Design of a tubular steel spaceframe for a Formula Student race car

A.J. Kemna

CST 2011.002

CST report

Eindhoven University of TechnologyDepartment of Mechanical EngineeringControl 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

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1 Preface

The goal of the rear frame was to make the best possible design and this report will summarize thedesign proces. However there are two additional goals of this report: (1) A good performance of thedesign event of the Formula Student competition and (2) The design of the successor of this rearframe. The reader is adopted to be the person who participate in one of the above points. To followthe 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 beenadded to the report. There are many different design concepts and layout concepts added, togetherwith 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 wellinformed (and hopefully impressed): a mockup has been build after the first design to give practicalprove to the theoretical design choices. Besides this a torsional stiffness test of the URE05e has beendone to get an indication of the design goal. The same will be done with the URE06 to verify thedesign.

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2 Abstract

Formula Student CompetitionFormula Student is a project for technical students to design, build, test, and race a single seated for-mula 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 morethen 450 different teams. Teams do not only get judged based on the race results, but also their tech-nical design, costs, and business presentations.

University Racing EindhovenURE exists since 2003 and has participated in various Formula student competitions around Europeever since. Every year a new race-car is developed in which improvements and new idea’s are imple-mented. Last year the team built its first electric car: the URE05e, which can be seen in figure 1. In2010-2011 URE will build its successor: the URE06. The URE06 will have an electric powertrain thatis an evolution of the URE05e powertrain. Besides this, improvements are made on the suspensionand chassis design.

Figure 1: A design impression of the URE05e

Thesis ObjectiveThe objective of this thesis is to design the rear frame of the URE06 in such a way that it can mountthe electric components. The URE06 will have a chassis consisting of a carbon fiber monocoque atthe front and a tubular space frame at the rear. The design of the monocoque and the pickup pointsof 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 tar-gets are explained. The design of the rear frame itself will be explained after which it is supportedby a structural calculation and analyzed using the Finite Element Method. Points of considerationsthat 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 rearframe.

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Contents

1 Preface 3

2 Abstract 4

3 List of symbols 6

4 Design specification 74.1 Working environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.1.1 Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.1.2 Working coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.1.3 Design constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.1.4 Suspension Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.2 Design targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.2.2 Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.2.3 Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.2.4 Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2.5 Weight distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2.6 Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5 Design 125.1 Design concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125.2 Lay-out concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135.3 First design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.4 Mockup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165.5 Final design choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

6 Analysis 226.1 Finite element analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

6.1.1 Chassis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226.1.2 Motor bracket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266.1.3 Suspension brackets: Standard system . . . . . . . . . . . . . . . . . . . . . . . 266.1.4 Suspension brackets: Specific loadcases . . . . . . . . . . . . . . . . . . . . . . 296.1.5 Tube P4 support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.1.6 Head restraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.2 Torsional stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

7 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

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3 List of symbols

Symbol Quantity Unit

k Safety factor [-]F Force [N]σ Stress [N/m2]u Deflection [m]L Total length [m]a Length [m]E Young’s modulus [N/m2]IO Second moment of area [m4]DO Outer diameter [m]DI Inner diameter [m]M Moment [Nm]α Angle [ ◦]∆z Difference in height [m]K Stiffness [Nm/ ◦]

Table 1: List of symbols

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4 Design specification

The design specification consists of two parts, both describing the essence of the assignment. Ev-ery team has particular rules which it has to maintain during the design, without these rules andconstraints the team will be unable to build a proper car. These are described in the working environ-ment. In the design targets section the different targets of the rear frame will be discussed. These arethe targets set to make sure that the rear frame of the URE06 is an improvement on the URE05 andURE05e.

4.1 Working environment

In this section the working principles of University Racing Eindhoven and the Formula Student com-petition will be discussed. There are certain rules that must be maintained in order to be able to driveduring the competition. The design constraints, systems that cannot be changed anymore, are thenexplained after which the suspension loads are given. The suspension loads are used for the loadcaseson 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 2011Formula SAE rules. Every Formula Student organization in the world uses these rules as a basicplatform for their competition and apply additional rules if considered necessary. University RacingEindhoven will participate in Formula Student England Class 1A, Formula Student Germany Electricand Formula Student Austria Electric. The different rules are stated in the list below, this means thatthe 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 ofwriting, therefore the rules of 2010 were used. The most important rules necessary for the rear frameare 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 basedon the international norm ISO 8855[9]. The point (x,y,z) = (0,0,0) is located on the road, directly underand 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. Thereare five systems which are fixed in both size and position. The global size and position are referred toin 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)

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Figure 2: Sign convention used by University Racing Eindhoven

• The chain, primary sprocket fixed in y plane of the drivetrain (red), (The primary sprocket onthe 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 constraintwhich involved a backup motor, controller and batterybox. This plan was rejected during the designphase and will therefore not be treated in this report. The design constraints which are fixed in sizebut 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)

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• 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 thesign convention used by University Racing Eindhoven there is also a naming convention for the sus-pension. This can be seen in figure 5. This figure will further explain table ??. The suspension loadsare 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 935 915 3505 7125 1986P2 249 -34 502 -2569 539P3 -85 -1090 -123 1480 -145P4 -371 -744 -95 1987 -818

P5 (Tie rod) -165 716 -2677 -6543 -330P6 (Pull rod) -874 -2174 -945 -3704 -1809

Table 2: Suspension forces for worst case scenario’s on the URE06 [4]. Negative values arecompressive forces.

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4.2 Design targets

In this chapter the design targets of the rear frame of the URE06 will be discussed. A summary isgiven beforehand in chapter 4.2.1 after which each subsection will go into detail about their specifictarget.

4.2.1 Overview

In table ?? an overview of the design targets can be seen.

Stiffness > 4000 Nm/ ◦

Battery removal time < 5 minutesMotor removal time < 5 extra minutesWeight < 13 kgProduction time < 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 UniversityRacing Eindhoven. The results have been summarized in table ??.

Car Chassis stiffness Car mass Specific Stiffness[Nm/ ◦] [kg] [Nm/ ◦/kg]

URE03 2828 240 11.8URE04 3500* 245 14.3URE05 4000* 231 17.3URE05e 3232 269 12.0

URE06 target 4000 245 16.3

Table 4: Measured stiffness and mass of the cars troughout the years. Numbers with a * areestimates.

Although the chassis stiffness does not need to be more than 2200 Nm/ ◦, according to WilliamB. Riley (Cornell Formula Student Team) [16], it is necessary that the stiffness of the chassis should atleast exceed its predecessor. The suspension geometry of the URE06 has been changed, to make surethat these changes can be verified, other variables of the car needs to be as constant as possible. Thestiffness of the URE06 should therefore be at least 4000 Nm/ ◦ (the real predecessor of the URE06is the URE05), and the specific stiffness should be higher than the previous car, as the decrease ofweight 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 tothe design and manufacturing phase, losing time during testing is an absolute killer for the team andmust be avoided at all times. The second and third quote found at the front page perfectly explainsthis main focus. The designers have to put in their ultimate effort to make sure the mechanics have aneasy 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.

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4.2.4 Weight

To determine the maximum weight of the rear frame a weight analysis has been made, this can beseen in the appendix, chapter 10. This weight analysis of the URE05e resulted in a weight budget forthe URE06. To make sure the weight of the URE06 is not excessively larger than its competitors itneeded a weight reduction of at least 30kg compared to the URE05e. In the appendix it can be seenhow this reduction can be achieved. A weight reduction of the rear frame by 5.5kg is needed whichgives 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. Fourwere 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 perfectweight distribution, the results were spreaded around the 50/50 percent range with a variation of 8percent. 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 tochange the weight distribution, the time and place needed to do this is very limited. Because the re-sults of "a perfect weight distribution" are - as of today - not proven, the possible advantages do notweigh 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 nothave excessively long production times. In the past it has been proven that a rear frame could be cutand 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 repairscan be easily done on track.

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5 Design

This section will have a chronological time line which is maintained during the assignment. Firsta design begins with concepts where different types of designs are discussed. When one concept ischosen various layout concepts of the different subsystems are shown. These are then worked out inthe first design after which a mockup will be build to verify the first design. When an early simplifiedFEM 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 FiberReinforced Plastic (CFRP) monocoque. The (dis)advantages of both concepts will be explained andweighted against each other to form a viable conclusion. In the comparison in table ?? the key designtargets will be compared. In addition several secondary targets as cost, design time and present designknowledge are added.

Steel space frame Full CFRP

Stiffness in bending 0 +Stiffness in tension 0 +Stiffness in torsion 0 ++

Weight 0 +Serviceability ++ 0Fabrication + -

Manufacturing time ++ –Cost ++ –

Design time 0 0Present design knowledge + 0

Total nr. of + 8 2

Table 5: Comparing steel rear frame vs. full CFRP

StiffnessIn the report of Andries van Berkum [1] can be seen that a plate construction is stiffer than a tubularspaceframe. A full CFRP monocoque will be 2 times stiffer in bending, 1.6 times in tension and 2.6times in torsion. This comparison is done with a maximum outside dimension and having identicalmaterial volume.

WeightA 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 spaceframe remains within the 10kg. Although a CFRP monocoque can be made slightly lighter, this isnormally not achieved in the first year of implementation where the CFRP monocoques are heavierthan 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 timeWhen taking a closer look at the time between the final design and final product, the steel spaceframecomes out as an absolute winner. A steel spaceframe takes around 1 to 2 weeks to fabricate in thepast years at URE. The monocoque of the URE05 took around 7/8 weeks. This was mainly due to thelong manufacturing time of the positive and negative molds. The molds are also the reason why theamount of actions needed to complete the product is much greater for a CFRP product.

Design time and knowledge

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Although the time needed to design the two chassis’ do not differ that much, it is especially the anal-ysis that makes the difference. A spaceframe requires basic mechanical knowledge and this is widelyknown in the team. This can also be analyzed using Marc Mentat which is offered by the EindhovenUniversity of Technology. The knowledge needed to analyse a CFRP chassis is still very new in theteam and not readily accessible to implement it.

ConclusionAs can be seen in table ?? it can be concluded that a steel rear spaceframe is favorable, mainly dueto the better serviceability. Besides this the manufacturing time and total cost is much lower than theCFRP chassis.

5.2 Lay-out concepts

Multiple layout concepts have been analyzed to make sure the best suitable solution is found for theURE06. In the concept phase it is important to look for every possible solution as it is easier to makechanges and it will cost less money and time, opposite to the fabrication/testing phase. Five differentoptions are shown in figures 6, 7, 8, 9 and 10. The explanation of the layouts are described in eachcaption.

The ”golden rule” in University Racing Eindhoven is that changes should not be made to thingsthat work. This means that gearing systems as a planetary set, direct gearing and the bevel are ruledout. To make the choice between the two chain geared layouts (figures 8 and 9), two extended designshave been made. It was discovered that the motors would collide with the suspension system inconcept 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 thedrivetrain.

(a) Topview (b) Sideview

Figure 6: Concept 1. The motors are located underneath the drivetrain and connected throughdirect gearing. The battery box is lying on its back.

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(a) Topview (b) Sideview

Figure 7: Concept 2. The motors are located next to the drivetrain and connected with a planetaryset. 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 boxand the drivetrain.

(a) Topview (b) Sideview

Figure 9: Concept 4. Chain reduction, the motors are located on top of the battery box which ison its back.

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(a) Topview (b) Sideview

Figure 10: Concept 5. The motors are located underneath the drivetrain, connected via a bevelor 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 FEManalysis, 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 rules2010 [7]. This rule makes it mandatory that the the motor, battery and controllers are protected by aside impact structure.

Figure 11: The first design of the rear frame in which only the left motor bracket is shown.

Motor bracketFigure 13 shows the motor bracket. It is statically determinate supported by a spring leaf and two rodaerials. 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 whenthe battery is removed.

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(a) Top view (b) Side view

Figure 12: The first design of the rear frame, including the different subsystems. Notice that themotors 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 mountingAt the time of writing the design of the battery box itself was not started. A mounting of the box wastherefore not designed and will not be discussed.

Damper mountingThe mounting for the dampers is shown in figure 14. The placement of the dampers is chosen to makesure that the mechanics can reach it very easily. To make sure that the damper forces are redirectedcorrectly a pyramid shape is needed. A force parallel to the plane of a cross is very weak but as soonas 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 necessaryas it gives them a much better insight and feeling of the structure. Beside for the visualization of thedesigner 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 andmotors.

• The designer will get a better insight which of the diagonals are really necessary and which areless important.

• The wiring loom can be made more accurately using a mockup.

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(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, thesupports are shown in green.

• The "reachability" and serviceability for the mechanics can be checked (the brushes of the elec-tric 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 5hours to manufacture it. This particular mockup is a 1:1 model made out of PVC tubes and duct-tapewith 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 opensquares 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 samestiffness as a diagonal tube.

Figure 15: The mockup made out of PVC tubes and duck-tape.

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(a) The diagonal under the battery tested as a plate cross.(b) The arrow is pointing towards the diagonal under themotors.

Figure 16: The diagonal under the motors and the battery were found to be crucial for the torsionalstiffness.

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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 willbe 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 isdone for three reasons:

– Throughout the year the management decided to use another type of controller. The di-mensions of this type was bigger than the regular one. This meant it could not fit betweenthe battery and monocoque anymore, as can be seen in figure 12. Rule B8.14 [7] made itmandatory that the controller is protected with a side impact structure. The controllers aretherefore moved to the back of the vehicle between the two drive trains. To make roomfor this the sprocket (and thus the motors) needed to move sideways, the motors weremirrored for this purpose.

– The mounting points of the motors were located on the inside of the frame (almost directlyon the (y,z) plane), the brackets would therefore be loaded in the middle of the tube. Mir-roring the motors made it possible that the brackets could be supported near stiff nodes ofthe chassis.

– With the chains on the inside of the frame it was very inconvenient to make a properbracket 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 fig-ure 18. The mounting strips are therefore horizontally instead of vertically in order to make itfit.

• 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 toaccommodate the bracket for the damper rocker. It now measures 25.4mm outer diameter and20mm inner diameter.

• The FEM analysis showed that the P1 mount wasn’t possible in the first version. The mountingpoint 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 bracketwill therefore not be included.

Figure 17: Isometric view. The controllers are placed between the drive trains which needed themotors to be rotated 180 ◦ in the z direction to make it fit.

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Figure 18: Side view. Notice that the battery box has been moved forward and nearly touchesthe monocoque to create more space for the motor. The side impact structure is now protectingall 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 determinedat the time of writing.

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(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 afterthe 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 heightenedto 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 berotated, 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 noteasily 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 therear 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 becauseof the welds and paint. The excess in weight is due to the fact that the battery, motor andcontrollers have to be protected by a side impact structure. These tubes are twice the weight ofthe physically required tubes and covers nearly the entire rear frame. The rear frame is thereforeover dimensioned with nearly a factor two.

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6 Analysis

In this section the chassis will be analyzed on both the maximum stress during operations and thetorsional stiffness. It is therefore divided in two subsections. In section 6.1 the FEM analysis of thedifferent parts of the chassis is given, this includes the chassis itself as well as the subsystems as themotor 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 particularsubsystem of/in the frame. The first section will describe the analysis of the chassis itself using MarcMentat. The second subsection describes the FEM analysis of the motor bracket. The third and fourthsection provides a standardized system for respectively the suspension brackets and the analysis ofeach suspension bracket itself. The latter two sections describe "vergeetmenietjes" for the suspensionforces.

6.1.1 Chassis

This section will give information about the FEM analysis of the entire chassis. The Finite ElementMethod package used to analyze this rear frame is Marc Mentat. This is due to the fact that the normalpackage used by University Racing Eindhoven (Unigraphics 5) is having trouble with meshing tubesin 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 systemhas 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 loadcasewith the forces on the other side of the chassis. For an indication of the boundary conditions seefigure 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 thestresses similar to the forces.

2. Choose the material of the tubes and get an indication of the available tube dimensions in themarket.

3. Choose the tube sizes according to the following steps. Also see chapter 12 for the excel file.

(a) Run the model to get the maximum forces going through each tube. See figure 23.(b) Give all tubes minimum wall thickness of 1 mm for welding purposes.(c) Choose outer diameter depending on the maximum force reached.(d) Make sure the tubes do not buckle due to compressive forces.(e) 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 therear frame. See figure 24.

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Figure 22: The boundary conditions used in the model. It is assumed that the monocoque isinfinitely stiff and the forces are going trough the connection rods to the brackets at their respectiveangle.

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Figure 23: Acceleration loadcase. This is step 3a of the plan. The numbers indicate the forcesgoing trough each tube. This is done for every loadcase in order to get the maximum force goingtrough the chassis in every possible loadcase.

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Figure 24: Bump loadcase, including the area, this is the loadcase in which the chassis undergoesthe maximum forces. This is step 4 of the plan, notice that the maximum stress does not exceed84 MPa (three times lower than the yield stress of steel).

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6.1.2 Motor bracket

The safety factor for the motor bracket is different compared to the regular safety factor. UniversityRacing Eindhoven uses a system for the drivetrain that makes sure that the chain is the first thing tobreak during driving. This means that instead of the maximum load on the part itself the loadcase isthe maximum load until the chain breaks, this means a chain force of 15000N. See figure 25 for theFEM results. The flanges that were added in the final design are not taken into account for simplicityreasons, 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 of300 MPa. Notice that this is only reached in the holes for the bolts where the tension force of thewashers 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 asshort as possible, a standardized system would therefore be convenient. In order to make this systemfor the brackets, four designs are analyzed on their strength. These four designs can be seen infigures 27, 28, 29 and 30. The first design (case 1) is the ultimate design from last years car, theURE06 combustion [5]. This design is optimized for the lowest stress, but the manufacturing time islong 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 toshow which of the three substitute designs are stronger and lighter than case 1. Case 2 is lighter thancase 1 but the forces go perpendicular into the tube, creating a lot of deformation. This problem issolved in case 3. The idea behind case 4 is that the welding spot will not go trough the tube, which willhappen in case 3. For this simulation, a tensile force Fr = 3500N is applied at an angle of 45 ◦s to thebracket, see figure 26.

Case 1 Case 2 Case 3 Case 4

Maximum stress [MPa] 0.61 1 0.34 0.26Mass [g] 1 0.65 0.68 0.69

Deformation of tube [mm] 0.78 1 0.84 0.87

Table 6: Results of the FEM cases for the pick up points, normalized to the maximum valuerespectively.

The normalized results are given in table ??. The standard system for the brackets is chosen tobe case 4 because the maximum stress is the lowest while the weight and maximum deformation ofthe tube are nearly the same. With this basic system in mind the suspension brackets are analyzed ontheir specific design and loadcase in section 6.1.4.

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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 stressof 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 stressof 300 MPa

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(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 stressof 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 stressof 300 MPa

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6.1.4 Suspension brackets: Specific loadcases

In this section the specific loadcases on the suspension brackets are analyzed to make sure that allthe systems will never fail during driving. The figures each show a different bracket and will give anindication of the maximum stress in the part. All the forces have a total safety factor of k = 1.5. It isassumed that the dynamical loading is calculated with this safety factor thus the maximum stress isσmax = 300 [MPa]. The load cases can be seen in the appendix, chapter 11. The results of the FEManalysis have been summarized in table ??.

Suspension point number Description

P1 See figure 32P4 The loads on the P4 suspension rod is more than 4 times lower then

other suspension brackets. It is therefore assumed that the bracket willhold under the load.

P5 See figure 31Damper rocker mount See figure 33

Damper bracket 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 stressis higher than 300 MPa. This can be neglected as the clamping of the ring and bolts were nottaken into account.

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(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 thestress 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 stressis 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 ishigher than 300 MPa. This can be neglected as the clamping of the ring and bolts were not takeninto account.

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6.1.5 Tube P4 support

The loads on the P4 suspension rod is more than 4 times lower then other suspension brackets. Itis therefore assumed that the bracket will hold under the load. However the attachment point of thebracket is in the middle of the tube (a few centimeters away from the fixed end), which makes itnecessary to calculate whether the tube will not deflect too much (see figure 35). Equation 1 gives thesolution for a built-in beam with a concentrated force, according to Fenner[14].

ua = −F (L− a)3a3

3EIoL3(1)

With ua the deflection of the beam directly under the force F = 2000N at a distance a = 45mm fromits end. Equation 2 gives the polar second moment of area of a thin hollow tube.

Io =π

64(D4

O −D4I ) (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

1/4π(D2O −D2

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 headrestraint consist of two tubes as the drivers heights differ, see figure 36). The yield stress of rolled steelis σyield = 300MPa which therefore makes the head restraint correct according to the rules.

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Figure 36: Isometric view of the rear frame, the head rest is shown in gray.

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6.2 Torsional stiffness

When the area’s of the tubes are chosen the torsional stiffness can be calculated. A vertical loadis applied to both rear wheel centers in opposite direction to simulate the torsional load while themonocoque is assumed to be infinitely stiff. The vertical load is recalculated in the force vectors goingtrough the suspension rod with help of Cadesh [4]. This is to make sure that the suspension stiffnessis not added to the chassis stiffness. The torsional stiffness K of the chassis can then be calculated bymeasuring the angular deformation in the rear bulkhead.

K =M

α(4)

M = 2Fl (5)

α = sin−1(∆zquickjack

Lquickjack) (6)

gives a torsional stiffness K = 10380 Nm/ ◦. This is in the same range as Erik Stoltenborg calculatedhis 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 overdimensioned due to the Side Impact rules.

7 Recommendations

• Try to reposition the dampers in such a way that the three major components can be repositionedwhere they are protected by just 1 side impact structure (SI structure). In this design thereare three separate SI systems which makes the rear frame over-dimensioned in weight( andstiffness).

• It is absolutely necessary to measure the (chassis)stiffness of the URE06 in order to evaluate thetheoretical torsion stiffness calculations.

• When designing the rear frame of the URE06 it is advised to make a full monocoque instead ofa hybrid. This will reduce the weight while increasing stiffness (no transition between carbonand steel). Plus the problem with the positioning of systems due to the side impact structure isdecreased. However this mean that the mold need to be redesigned and manufactured whichtakes time and money.

• In the past few years a torsional stiffness test has not been a high priority activity, in order tokeep improving on the chassis (and the suspension) it is very much recommended to do thetorsional stiffness test of the URE06 as soon as it is built.

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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, Jul2010.

[6] Formula SAE International, 2011 Formula SAE rules, http://students.sae.org/competitions/formulaseries/rules/

[7] Formula Student England, 2011 Formula Student Class 1A Rules,http://www.formulastudent.com/

[8] Formula Student Germany Electric, 2010 Formula Student Electric Rules,http://www.formulastudentelectric.de/

[9] Internation Organisation for Standardization , Road vehicles - Vehicle dynamics and road-holdingability - 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

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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

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10 Appendix B - Weight analysis

36

37

38

39

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11 Appendix C - Suspension Load cases

Bump Cornering Braking Acceleration

Vector componenten Normaal Kracht Kracht Kracht Kracht

P1 A 325,1737997 1 3417 tension 7125 tension 3505 tension 915 tension

Ax 95 0,292151459 998,2815 2081,57915 1023,991 267,3186

Ay -308 -0,947185783 -3236,53 -6748,6987 -3319,89 -866,675

Az -43 -0,132236976 -451,854 -942,18846 -463,491 -120,997

P4 A 277,2183255 1 818 comp 1987 tension 95 comp 744 comp

Ax 120 0,432871816 354,0891 860,116298 41,12282 322,0566

Ay -235 -0,847707306 -693,425 -1684,3944 -80,5322 -630,694

Az -85 -0,306617536 -250,813 -609,24904 -29,1287 -228,123

P5 A 305,6354037 1 330 comp 6543 comp 2677 comp 716 tension

Ax 0 0 0 0 0 0

Ay -302 -0,988105423 -326,075 -6465,1738 -2645,16 -707,483

Az -47 -0,153777996 -50,7467 -1006,1694 -411,664 -110,105

P6 A 269,4567821 1 1809 comp 3704 comp 945 comp 2174 comp

Ax 83,2127 0,308816499 558,649 1143,85631 291,8316 671,3671

Ay -162,8143 -0,60423159 -1093,05 -2238,0738 -570,999 -1313,6

Az 197,9245 0,734531521 1328,768 2720,70475 694,1323 1596,872

Damper A 209,4618976 1 2621,739 comp 5368,11594 comp 1369,565 comp 3150,725 comp

Ax 38,9655 0,186026673 487,7134 998,612751 254,7757 586,1188

Ay -205,7925 -0,982481789 -2575,81 -5274,0762 -1345,57 -3095,53

Az -2,3288 -0,011118013 -29,1485 -59,68278 -15,2268 -35,0298

Rocker mount A 434,8058917 4030,442 comp 8252,49106 comp 2105,455 comp 4843,66 comp

Ax 122,1782 1046,362 2142,46906 546,6073 1257,486

Ay -368,6068 -3668,87 -7512,15 -1916,57 -4409,13

Az 195,5957 1299,619 2661,02197 678,9054 1561,842

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12 Appendix D - FEM results

On the next page the excel file of the FEM results is added.

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