Design of a tubular steel space
frame for a Formula Student race car
A.J. Kemna
CST 2011.002
CST report
Eindhoven University of Technology
Department of Mechanical Engineering
Control Systems Technology
Eindhoven, January 01, 2011
“A chassis is nothing more than the car’s largest bracket.”
Carrol Smith
”The race will start at 2 o’clock.
Prepare yourself for the race.
Are you not ready?
The race will start at 2 o’clock.”
Known since humanity began racing
”By failing to prepare you are preparing to fail.”
Benjamin Franklin
2
1
Preface
The goal of the rear frame was to make the best possible design and this report will summarize the
design proces. However there are two additional goals of this report: (1) A good performance of the
design event of the Formula Student competition and (2) The design of the successor of this rear
frame. The reader is adopted to be the person who participate in one of the above points. To follow
the red line of thinking of the design judges every part of the report is build up in three phases:
• What did you do?
• Why did you do it, including theoretical proof.
• Did the change work out, including practical evidence.
To make sure that the conversation with the design judges can be optimized a few things have been
added to the report. There are many different design concepts and layout concepts added, together
with a large number of pictures and drawings.
Also during the design itself a few things have been done to make sure that the judges will be well
informed (and hopefully impressed): a mockup has been build after the first design to give practical
prove to the theoretical design choices. Besides this a torsional stiffness test of the URE05e has been
done to get an indication of the design goal. The same will be done with the URE06 to verify the
design.
3
2
Abstract
Formula Student Competition
Formula Student is a project for technical students to design, build, test, and race a single seated formula style race-car. The project greatly improves knowledge and experience of the future engineer.
Teams around the world gather on big international events to compete with their car against more
then 450 different teams. Teams do not only get judged based on the race results, but also their technical design, costs, and business presentations.
University Racing Eindhoven
URE exists since 2003 and has participated in various Formula student competitions around Europe
ever since. Every year a new race-car is developed in which improvements and new idea’s are implemented. Last year the team built its first electric car: the URE05e, which can be seen in figure 1. In
2010-2011 URE will build its successor: the URE06. The URE06 will have an electric powertrain that
is an evolution of the URE05e powertrain. Besides this, improvements are made on the suspension
and chassis design.
Figure 1: A design impression of the URE05e
Thesis Objective
The objective of this thesis is to design the rear frame of the URE06 in such a way that it can mount
the electric components. The URE06 will have a chassis consisting of a carbon fiber monocoque at
the front and a tubular space frame at the rear. The design of the monocoque and the pickup points
of the suspension have been finished and will thus be considered as a design constraint.
This thesis consists of a design specification in which the working environment and the design targets are explained. The design of the rear frame itself will be explained after which it is supported
by a structural calculation and analyzed using the Finite Element Method. Points of considerations
that are taken into account during the design phase are the competition regulations, weight, stiffness,
costs and manufacturability. This thesis will be concluded with the recommendations for the next rear
frame.
4
Contents
1
Preface
3
2 Abstract
4
3
6
List of symbols
4 Design specification
4.1 Working environment . . . . . . .
4.1.1 Rules . . . . . . . . . . . .
4.1.2 Working coordinate system
4.1.3 Design constraints . . . . .
4.1.4 Suspension Loads . . . . .
4.2 Design targets . . . . . . . . . . .
4.2.1 Overview . . . . . . . . . .
4.2.2 Stiffness . . . . . . . . . .
4.2.3 Serviceability . . . . . . . .
4.2.4 Weight . . . . . . . . . . .
4.2.5 Weight distribution . . . .
4.2.6 Production . . . . . . . . .
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12
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15
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19
6 Analysis
6.1 Finite element analysis . . . . . . . . . . . . . .
6.1.1 Chassis . . . . . . . . . . . . . . . . . .
6.1.2 Motor bracket . . . . . . . . . . . . . .
6.1.3 Suspension brackets: Standard system .
6.1.4 Suspension brackets: Specific loadcases
6.1.5 Tube P4 support . . . . . . . . . . . . .
6.1.6 Head restraint . . . . . . . . . . . . . .
6.2 Torsional stiffness . . . . . . . . . . . . . . . .
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22
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26
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31
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33
5
7
Design
5.1 Design concepts . .
5.2 Lay-out concepts . .
5.3 First design . . . . .
5.4 Mockup . . . . . . .
5.5 Final design choices
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Recommendations
33
8 Bibliography
34
9 Appendix A - Important rules
35
10 Appendix B - Weight analysis
36
11 Appendix C - Suspension Load cases
41
12 Appendix D - FEM results
42
5
3
List of symbols
Symbol
Quantity
Unit
k
F
σ
u
L
a
E
IO
DO
DI
M
α
∆z
K
Safety factor
Force
Stress
Deflection
Total length
Length
Young’s modulus
Second moment of area
Outer diameter
Inner diameter
Moment
Angle
Difference in height
Stiffness
[-]
[N]
[N/m2 ]
[m]
[m]
[m]
[N/m2 ]
[m4 ]
[m]
[m]
[Nm]
[ ◦]
[m]
[Nm/ ◦ ]
Table 1: List of symbols
6
4
Design specification
The design specification consists of two parts, both describing the essence of the assignment. Every team has particular rules which it has to maintain during the design, without these rules and
constraints the team will be unable to build a proper car. These are described in the working environment. In the design targets section the different targets of the rear frame will be discussed. These are
the targets set to make sure that the rear frame of the URE06 is an improvement on the URE05 and
URE05e.
4.1
Working environment
In this section the working principles of University Racing Eindhoven and the Formula Student competition will be discussed. There are certain rules that must be maintained in order to be able to drive
during the competition. The design constraints, systems that cannot be changed anymore, are then
explained after which the suspension loads are given. The suspension loads are used for the loadcases
on the rear frame in the FEM analysis.
4.1.1
Rules
The first and most important thing that should be done prior to the designing is reading the rules.
The rules are separated into three different articles. The first and most important one is the 2011
Formula SAE rules. Every Formula Student organization in the world uses these rules as a basic
platform for their competition and apply additional rules if considered necessary. University Racing
Eindhoven will participate in Formula Student England Class 1A, Formula Student Germany Electric
and Formula Student Austria Electric. The different rules are stated in the list below, this means that
the rear frame will have to satisfy four different rule books.
• 2011 Formula SAE rules[6]
• Formula Student England Class 1A[7]
• Formula Student Germany Electric[8]
• Formula Student Austria Electric (These rules are not known yet.)
The additional 2011 rules for Formula Student Germany and Austria were not known at the time of
writing, therefore the rules of 2010 were used. The most important rules necessary for the rear frame
are stated in chapter 9.
4.1.2
Working coordinate system
In order to eliminate any misunderstandings, a sign convention is provided in figure 2 which is based
on the international norm ISO 8855[9]. The point (x,y,z) = (0,0,0) is located on the road, directly under
and between the rear wheel center points.
4.1.3
Design constraints
Beside the rules there are a number of design constraints which should be taken into account. There
are five systems which are fixed in both size and position. The global size and position are referred to
in figure 3.
• The carbon fibre monocoque (orange)
• The drivetrain, fixed in z and x direction (green)
• The suspension geometry (pink)
• The spring-damper system (blue)
7
Figure 2: Sign convention used by University Racing Eindhoven
• The chain, primary sprocket fixed in y plane of the drivetrain (red), (The primary sprocket on
the motor side can be repositioned)
(a) Isometric view
(b) Topview
Figure 3: The five different systems which are fixed in size and position.
In the beginning of the design phase for the rear frame there was an additional design constraint
which involved a backup motor, controller and batterybox. This plan was rejected during the design
phase and will therefore not be treated in this report. The design constraints which are fixed in size
but can be changed in their position in the rear frame are shown in figure 4.
• Two AGNI motors (light red)
• The battery box (light green)
• Two controllers (gray)
8
• The wiring loom (not shown)
(a) Isometric view
(b) Topview
Figure 4: The three systems which can be repositioned, now shown in the final position.
4.1.4
Suspension Loads
The loads going trough the connection rods of the suspension are depicted in table ??. Beside the
sign convention used by University Racing Eindhoven there is also a naming convention for the suspension. This can be seen in figure 5. This figure will further explain table ??. The suspension loads
are used for the FEM analysis done in chapter 6.
Figure 5: The naming convention for the suspension rods used by University Racing Eindhoven,
the names on the left size are the same on the right.
URE06 forces
Static position [N]
Acceleration [N]
Braking [N]
Cornering [N]
Bump [N]
P1
P2
P3
P4
P5 (Tie rod)
P6 (Pull rod)
935
249
-85
-371
-165
-874
915
-34
-1090
-744
716
-2174
3505
502
-123
-95
-2677
-945
7125
-2569
1480
1987
-6543
-3704
1986
539
-145
-818
-330
-1809
Table 2: Suspension forces for worst case scenario’s on the URE06 [4]. Negative values are
compressive forces.
9
4.2
Design targets
In this chapter the design targets of the rear frame of the URE06 will be discussed. A summary is
given beforehand in chapter 4.2.1 after which each subsection will go into detail about their specific
target.
4.2.1
Overview
In table ?? an overview of the design targets can be seen.
Stiffness
Battery removal time
Motor removal time
Weight
Production time
>
<
<
<
<
4000 Nm/ ◦
5 minutes
5 extra minutes
13 kg
1 week
Table 3: A summary of the design targets of the rear frame of the URE06
4.2.2
Stiffness
To get an indication of the chassis stiffness Helder [15] has measured the previous cars of University
Racing Eindhoven. The results have been summarized in table ??.
Car
Chassis stiffness
[Nm/ ◦ ]
Car mass
[kg]
Specific Stiffness
[Nm/ ◦ /kg]
URE03
URE04
URE05
URE05e
URE06 target
2828
3500*
4000*
3232
4000
240
245
231
269
245
11.8
14.3
17.3
12.0
16.3
Table 4: Measured stiffness and mass of the cars troughout the years. Numbers with a * are
estimates.
Although the chassis stiffness does not need to be more than 2200 Nm/ ◦ , according to William
B. Riley (Cornell Formula Student Team) [16], it is necessary that the stiffness of the chassis should at
least exceed its predecessor. The suspension geometry of the URE06 has been changed, to make sure
that these changes can be verified, other variables of the car needs to be as constant as possible. The
stiffness of the URE06 should therefore be at least 4000 Nm/ ◦ (the real predecessor of the URE06
is the URE05), and the specific stiffness should be higher than the previous car, as the decrease of
weight is one of the important design goals of the management.
4.2.3
Serviceability
The main focus of attention for the rear frame is the serviceability for the mechanics. Opposite to
the design and manufacturing phase, losing time during testing is an absolute killer for the team and
must be avoided at all times. The second and third quote found at the front page perfectly explains
this main focus. The designers have to put in their ultimate effort to make sure the mechanics have an
easy job servicing the vehicle. Three targets have been set that will improve the predecessors chassis:
• Remove the battery within 5 minutes and with less than 8 bolts.
• Remove the motors within 5 extra minutes and with less than 5 extra bolts.
• The brush holders of the motors must be easily accessible.
10
4.2.4
Weight
To determine the maximum weight of the rear frame a weight analysis has been made, this can be
seen in the appendix, chapter 10. This weight analysis of the URE05e resulted in a weight budget for
the URE06. To make sure the weight of the URE06 is not excessively larger than its competitors it
needed a weight reduction of at least 30kg compared to the URE05e. In the appendix it can be seen
how this reduction can be achieved. A weight reduction of the rear frame by 5.5kg is needed which
gives the new frame a weight budget of 13kg.
4.2.5
Weight distribution
Different studies have been done on the perfect weight distribution of a Formula Student car. Four
were conducted by team members of University Racing Eindhoven during the last years (Lamers [10],
Hopmans [11], Spierings [12] and Janssen [13]). Even though they all succeeded in finding the perfect
weight distribution, the results were spreaded around the 50/50 percent range with a variation of 8
percent. This means that the perfect distribution could be 42 percent or 58 percent to the front.
Although the placement of heavy objects as the battery box and motors are a very good tool to
change the weight distribution, the time and place needed to do this is very limited. Because the results of "a perfect weight distribution" are - as of today - not proven, the possible advantages do not
weigh up against the extra design time needed.
The weight distribution will therefore be neglected.
4.2.6
Production
To make sure that the car will be ready in April, it is necessary that the different components do not
have excessively long production times. In the past it has been proven that a rear frame could be cut
and welded within one week. The goal for the URE06 frame will be the same.
• The fabrication time of the rear frame should not exceed one week.
• The use of exotic material (i.e. titanium) needs to be as little as possible to make sure that repairs
can be easily done on track.
11
5
Design
This section will have a chronological time line which is maintained during the assignment. First
a design begins with concepts where different types of designs are discussed. When one concept is
chosen various layout concepts of the different subsystems are shown. These are then worked out in
the first design after which a mockup will be build to verify the first design. When an early simplified
FEM analysis shows that the design is feasible the final design is discussed.
5.1
Design concepts
In this section a comparison will be made between a steel tubular rear frame and a full Carbon Fiber
Reinforced Plastic (CFRP) monocoque. The (dis)advantages of both concepts will be explained and
weighted against each other to form a viable conclusion. In the comparison in table ?? the key design
targets will be compared. In addition several secondary targets as cost, design time and present design
knowledge are added.
Steel space frame
Full CFRP
Stiffness in bending
Stiffness in tension
Stiffness in torsion
Weight
Serviceability
Fabrication
Manufacturing time
Cost
Design time
Present design knowledge
0
0
0
0
++
+
++
++
0
+
+
+
++
+
0
–
–
0
0
Total nr. of +
8
2
Table 5: Comparing steel rear frame vs. full CFRP
Stiffness
In the report of Andries van Berkum [1] can be seen that a plate construction is stiffer than a tubular
spaceframe. A full CFRP monocoque will be 2 times stiffer in bending, 1.6 times in tension and 2.6
times in torsion. This comparison is done with a maximum outside dimension and having identical
material volume.
Weight
A empirical comparison has been done between the weights of the best cars in the FSAE competition
[3][2]. It can be concluded that the difference between a full CFRP monocoque and full steal space
frame remains within the 10kg. Although a CFRP monocoque can be made slightly lighter, this is
normally not achieved in the first year of implementation where the CFRP monocoques are heavier
than the steel spaceframes. Looking only at the rear frame the difference would be smaller than 5kg.
This is nearly negligible for a team that focuses more on serviceability and time efficiency.
Fabrication and Manufacturing time
When taking a closer look at the time between the final design and final product, the steel spaceframe
comes out as an absolute winner. A steel spaceframe takes around 1 to 2 weeks to fabricate in the
past years at URE. The monocoque of the URE05 took around 7/8 weeks. This was mainly due to the
long manufacturing time of the positive and negative molds. The molds are also the reason why the
amount of actions needed to complete the product is much greater for a CFRP product.
Design time and knowledge
12
Although the time needed to design the two chassis’ do not differ that much, it is especially the analysis that makes the difference. A spaceframe requires basic mechanical knowledge and this is widely
known in the team. This can also be analyzed using Marc Mentat which is offered by the Eindhoven
University of Technology. The knowledge needed to analyse a CFRP chassis is still very new in the
team and not readily accessible to implement it.
Conclusion
As can be seen in table ?? it can be concluded that a steel rear spaceframe is favorable, mainly due
to the better serviceability. Besides this the manufacturing time and total cost is much lower than the
CFRP chassis.
5.2
Lay-out concepts
Multiple layout concepts have been analyzed to make sure the best suitable solution is found for the
URE06. In the concept phase it is important to look for every possible solution as it is easier to make
changes and it will cost less money and time, opposite to the fabrication/testing phase. Five different
options are shown in figures 6, 7, 8, 9 and 10. The explanation of the layouts are described in each
caption.
The ”golden rule” in University Racing Eindhoven is that changes should not be made to things
that work. This means that gearing systems as a planetary set, direct gearing and the bevel are ruled
out. To make the choice between the two chain geared layouts (figures 8 and 9), two extended designs
have been made. It was discovered that the motors would collide with the suspension system in
concept 4. Another problem with this concept was the chain which would collide with the battery box.
It was therefore chosen to use concept 3 where the motors will reside between the battery box and the
drivetrain.
(a) Topview
(b) Sideview
Figure 6: Concept 1. The motors are located underneath the drivetrain and connected through
direct gearing. The battery box is lying on its back.
13
(a) Topview
(b) Sideview
Figure 7: Concept 2. The motors are located next to the drivetrain and connected with a planetary
set. The battery box is lying on its back.
(a) Topview
(b) Sideview
Figure 8: Concept 3. Chain reduction, the motors are located between the standing battery box
and the drivetrain.
(a) Topview
(b) Sideview
Figure 9: Concept 4. Chain reduction, the motors are located on top of the battery box which is
on its back.
14
(a) Topview
(b) Sideview
Figure 10: Concept 5. The motors are located underneath the drivetrain, connected via a bevel
or hypoid. The battery box is lying on its back.
5.3
First design
The first design is the design in which every component fits properly and which was ready for FEM
analysis, see figures 11 and 12. The mockup, described in subsection 5.4, was made with this design.
This chapter will shortly describe the design choices for the different subsystems of the rear frame.
A very important point of notice is that the chassis complies to rule B8.14 of the FSUK Class rules
2010 [7]. This rule makes it mandatory that the the motor, battery and controllers are protected by a
side impact structure.
Figure 11: The first design of the rear frame in which only the left motor bracket is shown.
Motor bracket
Figure 13 shows the motor bracket. It is statically determinate supported by a spring leaf and two rod
aerials. A major problem with this design is that the chain is going straight through the upper tube.
This first design indicates a bracket of 300g and each motor can be removed with 4 bolts after when
the battery is removed.
15
(a) Top view
(b) Side view
Figure 12: The first design of the rear frame, including the different subsystems. Notice that the
motors are placed with the brush holders facing outside.
(a) Isometric view
(b) Side view
Figure 13: Section view of the motor bracket shown in green, with the (x,z) plane as cutting plane.
Battery mounting
At the time of writing the design of the battery box itself was not started. A mounting of the box was
therefore not designed and will not be discussed.
Damper mounting
The mounting for the dampers is shown in figure 14. The placement of the dampers is chosen to make
sure that the mechanics can reach it very easily. To make sure that the damper forces are redirected
correctly a pyramid shape is needed. A force parallel to the plane of a cross is very weak but as soon
as the pyramid is heightened it is a statically determined system.
5.4
Mockup
As soon as the first design has been made a mockup can be made. For a designer this is necessary
as it gives them a much better insight and feeling of the structure. Beside for the visualization of the
designer there are a number of things that can be checked:
• The designer will get a better feeling whether or not it is possible to remove the battery and
motors.
• The designer will get a better insight which of the diagonals are really necessary and which are
less important.
• The wiring loom can be made more accurately using a mockup.
16
(a) Isometric view
(b) Rear view
(c) Side view
Figure 14: The first design of the damper mounting. The spring/damper system are in blue, the
supports are shown in green.
• The "reachability" and serviceability for the mechanics can be checked (the brushes of the electric motor, cooling ducts, bolts and nuts, etc.).
The fabrication of the mockup is very simple. The materials used cost around 40 euro’s and it took 5
hours to manufacture it. This particular mockup is a 1:1 model made out of PVC tubes and duct-tape
with an accuracy estimated to be around 1 cm (see figure 15). The following was discovered:
• The diagonal under the battery box is needed. This diagonal fills up one of the largest open
squares in the frame, thus creating torsional weakness.
• The diagonal under the motors is needed for the same reason as stated above.
• The diagonal can be made out of a plate steel cross. This adds, roughly measured, the same
stiffness as a diagonal tube.
Figure 15: The mockup made out of PVC tubes and duck-tape.
17
(a) The diagonal under the battery tested as a plate cross.(b) The arrow is pointing towards the diagonal under the
motors.
Figure 16: The diagonal under the motors and the battery were found to be crucial for the torsional
stiffness.
18
5.5
Final design choices
After the first design and the mockup were analyzed, a few things were changed in the final design.
The most important changes are listed below, see figures 17, 18 and 19. The different sub systems will
be explained more thoroughly further down this chapter in the caption of figures 20 and 21. ,
• The position of the motors were mirrored such that the brush holders face each other. This is
done for three reasons:
– Throughout the year the management decided to use another type of controller. The dimensions of this type was bigger than the regular one. This meant it could not fit between
the battery and monocoque anymore, as can be seen in figure 12. Rule B8.14 [7] made it
mandatory that the controller is protected with a side impact structure. The controllers are
therefore moved to the back of the vehicle between the two drive trains. To make room
for this the sprocket (and thus the motors) needed to move sideways, the motors were
mirrored for this purpose.
– The mounting points of the motors were located on the inside of the frame (almost directly
on the (y,z) plane), the brackets would therefore be loaded in the middle of the tube. Mirroring the motors made it possible that the brackets could be supported near stiff nodes of
the chassis.
– With the chains on the inside of the frame it was very inconvenient to make a proper
bracket for the suspension rods P1 and P4, the replacement of the motors made this easier.
• The damper support pyramid has been made higher to increase the systems stiffness, see figure 18. The mounting strips are therefore horizontally instead of vertically in order to make it
fit.
• The motor bracket has an extra flange attached to withstand the torsion moment.
• The tube on which P1, P4 and the damper rocker mount support on, has been made thicker to
accommodate the bracket for the damper rocker. It now measures 25.4mm outer diameter and
20mm inner diameter.
• The FEM analysis showed that the P1 mount wasn’t possible in the first version. The mounting
point has been changed that it can accommodate the forces.
• The battery box was not ready on the time of writing this report, the final design of this bracket
will therefore not be included.
Figure 17: Isometric view. The controllers are placed between the drive trains which needed the
motors to be rotated 180 ◦ in the z direction to make it fit.
19
Figure 18: Side view. Notice that the battery box has been moved forward and nearly touches
the monocoque to create more space for the motor. The side impact structure is now protecting
all the high voltage components.
Figure 19: Top view. There is still room near the motors and controllers for a cooling system.
Notice that the bracket for the controllers are not designed yet as the placement is not determined
at the time of writing.
20
(a) Isometric view
(b) Side view
Figure 20: The bracket of the motor is shown in green. It can be removed with just 3 bolts after
the battery box has been removed.
(a) Isometric view
(b) Rear view
(c) Side view
Figure 21: The final design of the damper changed in two ways: The pyramid has been heightened
to withstand the forces better and the bracket itself is horizontally oriented instead of vertically.
The black cylinder shows the maximum clearance the damper needs.
There are however two design targets that did not make it into the final design:
• The brush holders are not easily reachable. This is due to the fact that the motors had to be
rotated, see above for the explanation. However because of the short removal time of the motors
(within 10 minutes) the brush holders can be reached easily after the motors have been removed.
This is a very big progression compared to the URE05e in which the brush holders were not
easily reachable plus it took more than 45 minutes to remove the motor.
• The weight will probably exceed 13 kg. At the moment of writing this is not sure yet as the
rear frame has not been manufactured. The theoretic design showed a weight of around 12.6kg
(excluding the main roll hoop) but in practice the weight will probably exceed the target because
of the welds and paint. The excess in weight is due to the fact that the battery, motor and
controllers have to be protected by a side impact structure. These tubes are twice the weight of
the physically required tubes and covers nearly the entire rear frame. The rear frame is therefore
over dimensioned with nearly a factor two.
21
6
Analysis
In this section the chassis will be analyzed on both the maximum stress during operations and the
torsional stiffness. It is therefore divided in two subsections. In section 6.1 the FEM analysis of the
different parts of the chassis is given, this includes the chassis itself as well as the subsystems as the
motor bracket and suspension brackets. In 6.2 an analysis of the torsional stiffness is shown.
6.1
Finite element analysis
This section is divided in 6 different subsections, each describing the FEM analysis of a particular
subsystem of/in the frame. The first section will describe the analysis of the chassis itself using Marc
Mentat. The second subsection describes the FEM analysis of the motor bracket. The third and fourth
section provides a standardized system for respectively the suspension brackets and the analysis of
each suspension bracket itself. The latter two sections describe "vergeetmenietjes" for the suspension
forces.
6.1.1
Chassis
This section will give information about the FEM analysis of the entire chassis. The Finite Element
Method package used to analyze this rear frame is Marc Mentat. This is due to the fact that the normal
package used by University Racing Eindhoven (Unigraphics 5) is having trouble with meshing tubes
in large quantities. Marc Mentat gives the opportunity to easily analyze a truss and beam system,
without having to calculate the entire 3D system as Unigraphics does. The safety factor of the system
has chosen to be the normal system of University Racing Eindhoven:
• Forces acted on the chassis: kchassis = 1.2
• Maximum yield stress: kstress = 0.8 (Which results in a smaller yield stress.)
There are four basic loadcases, as described in the design chapter 4.1.4, and an extra cornering loadcase
with the forces on the other side of the chassis. For an indication of the boundary conditions see
figure 22 which shows the bump loadcase.
• Bump
• Left cornering
• Right cornering
• Braking
• Acceleration
With the safety factor and loadcase in mind the plan shown below is followed:
1. Model the rear frame using trusses and choose the surface A to be 1 mm2 , this makes the
stresses similar to the forces.
2. Choose the material of the tubes and get an indication of the available tube dimensions in the
market.
3. Choose the tube sizes according to the following steps. Also see chapter 12 for the excel file.
(a)
(b)
(c)
(d)
(e)
Run the model to get the maximum forces going through each tube. See figure 23.
Give all tubes minimum wall thickness of 1 mm for welding purposes.
Choose outer diameter depending on the maximum force reached.
Make sure the tubes do not buckle due to compressive forces.
Give the tubes the minimum sizes due to rules.
4. Assign the dimensions to the trusses and run the analysis to get the maximum stresses in the
rear frame. See figure 24.
22
Figure 22: The boundary conditions used in the model. It is assumed that the monocoque is
infinitely stiff and the forces are going trough the connection rods to the brackets at their respective
angle.
23
Figure 23: Acceleration loadcase. This is step 3a of the plan. The numbers indicate the forces
going trough each tube. This is done for every loadcase in order to get the maximum force going
trough the chassis in every possible loadcase.
24
Figure 24: Bump loadcase, including the area, this is the loadcase in which the chassis undergoes
the maximum forces. This is step 4 of the plan, notice that the maximum stress does not exceed
84 MPa (three times lower than the yield stress of steel).
25
6.1.2
Motor bracket
The safety factor for the motor bracket is different compared to the regular safety factor. University
Racing Eindhoven uses a system for the drivetrain that makes sure that the chain is the first thing to
break during driving. This means that instead of the maximum load on the part itself the loadcase is
the maximum load until the chain breaks, this means a chain force of 15000N. See figure 25 for the
FEM results. The flanges that were added in the final design are not taken into account for simplicity
reasons, the flanges do not add strength in the radial direction.
(a) Isometric view
(b) Side view
Figure 25: The maximum stress is given in MPa, black indicates a value above the yield stress of
300 MPa. Notice that this is only reached in the holes for the bolts where the tension force of the
washers have not been taken into account.
6.1.3
Suspension brackets: Standard system
The suspension brackets will be chosen to be as simple as possible and the manufacturing time as
short as possible, a standardized system would therefore be convenient. In order to make this system
for the brackets, four designs are analyzed on their strength. These four designs can be seen in
figures 27, 28, 29 and 30. The first design (case 1) is the ultimate design from last years car, the
URE06 combustion [5]. This design is optimized for the lowest stress, but the manufacturing time is
long and expensive and the weight is enormous.
Case 2, 3 and 4 are therefore designed as a substitute for the original system. They are analyzed to
show which of the three substitute designs are stronger and lighter than case 1. Case 2 is lighter than
case 1 but the forces go perpendicular into the tube, creating a lot of deformation. This problem is
solved in case 3. The idea behind case 4 is that the welding spot will not go trough the tube, which will
happen in case 3. For this simulation, a tensile force Fr = 3500N is applied at an angle of 45 ◦ s to the
bracket, see figure 26.
Maximum stress [MPa]
Mass [g]
Deformation of tube [mm]
Case 1
Case 2
Case 3
Case 4
0.61
1
0.78
1
0.65
1
0.34
0.68
0.84
0.26
0.69
0.87
Table 6: Results of the FEM cases for the pick up points, normalized to the maximum value
respectively.
The normalized results are given in table ??. The standard system for the brackets is chosen to
be case 4 because the maximum stress is the lowest while the weight and maximum deformation of
the tube are nearly the same. With this basic system in mind the suspension brackets are analyzed on
their specific design and loadcase in section 6.1.4.
26
Figure 26: Pick up point loadcase
(a) View in zx plane.
(b) View in zy plane.
Figure 27: Case 1, maximum stress given in MPa, black indicates a value above the yield stress
of 300 MPa
(a) View in zx plane.
(b) View in zy plane.
Figure 28: Case 2, maximum stress given in MPa, black indicates a value above the yield stress
of 300 MPa
27
(a) View in zx plane.
(b) View in zy plane.
Figure 29: Case 3, maximum stress given in MPa, black indicates a value above the yield stress
of 300 MPa
(a) View in zx plane.
(b) View in zy plane.
Figure 30: Case 4, maximum stress given in MPa, black indicates a value above the yield stress
of 300 MPa
28
6.1.4
Suspension brackets: Specific loadcases
In this section the specific loadcases on the suspension brackets are analyzed to make sure that all
the systems will never fail during driving. The figures each show a different bracket and will give an
indication of the maximum stress in the part. All the forces have a total safety factor of k = 1.5. It is
assumed that the dynamical loading is calculated with this safety factor thus the maximum stress is
σmax = 300 [MPa]. The load cases can be seen in the appendix, chapter 11. The results of the FEM
analysis have been summarized in table ??.
Suspension point number
P1
P4
P5
Damper rocker mount
Damper bracket
Description
See figure 32
The loads on the P4 suspension rod is more than 4 times lower then
other suspension brackets. It is therefore assumed that the bracket will
hold under the load.
See figure 31
See figure 33
See figure 34
Table 7: Results of the FEM cases for the specific mounting brackets of the suspension rods
(a) Side view.
(b) Close up of the stressed parts.
Figure 31: P5 suspension bracket. Results of the FEM analyis: the gray area is where the stress
is higher than 300 MPa. This can be neglected as the clamping of the ring and bolts were not
taken into account.
29
(a) Side view.
(b) Close up of the stressed parts.
Figure 32: P1 suspension bracket. Results of the FEM analyis: There are no areas where the
stress is higher than 300 MPa.
(a) Side view.
(b) Close up of the stressed parts.
Figure 33: Damper rocker mount. Results of the FEM analyis: the black area is where the stress
is higher than 300 MPa. This can be neglected as the welding of the tubes is unpredictable.
(a) Top view.
(b) Close up of the stressed parts.
Figure 34: Damper bracket. Results of the FEM analyis: the black area is where the stress is
higher than 300 MPa. This can be neglected as the clamping of the ring and bolts were not taken
into account.
30
6.1.5
Tube P4 support
The loads on the P4 suspension rod is more than 4 times lower then other suspension brackets. It
is therefore assumed that the bracket will hold under the load. However the attachment point of the
bracket is in the middle of the tube (a few centimeters away from the fixed end), which makes it
necessary to calculate whether the tube will not deflect too much (see figure 35). Equation 1 gives the
solution for a built-in beam with a concentrated force, according to Fenner[14].
ua = −
F (L − a)3 a3
3EIo L3
(1)
With ua the deflection of the beam directly under the force F = 2000N at a distance a = 45mm from
its end. Equation 2 gives the polar second moment of area of a thin hollow tube.
Io =
π
(D4 − DI4 )
64 O
(2)
These equations give a deflection ua of 0.012mm which can be neglected.
Figure 35: Close up of the rear frame, the tube is shown in green and the P4 bracket in red.
6.1.6
Head restraint
According to the rules [6] the head restraint should be capable of holding a force of Fr = 900N.
Equation 3 gives the maximum stress of a tube under a force F.
σmax =
F
2 − D2 )
1/4π(DO
I
(3)
A tube with outer and inner diameter of 8 and 6 mm respectively results in a maximum stress σmax =
40.1MPa. This is done in the ultimate case where the helmet is resting on only one tube (The head
restraint consist of two tubes as the drivers heights differ, see figure 36). The yield stress of rolled steel
is σyield = 300MPa which therefore makes the head restraint correct according to the rules.
31
Figure 36: Isometric view of the rear frame, the head rest is shown in gray.
32
6.2
Torsional stiffness
When the area’s of the tubes are chosen the torsional stiffness can be calculated. A vertical load
is applied to both rear wheel centers in opposite direction to simulate the torsional load while the
monocoque is assumed to be infinitely stiff. The vertical load is recalculated in the force vectors going
trough the suspension rod with help of Cadesh [4]. This is to make sure that the suspension stiffness
is not added to the chassis stiffness. The torsional stiffness K of the chassis can then be calculated by
measuring the angular deformation in the rear bulkhead.
K=
M
α
M = 2F l
α = sin−1 (
∆zquickjack
)
Lquickjack
(4)
(5)
(6)
gives a torsional stiffness K = 10380 Nm/ ◦ . This is in the same range as Erik Stoltenborg calculated
his rear frame for the (never build) URE06 [5], we therefore assume that the model is correct.
This is much higher as anticipated but can be related to the fact that the entire chassis is over
dimensioned due to the Side Impact rules.
7
Recommendations
• Try to reposition the dampers in such a way that the three major components can be repositioned
where they are protected by just 1 side impact structure (SI structure). In this design there
are three separate SI systems which makes the rear frame over-dimensioned in weight( and
stiffness).
• It is absolutely necessary to measure the (chassis)stiffness of the URE06 in order to evaluate the
theoretical torsion stiffness calculations.
• When designing the rear frame of the URE06 it is advised to make a full monocoque instead of
a hybrid. This will reduce the weight while increasing stiffness (no transition between carbon
and steel). Plus the problem with the positioning of systems due to the side impact structure is
decreased. However this mean that the mold need to be redesigned and manufactured which
takes time and money.
• In the past few years a torsional stiffness test has not been a high priority activity, in order to
keep improving on the chassis (and the suspension) it is very much recommended to do the
torsional stiffness test of the URE06 as soon as it is built.
33
8
Bibliography
References
[1] van Berkum, A., Chassis and suspension design FSRTE02, pp. 27-28, March 2006.
[2] Website Rennteam Stuttgart, www.rennteam-stuttgart.de
[3] Website Joanneum Racing, www.joanneum-racing.at
[4] Ozturk, C., Design and development of the URE06 rear suspension, pp. 32-38, Nov 2009.
[5] Erik Stoltenborg, Design of a rear frame for a formula student race car, CST 2010.051, pp. 18-19, Jul
2010.
[6] Formula SAE International, 2011 Formula SAE rules, http://students.sae.org/competitions/formulaseries/rules/
[7] Formula
Student
England,
http://www.formulastudent.com/
2011
[8] Formula Student Germany Electric,
http://www.formulastudentelectric.de/
Formula
2010
Student
Formula
Class
Student
1A
Electric
Rules,
Rules,
[9] Internation Organisation for Standardization , Road vehicles - Vehicle dynamics and road-holding
ability - Vocabulary, http://www.iso.org/
[10] Lamers, W., Development and analysis of a multi-link suspension for racing applications, pp. 19-21,
May 2008.
[11] Hopmans, J.A.M., Analysis and development of Formula Student racing tyres, pp. 67-70, Feb 2010.
[12] Spierings, J.T., Performance analysis of a Formula Student racing car, pp. ??-??, Dec 2010.
[13] Janssen, M., ???, pp. ??-??, Nov 2009.
[14] Fenner, R.T., Mechanics of Solids, pp. 350-352, 1999, CRC Press LLC.
[15] Helder, R Project Report: Torsional test bench, pp. 22-25, year unkown
[16] Riley, W.B. and George, A.R. Design, Analysis and Testing of a Formula SAE Car Chassis, pp. 17,
Dec 2002
[17] Rosielle, P.C.J.N. Constructieprincipes, Hfd. 1, Maart 2008
34
9
Appendix A - Important rules
2010 FSAE Rules (Also see 2010 FSAE rules explained PDF.)
• B3.3 Minimum Material Requirements
• B3.4 Alternative Tubing and Material - General
• B3.5 Alternative Steel tubing
• B3.6 Aluminium Tubing Requirements
• B3.8 SEF
• B3.9 Main and Front Roll Hoops - General Requirements
• B3.10 Main Hoop
• B3.12 Main Hoop Bracing (Especially B3.12.7)
• B3.14 Other Bracing Requirements
• B3.15 Other Side Tube Requirements
• B3.16 Mechanically Attached Roll Hoop Bracing
• B3.24 Side impact structure for tube cars
• B4.5 Firewall
• B5.4 Shoulder Harness
• B5.6 Head Restraint
• B6.2 Ground Clearance
• B6.6 Jacking Point
• B8.13 Drive Train Shields and Guards
• B11.1 Master switches
• B11.2 Primary master switch
• B11.4 Batteries
FSUK Class 1A rules 2010
• B4.5 Firewall
• B8.14 Powertrain System location
FSE Germany Rules 2010
• 3.4 Drive Train
35
10
Appendix B - Weight analysis
36
37
38
39
40
11
Appendix C - Suspension Load cases
Vector componenten
Normaal
Bump
Kracht
Cornering
Kracht
Braking
Kracht
Acceleration
Kracht
P1
A
Ax
Ay
Az
325,1737997
1
3417 tension
95 0,292151459 998,2815
-308 -0,947185783 -3236,53
-43 -0,132236976 -451,854
7125 tension
2081,57915
-6748,6987
-942,18846
3505 tension
1023,991
-3319,89
-463,491
915 tension
267,3186
-866,675
-120,997
P4
A
Ax
Ay
Az
277,2183255
1
818 comp
120 0,432871816 354,0891
-235 -0,847707306 -693,425
-85 -0,306617536 -250,813
1987 tension
860,116298
-1684,3944
-609,24904
95 comp
41,12282
-80,5322
-29,1287
744 comp
322,0566
-630,694
-228,123
P5
A
Ax
Ay
Az
305,6354037
1
0
0
-302 -0,988105423
-47 -0,153777996
330 comp
0
-326,075
-50,7467
6543 comp
0
-6465,1738
-1006,1694
2677 comp
0
-2645,16
-411,664
716 tension
0
-707,483
-110,105
P6
A
Ax
Ay
Az
269,4567821
83,2127
-162,8143
197,9245
1
1809 comp
0,308816499 558,649
-0,60423159 -1093,05
0,734531521 1328,768
3704 comp
1143,85631
-2238,0738
2720,70475
945 comp
291,8316
-570,999
694,1323
2174 comp
671,3671
-1313,6
1596,872
Damper
A
Ax
Ay
Az
209,4618976
1 2621,739 comp
38,9655 0,186026673 487,7134
-205,7925 -0,982481789 -2575,81
-2,3288 -0,011118013 -29,1485
5368,11594 comp
998,612751
-5274,0762
-59,68278
1369,565 comp
254,7757
-1345,57
-15,2268
3150,725 comp
586,1188
-3095,53
-35,0298
Rocker mount
A
Ax
Ay
Az
434,8058917
122,1782
-368,6068
195,5957
8252,49106 comp
2142,46906
-7512,15
2661,02197
2105,455 comp
546,6073
-1916,57
678,9054
4843,66 comp
1257,486
-4409,13
1561,842
4030,442 comp
1046,362
-3668,87
1299,619
41
12
Appendix D - FEM results
On the next page the excel file of the FEM results is added.
42