ROSE-HULMAN INSTITUTE OF TECHNOLOGY
Structural Analysis of a
Suspension Member
ME522
Advanced Finite Elements
Dr. L. Olson
Stephen Sakai
5/20/2011
Stephen,
This is a very nice report. I marked one or two
typos, but everything else is great.
I am really curious about what was wrong with
the models you presented in class-- obviously you
fixed the problems.
L. O.
Project Grade: 100
Table of Contents
Figures and Tables ............................................................................................................... 2
Introduction .......................................................................................................................... 3
Model .................................................................................................................................. 5
Finite Element Model .......................................................................................................... 7
Forces and Boundary Conditions ......................................................................................... 8
Analysis ............................................................................................................................... 10
Results .................................................................................................................................. 12
Further Results and Analysis ............................................................................................... 13
Conclusion and Future Work ............................................................................................... 16
Appendix .............................................................................................................................. 17
1
Figures and Tables
Figures
1.
Previous generation RhEV vehicle ......................................................................... 3
2.
New generation RhEV vehicle ................................................................................ 4
3.
3-D model of new RhEV vehicle ............................................................................ 4
4.
New front suspension design (Top), Right side with wheel removed (Bottom) .................. 5
5.
Right side of front suspension (Left), 3-D model created in Solidworks (Right) ................ 6
6.
Initial mesh produced in ANSYS ........................................................................................ 7
7.
Points of fixed displacement in finite element analysis ....................................................... 8
8.
Front/Rear load distribution ................................................................................................ 8
9.
Resultant force and moments acting on wheel center (Left),
Resultant force and moments acting on wheel axle (Right) ................................................ 9
10.
Probe measuring deformation of upper mount .................................................................... 10
11.
3-D Element Size: 0.100 in, Displacement: 0.00895 in ....................................................... 11
12.
3-D Element Size: 0.100 in, Displacement: 0.00896 in ....................................................... 11
13.
Results from initial simulation: Stress in psi (Left) and deformation in inches (Right) ...... 12
14.
Alternative upright designs (left to right): Original, Angle Removed,
Reduced Thickness, Reduced Thickness with Angle Removed .......................................... 13
15.
ANSYS results for upright with angle removed .................................................................. 14
16.
ANSYS results for upright with thickness reduced ............................................................. 15
17.
ANSYS results for upright with angle removed and thickness reduced .............................. 15
Tables
1.
RhEV Shell Eco-Marathon Americas Results ..................................................................... 3
2.
Results from finite element simulations .............................................................................. 15
2
Introduction
The Rose-Hulman Efficient Vehicle team (RhEV) works every year to design and create a vehicle
to obtain the highest possible fuel mileage in national competitions. For the four years prior to the
beginning of the 2010-2011 academic year, the RhEV team has been concentrating on optimizing a single
vehicle design. While the vehicle was competitive, placing in the top 5 in 3 of the last 4 years, the fuel
mileage appeared to be limited despite further optimization attempts. This led the team to develop a
completely new vehicle in an effort to overcome some of the
Table 1: RhEV Shell Eco-Marathon
Americas Results
Year
Mileage
Place
2007
1637
2nd
2008
0
N/A
2009
1800
4th
2010
1803
3rd
current design limitations
The previous vehicle was a flat bottom design based on a
plate made from corrugated aluminum with all of the
aerodynamic elements in the cover. The corrugated aluminum
base was chosen for its high rigidity. Chassis stiffness is an
important component in achieving the most fuel mileage.
In
discussions with other teams who achieve some of the highest fuel mileages in the world, the common
belief is that any unwanted movement in vehicle components results in energy that is lost and not put into
the vehicle’s forward motion. As a result, any twist or bending in the chassis or suspension deflection can
lead to lost fuel mileage.
One of the primary goals with the new chassis
was to increase its aerodynamic efficiency. To do so,
a completely new design was created using carbon
fiber in order to allow the inclusion of more curvature
in the shape. Since the chassis design is completely
Figure 1: Previous generation RhEV vehicle
new, the majority of the internal components needed to
3
be re-designed as well. The front suspension components were the most difficult part of this design, with
concerns such as driver space, sufficient space for easy driver egress, and steering function to consider.
As
discussed
earlier,
suspension rigidity is an important
design criterion, one that is difficult to
maintain given the constraints just
mentioned.
Unfortunately, due to
Figure 2: New generation RhEV vehicle
delays, vehicle construction began
three months late not allowing testing in the design until actually put into use at competition. One of the
purposes of this study is to try to determine if significant deflection of the suspension members can or
should be expected and if the design can be altered to reduce weight and/or size. Here significant
deflection is termed as deflection greater than 0.050 inches.
Figure 3: 3-D model of new RhEV vehicle
4
Model
The new suspension design is pictured in Figure 4. It consists of a base frame which is attached
to the car, with uprights made from aluminum angle attached at either end. To each angle, a knuckle, to
which the wheel and brake is attached, is fixed to each angle using two spherical joints to allow the
knuckle to pivot for turning. The first step in developing a model for the front suspension was to
determine how much of the suspension would need to
Uprights
be modeled in order to produce useful results. Since
the front suspension is symmetrical and total
Knuckle
deflection is the primary component of interest, it was
decided that only one half of the front suspension
would need to be modeled for this analysis.
Base
Once this was decided, a 3-D model of the
Upright
right side of the suspension was created using
Solidworks CAD software (Figure 5). To properly
Spherical
Joints
recreate the spherical joints in the suspension, shown
in Figure 4, point connections were created in the solid
Knuckle
model. Again, because of the symmetrical nature of
the front suspension design and in an effort to reduce
calculation time only one half of the front suspension
was modeled.
Figure 4: New front suspension design (Top)
Right side with wheel removed
(Bottom)
5
Figure 5: Right side of front suspension (Left), 3-D model created in Solidworks (Right)
6
Finite Element Model
Once the solid model was created in Solidworks, it was imported into the ANSYS 12 finite
element software package. The primary component of interest in this analysis is the upright itself so the
total number of elements in the analysis could be minimized. Thus, the finite element model was created
using 3-D elements to simplify the analysis setup.
After the model was imported into ANSYS,
connections and material properties were set. The base and
upright were modeled as aluminum alloy; however, because the
remaining components are simply transmitting force, they were
modeled as steel.
As mentioned earlier, the connection
between the knuckle and upright were set as spherical
connections.
Spherical connections will transmit forces;
however, moments will not be transmitted.
The remaining
connections were all treated as bonded.
After the connections were setup, an initial mesh was
generated with a body sizing of 0.100 inches applied to the
upright. This produced the mesh shown in Figure 6. This
Figure 6: Initial mesh produced in
ANSYS
element sizing ensured at least two elements through the
thickness of the upright member. As the anticipated deflection
of the upright is small, the simulation is setup for linear behavior, with all of the components behaving
elastically.
7
Forces and Boundary Conditions
Before the finite element model could be
analyzed, it was necessary to determine and apply the
proper boundary conditions. For this analysis, there
were two main areas which needed to have
displacement defined. These areas were the mounting
points on the base, and one point on the knuckle. The
base of the front suspension is secured to the vehicle
using 6 bolt connections.
Due to symmetry, this
Figure 7: Points of fixed displacement in finite
element analysis
becomes two complete holes and two halves. The locations of these are shown in Figure 7. The other
location where displacement must be limited is on the knuckle. Because the knuckle is connected using
spherical joints, during the analysis, the knuckle may rotate. To prevent this rotation from occurring, one
corner of the knuckle is fixed in the X-Z plane.
To determine the proper forces to apply to the model required several steps. First, a statics
analysis was performed on the entire vehicle to determine the load on the front axle. The total static
weight of the car including driver is approximately 300 lbs. Given the center of gravity of the car and the
location of the driver, the total center of gravity for the vehicle is located approximately 27 inches
rearward of the front axle. With a total axle-axle length of 67 inches, the weight on both front wheels is
180 lbs (Figure 8). Since each front
wheel carries half of the front axle
load, each front wheel supports 90 lbs.
Another consideration for the
front wheel load is the camber and
Figure 8: Front/Rear load distribution
8
caster angles of the wheel and how those angles affect the forces applied to the knuckle and, as a result,
the upright. The camber angle refers to the vertical angle of the wheel when viewed from the front or rear
of the vehicle. The caster angle refers to the angle of the line drawn through the upper and lower pivot
points with relation to vertical. This angle is measured when looked at from the side of the vehicle. The
current front suspension geometry is setup such that the camber angle is approximately 8 degrees negative,
i.e. the top of the wheel is 8 degrees further inboard than the bottom, and the caster angle is approximately
10 degrees positive, i.e. the upper steering mount (spherical bearing) is 10 degrees rearward than the
lower mount.
The combination of these two angles increases the difficulty of determining the actual forces
acting on the upright from the ground contact point of the wheel. In an effort to simplify this, the knuckle
was modeled along with the wheel axle which extends to the centerline of the wheel. The reaction force
and moment acting at the center point of the wheel was then calculated and applied to the same point on
the axle of the finite element model.
Very nice
graphic.
Figure 9: Resultant force and moments acting on wheel center (Left)
Resultant force and moments acting on wheel axle (Right)
9
Analysis
Once the proper loads and boundary conditions were placed on the model, an initial solution was
generated. For this analysis, since the interest lies in the deformation of the upright component, a
deformation probe was placed on the upper mounting point for the knuckle as shown in Figure 10. In
addition to the deformation probe, equivalent stress and total
deformation for the upright were reported. An initial simulation was
run which produced a result of 0.00895 inches displacement at the
deformation probe.
To determine whether or not the mesh was
sufficiently small, a second simulation was performed with a mesh
element size of 0.075 inches. This produced a result of 0.00896 inches
of deformation. The two different mesh sizes are shown in Figures 11
and 12. This represents a percent difference of 0.11% between the two
solutions and indicates that the original mesh should be sufficiently
small.
Figure 10: Probe measuring
deformation of
upper mount
10
Figure 11: 3-D Element Size: 0.100 in
Displacement: 0.00895 in
Figure 12: 3-D Element Size: 0.100 in
Displacement: 0.00896 in
0.075
inches
11
Results
Results from the initial simulation, shown in Figure 13, were promising. The maximum stress
was reported as being approximately 6050 psi and a maximum deflection of 0.00981 inches. These
appear to be realistic results. The maximum stress occurs in the mounting locations, and the maximum
deflection occurs in the uppermost point of the upright. Both of these results are expected and the
reported values are in a realistic range.
Figure 11: Results from initial simulation: Stress in psi (Left) and deformation in inches (Right)
12
Further Analysis and Results
Given these results, further studies of the upright design were performed. These studies involved
modifying the design of the upright with the following main ideas in mind: 1 – remove the angle
component of the member, 2 – decrease the thickness of the member, and 3 – both 1 and 2 together.
These designs are displayed in Figure 14.
Figure 12:
Alternative upright designs (left to right): Original, Angle Removed,
Reduced Thickness, Reduced Thickness with Angle Removed
Again, the results from the new analyses appear realistic and are expected. These results are shown in
Table 2 as well as Figures 15-17. With each modification to the upright, the total deflection of the upper
mount increases. Also, the maximum equivalent stress increases as well, with the final iteration
producing the highest reading of approximately 32 ksi. The reduced thickness of the material contributes
greatly to the increased stress; however, this value is still well below the compressive yield strength of
aluminum of 40.6 ksi.
13
Table 2: Results from finite element simulations
Model
Original
No Angle
Thin
Thin + No Angle
Deflection
of Probe
(in)
0.00895
0.01071
0.01418
0.01454
Total
Deformation
(in)
0.00981
0.01133
0.01792
0.02028
Maximum
Stress
(psi)
6054
8385
19632
32119
Figure 13: ANSYS results for upright with angle removed
14
Figure 14: ANSYS results for upright with thickness reduced
Figure 15: ANSYS results for upright with angle removed and thickness reduced
15
Conclusion and Future Work

A finite element model was created for a front suspension member and a static structural analysis
performed.

The results produced by the analysis of the original design were realistic and encouraging enough
to perform similar analyses on modified versions of the structure.

As with the first simulation, the results produced from the additional model analyses were
realistic and expected.

In the future, one goal will be to take experimental data to correlate and validate the FE model.

Once the model can be compared to experimental data, the finite element model can be refined to
improve the accuracy of the model.
16
Appendix
Aluminum Material Properties
Density – 172.9 lb/ft^3
Young’s Modulus – 10297 ksi
Poisson’s Ratio – 0.33
Tensile Yield Strength – 40.6 ksi
Compressive Yield Strength – 40.6 ksi
[Source: ANSYS 12.1 Engineering Data]
17