ASME Human Powered Vehicle Team
Structural Analysis
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Honors Research Project/Senior Design Project
Samantha Bittinger
The University of Akron
April 2012
Contents
Abstract
3
Introduction
3
Frame Material Considerations
4
Frame Stress Analysis
5
Frame Modal Analysis
7
Roll Bar Analysis
8
Roll Bar Testing
11
Conclusion
12
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Abstract
The ASME Human Powered Vehicle (HPV) Competition pits student design teams against one
another in a series of human-powered vehicle races. It’s a program that encourages its
participants to think outside the box and beyond the realm of current non-renewable energy
sources. This marks The University of Akron’s second year in the HPV competition.
One of the core capabilities added this year was finite element analysis (FEA). This is a powerful
tool used extensively in the vehicle industry to optimize products. A frame model is imported,
boundary and loading conditions are applied, and the program uses a nodal process to calculate
stress, displacements, and more over the entire structure. It enables the analyst to determine
structural integrity from an overall standpoint, down to spot-treatment as the design progresses.
Raw material usage can be minimized while maintaining strength and stiffness in critical
locations.
Several key analyses were performed on many iterations of the bike’s design. Presented here are
the final accepted designs and how they have responded to anticipated loading conditions. The
frame itself has been analytically rated for a 200 lb rider, with factors added for dynamic events
and safety. Additionally, the rules of the HPV Competition state that the roll bar must withstand
600 lb at 12 degrees from vertical, and 300 lb at the horizontal. The final design meets both
strength and displacement requirements for each load case. The FEA results for the roll bar shall
be verified with physical testing to ensure safety of the riders.
Introduction
The ASME Human Powered Vehicle Competition is a race between vehicles that use no power
source other than its rider. Engineering student teams from all over the world will compete to test
their unique ideas against the field. The competition challenges participants to think beyond the
realm of current technology and develop new ways of travel, to mitigate our dependence on oil
and think progressively about the future. Zephyr was developed with these critical issues in
mind.
This is the second year the University of Akron will be competing in the ASME Human Powered
Vehicle Competition. Last year, the team created The Blue Streak, a tadpole configured tricycle.
Much was learned from the design, fabrication, and competition in 2011. The nature of the
competition was better understood, and this lent valuable insight into the design process for
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2012. Our objective is to improve upon the success and lessons learned during fabrication and
competition of the Blue Streak.
Several goals guided the design and construction of Zephyr (Figure 1). First and foremost, the
design was created to be able to win the race, based on past competitions. Secondly, the vehicle
would be self-sufficient – the rider should need no outside help in any phase of a ride. Third, the
vehicle would be safe and practical – realistic for replacing an internal combustion engine
vehicle for local travel. Other goals included aesthetics, comfort, and simplicity. By keeping
these goals in mind at all times, the trike that the team initially wanted is becoming a reality.
Figure 1: Zephyr Design
The core innovation introduced in this year’s model is the tilting mechanism. For stability, the
recumbent tricycle was designed with three wheels, but a rear linkage mechanism allows the rear
wheels to tilt as the weight of the rider moves from side to side. This provides the vehicle with
both stability and speed allowance. Also newly included this year is a full fairing to limit the
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effect of air drag. FEA and CFD analyses were also used extensively this year. Both proved to be
extremely useful in creating a strong, lean, and fast design in both the frame and fairing.
For the established goals to be achieved, it was determined that several frame variables should be
optimized – strength, stiffness, mass, ease of fabrication, simplicity, and cost. Iterative
computational processes using FEA software packages were adapted this year to evaluate the
effects of design changes and optimize the frame.
Frame Material Considerations
Material choice is a critical decision in the construction of any vehicle. Our initial options were
steel (AISI 4130, yield strength 66 ksi) and aluminum (6061-T6, yield strength 40 ksi).
Aluminum and steel are standard vehicle structural options, but each one provides different
benefits. Steel is a strong, cheap material with good stiffness and weldability. On the other hand,
aluminum provides a 2/3 weight reduction over steel. However, aluminum is also less stiff, more
difficult to weld, and more expensive (Table 1).
Due to the team’s limited budget, low-carbon steel (A-513, yield strength 50 ksi) was chosen for
most of the frame, with the exception of the rear knuckles, spindles, and seat. These components
were made of aluminum on last year’s bike, and performed well, so we believe aluminum is a
proper choice for these parts. Table 1 shows the relative ranking for the frame material design
criteria, where 10 represents a high score and 1 represents a low score (Table 1):
Table 1: Point system for material selection
A-513 steel best fit the design criteria. However, all finite element analysis had been performed
using 4130 steel. But since stress results depend mostly on geometry, the new yield strengths for
the weaker steel can be compared to the stresses identified in the model results for the stronger
steel. After the comparison, it was determined that the current geometry could support the given
loading conditions with the weaker steel. Additionally, all steel has the same stiffness. Frame
loading and geometry determine the resultant stress. After reviewing the analysis, we were able
to successfully substitute lower-cost A-513 steel in the design.
Frame Stress Analysis
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One of the prominent improvements over last’s year’s design process was the extent to which
finite element analysis (FEA) was implemented throughout the design process to optimize part
geometry. It is an invaluable tool that can save countless hours spent rebuilding broken parts that
could have been designed properly with the virtual first-cut analysis that FE provides.
The analysis of the frame was performed in Autodesk’s Multiphysics Simulation 2012. The
material was selected as AISI 4130 steel. A beam model was created in SolidWorks in order to
provide a simple basis to import for the finite element analysis. Beam models run in far less time
than 3D models, while still maintaining accuracy. Since the head tube and rear linkage are not
yet completed, the boundaries constrained were the points of connection into the head tube and
the rear linkage. The boundaries were constrained in translation on the inner connection surfaces.
The distributed force applied to the lower frame member is 600 lb in the –y direction. This
represents an overestimation of the weight of the rider and of the bike, multiplied by two for
dynamic events such as bumps in the road. A distributed load was used because the seat
attachment location and thus center of mass had not yet been determined. The additional force
applied to the head of the frame is representative of the pedaling force at the crank. The force is
estimated at 600 pounds, directed mostly outward in the –x direction, and slightly downward in
the –y direction (Figure 2).
Figure 2: Boundary conditions (pink) and loading conditions (magenta) for frame analysis
It can be seen in the screenshot below that the results indicate most of the frame to be structurally
sound in a typical riding environment. There are some areas of high stress at corners and welds.
These areas are false stresses that the FEA magnifies due to sharp geometry. FEA does not
recognize model welds, so they are left out of the model for analysis. In reality, welds alleviate
the stress and spread it to surrounding areas. So after eliminating these anomalies from stress
consideration, the highest stress is seen between the head tube and crank at about 25 ksi. This is
much lower than the yield strength of the 4130 alloy (66 ksi) (Figure 3).
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Figure 3: Stress results: Frame Analysis
Displacement is another critical measure of frame performance. It indicates the stiffness of the
design, which is determined by both the geometry and the material. The results below show a
maximum relevant displacement magnitude of 0.09 inches at the crank. This low value is an
indication of good handling and minimal loss of torque and power at the crank. If the
displacements were too high, the rider would spend his energy moving the frame around, instead
of using that energy to transfer torque to the front wheel (Figure 4). The force in the z-direction
was not considered in this analysis, but due to the geometry and strength of material, the
deflection due to moment should not be a large issue.
Figure 4: Displacement results: Frame analysis
Frame Modal Analysis
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Finally, a normal modes finite element analysis was performed using no forces and no
constraints on the model. This dynamic analysis identifies natural modes - frequencies and
shapes which a model tends toward. The frequencies at which these modes are excited are
termed ‘resonant modes.’ If the bike is excited at one of these frequencies for a duration, the bike
can vibrate out of control and even break the material. Modal mass percentage is a good measure
of the potential danger of a mode. It identifies the percentage amount of mass in the model that
moves in a certain direction. The higher the modal mass percentage, the more dangerous the
mode, if excited. Typically, a value under 5% is negligible (Table 2).
Unfortunately, excitation data for the course is not available. However, excitation frequencies
borne of small bumps in typical roads are usually over 50 Hz, and are low in amplitude. Pedaling
excitation is also out of range, usually under 3 Hz. If any further pavement information were
available, the following modes would be matched up to the excitations. If any were the same, the
geometry would be changed to alter a natural frequency in a chosen direction by using various
stiffening and de-stiffening methods.
Modal Mass %
X
Y
Z
14% 28% 0%
0% 0% 16%
0% 0% 18%
1% 11% 0%
12% 25% 1%
Mode Frequency
1
3.5 Hz
2
7.2 Hz
3
26.7 Hz
4
31.1 Hz
5
49.9 Hz
Table 2: Frequency analysis/Normal modes results: Frame
Roll Bar Analysis
As per the rulebook for the HPV competition, the roll bar shall be analyzed and tested according
to two load cases. Two requirements, one for material yielding and one for displacement, must
be met for each load case. To satisfy these requirements, a finite element analysis was performed
for both load cases.
Case 1: Top Loading
This analysis was also performed using Autodesk Simulation Multiphysics 2012, along with the
material application of AISI 4130 steel. The same SolidWorks beam model was imported and the
same boundary conditions were used as in the analysis if the frame. As per the rulebook, a 600 lb
force was applied to the top of the roll bar, directed at 12 degrees from the vertical, acting
downward at –y and backward at +x. The purpose of this analysis is to assure the structural
integrity of the roll bar in the event of a full roll-over (Figure 5).
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Figure 5: Boundary conditions (green) and loading conditions (dark green) for top loading analysis
The first requirement states that there shall be no indication of permanent deformation, fracture,
or delamination on the frame. The results of the FEA indicate that most of the vehicle
experiences minimal stress, and the maximum stress in the material is about 30 ksi, well below
the yield strength of our material. This indicates no permanent deformation or fracture. Again,
the higher stresses are due to the unrealistic point load application and sharp geometry, and
should not be an issue in the actual vehicle (Figure 6).
Figure 6: Stress results: Roll Bar Analysis: Top loading case
The second requirement identified in the rule book states that the displacement needs to be less
than 2 inches. The maximum deformation in this model is 0.33”, and thus meets the requirement
(Figure 7).
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Figure 7: Displacement results: Roll Bar Analysis: Top loading case
Case 2: Side Loading
A second roll bar load case was tested according to the guidelines of the rule book. A 300 lb
force was applied at shoulder height to the side of the roll bar, acting in the +z direction, while
constraining the opposite side in translation. The purpose of this analysis is to assure roll bar
integrity and thus rider safety in the event of a tip-over (Figure 8).
Figure 8: Boundary conditions (teal) and loading conditions (green) for side-loading analysis
Again, the first requirement states that there shall be no indication of permanent deformation,
fracture, or delamination on the frame. The results of the FEA indicate that most of the vehicle
experiences minimal stress, and the maximum stress in the material is about 40 ksi, well below
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the yield strength of our material. This indicates no permanent deformation or fracture (Figure
9).
Figure 9: Stress results: Roll Bar Analysis: Side loading case
The second requirement identified in the rule book states that the displacement needs to be less
than 1.5 inches. The maximum deformation in this model is 0.23”, and thus meets the
requirement (Figure 10).
Figure 10: Displacement results: Roll Bar Analysis: Side loading case
Roll Bar Testing
After welding the components of the main frame, the roll bar was tested to validate FEA results
(Figure 11). To test the roll-over case, the vehicle was oriented at a 12 degree angle, and a steel
base was tied from the top of the bar. Weights were incrementally added to the base up to 650
pounds, all while displacement measurements were taken by a dial indicator. To test the side
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loading case, the process was repeated with the frame oriented on its side. For this case, 300
pounds was achieved.
Figure 11: Roll Bar Test Setup
To verify a lack of inelastic deformation, data points were taken incrementally as weight was
added. The chart below shows a linear trend on both tests, indicating solely elastic deformation
(Figure 12). The total deflections of 0.75 and 0.25 inches, respectively, are in close range of the
analytical results (0.33 and 0.23 inches).
Figure 12: Roll Bar Test Results
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Conclusion
The frame design has been verified by several analyses. First, standard riding forces were
applied, with loading factors applied for dynamic events. Second, a modal analysis of the frame
was performed to identify the natural modes and their frequencies. Third, the two required
analyses of a rollover and side-impact test were run, yielding acceptable results for all three.
Additionally, analysis results were verified by physical testing of the roll bar. This is a critical
part of the process to verify that the steel received was as strong as required, and the welds were
properly made. The physical testing showed no signs of material yielding, and showed deflection
results similar to that of the analysis.
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