1. Analysis of a Recumbent, Three Wheeled Tricycle Frame
Michael Hamman, William Steppe
Abstract-The recumbent trike was designed for an
upcoming tricycle competition in May of 2016. A
finite element analysis was performed on the
frame to ensure the safe operation under
competition loading constraints. After the initial
model was analyzed using Von Mises Stress and
Total Displacement methods, it was reiterated
twice to lower the stress and increase the Factor of
Safety. A CFD analysis was performed on a
model fairing to determine an approximate drag
force at the maximum riding velocity. The drag
force was found to be negligible and was omitted
from the analysis loading configuration. A mesh
independent study was performed on the final
design to ensure accurate results.
I. Introduction
he American Society of Mechanical
Engineers is competing in the
Human Powered Vehicle Competition in
May, 2016, and must build a recumbent
tricycle. This paper involves a static analysis
of tricycle frame for supporting the tricycle
design. Figure 1 presents a CREO 3.0 [1]
model of the competition design. The frame
will be custom built to support an 81.6 Kg
person pedaling with a force of 1000 N [1].
The forces from the mass of the rider
equated to 800 N, with a 1000 N force
applied in the negative x-direction and an
800 N force applied in the negative y-
direction. Figure 2provides a model with
the constraints and forces.
Figure 1: Frame model
Figure 2: Loading and Constraints on Frame
The tubing will be welded together at all
angles for ease of connection and the weight
savings it will offer compared to brackets or
nuts and bolts. The frame will be designed
using a factor of safety of 1.5, since it is
only being used in a certain scenario, and
the goal is to make the bike as light as
possible while still being structurally sound.
II. Methodology
The trike model was designed with CREO
3.0. This software was used because there
will have to be many changes to the
geometry in order to optimize the frame, and
CREO makes it relatively easy to apply
those changes. ANSYS 14.5 Workbench [3]
was used to perform a stationary Finite
Element Analysis on the model. The Shear
Strain Energy theory was used as the design
failure criteria so Von Mises Stress and
T

2. Total Displacement distributions were
analyzed through the simulation process.
The geometry was iteratively modified
based on the results attained in CREO. Star-
CCM+ [4] was used once to perform a CFD
analysis on the fairing, Figure 3, which will
fully enclose the bike and rider reducing
drag force effects.
Figure 3: Fairing Shell Model
III. Initial Simplification
The model from Figure 1 was simplified on
the basis that certain objects are not required
for the frame analysis. Figure 4provides the
simplified model that was imported to
ANSYS.
Figure 4: Initial Simplification of Frame
The rear wheel was removed. The rear
wheel was analyzed as a frictionless support
because it is mounted on the frame as a
bearing instead of a static object. The front
wheels and the suspension were removed
and analyzed as a vertical constraint on the
bolt holes where the suspension components
would mount to the frame. This is because
the wheels will not be able to change their
vertical displacement, but they can change
their horizontal displacement if the force is
strong enough.
IV. Initial Analysis and Results
The initial design was modeled with square
tubing having cross-sectional dimensions of
0.0381 m for height and width, and a wall
thickness of 0.003175 m. The material
chosen for the frame tubing 6061-T6
Aluminum because of its success in
commercial bike frames thus far. The mass
for the frame will equate to 2.4 Kg using this
material for all of the beams. The static
analysis was performed on the model to
obtain the initial stress and displacement
results. Figure 5 and Figure 6 provide the
Von Mises stress and total displacement
results, respectively.
Figure 5: Initial Von Mises Stress Analysis
Figure 6: Initial Total Displacement Analysis

3. The Von Mises stress analysis resulted in a
maximum stress of 3.81 MPa. This stress
would result in failure according to Von
Mises failure criterion since 6061-T6
Aluminum has a yield stress of nearly 2.16
MPa. The maximum displacement that
occurred was 0.0115 m at the pedal location,
which, if under continuous fatigue could
lead to failure if the maximum stress was not
reached first.
V. CFD Analysis and Results
A CFD analysis was performed using
STARCCM+ computational software to
determine the influence of the air drag on
the structural frame members [2].
STARCCM+ is a finite volume modeling
software. A non-structured block mesh was
used with a boundary laying scheme for the
near wall regions. Figure 7 shows the mesh
domain for the fairing CFD analysis along
the fairing’s symmetry line. The fairing was
treated as a wind tunnel flow with 1m
spacing from the tunnel walls to the fairing
top and sides. Standard air conditions where
used for defining the air fluid properties.
The Reynolds number defined by the fairing
height is given in Table 1 is clearly in the
turbulence flow regime. The turbulence was
modeled using the steady state Realizable k-
ε Reynolds Averaged Naiver-Stokes
turbulence model. The model used a two-
layer y+ wall treatment. Since the Mach
number was nearly .08 the flow was highly
incompressible and an uncoupled solver
configuration was used to improve the
computational speed.
Figure 7: Fairing mesh and dimensions
The simulation converged to a nearly 20N
for several mesh refinement configurations.
A drag coefficient was defined using the
largest normal fairing cross-sectional area
and is given in Table 1. The drag force was
considered to have adequately converged
since the drag coefficients predictions of
same order of magnitude and nearly have
the Reynolds number are reported for a CFD
study of an Ahmed body [5]. This included
several numerical schemes for turbulence
treatment and reported an experimental
baseline coefficient.
Table 1: CFD flow condition and results summary.
Re (-)
Drag
Force
(N)
Drag
Coefficient
(-)
Elements
1.3E6 20 .0404 2.5E6
Figure 8 presents a velocity distribution
along the symmetry plane. The flow profiles
shown correspond with typical blunt body
flows. Since the predicted drag force of 20N
corresponding to maximum trike speed of
64.37kph is minimal compared to pedaling
and rider loads it was considered negligible
in the FEA.
Figure 8: Velocity profile of fairing along
symmetry plane.

4. VI. Second Simplification
In attempting to achieve a higher accuracy
in the meshes, the computer started to fail at
completing the analysis. To remedy this,
symmetry was introduced to the model, and
the roll cage was removed, which is describe
in Figure 9.
Figure 9: Second Simplification Model
Figure 10: Second Simplification Loading and
Constraints
Symmetry, Figure 10, was able to be applied
because the frame is symmetric about the
vertical plane that is normal to the direction
of motion. This reduced the computational
effort. The roll cage was able to be removed
because there was no displacement and
minimal stress applied to it, so the need to
analyze the material there was unnecessary.
VII. Second Analysis and Results
The first step taken to decrease the stresses
on the bike frame was to change the
material, which was also the easiest. The
material chosen was Alclad 2014-T6. The
new material only has 0.1 g/cc higher
density than 6061-T6 Aluminum, which lead
to a new mass of 2.49 Kg. It also has a
higher yield stress, at 414 MPa, compared to
6061-T1 at 110 MPa. The second step taken
to reduce the stresses on the frame was to
add fillets at some of the critical locations.
The final step taken was to increase the
height of the tube cross-section to 0.04445
m. This would assist in decreases the
stresses since they are not applied
horizontally on the tube. The static analysis
was run on the new model; Figure
11provides the corresponding Von Mises
stress and Figure 12provides the
corresponding Total Displacement:
Figure 11: Second Von Mises Stress Analysis
Figure 12: Second Total Displacement Analysis
The new Von Mises stress analysis provided
a maximum stress of 2.6878 MPa, which
provides a factor of safety of 1.540.
Although this is slightly larger than the
initial design goal, a third analysis was
performed with an updated model in an
attempt to minimize the maximum Von

5. Mises stresses, which will provide an
increased factor of safety.
VIII. Final Analysis and Results
The only step taken to decrease the stresses
on the bike frame after the second analysis
was to increase the size of the fillets on the
previous model and add a few more to some
the high stress locations. Figure 13 and
Figure 14 provide the corresponding Von
Mises stress results and total displacement
results, respectively.
Figure 13: Final Von Mises Stress Analysis
Figure 14: Final Total Displacement Analysis
The final Von Mises stress analysis recorded
a maximum stress of 2.678 MPa. This
provided a factor of safety of 1.549. This
meant, unless the material was changed, the
wall thickness was increased, or the height
of the beam was increased again, there was
not much room for improvement on the
design.
IX. Mesh Independent Study
A series of static structural simulations were
performed with decreasing element size for
eliminating the influence of element size on
the accuracy of the simulation. Figure 15
presents the results of the mesh
independence study. Both maximum Von
Mises Stress and Total Deformation were
monitored for convergence. The
deformation converges quickly while the
Von Mises stress converges at nearly half a
million elements.
Figure 15: Mesh Independence Study
X. Natural Frequency Analysis
Following the mesh convergence study a
modal analysis was performed using
the .002m mesh size from the
convergence study. The modal study
resulted in an approximation of the first 6
modal frequencies and the respective
shapes. Figures Figure 16 through Figure
21.
Figure 16: Modal shape at resonance frequency
of 65.759Hz

6. Figure 16 major deformation occurring in
the vicinity of the main frame member.
Figure 17: Modal shape at resonance frequency
of 92.756Hz
Figure 17 shows a single high
deformation near the axel mounts.
Figure 18: Modal shape at resonance frequency
of 100.82Hz
Figure 18 show two dominate loading
locations one near the rear axial mount and
a second near the lower seat mount.
Figure 19: Modal shape at a 215.89Hz resonance
frequency
Figure 19 gives a single dominate
deformation near the pedal bearing mount.
Figure 20: Modal shape at a 334.32Hz resonance
frequency
Figure 20 shows high deformation due to
buckling near the rear axel mount.
Figure 21: Modal shape at a 558Hz resonance
frequency
Figure 21shows twisting and buckling of
the frame member near the rear axel
mount.
XI. Conclusions
The frame for a recumbent tricycle must be
able to support many large forces and
remain rigid. The frame being analyzed was
modeled in CREO 3.0 and analyzed in
ANSYS Workbench. The analysis used the
Von Mises Stress and total displacement
criterion to measure the factor of safety and
displacement from loading, respectively. A
CFD analysis was applied to the fairing
which produced drag forces of only 20 N at
a maximum riding velocity of 64.37 Kph.
Because the drag forces were small
compared to the rider mass and pedaling
force, they were able to be ignored. The

7. initial material was 6061-T6 aluminum
because of its known success in
commercially designed tricycles and low
density, which resulted in a bike frame that
only weighed 2.39 kg. After the initial
analysis however the mechanical properties,
specifically the yield strength of 2.16 MPa,
were unacceptable. The first modification to
decrease the maximum Von Mises stress
was to change the material that had a higher
yield strength, with a similar density in order
to keep the mass similar. The new material
chosen was Alclad2014-T6 Aluminum,
which has a yield strength of 414 MPa and a
provided a new mass of 2.48 Kg. The beam
height was also increased to 0.044 m in
order to increase the strength of the beam in
the main directions that the forces were
applied, without bulking it up too much.
The final results provided a factor of safety
of 1.55, which was almost exact to the
desired factor of safety. These results end in
a frame that has a low weight, high strength,
and optimal performance. A modal analysis
was performed determining the modal
shapes corresponding six approximated
resonance frequency. Though not in the
scope of this study these modal result could
be used in conjunction with dynamic loading
to evaluate the fatigue life and design
against harmonic loading.
XII. Works Cited
[1
]
PTC, "PTC CREO," [Online]. Available:
http://www.ptc.com/product/creo/ne
w. [Accessed December 2015].
[2
]
J. Stokes, Marshall Space Flight Center,
1976.
[3
]
ANSYS INC, "ANSYS.com," ANSYS INC,
2015 . [Online]. Available:
http://www.ansys.com/. [Accessed
NA].
[4
]
CD-adapco, "cd-adapco.com," 2014.
[Online]. Available: http://www.cd-
adapco.com/. [Accessed 31 11 2015].
[5
]
A. M. Y. Liu, "Numerical modeling of
airflow over the Ahmed body," in
Eleventh annual conference of the CFD
Society of Canada, 2003.