The document summarizes the analysis and optimization of steering components for a human-powered vehicle (HPV). It describes the goals of reducing component weights by 60-80% while maintaining a safety factor above 1.5. The methodology included understanding load paths, applying finite element analysis to evaluate stresses, and iteratively modifying designs. All components met safety factor goals except the steering plate, which fell just short at 1.46. The optimizations achieved weight reductions but did not fully meet all initial percentage targets.

1.
California State University, Northridge
Department of Mechanical Engineering
Computer­Aided Analysis and Design
ME 386/L
Professor Khachatourians
Spring 2015
Robert Timm
Rachel Foreman
Kevin Matsuno
Piotr Orzechowski
Mario Solorzano
Jeremy Ward
May 6, 2015
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2. Table of Contents
Executive Summary…………………………………………………………………....………….2
Design Methodology………………………………………………………………………...…….3
Load Path and Boundary Conditions……………………………………………………..……….5
Critical Component Analysis………………………………………………………………....…...9
SS­1001: Left Lever Arm…………………………………………………………...…….9
SS­1002 & SS­1004: Input and Output Tie Rod………………………………...………22
SS­1003: Steering Plate……………………………………………………………….…30
SS­1005: Steering Knuckle……………………………………………………………....38
Conclusion……………………………………………………………………………………….46
References………………………………………………………………………………………..47
APPENDIX....……………………………………………………………………………………48
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3. Executive Summary
The Human Powered Vehicle Challenge (HPVC) is a yearly competition hosted by the
American Society of Mechanical Engineers (ASME). Students work in teams to develop
sustainable and practical human­powered transportation alternatives. The specific objective of
this project was to improve the steering components of the existing California State University,
Northridge (CSUN) HPV team vehicle. Goals were set to reduce the weights of each component;
60% reduction for the lever arm, 40% reduction for each tie­rod, 50% reduction for the steering
plate, and 40% reduction for the steering knuckle. Additionally, based on SolidWorks Simulation
finite element analysis (FEA), no part was to fall below a factor of safety (F.O.S.) of 1.5. By
changing the geometry of the lever arm, first tie rod, and second tie rod, their weights were
reduced by 60, 81, and 79 percent, respectively. By changing the geometry and material of the
steering plate and knuckle, their weights were reduced by 78 and 26 percent, respectively. Each
part met the minimum factor of safety except for the steering plate, which fell just short with a
factor of safety of 1.46.
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4. Design Methodology
The method used to optimize the steering system began with understanding the current
CSUN HPV steering system. This definition came from the HPV team. They provided models
and identified each of the components in the system. The interface between each of these
components, other HPV components, and the driver were clarified. Critical inputs into the
analysis were the maximum forces that could be applied by the driver, the limit of travel of the
steering plate, and the original materials selected for the each of the components.
With this geometric definition of the assembly, the kinematics of the system and its
components could be determined. The positional kinematics of the system were solved based on
the tie rod configuration. The forces acting on each of the components was quantified with free
body diagrams (FBDs) and hand calculations. With this information the loading and boundary
conditions for each of the system components was determined.
With solid models and boundary conditions for each component, the FEA effort could
begin. The team was separated into groups with each managing a component in the system. In
all cases, the components required some idealization to be meshed. Examples of idealization are
removing threading, adding fillets to shark, re­entrant corners, or simply fixing incorrect
geometries from the original HPV models. With meshing complete the static simulations could
be run to find the maximum stresses. To achieve better than 5% convergence, manual and
automated mesh iteration was used. Generally, all models required generous use of fillets to
achieve convergence. Achieving convergence on the original parts established baseline for
proper analysis of the optimized parts. The focus could now be turned to the optimization of
each of the parts.
The FEA process of creating a Solidworks CAD model, idealizing the model, meshing
the model, running the simulations, demonstrating convergence, and calculating the F.O.S. for
various material candidates was completed. This process was repeated as needed until the model
meshed properly, converged, and performed well relative to the set goals (F.O.S. and weight).
Meeting the F.O.S. requirements for the system was the primary requirement. Any design that
did not achieve the minimum FOS of 1.5 was rejected. The weight reduction goals for the
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5. project were important, but were best effort. The final designs (combination of geometry and
material changes) all showed improvements, but the per component weight reduction goals were
not all met. The time constraints for the project eventually required all of the optimization
efforts for the each of the components to end. In the case of the more complex parts (the lever
arm and the steering knuckle), more improvement (reducing weight while maintaining the
minimum FOS) was certainly possible. This additional optimization represents an area of
opportunity for future efforts. Additionally, the interfacing features of each of the parts were not
changed so that the system kinematic behavior and the integration of the system components in
Solidworks would be unaffected. Future work could involve improving these connections as well
as the individual components.
Figure 1:​ FEA driven design process.
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6. Load Path and Boundary Conditions
Referring to Figure 2, the user grips each of the lever arm handles. To turn, one lever arm
is pushed forward while the other is pulled towards the user (green arrows). This causes both
levers to rotate opposite to one another (yellow arrows). The input force from both lever arms
translate through each tie rod and into the the steering plate. Since both input tie rod forces are
off centered, the steering plate rotates and translates force into the output tie rods. Note that part
of the initial input forces will diffuse into the HPV frame from the hinged portion of the steering
plate. The remaining forces translate through both output tie rods to the steering knuckles, and
ultimately rotate the front wheels. The remaining forces dissipate into the portions of the frame
supporting the front tires as well as into the ground (blue arrows).
Figure 2:​ (Left) The load path of the steering subassembly. (Right) Colored legend of each arrow.
In addition to the load path, boundary conditions were established to better represent
realistic scenarios. First, in calculating the load for each part, the maximum amount of pushing or
pulling force generated from an average adult male arm needed to be determined. The National
Aeronautics and Space Administration (NASA) published a paper that measured the average
adult male strength to the 95th percentile. The acquired results were used for the HPV steering
subassembly and can be seen in Figure 3.
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7.
Figure 3:​ Charts from NASA Human Strength Study showing a maximum force of 56 lb.
Another boundary condition established was the operating condition. All analysis was
conducted in ambient, non­corrosive, environmental conditions. As a result, any failure from the
component is due to the stress from the applied loads. In addition, each component of the
subassembly was examined under a “locked,” static scenario in order to calculate the maximum
loading conditions.
The final boundary conditions were determined by describing the system kinematics
mathematically. The steering system kinematics can be described by a four bar linkage. The
four linkages on the HPV vehicle are (Figure 4):
● The steering plate edge “a”. This is the driving link length 5.00 inches.
● The tie rod “b”. This is the coupling link of 14.25 inches.
● The steering knuckle “c”. The is rocker link of 3.79 inches.
● The fixed link “d”. This link is fixed at both ends to the frame. It is 15.78 inches.
The four bar linkage position equations are derived by understanding each linkage is a
vector and the four vectors always add to zero (even as the angle of the driving link is changed).
The inputs into the equation are the lengths of each link and the angle of the driving link.
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8. The range of motion possible from for the steering plate was given by the HPV team. It
is +/­18° from straight. With this input and trigonometry, the angles for each of the other
linkages can be solved. The angle for each linkage is defined relative to the ground link, “d”.
● Θ​2​ ­ angle between a and d. 78.84° when steering is straight. Can vary from
60.84 to 96.84. This is an input into the four bar linkage equations. This angle
drives the position of the other linkages.
● Θ​3​ ­ angle between b and d.
● Θ​4​ ­ angle between c and d.
Figure 4:​ The steering system geometry with the four linkages defined.
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9.
Figure 5:​ The four bar linkage solution for Θ​3​ and Θ​4​ (as a function of the steering angle). The
steering angle is 0° when the steering is straight.
Figure 6:​ The graphical representation of the travel of the steering system when the steering
plate is rotated +/­18°. The top linkage (“d”) is the ground link; it does not move.
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10. Critical Component Analysis
Left Lever Arm (SS­1001)
The HPV team’s left lever arm (Figure 2) is used to initiating motion within the steering
subassembly. The lever arm has already been built by the HPV team to the dimensions specified
in their original SolidWorks model. The arm spans approximately 22 in. by 18 in. and its total
width is approximately 3 in. (Figure 7). The lever arm is made of Aluminum 6061­T6, and it
weighs approximately 1.91 lb. (Table 1). It is a 1” by 2” rectangular beam weldment with a
thickness of 0.125” (Figure 8).
Figure 7:​ Original lever arm left and front view with dimensions.
Figure 8:​ Lever arm body cross­section with dimensions (handle has different dimensions).
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11. The lever arm is made up of nine separate pieces. They were welded together using filler
weld rod 4043 (Figure 9). Yield strength of aluminum 60601­T6 is 39,885 psi. Yield strength of
post­weld, heat­treated, and aged alloy 4043 with aluminum 6061 is approximately 40,000 psi
(see Appendix, Figure 44). Therefore, for FEA purposes the lever arm can be considered one,
solid component with a uniform stiffness matrix and a yield strength of 39,885 psi.
Figure 9:​ Original lever arm weldment showing each separate section.
The HPV team provided the fully dimensioned model of their original lever arm design.
Since our goal was to optimize the model by reducing weight while achieving a minimum F.O.S.
of 1.5, we needed to: (1) identify the worst case loading scenario, (2) draw a free body diagram,
(3) apply the HPV team loading conditions and fixtures, (4) verify the HPV team FEA model
and results, and (5) optimize the lever arm model and compare its FEA driven results to the
original HPV team data.
Based on the previously determined force of 56 lb, as well the fixtures assumed from the
“locked” scenario, a FBD was created using the original SolidWorks model (Figure 10).
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12.
Figure 10:​ Lever arm’s FBD with maximum input force of 56 lb.
Defining all distances and taking a moment about the lever arm’s pivot point, Newton’s Second
law produces a general equation of the output force for the lever arm (Eq.1). The “Force­out” in
Figure 10, represents the reaction force exerted by the tie­rod back onto the Lever Arm.
(Eq. 1)
Applying 56 lb. on the handle results in the tie­rod experiencing 425 pounds of force. Table 1
summarizes all FBD findings.
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13. Table 1:​ Given and calculated FBD lever arm values.
Although the HPV Team had previously performed FEA analysis, they were not able to
locate their numerical results to pass on to our team. However, they provided their lever arm
model and the external loads and fixtures that they applied to their model (Figure 11). The HPV
Team applied a standard fixed geometry to the inner circumference of the pivot pin surface.
Unfortunately, the HPV Team did not consider the reactionary force from the tie­rod, which is
necessary in the analysis of this part.
Figure 11:​ HPV team FEA model.
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14.
The HPV team treated the entire box­cross section of the model as a solid. The cylindrical
handles (Part 7 and 8, Figure 9) were treated as shells with thickness of 0.125”. The end surfaces
of the cylindrical shells were manually bonded to each other and to the solid Lever Arm section
(Part 6, Figure 9). The results of coarse, default, and fine mesh densities are shown in Table 2.
Table 2:​ FEA results driven by HPV Team interpretation of loads and fixtures.
Although there appears to be a convergence in the maximum von Mises stress across
course, default, and fine mesh densities, using mesh control applied to a random re­entrant edge
revealed a slightly higher von Mises stress (Table 1, 4​th
column, Fine Mesh with Mesh Control).
An h­adaptive study confirmed that the maximum von Mises stresses did not converge (Figure
12). Therefore the results under course, default, and fine mesh density columns used by the HPV
team to identify quiet areas and minimum factor of safety in the Lever Arm were suspect.
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15.
Figure 12:​ H­adaptive study on HPV team lever arm model.
While each mesh refinement shown in Table 1 brings about an increase in the maximum
displacement, the difference between consecutive results decreases. Therefore, the only result in
the HPV Team’s FEA study that provides accurate values is the displacement (0.33”). Because
factor of safety is dependent on stress, it along with the von Mises stresses previously calculated
could not be used in our study. Due to the significant amount of stress singularities, the HPV
Team’s FEA Lever Arm model had to be cleaned up.
In order to eliminate all stress singularities, 0.1 inch radius fillets were applied to all
sharp re­entrant corners (Figure 13). Since maximum displacement would occur at the location
of the input load (56 lb), the cylindrical handles (Part 7 and 8, Figure 9) were removed and Part 6
of Figure 9 was extended in order to imitate the contact force (Figure 14). A circular split line
was created on the surface of the Lever Arm where the tie rod is attached. The split line
represented a washer that would be placed under the tie rod bolt, holding it in place. Standard
fixed geometry was applied to the split line surface and to inner wall (Figure 13). A shaft was
created and inserted into the Lever Arm’s pivot point hole. This shaft was necessary to It was
bonded to the Lever Arm and a “fixed hinge” was applied to the inner walls of the shaft (Figure
13).
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16.
Figure 13:​ Fixtures and fillets added to lever arm FEA model.
Figure 14:​ Applied fixtures and external Loads on cleaned­up FEA lever arm model.
15

17. After applying the necessary fixtures and loads (Figure 14), an h­adaptive study revealed
(after 3 loops and convergence of 0.66%) a maximum von Mises stress of 27,367 psi with a
minimum factor of safety of 1.46 (Figure 15). Results from the h­adaptive study are shown in
Table 3.
Table 3:​ FEA driven results for modified (cleaned­up) lever arm model.
Maximum von Mises stress and minimum factor of safety occurred at the intersection of Part 1
and Part 2 (see Figure 9 for reference) (Figures 15 & 16). Displacement from Table 3 was
disregarded since the handle was not necessary for the h­adaptive stress study. Maximum
displacement was taken from Table 1. The Modified FEA Lever Arm model was created in order
to determine the maximum von Mises stress in the original HPV Team’s model. Displacement
from Table 1 and maximum von Mises Stress from Table 3 will be used to compare the
optimized model with HPV Team’s model.
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18.
Figures 15 & 16:​ Locations of maximum von Mises stress (left) and minimum FOS (right) on
modified lever arm model.
The decision was made to continue the use of 6061­T6 aluminum for the optimized lever
arm. The initial optimized design included large radii at the bends (Figure 17, left). The purpose
of this was to immediately reduce the chance for stress singularities in the analysis. Rather than
using weldments in SolidWorks, the part was modeled as one solid piece. The handle of the lever
was shortened and its thickness was reduced to lower the overall weight (Figure 18, bottom).
Figure 17:​ Initial lever arm optimization with large radii (left) compared to original (Right).
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19.
Figure 18:​ Initial lever arm handle (top) versus reduced handle (bottom).
The original dimensions of the rectangular cross section were 2.00” x 1.00” x 0.125. To
continue to reduce the lever arm weight, the thickness of the rectangular body was first reduced
to 0.056” – the smallest standard thickness of 2” by 1” tubing based on SolidWorks Weldment
Profiles. This thickness was found to produce stresses well above the yield strength of the
material. The thickness was gradually increased based on standard available rectangular pipe
sizes until a suitably low stress was achieved. The thickness eventually chosen was 0.09375, or
3/32 inches (Figure 19).
To further reduce the weight, the outer dimensions of the rectangular tube were shortened
as much as possible. This was also an iterative process; the longer side of the tube was reduced
by 1/8” increments until the factor of safety no longer met the goal of 1.5. After the smallest
acceptable dimension was determined to be 1.75” for the long side, the same procedure was
repeated for the short side. After numerous iterations, the final dimensions of the rectangular
tube were 1.75” x 0.75” x 0.09375” (Figure 19).
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20.
Figure 19:​ Original lever arm cross section (left) and optimized lever arm cross section (right).
With the new dimensions, the part was analyzed using second order solid elements. A
default, curvature based mesh was used to more accurately solve for the stresses. In addition, an
h­adaptive study was implemented with a target accuracy of 99% and a maximum of three loops.
By fully fixing the hole where the tie rod connects, putting a fixed hinge at the second hole, and
applying a 56 pound force normal to the handle, the stress results seen in Figure 20 were
obtained.
The stress results between the second and third loop had a convergence error of 2.00%;
within the 5% convergence criteria. This resulted in a factor of safety of 1.58, above the required
minimum of 1.5. This also reduced the weight by 47% in comparison to the original model
(Table 4). While this did not quite meet the reduction goal of 60%, the results were acceptable,
and thus were presented in the group’s critical design review (CDR) on Monday, April 20, 2015.
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21.
Figure 20:​ FEA von Mises stress results on optimized lever arm.
Table 4:​ FEA driven results from original and optimized lever arms.
Although the results of the optimized design were already an improvement on the
original lever arm, further optimization was performed after the CDR presentation. To more
accurately represent the model, the design was altered back to weldments per the original HPV
model. The handle was still shortened and reduced in diameter and thickness to begin to reduce
the weight. The final handle was 0.75” diameter by 0.035” thickness; this is the smallest
thickness available at this diameter. 6061­T6 Aluminum was still used.
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22. The rectangular tubing was reduced to 1.75” x 0.75” based on the results of the first
optimization. However, the thickness was reduced to 0.064” to see if the weldment geometry
could handle the forces with less material. To prevent stress singularities, 0.2” fillets were added
to all of the interior edges of bends along the lever arm. The same fixtures and force that were
applied to the first optimized lever arm were applied to this second optimization. The same mesh
properties were used, with the exception of the maximum number of loops being raised to five.
The results of the second optimization surpassed those of the first optimization. The new,
lower stress results can be seen in Figure 21. The lower maximum stress yielded an improved
factor of safety of 1.78. Most importantly, the new optimization reduced the part weight to 0.80
pounds. Based on the original weight, this would be a 58% weight reduction. However, an error
was found in the original weight calculation (the weight was initially measured without both
sections of the handle included); in comparison to the corrected original weight, this part met the
weight reduction goal with a total reduction of 60.2%. The comparison between the original,
first, and second optimizations with the adjusted original weight can be viewed in Table 5.
Figure 21:​ FEA von Mises stress results on the second optimized lever arm.
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23. Table 5:​ FEA driven results for the original, first optimized, and second optimized lever arm models
with corrected weight values.
Input Tie Rod (SS­1002) and Output Tie Rod (SS­1004)
Figure 22:​ Tie rod location within steering subassembly.
Shown highlighted in red in Figure 22 are both tie rods, their general dimensions, and
placement in the steering subsystem. In optimizing the tie rods, one of the main constraints on
optimization was to keep the original lengths of the members, and to not change the tie rod ends
that connect the system. Both tie rods were run using similar analyses, therefore analysis of these
parts will have results shown together to compare and contrast between the two. The input and
output tie rods are simple, two­force members. The input tie rod receives load from the lever arm
via its tie­rod end connection to the member. This force is translated into the rod, where the load
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24. then distributes to the ternary plate via a similar connection. The ternary then translates the
forces into the output tie rods, and finally that load is transferred to the knuckle through the
output tie rod. With the “locked” steering scenario, the opposite sense of the forces on each
respective side of the system mean that the tie rods can and will be subjected to both tensile and
compressive loading in right and left turn scenarios, respectively. These two loading scenarios
are shown in Figure 23 below:
Figure 23:​ Loading conditions applied to each tie rod.
Being long, slender members that are subjected to compressive loads, it is obvious that
another mode of failure for these parts is buckling. Therefore, compressive and tensile static
linear structural analyses were carried out, along with buckling analysis for both members in
hopes of reducing the weight of these components by a minimum of 40% through optimization.
Interestingly, the output tie rod sees much less force than the input receives, at just 152 pounds
of force versus 425 pounds of force for the input tie rod. This was taken into consideration, but
because of the differing lengths of the two rods, static stress analysis and buckling analysis were
performed on both to confirm that the input tie rod was indeed the critical member.
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25. The first step in the analysis process of these components was defeaturing and
idealization of the model. This process included removal of the threads on the two ends of the
rods, and the addition of some generous fillets on the interior change in diameters of the rod.
Additionally, it should be noted that the two ends of the rods have inserts to place the smaller
quarter inch nominal threads into the much larger inner diameter of the rod material coming from
McMaster Carr. For this analysis these inserts are assumed to be solid and a part of the rod itself
and this was part of the idealization of the tie rods. In practice these inserts would either need to
be welded, press fit, or glued into the ends of the rods themselves. Figure 24 below shows some
of the defeaturing and idealization of the model.
Figure 24:​ Defeaturing, idealization, and addition of fillets to the tie rods.
In order validate the idealization made by removing the threads from the model, a quick
thread tearout hand calculation was performed to make sure that the threads would not tear out
under the applied loading. This calculation was absolutely necessary prior to performing any
FEA analysis on this rod. If the threads would have failed on this part, the loading applied to the
rest of the rod would never reach the value being put into the FEA model. Because only three
threads typically yield and hold load, three times the pitch was used for the thread engagement
24

26. length for a conservative estimate. This calculation confirmed that the threads would not be a
problem, so long as 6061 T6 was the aged state of the threads. The factor of safety found for the
thread tearout was about 7.2. The results of these hand calculations can be seen in Figure 25.
Figure 25:​ Thread tearout calculations to validate idealization assumptions.
​After defeaturing and idealizing the tie rods, the restraints and loads were applied. It was
determined that it would be beneficial to split the model in half and apply symmetry boundary
conditions to the model. This had twofold benefits; it reduced the amount of time to mesh and
run each of the many studies needed, and made the visualization of maximum stress locations
much easier. This also allowed for quick updates to non­convergent areas like the interior fillets.
A fixed restraint was applied to the cylindrical face on one side of the rod, where the threads
would be taking the load. Similarly, the load was applied to the opposite end of the rods on the
same cylindrical face where the threads would take the load. Because of the symmetry boundary
conditions, half the expected load was applied to this cylindrical surface, normal to the end face
of the rod in both tensile and compressive loading scenarios, respectively. Figure 26 shows the
symmetry boundary condition, restraints and loads applied to the model.
25

27.
Figure 26:​ Restraints and loads applied to tie rod models.
Once all of the idealization and boundary conditions were applied, a mesh was created.
Solid, standard, high quality elements were used for these parts since the added inserts at the end
of the rod didn’t allow for shell or beam elements to be used in this case. A static linear study
was then carried out for the initial tubing size to find out how high a factor of safety the tie rods
had before moving forward with optimization. The mesh was manually edited, using coarse,
default, and then fine element size in order to confirm convergence of the model. This
convergence was calculated for each step by finding the convergence error between the default
and fine mesh steps. Other than the first static study performed, and one other study on the
output tie rod with extremely low stresses, all models achieved convergence on the first try. For
the output tie rod study that failed the first convergence test, a quick change of the mesh to a
curvature based fine mesh compared with the last fine mesh produced convergent results. The
initial factor of safety for the input tie rod with an outer diameter of ¾” was found to be 29.
Since this factor of safety was so high, the tubing size selected for the second iteration was cut in
half, with a ⅜” outer diameter. This resulted in a factor of safety for stress of 11.68 for both
tensile and compressive loading scenarios. FEA von Mises plots for the tensile loading scenario
26

28. are shown in Figure 27. The results showing von Mises Stress, max deflection and minimum
factor of safety from these static studies for both loading scenarios are shown in Table 6.
Figure 27:​ FEA static von Mises stress for original (left) and optimized (right) tie rod models.
Table 6:​ FEA driven static results of original and optimized tie rods.
As is evident in looking at Table 6, stress values were still nowhere near the yield stress
of aluminum 6061 T6, however it was necessary to confirm that these studies for compression
and tension were actually the critical mode of failure for the part moving forward. Since they are
long and slender members, buckling analysis was carried out for each rod. Buckling plots are
shown in Figure 28, whereas Table 7 lists the buckling load factors found for each tube size.
Mode 1 was the first positive BLF value found, so this mode was taken to give the BLF for all
buckling tests performed.
27

29.
Figure 28:​ Buckling plots for original (left) and optimized (right) tie rod sizes.
Table 7:​ BLF factors from mode one of buckling analysis for each rod and size.
From Table 7 and Table 6, it is clearly evident that the input rod is the critical member of
the two tie rods in the system. Even with the longer length of the output rod, the BLF still comes
out higher due to the lower force exerted into this member by the ternary. With a BLF of just
1.845, the input tie rod was deemed to be fully optimized, as the next size down from ⅜” would
have produced a member that buckled under the same loading conditions. Additionally, the next
size down from ⅜” would also require reducing the size of the tie rods, as the major thread
diameter would then be larger than the outer diameter of the next size down in tubing from
McMaster Carr. This would have defeated the optimization intent of keeping the original tie
rods, therefore ⅜” outer diameter tubing was the final optimized sizing selected for the tie rods
based on buckling failure, having a critical factor of safety of 1.845. Multiplying the BLF factor
by the applied load of 425 pounds gives a buckling load of 784 pounds allowed for the input tie
rod.
Changing the material of the tie rods was really out of the question for this optimization
project. The only material that could have reduced the weight significantly would have been
magnesium, but because of the ability to get the stock for this part off the shelf in aluminum
28

30. 6061, it was pointless to try and fabricate this part out of magnesium to try and shave off a few
extra ounces.
Table 8:​ FEA driven results for original and output tie rods in static and buckling analysis.
Optimization of the tie rods resulted in about an 80% reduction in weight from the
original design (Table 8), which was double the goal of 40% weight reduction that was originally
set to achieve. The original design was very overdesigned, and this optimized sizing will result in
better steering response and a lighter vehicle overall. Not much else can be done with the tie rods
moving forward, a sensitivity study on this part would likely show negligible gains by removing
more material. Looking at reducing the tie rod end size would be the next step in reducing weight
of this part of the steering subsystem.
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31. Steering Plate (SS­1003)
Figure 29:​ Envelope dimensions of the steering plate.
The steering plate receives the input force from the two lever arms and then translates it
to the steering knuckles; this causes the front tires to rotate. Like other components, the steering
plate was studied as a linear, static structural analysis. To begin analysis, the maximum forces
experienced by the part needed to be determined. As a result, two FBDs were created that varied
the steering plate’s and output tie rods’ positions: one in the idle position (no rotation) and one at
the maximum rotation (18° from the y­axis). The rest of the steering subassembly components
have mirror parts; as a result, loads from only one of each of these parts is needed for the
analysis of those parts. Alternatively, the steering plate’s loading scenario must include the
forces from all duplicates parts. Ultimately, the fully rotated scenario experienced the greatest
forces. Both output tie rods generated a resultant force of 152 lb. on the steering plate. Below is
the FBD for this loading scenario in (Figure 30) (Scenario 1 can be found in the Appendix,
Figure 45).
30

32.
Figure 30:​ (Right) FBD of the original steering plate at full rotation. (Left) Summary of forces
and assumptions.
Next, SolidWorks Simulation was used to determine the original plate design weight,
maximum von Mises stress, maximum deflection, and minimum F.O.S. Due to its simplistic
design and clean CAD model, no defeaturing or cleanup was needed to begin the analysis.
Model preparation was completed by adding split lines to divide the two smaller holes’
cylindrical faces in half. This was necessary to simulate the approximate area on which the tie
rod input and output forces would act. When applying loads, the resultant output tie rod force
was broken into cartesian (x and y) components. These components accounted for both the
steering plate and tie rods' angles of rotation with respect to one another. Finally, the direction of
each force was applied normal to either the standard front, right, or top plane and placed on only
one side of the split line face. In order to fix the plate, an advanced fixture was used on the
larger (bottom) cylindrical face that restrained the part from moving in the radial,
circumferential, and axial directions. Figure 31 shows the FEA model used for analysis.
31

33.
Figure 31:​ FEA model with boundary conditions for original static analysis.
Due to the steering plate volume, second order solid elements were used. To obtain
accurate results, a finer mesh density was used in every successive iteration. Coarse, default, and
fine meshes were tried for the original and each optimized geometry. If more iterations were
needed, mesh control and curvature based meshes were applied in local areas. For each
iteration, a standard spreadsheet established by the group was filled out (see Appendix, Figure
46). Finally, the official data was collected once the von Mises stress between two consecutive
runs met the 5% convergence criteria. The results can be seen in Figure 32.
32

34.
Figure 32: ​(Top) FEA von Mises stress results of the fifth iteration of analysis. (Bottom)
Summary of manual convergence iteration results.
The maximum von Mises stress, maximum deflection, and minimum F.O.S. occur at the
upper right corner of the steering plate. This is the case when the steering plate was rotated
completely to the right. Due to symmetry, the upper left corner would have identical results if
the plate was rotated fully to the left.
Based on the results, the plate geometry, material, and thickness could be altered to reach
the 50% weight reduction goal while maintaining a F.O.S. of 1.5 or greater. To find the best
optimized design, a manual sensitivity study was conducted. First, keeping the geometry and
thickness fixed, each material from the table of material candidates was applied (see Appendix,
Table 16). The same data and convergence criteria from analysis of the original design was
33

35. used. Next, the geometry of the design was changed while the material and thickness were
maintained. In optimizing the geometry, two designs were chosen (Figure 33).
Figure 33:​ Original, first optimized, and second optimized steering plate designs as labeled.
In addition, all combinations of geometric designs and material candidates went through
a linear, static structural study with the same data objectives and convergence criteria. Finally,
the thickness was altered in combination with the geometric design and material candidates.
Originally, the thickness of the plate was 0.25 inches. The optimized thickness, 0.16 inches, was
chosen from McMaster Carr’s standard sheet/bar/strip 6061­T6 thickness list. The individual
material and geometric design variable studies underwent the same manual convergence process.
However, due to the limitation of time, the studies combining material, geometry, and thickness
were solved using h­adaptive studies with a 99% target accuracy. Tables 9 and 10 provide a
summary of all the studies performed.
34

36. Table 9:​ Summary of analysis results for each steering plate geometry and each material tried.
Dark orange cells indicate both weight and F.O.S. goals were met.
Table 10:​ Final analysis with previous proposed geometries and material AND reduced thickness.
35

37. Figure 34 shows the chosen optimized design. Based on the manual sensitivity study, the
best design is optimized design 1, and should be made from AZ61A­F magnesium alloy with a
thickness of 0.16 in. Unlike the original design, the optimized design has its maximum von
Mises stress, maximum deflection, and minimum F.O.S. in the upper left corner. Although the
minimum F.O.S. is below the required 1.5, it is highly localized. The majority of the part has a
calculated F.O.S. well above 1.5. As a general observation, cutting the geometry introduces
more stress concentrations. As a result, optimized design 2 was rejected due to the increased
amounts of critical stresses produced in the part. The results using a AZ61A­F, optimized design
2, and a 0.16 in. thickness can be seen in the Appendix (Figure 47).
Figure 34:​ FEA von Mises stress plot and summary of results for optimization 1 (chosen design).
Another study was conducted to calculate the minimum F.O.S. at the tie rod holes due to
tearout shear and direct bearing stresses. The tabulated summary, formulas, and minimum
F.O.S. for each material can be seen in Figure 35. In the optimized design, tearout and bearing
stresses will not cause the part to fail.
36

38.
Figure 35:​ (Left) Summary of tearout shear stress calculations. (Right) Summary of bearing
stress analysis. Verification that the part with not fail due to tearout.
In summary, the optimized design can successfully reduced the weight by 78% and still
maintain a F.O.S. of 1.5 and above. The changes in material, geometry, and thickness allowed
the component to perform in the worst case scenario. A comparison between the original and
optimized steering plate can be seen in Figure 36. In terms of manufacturing, optimized design 1
would need to be milled to remove the interior material. In addition, plate can be purchased with
the 0.16 thickness or machined to achieve this. Future work for this part includes performing
buckling analysis on the chosen optimized design.
Figure 36:​ (Left) Chosen steering plate geometry. (Right) FEA driven results for original and
chosen optimized designs.
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39. Steering Knuckle (SS­1005)
The boundary conditions for the steering knuckle were established based on input from
the HPV team, assuming the “locked” scenario, and guided by the previously determined
kinematic positional results (Figure 37). The knuckle attaches to the frame, the wheel hub, the
output tie rod, and the brake calipers. The forces applied during breaking were given by the
HPV team. From the kinematic analysis, the tie rod force vector is known to be nominally at an
angle of +14.0° (Figure 5). When the turning fully to the left, the tie rod vector is at an angle of
+44.2°. When the steering is hard right, the tie rod vector is at ­10.8°. There are many different
possible combinations for the steering position, brake application, and turning force direction
between these two angles. The worst case condition used for modeling and optimization was
steering fully left (or right), maximum applied force from the rider, and brakes applied. The
sensitivity of the design to changes in the boundary conditions was tested and will be discussed.
Figure 37:​ Fixtures and loads applied to the original steering knuckle model.
38

40.
Figure 38:​ Angle of the force input to the left steering knuckle.
At the tie rod mounting, the angle of force input to the left knuckle varies. For a hard left
turn, the angle is 44.2°; on the other hand, a hard right turn yields an angle is ­10.8°. For initial
analysis the nominal, 14° angle was used (Figure 38).
Figure 39:​ Explanation of “in” and “out” forces.
39

41. The force from the tie rod can be either in the “in” direction or the “out” direction, as seen in
figure 39. Both boundary conditions were analyzed and gave very similar results.
The FEA effort began with the analysis of the existing HPV team part (the left side
steering knuckle). Due to the presence of sharp corners, the model required idealization in the
form of adding fillets to obtain convergence (Figure 40). The model was manually meshed and
the convergence criteria of 5% was met. The maximum von Mises stress was found to be 17,627
psi and the minimum F.O.S. was 2.26. The maximum stress was located on the transition to the
flat section of the part, where the frame mounts to the knuckle. The results for both the tie rod
“in” and “out” forces were very similar (Table 11).
Table 11:​ FEA driven results for the original steering knuckle design.
40

42.
Figure 40:​ FEA results for the original design with the “in” force applied.
For the optimized design, material was removed from “quiet” areas of the part based on
the original FEA. The stress concentration at the transition to the flat surface was addressed by
adding material at this corner. Additionally, ribs were added to resist the moment created by the
tie rod force (Figure 41). The result was approximately a 60% reduction in maximum stress.
Although the part volume was increased approximately 10% which these changes, the weight
was still reduced by switching to a lighter, magnesium alloy material. The minimum F.O.S. for
this critical part was increased from 2.3 to 5.0 while the weight was cut from 0.27 lb. to 0.20 lb.
(Table 12).
41

43. Table 12:​ FEA driven results for the improved knuckle design using non­adaptive studies.
Figure 41:​ FEA results of the optimized design with the “in” force applied.
42

44. Analysis was conducted to understand the sensitivity of the FEA results to changes in the
boundary conditions. It was determined that the analysis was insensitive to a reversal in the
direction of the tie rod force from the nominal. However, changes in the tie rod force angle
(representing turning fully to the left or right) did have a significant effect on the maximum
stress FEA result. Although the quantitative result was different for these varying boundary
conditions, the overall trend was the same. The optimized knuckle design had lower maximum
stress and greater stiffness (Figures 42 and 43, Table 13).
Figure 42:​ Changing the tie rod force angle from 44.2° (top) to ­10.8°(bottom) on the original
knuckle had a significant effect on the max stress quantity and location.
43

45.
Figure 43:​ As with the original design, changing the tie rod force angle had a significant effect
on the max stress quantity and location for the improved design.
Table 13:​ The effect of changing the tie rod input force direction for original and optimized designs.
44

46. There is ample opportunity for future work to be conducted on the steering knuckle. The
design could be further optimized to improve manufacturability while reducing weight and
maintaining the the use of inexpensive and widely available 6061­T6 aluminum alloy. Ideally,
the effect of other variations to the boundary conditions would be studied taking into account
weight transfer due to breaking. This would also call for verification of the braking caliper input
forces obtained from the HPV team.
Table 14:​ FEA driven results for both force scenarios for the original and optimized designs.
45

47. Conclusion
In summary, the CSUN HPV steering subassembly was optimized. Based on the
established boundary conditions, each part had a target weight reduction goal to make the senior
design vehicle lighter. In addition, a minimum F.O.S. of 1.5 was established to constrain the
amount of optimization and ensure the rider’s safety.
Using FEA, a sensitivity study was conducted for each part to select the best combination
of design variables, material, thickness, and geometry. Adjusting the thickness in each part was
determined to be most effective in reducing the weight. Out of the five components, only the
steering knuckle was unable to fulfill its weight reduction goal (Table 15). Still, the overall
weight of the optimized subassembly is 1.20 lb, which is a 62% reduction of the initial weight.
A minimum F.O.S. of 1.5 was met for each part of the subassembly under the worst case
conditions. The steering plate has the lowest F.O.S., and therefore would be the “weakest”
component in the subassembly.
For future improvements, redesigning the steering knuckle to further reduce weight is
desired. Additionally, designing a simpler lever arm with less complex angles would make the
component easier to manufacture. One area that would be beneficial to research is the corrosive
resistance of each part in regards to human sweat and other environmental factors.
In terms of lessons learned, being in constant communication is essential in streamlining
the design process. Attending group meetings and responding to group members’ messages
allows all members to gauge the group’s overall progress.
Table 15:​ A summary of the optimized steering subassembly weight and minimum F.O.S.
46

48. References
[1] ASME. ​Rules For The 2015 Human Powered Vehicle Challenge​. Chicago: ASME, 25
Sept. 2014. PDF.
[2] “Beams and Trusses Overview.” 2013 SOLIDWORKS Help. Dassault Systemes, n.d.
Web. 19 Apr. 2015.
[3] Jeeverajan, Anthony. “HUMAN PERFORMANCE CAPABILITIES.” ​HUMAN
PERFORMANCE CAPABILITIES​. nasa, 7 May 2008. Web. 17 Mar. 2015.
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49. Appendix
Figure 44:​ Data sheet for 4043 weld wire.
48

50.
Figure 45:​ FBD of the steering plate in idle position. Forces, equations, and assumptions used.
Figure 46:​ (Top) A standard table used for each group member to track analysis iterations.
(Bottom) A standard table for verifying convergence between iterations.
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51. Table 16:​ List of material candidates for all subassembly components.
Figure 47:​ FEA von Mises stress plot and summary of results for optimization 2 (not chosen).
50