Upload
matthew-gaudioso
View
216
Download
2
Embed Size (px)
DESCRIPTION
This is a status update presentation for the design of a composite material shuttle boom arm for a group academic project at UCSB. The design need to meet a specific weight, deflection, vibrations and thermal performance requirements. This presentation explains our initial choices and their justifications. It also includes our recommended changes needed for the project to meet the given performance requirements.
Citation preview
Team 1: Matthew Gaudioso, Jeff Kandel, Armin Moosazadeh, Stephen Potter, John Emoto-Tisdale
Professor Kedward TA: Zi Yie ME 154
Y
Z
X
Ea, Ia
La
Eb, Ib
Lb
Ro=6.5in
D
Ri
h
t
t
b
For our design, we considered these three cross-sections.
The hollow cylinder cross-section was used for Beam A in all configurations.
All three cross-sections were constrained so that the diagonal is 13 inches max.
hi
I-beam
Circle
Square
Deflection Stiffness: Case 1 ◦ The result for the deflection was found using a
finite element method and was also found using Castigliano’s Theorem.
Deflection Stiffness: Case 1
Castigliano’s Theorem
Energy method for deflection analysis
Very useful when forces act on elastic systems subject to small displacements
bending
Deflection Stiffness: Case 2 ◦ Using theory of superposition and using a finite element
method
Deflection Stiffness: Case 3 ◦ Using theory of superposition
Bending Strength ◦ Bending Moment at which the structure will fail
given the material’s failure stress Fu. ◦ For composite materials the lowest failure stress
was always the compressive failure stress.
Hollow cylinder I-Beam Hollow Square
Thermal Deflection ◦ V is the maximum deflection due to thermal expansion.
◦ The section with the higher deflection due to thermal expansion is shown on the tables on the later slides.
T1
T2
Stowed
Released
Stowed Frequency
Minimum Flexural
Frequency
32 Hz
Boundary Conditions Pinned ends on beam
Weight ◦ Section A for all situations uses the hollow cylinder
geometry to reduce torsion.
𝑊 = 𝜌𝑉 Hollow cylinder
I-Beam
Hollow Square
Hollow Cylinder Ro=6.5in Ri=6.44in
I-Beam h=b=9.19in
hi=9.08in t=.056in
Hollow Square D=9.19in T=.07in
Restriction
Deflection 1 (in) 3.4727 3.9228 3.6642 1 in max
Deflection 2 (in) 0.7597 1.2098 0.9511 1 in max
Deflection 3 (in) 4.3743 6.9865 4.5657 1 in max
Failure Bending Moment (in-lb)
2.82*105 2.82*105 2.82*105 550,000 in-lb Minimum due to dynamic launch conditions
Applied Bending Moment due to Temperature gradient (in-lb)
1.96*105 1.36*105 1.92*105 Must be less than failure bending moment above
Weight(lb) 142.7 146.7 146.06 150 lb max
No geometry passed all conditions with Aluminum.
Many conditions failed by too large of a margin to consider Aluminum a viable choice.
We considered Titanium next.
Hollow Cylinder Ro=6.5in Ri=6.46in
I-Beam h=b=9.19in
hi=9.125in t=.033in
Hollow Square D=9.19in T=.04in
Restriction
Deflection 1 (in) 3.3803 3.8419 3.6119 1 in max
Deflection 2 (in) 0.7395 1.2010 0.9710 1 in max
Deflection 3 (in) 4.1873 6.8301 4.4189 1 in max
Failure Bending Moment (in-lb)
5.84 *105 5.84 *105 5.84*105
550,000 in-lb min due to launch conditions
Applied Bending Moment due to Temperature gradient (in-lb)
7.86 *104 5.3 *104 7.2 * 104 Must be less than failure bending moment above
Weight (lb) 147.3656 149.3139 145.2912 150 lb max
Stowed Frequency: Hollow Cylinder
Material Natural Frequency Passes 32 Hz requirement?
Aluminum 9.01 Hz No
Titanium 9.05 Hz No
Aluminum and titanium failed the vibrations test as well. So, we moved on to composites.
No basic geometry can allow Titanium to satisfy our requirements.
Part still failed by too large of a margin to consider Titanium a viable design choice.
Isotropic materials are a poor choice.
Composites are now considered.
Hollow Cylinder Ro=6.5in Ri=6.43in
I-Beam h=b=9.19in
hi=9.12in t=.036in
Hollow Square D=9in T=.081in
Maximum Spec
Deflection 1 (in) 1.0834 1.4173 1.1756 1 in
Deflection 2 (in) 0.2646 0.7265 0.3722 1 in
Deflection 3 (in) 2.2262 3.9934 2.3570 1 in
Failure Bending Moment (in-lb)
5.943*105
compression
2.295*105
Compression
5.534*105
compression 550,550 in-lb
Bending Moment due to Temperature gradient (in-lb)
5.525*104 6.55*104 5.592*104 550,550 in-lb
Weight (lb) 149.27 149.1 149.47 150 lb
Of the cross-sections tested, the hollow circular cross-section proved to be the best for all requirements
Changes in Length ◦ Adding Length to Beam A and removing from beam
B reduces deflection due to torsion by decreasing the lever arm that is deflected.
Changes in Thickness ◦ Adding thickness to beam A decreases all deflection
at the risk of adding more weight.
Choosing more 45⁰ Plies to limit deflection ◦ A higher Shear Modulus can decrease the deflection due
to torsion in case 3, but since it corresponds to a lower Young’s modulus the bending deflection in all cases will increase
Choosing Plies to increase Ftu & Fcu
◦ Decreasing the % 45 plies results in higher values of Ftu & Fcu. The higher the values, the better it can withstand maximum applied bending moment
Addition of Torsional springs at elbow may decrease deflection due to torsion for the case 3 out of plane load.
Other composite materials were next considered.
• For beam A, CFRP, epoxy matrix (isotropic) was used with 40% +/- 45 deg plies and 60% 0 deg plies. For beam B, Boron Carbide was used.
• The strategy for picking the beams was as follows: Beam A: look for an optimization of low density and high
shear modulus Beam B: look for an optimization of low density and high
Young’s modulus • A hollow cylinder was used for both beams. Beam A used the
maximum envelope, whereas beam B used a slightly smaller outer diameter.
• Torsional springs were going to be added to decrease δ3, but the trade-off for decreased δ3 did not outweigh the negative consequence of increased weight.
Materials from CES Software Database
Characteristic Value
Length Beam A 300 in
Length Beam B 300 in
Young’s Modulus Beam A 17.08*10^6 psi
Young’s Modulus Beam B 68.5*10^6 psi
Outer Radius Beam A 6.5 in
Inner Radius Beam B 6.357 in
Inner Radius Beam A 6.25 in
Inner Radius Beam B 6.194 in
Shear Modulus Beam A 6.84*10^6 psi
Density Beam A .054 lb/in^3
Density Beam B .085 lb/in^3
Ultimate Tensile Strength Beam A 130.34*10^3 psi
Ultimate Tensile Strength Beam B 81.2*10^3 psi
Ultimate Compressive Strength Beam A 98.6*10^3 psi
Ultimate Compressive Strength Beam B 825*10^3 psi
Coefficient of Thermal Expansion Beam A 2.22e-6
Coefficient of Thermal Expansion Beam B 1.89e-6
Final Design Parameters
Stowed Frequency: Hollow Cylinder
Different weight and dimensions (inner/outer radii) in both members of the beam
Cannot treat it as beam with uniformly distributed mass
Solution: Add third pin in middle and treat it as 2 beams
Material Natural Frequency Passes 32 Hz requirement?
CFRP Epoxy Matrix
(40% 45o, 60% 0o)
Boron Carbide
27.74 Hz (Beam A)
42.85 Hz (Beam B)
No
Yes
Beam A Beam B
Stowed Frequency: Hollow Cylinder
3 pins (both ends and middle) did not pass minimum requirement of 32 Hz for both beams
Beam A (left beam) failed
Solution: Add fourth pin in midpoint of Beam A and treat it as 3 beams
Beam A1 Beam A2 Beam B
Material Natural Frequency Passes 32 Hz requirement?
CFRP Epoxy Matrix
(40% 45o, 60% 0o)
Boron Carbide
110.95 Hz (Beam A1)
110.95 Hz (Beam A2)
42.85 Hz (Beam B)
Yes
Yes
Yes
Design Spec Current Spec Achieved
δ1 1 in 0.85 in
δ2 1 in 0.16 in
δ3 1 in 0.60 in
Frequency
Section 1, Section 2, Section 3
> 32 hz 110.94 hz, 110.94 hz, 42.85 hz
Geometry (length) 50 ft 50 ft
Geometry (Maximum envelope) 13 inches diameter 13 inches diameter
Maximum Weight 150 lb 149.4 lb
Withstand maximum moment 550,000 lb-in 550,570 lb-in
Thermal deflection stowed NA 3.07 in
Thermal deflection released NA -.0102 in
Design Spec vs. Current Spec Achieved
Other materials can be tested for more desirable properties that allow the implementation of a safety factor in the design.
More ply orientations can be tested to meet more desirable material properties as well.
Geometrical considerations such as tapering
could be explored to enhance performance. Mechanical behavior such as fatigue strength and
fracture toughness could be studied to ensure a more robust design.