz)
2j
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
74
201
243
264
336
345
13.39
Table 24: Tube Sample 2j
37
Sample 2k: Tube with Bend and Two Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and U shape beam added to bend tube. Respect
baseline (Sample 2a) results, HCF stress increased from 11.37 ksi to 12.49 ksi and
Natural Frequency decreased from 80 Hz to 77 Hz for first mode as shown in Figure 31
and Table 25. It is clear that adding U shape beam did not help to decrease HCF stress
and it is not a valid option for replacement of clamp hardware.
Figure 31: Tube with Bend, Two Clamps and U Shape Beam
Mode (Hz)
2k
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
77
208
254
268
352
360
12.49
Table 25: Tube Sample 2k
38
Sample 2l: Tube with Bend and Two Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and rectangular shape beam with through hole
added to bend tube. Respect baseline (Sample 2a) results, HCF stress increased from
11.37 ksi to 12.69 ksi and Natural Frequency decreased from 80 Hz to 76 Hz for first
mode as shown in Figure 32 and Table 26. It is clear that adding rectangular shape beam
with through hole did not help to decrease HCF stress and it is not a valid option for
replacement of clamp hardware.
Figure 32: Tube with Bend, Two Clamps and Rectangular Shape Beam with Through
Hole
Mode (Hz)
2l
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
76
202
249
264
343
353
12.69
Table 26: Tube Sample 2l
39
Sample 2m: Tube with Bend and Two Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and Z shape beam added to bend tube. Respect
baseline (Sample 2a) results, HCF stress increased from 11.37 ksi to 13.31 ksi and
Natural Frequency decreased from 80 Hz to 76 Hz for first mode as shown in Figure 33
and Table 27. It is clear that adding Z shape beam did not help to decrease HCF stress
and it is not a valid option for replacement of clamp hardware.
Figure 33: Tube with Bend, Two Clamps and Z Shape Beam
Mode (Hz)
2m
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
76
206
247
274
342
350
13.31
Table 27: Tube Sample 2m
40
Sample 2n: Tube with Bend and Two Clamps (One Clamp Removed/Beam
Added)
In this analysis, one clamp removed and L shape beam added to bend tube. Respect
baseline (Sample 2a) results, HCF stress increased from 11.37 ksi to 12.67 ksi and
Natural Frequency decreased from 80 Hz to 77 Hz for first mode as shown in Figure 34
and Table 28. It is clear that adding L shape beam did not help to decrease HCF stress
and it is not a valid option for replacement of clamp hardware.
Figure 34: Tube with Bend, Two Clamps and L Shape Beam
Mode (Hz)
2n
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Stress (Ksi)
77
206
252
266
350
358
12.67
Table 28: Tube Sample 2n
41
4.Conclusions
4.1 Summary of Results
The eleven different beam models have been analyzed to understand, if adding different
beam types helps decrease High Cycle Fatigue (HCF) stress and the natural frequency
modes. In the first case, a straight tube has been analyzed with three tube clamps and
result show that the straight tube with three clamps had 4.24 ksi Von Mises stress. In the
second case, one clamp was eliminated and the straight tube was analyzed with two tube
clamps. Results showed that the straight tube with two clamps had 10.57 ksi Von Mises
stress. Eliminating the tube support resulted in an increased of High Cycle Fatigue
(HCF) stress as expected. Additional analysis was performed for the tube with a bend. In
first case, a tube with a bend and three clamps was analyzed and results showed that the
tube had 4.09 ksi Von Mises stress. In second case, one clamp was eliminated and the
tube with a bend and two clamps was analyzed. Results showed that the tube with bend
and two clamps had 11.37 ksi Von Mises stress. After elimination of the one tube
support from each tube model, different beam types were added to both tube routings
and HCF/Modal analysis was performed again. Analysis showed that the addition of any
beam types did not help decrease HCF stress instead adding beam increased the stress.
Summary of analysis results can be seen at Table 29. The final recommendation
resulting from this study is to use clamps instead of using any kind of welded beam on a
tube.
Mode (Hz)
1
1a
1b
1c
1d
1e
1f
1i
1j
1k
1l
1m
1n
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
262
268
286
297
350
365
107
109
282
296
356
376
93
128
246
311
322
388
86
139
225
285
324
355
96
127
252
319
323
398
84
140
221
279
325
348
100
133
262
332
336
416
101
122
267
321
337
401
98
125
257
324
326
407
102
119
269
317
340
396
101
125
264
323
334
406
100
124
262
323
332
405
101
123
267
323
338
404
σ (Ksi)
4.24
10.57
13.80
16.24
13.16
16.99
12.00
11.78
12.60
11.55
11.86
12.19
11.72
Mode (Hz)
2
2a
2b
2c
2d
2e
2f
2i
2j
2k
2l
2m
2n
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
258
261
269
279
356
374
80
209
254
265
354
370
71
195
233
259
321
329
73
198
242
262
330
342
70
193
230
259
316
325
65
182
211
254
286
296
76
204
248
270
341
351
74
202
243
272
333
344
74
201
243
264
336
345
77
208
254
268
352
360
76
202
249
264
343
353
76
206
247
274
342
350
77
206
252
266
350
358
σ
4.09
11.37
14.61
14.04
14.47
17.64
12.59
13.60
13.39
12.49
12.69
13.31
12.67
(Ksi)
Table 29: HCF/Natural Frequency Results
42
References
[1] Giddens Industries. (2009). “Giddens Sheet Metal Capabilities ”, Retrieved from;
http://www.giddens.com/Capabilities.aspx
[2] B.A. Cowles. (1996). High cycle fatigue in aircraft gas turbines - an industry
perspective. International Journal of Fracture 80: 147-163, 1996. Kluwer Academic
Publishers. Retrieved from;
[3] ASM International. (2008). “Elements of Metallurgy and Engineering Alloys and
High Cycle Fatigue”, Retrieved from;
www.asminternational.org/content/ASM/StoreFiles/05224G_Chapter14.pdf
[4] Joseph C. Slater. (2005). “Natural Frequency and Resonance”, Retrieved from;
www.cs.wright.edu/~jslater/SDTCOutreachWebsite/nat_frequency.htm
43