Chassis and suspension design FSRTE02

Chassis and suspension design FSRTE02
Chassis and suspension design FSRTE02
A. van Berkum
DCT 2006.23
Master’s Thesis
Coach:
Supervisor:
Dr.ir. P.C.J.N. Rosielle
Prof.dr.ir. M. Steinbuch
Technische Universiteit Eindhoven
Department of Mechanical Engineering
Section Dynamics and Control Technology
Eindhoven, March 2006
1
Dutch summary
Achtergrond informatie
De Formula Student competitie is een competitie waaraan universiteiten vanuit de hele
wereld deelnemen. In 2004 heeft het Formula Student Racing Team Eindhoven (FSRTE)
voor het eerst deelgenomen in klasse 3. In deze klasse wordt het ontwerp beoordeeld.
In 2005 heeft het FSRTE voor de 2e keer meegedaan en dit keer in klasse 2 met een
onafgebouwde wagen. Het doel voor 2006 is om deel te nemen met een rijdende auto in
klasse 1. In deze klasse kan daadwerkelijk worden geraced met de zelfgebouwde
eenzitter. Het maximale vermnogen ligt hierbij op 65 kW.
Opdracht
Het doel van de race is om studenten te leren om een raceteam op te zetten dat in staat is
om een auto te ontwerpen, te bouwen en er uiteindelijk ook mee te kunnen racen.
Het team moet zich voorstellen dat ze een prototype moeten bouwen voor een bedrijf.
Uiteindelijk wil het bedrijf 1000 auto’s per jaar gaan maken voor de niet-professionele
weekend courour. De auto mag niet meer dan €21.000 gaan kosten, maar tegelijkertijd
moeten de prestaties en wegligging goed zijn. De uitdaging is om hier zo goed mogelijk
aan te voldoen.
Doel
Het doel van dit project is om het ontwerp voor het chassis en de wielophanging van de
FSRTE02 te maken, dat zo goed mogelijk voldoet aan de gestelde eisen.
Ook moet er een assemblage van de complete auto worden gemaakt in Unigraphics.
Conclusies
Het FSRTE02 chassis is grotendeels gebaseerd op het FSRTE01 chassis maar is
geoptimaliseerd naar torsie strijfheid. De wielophangings eigenschappen zijn bepaald
voor een goede wegligging. Het chassis is gemaakt van ALUCORE aluminium
honingraat panelen. De delen zijn waterstraal gesneden en gebogen waarna ze aan elkaar
gelijmd zijn. De dunne aluminium platen in het chassis zijn gesneden met laser voor een
hoge presicie. De voorste en achterste rol beugels zijn buitenom geplaatst en van
binnenuit bevestigd.Het dashboard is een sandwich structuur met een polyurethaan kern.
De stuuroverbrenging is verzonken in het dashbord. Bij het ontwerp van de
bevestigingspunten van de wielophanging is rekening gehouden met de maakbaarheid.
De aandrijving wordt verzorgd door een 600 cc Suzuki motorblok dat via een ketting de
achterwielen aandrijft. Voor het veerssysteem worden twee enkele veerdempers gebruikt.
Spiraalveren zorgen voor de roll stijfheid en twee motorfiets stuurdempers worden
gebruikt voor de roll demping. Alle onderdelen van het veersysteem en het anti-roll
systeem zitten ingebouwd in een rechthoekige aliminium koker, “de suspension box”.
Aanbevelingen
In het FSRTE02 ontwerp is weinig aandacht besteed aan de banden, hier zou uitgereider
naar gekeken moetn worden. Ook zal er een keuze gemaakt moeten worden voor een
specifike veerdemper zodat het ontwerp voor de suspensionbox definitief gemaakt kan
worden.
2
Voor het FSRTE03 ontwerp moet er goed gekeken worden naar de manier waarop het
Unigraphics model wordt opgebouwd. Er moet een zogenaamde “bottom up” assembly
gemaakt worden die helemaal parametrisch opgebouwd is.
Het Aprilia SXV 5.5 blok is een alternatief voor de Suzuki. Het blok vraagt wel om een
compleet andere auto. Carbon kan hierbij wellicht interressant zijn.
3
English summary
Background
The Formula Student competition is a competition in which university teams from all
over the world compete. In the 2004 event the Formula Student Racing Team Eindhoven
(FSRTE) competed with a design in class 3 and in 2005 the FSRTE competed with an
unfinished car in class 2. This year’s aim is to compete in the 2006 event in class 1.
In this class, a single seated race car has to be built. The maximum cylinder capacity is
600cc and an intake restrictor is obligated, reducing the maximum engine power to 65kW.
Objective
The objective is to design and build a car, manage and market it and finally to compete
with the car in the race. Therefore, the teams have to assume that a manufacturing firm
has engaged them to produce a prototype car for evaluation. In the future the firm is
planning to produce 1000 cars each year for the nonprofessional weekend autocross racer.
Therefore the car has to be produced at a cost below €21.000. On the other hand the car
should have a very high performance in terms of acceleration, braking and handling
qualities. The challenge is to design a prototype car that best meets these objectives.
General aim
The aim for this project is to make a design for the FSRTE02 chassis and suspension,
considering the desired car handling and the regulations determined by the Formula
Student organization. Furthermore all parts have to be assembled onto the chassis using
Unigraphics.
Conclusions
The chassis shape is based on the earlier designed FSRTE01 but optimized on torsion
stiffness. The suspension properties are set for optimum road holding.
The chassis consists out of two nearly symmetrical halfs made out of watercutted
ALUCORE honeycomb sandwich panels. Thin plate part layouts are lasercutted to obtain
high precision. The front and rear roll hoops are placed around the chassis and mounted
from the inside. The dashboard is a sandwich structure with a polyurethane core. The
steering system transmission is countersunk into the dashboard. The suspension mounting
points are designed for make-ability. A Suzuki 600 cc motorcycle engine is used to drive
the rear wheels using a chain. The suspension system is equipped with two monoshocks.
Front and rear roll stiffness is added using helical springs. A motorcycle steering damper
is used for roll damping. All is mounted into two suspension boxes front and rear.
Recommendations
In FSRTE02 design little attention is paid to the tires.
Furthermore work has to be done on the suspension boxes; they can be finalized when a
specific monoshock is chosen. Considering the FSRTE03 design, attention has to be paid
to the way the Unigraphics assembly is set up. So called “bottom up” assembly should be
applied and the Unigraphics assembly should be completely parametric. The Aprilia SXV
5.5 engine has to be looked at seriously as alternative for the Suzuki engine. This engine
demands a completely different design, a laminated carbon structure can be examined.
4
Preface
In september 2003 six enthusiastic students with a passion for wheels raised the Formula
Student Racing Team Eindhoven or FSRTE. They were determined to join the Formula
Student competition in the U.K., a racing competition among universities from all over
the world. In november 2003, the FSRTE found Wouter Berkhout willing to be the head
designer of the FSRTE01. The FSRTE was planning to compete in the design class of the
2004 event. In December 2003 I performed an internal traineeship for the FSRTE on the
final drive for the FSRTE01. At that time I got enthusiastic for designing a race car. In
july 2004, I visited the Formula Student event together with seven other students and my
coach Nick Rosielle. The Technische Universiteit Eindhoven obviously had to compete
with a built car. Half a year later in february 2005 I was asked to do the chassis and
suspension design for the FSRTE02, several weeks later I started graduating.
In my point of view it had to be a continuation of the work of Wouter Berkhout.
The FSRTE02 chassis and suspension design had to be feasible, makeable and
completely finished. Meanwhile the FSRTE01 was being built to compete in the 2005
event. This is when problems occurred, detailing was under estimated and little attention
was paid to accuracy. This enhanced my effort to generate a fully detailed chassis and
suspension design including building instructions. In september 2005, the FSRTE started
with a new committee. Many students joined the team to help to realize the FSRTE02.
I enjoyed inspiring them to think of new ideas and helping them to design the parts.
It took me quite some effort to finish my graduation. I wanted a perfect final assembly so
not a single part would interfere. While the chassis was being built I had to write my
report but I also wanted to see if everything went right on the building site.
During the project Nick Rosielle has been my coach as head of the Constructions and
Mechanisms group. His knowledge and common sense have been very useful for me.
Therefore I want to thank him. Every week, the students of the constructions and
mechanism group have been helpful and inspiring to me, so I would like to thank all of
them. Furthermore I would like to thank Ton Serné, Igo Besselink and Antoine Schmeitz
for their help on suspension geometry and tires.
And of course I would like to thank the FSRTE committees of 2005 and 2006 and the
FSRTE team members for the pleasant corporation.
5
Dutch summary................................................................................................................. 2
English summary .............................................................................................................. 4
Preface................................................................................................................................ 5
1 Introduction.................................................................................................................. 12
1.1 Project backround ................................................................................................... 12
1.2 Objective ................................................................................................................. 12
1.2.1 Project aim ....................................................................................................... 13
1.2.2 Project approach............................................................................................... 13
2 General FSRTE02 properties ..................................................................................... 14
2.1 Engine ..................................................................................................................... 14
2.1.1 The aprilia SXV5.5 engine .............................................................................. 15
2.1.2 The Suzuki GSX-R600 engine......................................................................... 16
2.2 Car dimensions........................................................................................................ 17
2.3 Tires ........................................................................................................................ 18
2.3.1 Slip angle ......................................................................................................... 18
2.3.2 Friction model.................................................................................................. 21
2.4 Design forces .......................................................................................................... 22
2.4.1 Bump forces ..................................................................................................... 22
2.4.2 Braking and accelerating forces....................................................................... 23
2.4.3 Cornering forces............................................................................................... 25
3 Chassis properties ........................................................................................................ 27
3.1 Chassis requirements .............................................................................................. 27
3.2 Chassis type ............................................................................................................ 27
3.3 Chassis material ...................................................................................................... 29
3.3.1 ALUCORE honeycomb panel properties ........................................................ 29
3.3.2 ALUCORE honeycomb panel cutting ............................................................. 30
3.3.3 ALUCORE honeycomb panel bending ........................................................... 30
3.3.4 ALUCORE honeycomb panel gluing .............................................................. 33
3.4 Chassis shape .......................................................................................................... 34
3.4.1 Chassis torsion stiffness................................................................................... 34
3.4.2 Chassis strength ............................................................................................... 36
4 Suspension properties.................................................................................................. 37
4.1 Suspension stiffness and damping .......................................................................... 37
4.2 Lateral suspension properties.................................................................................. 38
4.2.1 Roll center height............................................................................................. 38
4.2.2 Roll stiffness and damping............................................................................... 40
4.2.3 Camber............................................................................................................. 41
4.3 Longitudinal suspension design.............................................................................. 43
4.3.1 Acceleration; squat effect ................................................................................ 43
4.3.2 Braking; dive and rise effect ............................................................................ 45
4.4 Steering properties .................................................................................................. 46
4.4.1 Steering geometry ............................................................................................ 46
6
4.4.2 Kingpin inclination and scrub radius ............................................................... 47
4.4.3 Caster and trail ................................................................................................. 48
4.4.4. Bump steer ...................................................................................................... 49
5 Chassis design............................................................................................................... 51
5.1 Main structure ......................................................................................................... 51
5.1.1 ALUCORE side panels .................................................................................... 51
5.1.2 ALUCORE front and seat panel ...................................................................... 52
5.1.3 Rearframe......................................................................................................... 53
5.1.4 Suspension support beams ............................................................................... 54
5.1.5 Torsion tubes.................................................................................................... 55
5.1.7 Front and rear roll hoop ................................................................................... 56
5.1.8 Dashboard ........................................................................................................ 58
5.1.9 Rear and front covering plates ......................................................................... 59
5.2 Side impact and sloped floorpanel assembly .......................................................... 60
5.3 Steering system ....................................................................................................... 63
5.4 Power train and drive train...................................................................................... 65
6 Suspension design......................................................................................................... 70
6.1 Suspension center lines ........................................................................................... 70
6.2 Chassis connection points ....................................................................................... 70
6.2.1 Mounting point “type 1” .................................................................................. 71
6.2.2 Mounting point “type 2” .................................................................................. 72
6.3.3Mounting point “type 3” ................................................................................... 72
6.3 Connection rods and uprights ................................................................................. 73
6.4 Suspension unit concepts ........................................................................................ 75
6.4.1 Original FSRTE01 design................................................................................ 76
6.4.2. Anti-roll concept 1 .......................................................................................... 78
6.4.3. Anti-roll concept 2 .......................................................................................... 79
6.4.4. Anti-roll concept 3 .......................................................................................... 80
6.4.5. Anti-roll concept 4 .......................................................................................... 81
6.4.5. Anti-roll concept 5 .......................................................................................... 82
6.5 Suspension unit design............................................................................................ 83
6.5.1 Suspension ratios ............................................................................................. 83
6.5.2 Anti-roll helical spring stiffness....................................................................... 85
6.5.3 Steering damper specifications ........................................................................ 88
6.5.4 Monoshock specifications................................................................................ 90
6.5.5 Suspension box design..................................................................................... 92
7 FSRTE02 assembly ...................................................................................................... 96
7.1 Unigraphics assembly ............................................................................................. 96
7.2 FSRTE02 construction............................................................................................ 98
8 Conclusions and recommendations .......................................................................... 100
8.1 Conclusions........................................................................................................... 100
8.2 Recommendations................................................................................................. 101
Bibliography .................................................................................................................. 103
7
Appendices..................................................................................................................... 105
Appendix A: Static mass distribution ......................................................................... 105
Appendix B: friction coefficients on dry and wet road............................................... 107
Appendic C: Sandwich material core table................................................................. 108
Appendix D: FSRTE02 chassis FEM analysis results................................................ 108
Appendix D: FSRTE02 chassis FEM analysis results................................................ 109
Appendix E: Radial tire stiffness ................................................................................ 110
Appendix F: Standard driver seated in FSRTE02 chassis .......................................... 111
Appendix G: suspension coordinates.......................................................................... 112
Appendix H: Rod end specification ............................................................................ 113
Appendix I: Third rocker ballbearing specifications .................................................. 114
Appendix J: Suspension box mainshaft ball bearing specifications ........................... 115
Appendix K: Ball monorail guidance system specifications ...................................... 116
Appendix L: WP steering damper measurements....................................................... 117
Appendix M: Chassis construction sequence ............................................................. 118
List of figures
Figure 2.1: The DUT04 from Delft Uiversity of technology…………………………………………………. 14
Figure 2.2: The UT03 from the University of Toronto……………………………………………………….. 14
Figure 2.3: The aprilia SXV5.5 engine and its specifications………………………………………………… 15
Figure 2.4: The Suzuki GSX-R600 engine and its specifications………………………………….…………. 16
Figure 2.5: Skidpad track………………………………………………………………………………………17
Figure 2.6: Endurance and fuel economy event………………………………………………………………. 17
Figure 2.7: Force equilibrium during steady state cornering ………………………………………………… 18
Figure 2.8: Avon 7.0/20.0-13 3 ply pro-series, cornering force against slip angle………………………...... 19
Figure 2.9: Forces acting on one tire…………………………………………………………………………. 19
Figure 2.10: Avon 7.0/20.0-13 3 ply pro-series, cornering stiffness at Fn is 1500 N……………………….. 20
Figure 2.11: Tire on surface with lateral and longitudinal µ…………………………………………………. 21
Figure 2.12: µlat and µlong at a slip angle of 7o for the front tire on dry road………………………………… 21
Figure 2.13: Forces acting on a formula one car taken (copied from “racecar engineering” nov 2003)……... 22
Figure 2.14: Force equilibrium during maximum braking……………………………………………………. 23
Figure 2.15: Force equilibrium during maximum acceleration……………………………………………...... 24
Figure 2.16: Force equilibrium during maximum cornering………………………………………………...... 25
Figure 2.17: Flat-r plotted as a function of FN-r………………………………………………………………… 26
Figure 3.1: Limiting volume………………………………………………………………………………….. 27
Figure 3.2: Three possible configurations for the closed section tube……………………………………….. 27
Figure 3.3: Tubular spaceframe………………………………………………………………………………. 28
Figure 3.4: Honeycomb panel compared to a solid plate for out of plane bending load……………………… 29
Figure 3.5: Water cutting……………………………………………………………………………………… 30
Figure 3.6: SAFAN hydraulic press brake with ALCAN bending instructions………………………………. 30
Figure 3.7: Bending on the SAFAN press brake and measuring the outer skin radius……………………..... 31
Figure 3.8: Bent corner with different deformation zones and the applied FEM loadcase…………………… 31
Figure 3.9: Four bend finish options and their FEM results………………………………………………….. 32
Figure 3.10: Gluing test to convince the jury…………………………………………………………………. 33
Figure 3.11: FEM torsion test loadcase………………………………………………………………………. 34
Figure 3.12: Torsion stiffness of three different chassis……………………………………………………… 35
Figure 4.1: Graphical roll center determination ……………………………………………………………… 38
Figure 4.2 a: Force equilibrium RC above road ……………………………………………………………… 39
Figure 4.2 b: Force equilibrium RC below road …………………………………………………………….. 39
Figure 4.3 a: Time force graphs with RC above road ……………………………………………………….. 39
Figure 4.3 b: Time force graphs with RC below road ……………………………………………………….. 39
Figure 4.4: Three different outer wheel camber situations in a left corner …………………………………... 41
8
Figure 4.5: Parallel A-arm, body roll causes negative camber on both wheels………………………............. 42
Figure 4.6: Suspension lay-out with camber change rate…………………………………………………….. 42
Figure 4.7: Pitching causes……………………………………………………………………………………. 43
Figure 4.8: Anti-squat geometry………………………………………………………………………………. 43
Figure 4.9: Anti-rise and ainti-dive geometry………………………………………………………………… 45
Figure 4.10: Front wheel in front view with king pin inclination and scrub radius…………………………... 47
Figure 4.11: Front wheel in side view with caster angle and trail ……………………………………………. 48
Figure 4.12: Graphical determination of anti-bump steer geometry ………………………………………..... 49
Figure 4.13: Toe characteristics of front and rear wheels…………………………………………………….. 50
Figure 5.1 a: Layout ALUCORE panels……………………………………………………………………….51
Figure 5.1 b: Joining both symmetrical half’s ………………………………………………………………. 51
Figure 5.1 c: Gluing both half’s………………………………………… ……………………………………. 51
Figure 5.2 a: Placement of front and seatpanel……………………………………………………………….. 52
Figure 5.2 b: Attachment details ……………………………………………………………………………… 52
Figure 5.3: The rearframe and its placement in the chassis…………………………………………………… 53
Figure 5.4: Rearframe attachment…………………………………………………………………………...... 54
Figure 5.5: Suspension support beam placement with detailed attachment view…………………………….. 54
Figure 5.6: Torsion tube layout, placement and sub-parts……………………………………………………..55
Figure 5.7 a: Glued in flaps…………………………………………………………………………………… 56
Figure 5.7 b: Sidepanel - torsion tube attachment.……………………………………………………………. 56
Figure 5.8: Front and rear roll hoop placement and rear hoop bracing……………………………………...... 56
Figure 5.9 a: Cross section plane a……………………………………………………………………………. 57
Figure 5.9 b: Cross section plane b……………………………………………………………………………. 57
Figure 5.9 c: Cross section plane c……………………………………………………………………………. 57
Figure 5.10: Exploded view of the dashboard………………………………………………………………… 58
Figure 5.11: Dashboard placement and attachment…………………………………………………………… 58
Figure 5.12: Attachment traverse beams onto support beam ………………………………………………… 59
Figure 5.13: Front and rear covering plates…………………………………………………………………… 59
Figure 5.14: Side impact cross section………………………………………………………………………... 60
Figure 5.15: Sloped floorpanel layout and folded sloped floorpanel…………………………………………. 60
Figure 5.16: Side impact tube lay out and folded joint……………………………………………………….. 61
Figure 5.17: Sloped floorpanel and side impact assembly……………………………………………………. 61
Figure 5.18: Sloped floorpanel and side impact placement…………………………………………………… 62
Figure 5.19: Steering transmission with four eccentric disks…………………………………………………. 63
Figure 5.20: Placement and attachment steering system……………………………………………………… 64
Figure 5.21: Second sloped floorpanel for steering rack protection………………………………………….. 64
Figure 5.22: Suzuki engine mounting points…………………………………………………………………. 65
Figure 5.23: Topview of differential mounting plates with differential, sprocket and brake disk……………. 66
Figure 5.24: Drivetrain exploded view and assembly………………………………………………………… 67
Figure 5.25: Placement and attachment drivetrain and engine……………………………………………….. 68
Figure 5.26: Placement of battery, fuel tank and radiator……………………………………………………. 69
Figure 6.1: Suspension center lines…………………………………………………………………………… 70
Figure 6.2: “Type 1” mountingpoint…………………………………………………………………………. 71
Figure 6.3: Suspension angles……………………………………………………. ………………………….. 71
Figure 6.4: Mounting point “type 2” …………………………………………………………………………. 72
Figure 6.5 Mounting point “type 3” …………………………………………………………………………. 72
Figure 6.6: Overview of connection rods and uprights……………………………………………………….. 73
Figure 6.7: Connection rod cross section……………………………………………………………………... 73
Figure 6.8: Flexplate intersects with the pushrod centerline, special A-arm connecter design………………. 74
Figure 6.9: Steering rack with extension……………………………………………………………………... 74
Figure 6.10: Schematic presentation of rocker in both utmost positions…………………………………….. 75
Figure 6.11: Most common used system with two shocks……………………………………………………. 75
Figure 6.12: Monoshock system………………………………………………………………………………. 75
Figure 6.13 a: Rocker rotation in pure bump…………………………………………………………………. 76
Figure 6.13 b: Rocker rotation in pure roll……………………………………………………………………. 76
Figure 6.14: Original FSRTE01 anti-roll system design……………………………………………………… 76
Figure 6.15 a: FSRTE01 anti-roll system in pure bump……………………………………………………… 77
9
Figure 6.15 b: FSRTE01 anti-roll system in pure roll………………………………………………………... 77
Figure 6.16: Pneumatic anti-roll concept………………………………………………………………………78
Figure 6.17: Schematic topview of anti-roll concept 2……………………………………………………….. 79
Figure 6.18: Anti-roll spring compression in pure bump for concept 2………………………………………. 79
Figure 6.19: Anti-roll concept 3 in frontview…………………………………………………………………. 80
Figure 6.20: SAM model results anti-roll concept 3………………………………………………………….. 80
Figure 6.21: Anti-roll concept 4………………………………………………………………………………. 81
Figure 6.22: Topview of anti-roll concept 5…………………………………………………………………... 82
Figure 6.23: Sideview of suspension box placement and pushrod plane sections……………………………. 83
Figure 6.24: Rocker and parallelogram dimensions of front and rear suspension box……………………….. 84
Figure 6.25: Rocker and lever arm dimensions of front and rear suspension box……………………………. 84
Figure 6.26: Tevema helical spring for the anti-roll mechanism …………………………………………….. 85
Figure 6.27: Third rocker block preloaded by two helical compression springs………………………………86
Figure 6.28: Schematic view of the absolute roll stiffness adjustments front and rear……………………….. 87
Figure 6.29: WP steering damper and mounting bracket……………………………………………………... 88
Figure 6.30 a: WP measurement data…………………………………………………………………………. 88
Figure 6.30 b: Speed-force graph extracted from WP data…………………………………………………… 88
Figure 6.31: Setup to determine WP damping coefficient……………………………………………………. 89
Figure 6.32: Exploded view of triangulalar plates, bearings and parallelogram links………………………... 92
Figure 6.33: Placement of main shaft together with anti-roll lever arm and rocker………………………….. 92
Figure 6.34: Mainshaft cross section………………………………………………………………………….. 93
Figure 6.35: Exploded view of the third rocker rotation an translation system……………………………… 94
Figure 6.36: Placement of ball monorail guidance system using brackets……………………………………. 94
Figure 6.37: Spring and damper placement…………………………………………………………………… 95
Figure 6.38: Final design front suspension box……………………………………………………………….. 95
Figure 7.1: Front suspension box with bend mounting plates and corner profiles……………………………. 96
Figure 7.2: Placement of the suspension boxes front and rear onto the FSRTE02 chassis…………………… 97
Figure 7.3: Final FSRTE02 assembly with driver seated …………………………………………………….. 97
Figure 7.4: Watercutted layouts and bending both halfs on the press brake …………………………………. 98
Figure 7.5 a: Gluing the bottom seam………………………………………………………………………… 99
Figure 7.5 b: Gluing in the rearframe…………………………………………………………………………. 99
Figure 7.6 : Bending of torsion tube…………………………………………………………………………. 99
Figure A.1: Car side view with all parts over 5 kg……………………………………………………………. 105
Figure B.1: µlat and µlong at a slip angle of 7o for the front tire on wet road…………………………………. 107
Figure B.2: µlat and µlong at a slip angle of 7o for the rear tire on dry road………………………………….. 107
Figure B.3: µlat and µlong at a slip angle of 7o for the rear tire on wet road…………………………………... 107
Figure D.1: Stresses during maximum acceleration…………………………………………………………... 109
Figure D.2: Stresses during maximum braking……………………………………………………………….. 109
Figure D.3: Stresses during maximum cornering……………………………………………………………... 109
Figure E.1: Tire compression as a function of tire normal force for the front tire……………………………. 110
Figure E.2: Tire compression as a function of tire normal force for the front tire……………………………. 110
Figure F.1: Sideview and cross section at the elbow of standard driver……………………………………… 111
Figure G.1: Suspension points naming………………………………………………………………………... 112
Figure H.1: Rod end specifications…………………………………………………………………………… 113
Figure I.1: Suspension box third rocker ballbearing specifications…………………………………………... 114
Figure J.1: Suspension box mainshaft ball bearing specifications……………………………………………. 115
Figure K.1: Ball monorail guidance system specifications…………………………………………………… 116
Figure N.1: WP steering damper measuring data……………………………………………………………... 117
10
List of tables
Table 2.1: Bump Forces……………………………………………………………………………………….. 22
Table 2.2: Braking forces……………………………………………………………………………………... 24
Table 2.3: Acceleration forces………………………………………………………………………………… 24
Table 2.4: Cornering forces…………………………………………………………………………………… 25
Table 3.1: Comparison tubular spaceframe and plate construction on specific stiffness……………………... 28
Table 3.2: Maximum occurring Von Mises stress on different load cases……………………………………. 36
Table 4.1: Camber angle and lateral tire force………………………………………………………………....41
Table 4.2: Wheel travel and pitch angle during maximum acceleration……………………………………… 44
Table 4.3: Wheel travel and pitch angle during maximum braking…………………………………………... 45
Table 6.1: Tevema helical spring for the anti-roll mechanism dimensions and specifications……………….. 85
Table 6.2: Adjustments range for front and rear antiroll stiffness and corresponding lever arm lengths ……. 87
Table 6.3: Possible rear to front roll stiffness ratios…………………………………………………………... 87
Table 6.4: Three different options for the monoshock spring front and rear…………………………………. 91
Table A.1: Sprung and unsprung (front- and rear wheels) masses and positions……………………………..105
Table A.2: Combined centers of mass………………………………………………………………………... 106
Table C.1: Sandwich core materials………………………………………………………………………….. 108
Table G.1: Description and coordinates of each suspension point…………………………………………… 112
Table M.1: Chassis construction sequence……………………………………………………………………. 118
11
1 Introduction
1.1 Project backround
The Formula SAE competition is a competition in which university teams from all over
the world compete. The main aims are to teach students to raise a team which is able to
design and build a car, manage and market it and finally to compete with the car in the
race.
Six different Formula SAE competitions are held in 2006:
1. Formula SAE held in Michigan, USA and organized by SAE
2. Formula SAE West held in California, USA and organized by SAE
3. Formula SAE Australasia held in Australia and organized by SAE Australasia
4. Formula SAE Brasil held in Brasil and organized by SAE Brasil
5. Formula SAE Italy held in Italy and organized by ATA
6. Formula Student held in the United Kingdom and organized by IMechE
All competitions use equal rules and have open registration policies accepting
registrations by student teams representing universities in any country.
The Formula Student competition started in 1998 as demonstration event in which two
U.S. cars and two U.K. cars competed.
Formula Student has three classes, The Formula Student Racing Team Eindhoven
(FSRTE) started competing in the Formula Student competition in 2004, in class 3, which
means only a design was presented and judged.
For 2005 the FSRTE competed with an unfinished car (designed in 2004), in class 2.
The aim for the 2006 event is to compete with a finished and fully tested car in class 1.
The main conclusion of the 2005 “unfinished car” experience was that a fully detailed
design was needed in time. Therefore the aspects of planning and managing were
reconsidered.
1.2 Objective
The teaching aspect of the competition can be seen in its objective. The objective stated
by the organization is quoted below:
“For the purpose of this competition, the students are to assume that a manufacturing
firm has engaged them to produce a prototype car for evaluation as a production item.
The intended sales market is the nonprofessional weekend autocross racer. Therefore, the
car must have very high performance in terms of its acceleration, braking, and handling
qualities. The car must be low in cost, easy to maintain, and reliable. In addition, the
car’s marketability is enhanced by other factors such as aesthetics, comfort and use of
common parts. The manufacturing firm is planning to produce four (4) cars per day for a
limited production run and the prototype vehicle should actually cost below $25,000. The
12
challenge to the design team is to design and fabricate a prototype car that best meets
these goals and intents. Each design will be compared and judged with other competing
designs to determine the best overall car.”
1.2.1 Project aim
The aim for this project is to make a design for the formula student chassis and
suspension 2006, considering the desired car handling and the regulations determined the
formula student organization. Furthermore the complete car’s assembly will be made to
ensure that all part will fit.
1.2.2 Project approach
In 2004 Wouter Berkhout designed the first formula student car on the Technische
Universiteit Eindhoven. This car was built partly in 2005 and was then called the
“FSRTE01”, therefore the design of Wouter Berkhout will henceforth be referred to as
the “FSRTE01”. This design is studied intensively; also the recommendations were taken
into account. Some effort has been put into an alternative and completely new chassis
design. But a completely detailed and performable design was preferred and therefore the
FSRTE01 chassis design has been used as a base for the FSRTE02 design.
First the general properties are determined for the FSRTE02 car, the car dimension and
the tires determine the design forces. Then the chassis properties are determined. The
chassis type choice is made by comparing a plate structure with a tubular spaceframe
structure. A suitable and machineable material is chosen. The chassis shape is determined
using FEM analysis to compare on stiffness. The FEM analysis is also used to check the
chassis strength. Then the suspension properties are determined in chapter 4.
Chapter 5 describes the complete chassis design step by step using Unigraphics figures.
The suspension design is treated in chapter 6. First the suspension properties are
translated to a suspension lay-out in Unigraphics. Then several suspension system
concepts are shown. The best concept is worked out and its assemblage is shown step by
step. Finally the complete FSRTE02 assembly in Unigraphics is shown and the chassis
construction process till thus far is described and illustrated using photographs.
This report will be finalized with conclusions and recommendations.
13
2 General FSRTE02 properties
In this chapter the general properties of the FSRTE02 are discussed.
First the engine is chosen and the matching car mass is determined. Then the car’s
dimensions are explained. The tires are chosen and shortly discussed.
Finally the design forces are calculated for different handling situations.
2.1 Engine
The engine is the heaviest part of the car. The maximum permitted cylinder capacity is
600cc, furthermore the engine must have an air intake restrictor of 19 mm.
The resulting engine power and mass play an important role in the overall car design. To
be able to make an approximation of the total car mass two completely different
competitors have been examined;
Figure 2.1: The DUT04 from Delft Uiversity of technology
The first car is an extremely light car, the DUT04 from Delft University of technology.
Delft made a very small chassis with very small wheels (10 inch) almost like a go-kart.
Its total mass is only 125 kg and a Yamaha WR 450F engine of 32kg (oil included) is
used. The Yamaha has approximately 30 kW with an air intake restrictor.
Figure 2.2: The UT03 from the University of Toronto
The second car is the Formula student 2005 event winner, the UT03 from the University
of Toronto. This car has a total mass of 213 kg and uses a Honda CBR-600 engine of 55
kg (oil included). This engine has about 60 kW with an air intake restrictor.
The UT03 is chosen to represent the lightest cars using a 600 cc, four cylinder engine.
14
The DUT04 has about 0.24 kW/kg, while the the UT03 has 0.28 kW/kg.
Therefore the UT03 will be faster on a straight track, but the DUT04 has the advantage
that it will be faster in tight and fast cornering due to its low mass. Each team has its own
view onto this subject.
But both cars do have in common their “car mass : engine mass” ratio of 3.9.
So when saving mass on the engine one is also able to save mass on the rest of the car.
The FSRTE02 design depends on the engine choice, therefore two different engines are
considered, the aprilla SVX5.5 engine and the Suzuki GSX-R600.
2.1.1 The aprilia SXV5.5 engine
The aprilia SXV5.5 engine is an off-road motorcycle engine which is also used for
supermoto. The engine and its stock specifications are shown in figure 2.3.
Cycle
Cylinder line-up
Cylinder
capacity
Transmission
Starter
Carburetion
Cooling
Valve actuation
Max. power
Max. torque
Bore x stroke
Engine weight
Power: weight
Four stroke
2 cyl, 77º V-twin
550 cm3
5-speed sequential
Electric
Injection
Liquid
Single overhead cam,
4 valves/cyl
53 kW @ 11.500 rpm
Unknown
80 x 55 mm
31 kg (oil included)
1.71 kW/kg
Figure 2.3: The aprilia SXV5.5 engine and its specifications
This engine has very high power to weight ratio and would therefore be very suitable
for the formula student racing car. The expected power with an intake restrictor is 41 kW.
Using the SXV5.5 engine it should be possible to design a car of approximately 125 kg
using the “car mass : engine mass” ratio of 3.9. The power to weight ratio will then
become 0.33 kW/kg.
15
2.1.2 The Suzuki GSX-R600 engine
This engine is used on the Suzuki GSX-R600 motorcycle which is a sports motorcycle.
It is the most powerful 600 cc sports bike engine. The engine and its stock specifications
are depicted in figure 2.4.
Cycle
Cylinder line-up
Cylinder
capacity
Transmission
Starter
Carburetion
Cooling
Valve actuation
Max. power
Max. torque
Bore x stroke
Engine weight
Power:weight
Four stroke
4 cyl, inline
600 cm3
6-speed sequential
Electric
Injection
Liquid
DOHC
88.3 kW @ 13000 rpm
69.6 Nm @ 10800 rpm
67 x 42.5 mm
55 kg (oil included)
1.61 kW/kg
Figure 2.4: The Suzuki GSX-R600 engine and its specifications
This engine is expected to have a maximum power of 65 kW with an air intake restrictor.
The aim is to design 215 kg car using the “car mass : engine mass” ratio of 3.9.
The power to weight ratio will then become 0.30 kW/kg.
The main advantage is that the FSRTE already has two of these engines.
Therefore this engine will be used in the FSRTE02.
16
2.2 Car dimensions
The formula student competition has two racing days, on the first day, three events take
place; the acceleration test, the autocross and the skidpad test.
The first test is a straight run over 100 meter.
For the autocross event a tight sprint track must be completed in the quickest possible
time. The maneuverability and handling qualities of the car are tested in this event.
The skidpad test is a very narrow track marked by cones, this test is designed to measure
the cornering ability of the cars around a 15 meter diameter circle on a flat surface.
The average G-force can be calculated from the time it takes to complete the circle.
Ø 15 meter
2x
2x
Figure 2.5: Skidpad track
The second racing day the endurance & fuel economy event takes place. This test is
driven on a go-kart track, with a lot of tight corners. Some corners are even made
narrower by cones. The average speed during this test is about 40 km/h, and top speed
lies below 100 km/h.
Figure 2.6: Endurance and fuel economy event
Earlier research done by Wouter Berkhout on the final results of 2003, proved that a short
wheelbase is very important for the endurance and autocross. A minimum wheelbase of
1525 mm is required by the rules; the FSRTE02 will get a wheelbase of 1550 mm to stay
on the safe side. The front and rear track are important in the slalom parts. Cars having a
smaller rear track than the front track have scored best in 2003.
Therefore the FSTRE02 will front track of 1250 mm and a rear track of 1200 mm.
17
2.3 Tires
Tires play a very big role in the car’s handling. All the forces act on four small contact
patches on the tires. To be able to use the tire information a tire model is needed.
There are different suitable tires for the FSRTE02. Avon provides a lot of tire testing data,
furthermore Avon tires were used on the FSRTE01 (which did not drive) so they are
available. Therefore the Avon 3 ply pro-series tires will be used on the FSRTE02 and the
corresponding data will be analyzed in this paragraph. The front tire size will be 7.0/20.013 and the rear tire size will be 8.2/22.0-13, this is based on the front to rear mass
distribution ratio of 46/54 determined in appendix A.
2.3.1 Slip angle
When cornering the tires will make a slip angle to generate central tire forces.
Figure 2.7. shows a top view of the racecar during steady state cornering. Forces F1-F4
represent the four central tire forces. Angles α1- α4 are the corresponding slip angles. The
central tire force is the tire force component pointing at the actual turning point C1. Force
F5 represents the centrifugal force acting on the center of gravity CG. So when driving
the described path at constant speed there will be force equilibrium with forces F1-F5
pointing at/from point C1. When speed is increased C2 will become the actual turning
point, centrifugal force increases, slip angles and therefore central tire forces increase,
and a new equilibrium arises.
When speed is zero, point C0 will be the actual turning point, slip angles are zero, there
are no central tire forces and no centrifugal force.
α
α
1
F
F
1
2
2
descr
ibed
path
F
5
CG
C2
C1
C0
α
F
3
α
3
F
4
Figure 2.7: Force equilibrium during steady state cornering
18
4
In tire tests not the tire central force is measured but the tire lateral force is measured.
The characteristics for the Avon 7.0/20.0-13 3 ply pro-series front tire are depicted in
figure 2.8. The test is done at a camber angle of 2o and a tire pressure of 20 psi,
measuring slip angles from -7o to 7o with different tire normal forces.
Cornering Force [kN]
5
4
tire normal force 1500 N
tire normal force 2500 N
3
tire normal force 3500 N
2
1
0
-1
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-2
-3
-4
-5
Slip Angle [deg]
Figure 2.8: Avon 7.0/20.0-13 3 ply pro-series, cornering force against slip angle
To explain the difference between tire central force and tire lateral force a zoomed in
picture of one tire is shown in figure 2.9. The tire lateral force is always perpendicular to
the tire, while the tire central force is always pointing to the actual turning point of the car.
The tire lateral force is resolved into tire central and tire drag force.
α
F
F
tire central
teral
tire la
F
tire drag
Figure 2.9: Forces acting on one tire
The drag force is a disadvantage; especially for a formula student car this will cost engine
power. The equations for the Ftire central and the Ftire drag are:
Ftire −central = cos(α ) ⋅ Ftire −lateral
Ftire − drag = sin(α ) ⋅ Ftire −lateral
(equation 2.1)
(equation 2.2)
19
So the drag force needs to be as low as possible. On the other hand a large tire central
force is needed. This can be achieved by a large Ftire lateral at a low slip angle α.
The Ftire lateral is dependent on α as depicted in figure 2.10, the higher the initial slope the
higher the Ftire lateral at a low slip angle.
This is also known as a high cornering stiffness Cα.
2.5
Fn=1500N
2
Cornering Force (KN)
-7
.0
1.5
Cornering stiffness
Cα= 750 N/deg
1
0.5
7.
0
6.
0
5.
0
4.
0
3.
0
2.
0
1.
0
0.
0
-1
.0
-2
.0
-3
.0
-4
.0
-5
.0
-0.5
-6
.0
0
-1
-1.5
-2
-2.5
Slip Angle (deg)
Figure 2.10: Avon 7.0/20.0-13 3 ply pro-series, cornering stiffness at Fn is 1500 N
The cornering stiffness is dependent on the normal force Fn, the higher the normal force,
the higher the cornering stiffness. Therefore the cornering stiffness coefficient Cs is
introduced which is the cornering stiffness Cα divided by the normal force Fn, stated
below in equation 2.3. Cs is a non-dimensional constant tire parameter.
C
Cs = a
(equation 2.3)
Fn
In case of the Avon 7.0/20.0-13 3 ply pro-series front tire the Cα is 750 N/deg at a normal
fore Fn of 1500 N. This means the front tire cornering stiffness coefficient Cs=0.5 /deg.
This is good value for racing tires as it helps to keep the tire drag forces low.
Furthermore a high cornering stiffness coefficient has a positive effect on road-holding,
higher stiffness means a higher natural frequency, so a slalom can be done faster.
20
2.3.2 Friction model
The standard friction model is stated in equation 2.4.
F = µ ⋅ Fn
(equation 2.4)
This friction model can also used for simple tire modeling. The more normal force Fn in
the contact patch the more force between the tire and the ground plane (road surface) can
be transmitted. The friction coefficient µ provides a boundary for the tire performance.
A very often used method is the friction ellipse, this ellipse shows the friction coefficient
µ of the tire in both directions. Figure 2.11 shows the tire and its two main friction
directions.
long
µlat
lateral
longitudional
Figure 2.11: Tire on surface with lateral and longitudinal µ
The friction ellipse shows the µ distribution, with µlong and µlat the friction coefficients in
longitudinal and lateral direction. The µlong/µlat=1 for this kind of racing tires, this means
the friction ellipse is actually a friction circle. This produces realistic values for
acceleration and cornering performances in paragraph 2.4.
Another important tire characteristic is that the friction coefficient decreases as normal
force increases. This is a linear relation. This relation is extracted from the data in figure
2.8 by calculating the friction coefficients, for different normal forces (1500 N, 2500N,
and 3500 N) using equation 2.4. This is done at a slip angle of 7o, larger slip angles are
not interesting because of rapidly increasing drag forces (equation 2.2). The result is
plotted in figure 2.12
2
♦
1.8
µlat Avon measurements
linear approximation µlat = µlong
1.6
friction coefficient µ [-]
1.4
µlong= µlat = 1.74 –1.28e-4*FN-f
1.2
1
0.8
0.6
0.4
0.2
0
0
500
1000
1500
2000
2500
3000
3500
4000
tire norm al force Fn [N]
Figure 2.12: µlat and µlong at a slip angle of 7o for the front tire on dry road
21
The corresponding linear relation for the front tire on a dry road is shown in equation 2.5.
µ long = µ lat = 1.74 − 1.28 ⋅ 10 −4 ⋅ Fn − f
(equation 2.5)
Furthermore, functions are made for the tires on a wet surface using the assumption that
the µ on a wet surface is 0.5 times the µ on a dry surface. Appendix B shows all the
graphs and the corresponding linear relations for the front and rear tires.
The results will be used later on, to calculate the design forces.
2.4 Design forces
In Formula one monocoque design, forces are calculated looking at different handling
situations. An example of this can be seen in figure 2.13.
Figure 2.13: Forces acting on a formula one car taken (copied from “racecar engineering” nov 2003)
In case of the FSRTE02 aerodynamic forces are not taken into account. So the forces that
do act, are braking and accelerating forces, cornering forces and bump forces.
In case of acceleration or braking longitudinal load transfer takes place. When cornering
lateral load transfer takes place. Bump forces occur when a bump is taken. In the
following paragraph the corresponding forces will be calculated.
2.4.1 Bump forces
Formula one bump force can be up to 10 G which means the load on every wheel can
become 10 times the static load on that wheel.
For the FSRTE02 bump forces are assumed to be 2 G or smaller. The main reason is that
the FSRTE02 has no large aerodynamic forces. Furthermore speeds are much lower on
the go-kart circuit, so bumps are taken slower. Table 2.1 hows the maximum bump force
values per wheel.
Bump force [N]
Front wheel
1330
Rear wheel
1560
Table 2.1: Bump Forces
22
2.4.2 Braking and accelerating forces
The car mass will be 215 kg, together with the driver mass of 80 kg this results in a total
mass of 295 kg. Without load transfer, 46% of this mass will be on the front wheels and
54% will be on the rear wheels, this is calculated in appendix A.
During braking or accelerating the front/rear load distribution will change.
While braking, load is transferred to the front axle and when accelerating load is
transferred to the rear axle. In competition one should always brake and accelerate as fast
as possible. This is limited by the tire longitudinal friction coefficient µlong.
When braking, all tires are producing friction forces; this gives a force-equilibrium which
is depicted in figure 2.14.
b
a
CG
rearwheel
hcg
Fcg
Fg
frontwheel
FB-r
FB-f
+
+
With:
FN-r
Fg
Fcg
FN-f,r
FB-f,r
a, b
hcg
FN-f
gravity force
inertia force
normal force front and rear wheels
brake force, front and rear tires
distances rear/front axle to center of gravity
height center of gravity
Figure 2.14: Force equilibrium during maximum braking
To find the brake distribution during maximum braking four equations must be solved;
the equilibrium of moments around CG:
∑ M cg = 0
(equation 2.6)
b ⋅ FN -r + hcg ⋅ (FB-f + FB-r ) − a ⋅ FN -f = 0
And the force the equilibrium in vertical direction:
∑ Fy = 0
(equation 2.7)
FN -f + FN -r − Fg = 0
FB,f and FB,r can be written as functions of FN,f and FN,r using equation 2.4.
FB-f = µ long − f ⋅ FN -f
(equation 2.8)
FB-r = µ long −r ⋅ FN -r
(equation 2.9)
In paragraph 2.3.2 and appendix B, functions were derived for µlong-f and µlong-r on dry and
wet road, these functions are substituted into equations 2.8 and 2.9.
23
Table 2.2 shows the results of solving the system of equations for dry and wet road.
Dry road braking forces [N]
2230
660
900
3240
1250
4490
FN-f
FN-r
FLT-brake
FB-f
FB-r
Fcg
Wet road braking forces [N]
1800
1090
470
1360
990
2350
Table 2.2: Braking forces
The braking load transfer force FLT-brake is the normal force change on the front and rear
wheels compared to the static situation, it will be used to calculate pitch angles.
By dividing the inertia force Fcg through the gravity force Fg the braking G’s can be
calculated. On dry road the FSRTE02 brakes with 1.55 G and on a wet road the
deceleration is 0.81 G.
A similar calculation can be made for maximum acceleration. The main difference is that
the acceleration force is only applied on the rear wheels.
b
a
Fcg CG
rearwheel
+
+
FAcc
+
hcg
Fg
frontwheel
FB-r
FN-f
FN-r
Figure 2.15: Force equilibrium during maximum acceleration
FN-f
FN-r
FLT-acc
Facc
Fcg
Dry road acceleration forces [N]
610
2280
720
3600
3600
Wet road acceleration forces [N]
1020
1870
310
1550
1550
Table 2.3: Acceleration forces
The acceleration on a wet and a dry road are respectively 1.24 G and 0.54 G.
24
2.4.3 Cornering forces
Lateral load transfer takes place when cornering. The force equilibrium on the rear of the
car during cornering at constant speed is depicted below in figure 2.16.
tr
rear wheel left
rear wheel right
CGrear
hcg-r
Fcf-r
Fg-r
Flat-i-r
FN-o-r
FN-i-r
With:
Fg-r
Fcf-r
FN-i,o-r
Flat-i,o-r
tr
hcg-r
Flat-o-r
gravity force rear (54 % of total gravity force)
centrifugal force rear (54 % of total centrifugal force)
normal force inner and outer rear wheels
lateral force inner and outer rear wheels
track width rear
height center of gravity rear (calculated in appendix A)
Figure 2.16: Force equilibrium during maximum cornering
The equilibrium of moments around CG:
∑ M cg-r = 0
1
2
⋅ t r ⋅ FN -i-r + hcg −r ⋅ (Flat -i-r + Flat -o-r ) − 1 2 ⋅ t r ⋅ FN -o-r = 0
The equilibrium in vertical direction:
∑ Fy = 0
FN -i-r + FN -o-r − Fg -r = 0
Flat-i-r and Flat-o-r can be written as functions of FN-i-r and FN-o-r using equation 2.4.
Flat -i-r = µ lat −r ⋅ FN-i-r
Flat -o-r = µ lat −r ⋅ FN -o-r
µlat is a function of the tire normal force and is calculated in paragraph 2.3.2 and
appendix B for both wet and dry road. A similar force equilibrium can be made for the
front wheels. The lateral force equilibrium results, for both rear and front wheels, are
stated in table 2.4.
25
Dry road cornering forces [N]
20
1540
40
2640
2680
130
1200
220
1910
2130
FN-i-r
FN-o-r
Flat-i-r
Flat-o-r
Fcg-r
FN-i-f
FN-o-f
Flat-i-f
Flat-o-f
Fcg-f
Wet road cornering forces [N]
380
1180
370
1050
1420
390
1170
330
760
1090
Table 2.4: Cornering forces
The maximum lateral acceleration is 1.69 G
A low center of gravity is preferred, the reason for that can be now explained.
In figure 2.17 a graph is made in which the Flat-r is plotted as a function of FN-r.
3500
FN-o-r
3000
2000
Decrease of lateral tire force
due to load transfer
1500
FN-average=FN-static
Flat-r [N]
2500
1000
FN-i-r
500
0
0
200
400
600
800
1000
1200
1400
1600
1800
2000
FN-r [N]
Figure 2.17: Flat-r plotted as a function of FN-r
Lines are drawn at the FN-o-r and FN-i-r values for maximum cornering.
The difference between FN-o-r and FN-i-r depends on center of gravity height hcg-r, the
higher hcg-r the larger the difference. The FN-static represents driving straight, this is equal
to the average of FN-o-r and FN-i-r, the FN-average. But the corresponding maximum lateral
forces differ. This indicated difference is the average decrease of lateral force of one tire.
To get the total loss of two tires this value has to be doubled.
The conclusion is, the more load transfer the bigger the loss of lateral force.
26
3 Chassis properties
3.1 Chassis requirements
The chassis must be able to withstand the suspension forces. Therefore strong chassis
points are needed there. The suspension will be adjustable; the most important parameter
is the roll-stiffness. To be sure that the adjustment has the expected effect the chassis
must have sufficient stiffness.
To quantify this requirement an aim is set. The aim is that the chassis deformation
contributes less than 10% to the wheel travel displacement.
Therefore a torsion test is done with a FEM analysis in paragraph 3.4.1.
3.2 Chassis type
In the Formula Student competition two chassis types are used. The classic tubular space
frames and the box structures (monocoque). To compare these two, they will be analyzed
on specific stiffness.
A comparison is made between a square section plate construction and a frame of trusses
(tubular space frame, figure 3.3) on specific stiffness. To make it a fair comparison both
structures have to fit in the volume w*w*l and have to have the same material volume
(identical mass). Furthermore the square section plate construction has a constant wall
thickness and the trusses in the frame have an equal and constant truss section area.
Depicted in figure 3.1 are the limiting volume w*w*l and the three loadcases, tension,
bending (in two directions) and torsion, that will examined.
bending
y x
z
w
l
tension torsion
w
Figure 3.1: Limiting volume
First the most optimal geometry for both constructions within the volume is determined.
Starting with the closed section tube, three possible configurations are drawn in figure 3.2.
w
¼*w
½*w
y
z
Relative
stiffness
under:
tension
bending
torsion
x
1
1
1
1
≈8
≈8
1
≈64
≈64
Figure 3.2: Three possible configurations for the closed section tube
27
The bending and torsion stiffness rises as the outside dimensions of the tube are chosen
larger. So the best geometry in term of stiffness is to maximize the outside dimensions of
the cross-section within the given area w x w.
The best geometry for a tubular space frame within the volume is a traditional framework
depicted in figure 3.3. The angle α is 45o which is very close to the optimal angle for
maximum torsion stiffness.
α
Figure 3.3: Tubular spaceframe
Now both constructions can be compared on specific stiffness having identical material
volume i.e. identical mass. This is done in table 3.1, depicted below.
tubular spaceframe
Stiffness in tension
Comparing both axial
loaded areas will do, in
the tubular spaceframe
the diagonal trusses
stay unloaded.
Bending stiffness
(4 point bending test)
Bending stiffness is
linear with the area
moment of inertia I,
so those are being
compared.
Torsion stiffness
E and G are material
constants the
multiplication factor
of 2.6 is based on the
assumption that υ=0.3
Aload ,t =
4⋅ w⋅t
1+ 2
w3 ⋅ t
It =
(1 + 2 )
plate construction
Aload , p = 4 ⋅ w ⋅ t
2 ⋅ w3 ⋅ t
Ip =
3
w3 ⋅ t ⋅ G
w3 ⋅ t ⋅ E
kt =
kp =
2 ⋅ l ⋅ (2 + 2 )
l
ratio plate
over tube
Aload , p
Aload ,t
Ip
It
≈ 2.4
≈ 1.6
kp
≈ 2.6
kt
This comparison is from TUE lecture note 4007 “design principles”
Table 3.1: Comparison tubular spaceframe and plate construction on specific stiffness
The plate construction has more stiffness in all loadcases, therefore the FSRTE02 will get
a box structure chassis.
28
3.3 Chassis material
The box structure will be made from sandwich panels. These are lightweight, and have a
high stiffness perpendicular to the panel. A simple sandwich panel consists out of three
layers. The outer layers are thin aluminum sheets which are best for in-plane shear,
pressure and tensile forces. The core material is a low density material glued between the
outer sheets.
Different core materials can be used to produce the sandwich panel, appendix C gives an
overview of core materials with densities around 60 kg/m3, together with their main
properties.
Most core types have their own specific application. The PU (polyurethane) is the most
common foam type. The more expensive foam types like PVC-X (Polyvinylchloridecross linked) and PVC-L (Polyvinylchloride-linear) foams have higher strength and
stiffness. The most stiff and strong foam type is PMI (polymethacrylamide) with the
brand name Rohacell and is used for helicopter blades due to its good heat properties.
Furthermore two types of honeycomb structures are examined, aluminium honeycomb
and Nomex paper honeycomb. Both structures have a much higher strength and stiffness
than the foam-cores with the aluminium honeycomb having the highest stiffness.
The ALCAN factory produces sandwich panels called ALUCORE panels. These panels
consist of a 9 mm aluminum honeycomb core and two 0.5 mm thick aluminum skins.
These prefabricated aluminum honeycomb panels will be the building material for the
FSRTE02 chassis thereby limiting the gluing work on the assembly.
3.3.1 ALUCORE honeycomb panel properties
0.5
The properties of the prefabricated honeycomb panels are important for FEM analysis of
the chassis. The equivalent thickness is calculated in case of bending load, considering
only the aluminium cover sheets . In figure 3.4 two plates are depicted, the left plate is
the honeycomb panel and the right plate is a solid panel of 6.5 mm thickness. Both have
an equal second moment of area while the honeycomb panel weighs 3.3 kg/m2 and the
solid plate weighs 17.6 kg/m2.
neutral axis
0.5
6.5
9.0
aluminum
cover sheets
I1
I2
Figure 3.4: Honeycomb panel compared to a solid plate for out of plane bending load
29
3.3.2 ALUCORE honeycomb panel cutting
Due to the chassis layout the different honeycomb panels will get complex shapes.
Using a laser- or water cutting machine complex shaped sheets can be produced
accurately and fast.
Laser cutting is a faster technique but can not be used for cutting the ALUCORE
honeycomb panels because of reflection of the laser beam. However laser cutting will be
used to cut the solid plate layouts.
Water cutting offers a good alternative for cutting the ALUCORE. Figure 3.5 shows the
water cutting machine and a test piece that has made.
Figure 3.5: Water cutting
3.3.3 ALUCORE honeycomb panel bending
According to the ALCAN company it should be possible to bend the panels on a press
brake shown in figure 3.6.
Figure 3.6: SAFAN hydraulic press brake with ALCAN bending instructions
30
Bending tests have been done with different moulds and protection sheets. Figure 3.7
shows the best press brake setup and its result.
Figure 3.7: Bending on the SAFAN press brake and measuring the outer skin radius
The results of this test were satisfying, the outer skin radius corresponds perfect to the
values given by ALCAN and the bend looks smooth from the outside. Having done these
tests ensures the use of bending for the FSRTE02 chassis.
Three zones are distinguished in the bent corner, these are depicted in figure 3.8.
F
I
I
II
II
III
Figure 3.8: Bent corner with different deformation zones and the applied FEM loadcase
In zone I the honeycomb structure is undeformed. In zone II the honeycomb offers no
strength and stiffness to the construction anymore, all honeycomb walls are buckled.
Zone III has been deformed so extreme it adds strength and stiffness again. The bending
stiffness is linear with the cubic height. The height of zone III is 20% of the original
height. This means the bending stiffness of zone III is assumed to be approximately 1%
of the zone I stiffness. Figure 3.8 shows the load case used for the FEM analysis.
31
Four different options for finishing the bent corner are compared on strength and stiffness
using a FEM analysis. The strength is determined by looking at the maximum Von Mises
stress. The stiffness is compared by looking at the displacement at the point where the
force F is applied. All values are indexed to the values of option A in figure 3.9a.
Figure 3.9a shows the bent corner without any finish. In figure 3.9b the inner skin is
brought back by gluing in a sharp edged corner profile. Figure 3.9c shows the same
principle as 3.9b only the bend radius of the corner profile is enlarged.
The last option is shown in figure 3.9d, now the remaining gap is filled with glue.
To reduce weight micro balloons can be added to the glue.
A
Maximum Von Mises Stress: 142.3 Mpa
Stiffness bent corner: 30 Nm/rad
B
Maximum Von Mises Stress: 25.66 Mpa
Stiffness bent corner: 389 Nm/rad
C
D
Maximum Von Mises Stress: 10.28 Mpa
Stiffness bent corner: 1810 Nm/rad
Maximum Von Mises Stress: 11.26 Mpa
Stiffness bent corner: 740 Nm/rad
Figure 3.9 a, b, c, d : Four bend finish options and their FEM results
Option C shows the best results, it has the highest stiffness (60 x stiffness option A).
Furthermore, option C has the highest strength due to the equal stress distribution.
If one compares option D with option C it turns out that filling the remaining gap with
glue, only weakens the bent corner and adds more mass.
The bent corner finishing will be done by gluing in a corner profile with an inner radius
of 8 mm.
32
3.3.4 ALUCORE honeycomb panel gluing
The honeycomb panels will be glued using Araldite 2015, a two component epoxy paste
adhesive. The maximum shear strength is 16.5 N/mm2 (tested by Viba) for aluminium–
aluminium joints.
This test has been carried out by gluing two 25 mm strips together with an overlap of
12.5 mm creating a gluing spot of 25x12.5 mm
To convince the Formula Student jury of the strength of gluing, a special test can be done.
Two 5052-aluminium tensile test strips are made. These strips are glued on two large
aluminium blocks. This is depicted in figure 3.10.
Gluing spots
12.5 x 12.5 mm
Tensile test strips
expected to break
at 1700 N
Figure 3.10: Gluing test to convince the jury
Using the a gluing spot of 12.5 x 12.5 = 156 mm2 a tensile force of 156 x 16.5 ≈ 2500 N
can be generated causing the aluminium tensile test strips to break (F=>1700).
33
3.4 Chassis shape
The most important aspects of the chassis shape are chassis stiffness and strength,
ergonomics and crash safety, always carefully taking into account the mass.
The ergonomics determine the shape and the size of the driver compartment together with
the side-impact which is set by the rules.
The front impact can be added later to the design.
A FEM analysis is done to examine stiffness and strength.
Three different chassis analyzed with FEM and compared on torsion stiffness.
- The FSRTE01 chassis designed by Wouter Berkhout.
- The second chassis is a low and wide edged chassis, and will therefore be called TUB
chassis. This chassis could be suitable for the Aprilia engine (see paragraph 2.1.1)
- The FSRTE02 chassis, based on the FSRTE01 but optimized on stiffness
3.4.1 Chassis torsion stiffness
Torsion stiffness is the most important stiffness. If the chassis torsion stiffness and
suspension stiffness would be of the same order, suspension stiffness would be less useful.
Tuning of the suspension is then difficult and ineffective, one should not be guessing on
adjustments. Therefore chassis torsion stiffness should be high compared to suspension
stiffness.
The average axle force is approximately 1500 N. The torsion test is done by applying a
moment of 1500*1.25= 1875 N on the chassis. The corresponding load case is depicted
in figure 3.11. The rear tire road contact points are constrained in x, y and z direction and
x and z direction respectively. On the front tire road contact point patches two forces of
1500 N each are applied in z and –z direction. This load case corresponds with a 2 G
bump taken by a single front wheel so the resulting stresses are also representing a
realistic bump situation.
Translations
in x and z
constrained
Translations
in x, y and z
constrained
1500 N
1500 N
1.25 m
The FEM results are depicted in figure 3.12 a, b and c.
Figure 3.11: FEM torsion test loadcase
34
Torsion
stiffness
100 %
190 kNm/rad 100 %
Maximum Von
2
41.6 N/mm
Mises stress
FSRTE01
Torsion
stiffness
260 kNm/rad
Maximum Von
2
25.6 N/mm
Mises stress
TUB
137 %
62 %
Torsion
stiffness
575 kNm/rad
Maximum Von
2
16.4 N/mm
Mises stress
303 %
40 %
FSRTE02
A
B
C
Figure 3.12: Torsion stiffness of three different chassis
35
The FSRTE02 chassis has been optimized for torsion stiffness.
The main changes that have resulted in a 3 times higher torsion stiffness compared to the
FSRTE01 chassis, are stated below.
A rear cover around the engine has been added. It is expected to add about 1.5 kg
of weight but it offers much more torsion stiffness.
The FSRTE01 has torsion tubes to reduce the loss of stiffness due to the hole in
which the driver is seated. The cross section of these torsion tubes is enlarged
without limiting the driver’s freedom of movement.
Furthermore the torsion tubes where made longer, so the forces in the tubes are
spread better into the rest of the car. Now they extend from the engine cylinder
head, through the seat panel around the dashboard to the front suspension unit.
The aim is that the chassis deformation contributes less than 10% to the wheel travel
displacement. Therefore the chassis torsion stiffness is compared to the suspension roll
stiffness. It turns out that the roll stiffness is 3.8% of the chassis torsion stiffness.
3.4.2 Chassis strength
The chassis strength has only been examined for the FSRTE02 chassis.
Therefore different loadcases have been applied, for maximum acceleration, maximum
braking and maximum cornering situations using the forces calculated in paragraph 2.4.
The graphical results are depicted in appendix D, the maximum occurring Von Mises
stresses are stated in table 3.2.
Load case
Maximum occurring
Von Mises stress
Maximum acceleration
3.5 N/mm2
Maximum braking
9.3 N/mm2
Maximum cornering
26.3 N/mm2
Table 3.2: Maximum occurring Von Mises stress on different load cases
All stresses stay well below the yield stress of aluminium 3003 of 140 N/mm2 so the
FSRTE02 chassis has sufficient strength.
36
4 Suspension properties
All passenger cars are equipped with a suspension system to cope with bumps in the road.
The larger the bumps the larger the wheel travel.
A go-kart does not have a suspension system but its chassis only consists of an almost flat
tubular frame which can deform to keep all four wheels on the road surface.
The racetrack is partly a go-kart circuit and partly an airport runway, which means there
are no large bumps to expect. Therefore a car without a suspension system might be an
option; nevertheless the Formula Student rules require a fully operational suspension
system. Spring and shock absorbers must be added front and rear with a usable wheel
travel of 51 mm.
The FSRTE02 is constructed with a suspension system. Comfort is not an issue; the
longest event takes 20 minutes. Bumps will be small so the minimum required wheel
travel of 51 mm will be used. Furthermore the rules require the wheel travel to be divided
into 25.4 mm jounce and 25.4 mm rebound with a ground clearance of 50 mm to prevent
the car from hitting the ground. A double wishbone suspension system is to be used with
pushrods to transmit the spring and shock absorber forces to the uprights.
A double wishbone system has the most adjustment possibilities and can be constructed
with a low mass.
When cornering the lower triangle is always loaded more than the upper triangle.
The use of pushrods decreases the forces on the lower suspension triangle, therefore
pushrods are preferred. Furthermore an adjustable anti-roll system is added to control the
cars roll angle and to be able to set the under- and over steering properties.
4.1 Suspension stiffness and damping
Normal passenger cars have a natural bump frequency around 0.8-1.4 HZ, while racecars
have frequencies up to 5-6 Hz. Such high stiffness is needed to have a stable ground
clearance for the aerodynamics. The aerodynamic force pushing the car on the road can
be considered as an increase of weight.
The main aim of the stiffness is to keep wheel normal force variations as small as
possible to reach maximum tire grip.
The suspension stiffness of the FSRTE02 will have a natural frequency of 2.5 Hz.
Equation 4.1 can be used to calculate the wheel rates front and rear.
C wheel
ω bump =
(equation 4.1)
m
With Cwheel the suspension stiffness or wheel rate of a single wheel, m the mass resting on
this wheel and ωwheel the natural frequency in rad/sec.
The wheel rates front and rear are 16800 N/m and 19600 N/m respectively.
The wheel damping is determined by setting the non-dimension damping ratio ξ to 0.5
which is a commonly used value. To calculate the damping value equation 4.2 can be
used.
d wheel = 2 ⋅ ξ ⋅ ϖ bump ⋅ m
(equation 4.2)
The wheel damping for each front and rear wheel are 1070 Ns/m and 1250 Ns/m.
37
4.2 Lateral suspension properties
4.2.1 Roll center height
The most important parameter in the lateral suspension design is the roll center.
If lateral force is applied at the roll center the chassis will not roll.
The graphical determination of the roll center is shown in figure 4.1.
CG
h2
o1
o2
RC
P2
h1
P1
Figure 4.1: Graphical roll center determination
First the wishbone lines are extended creating intersection points O1 and O2. Then lines
are drawn from these intersection points to the contact patch points P1 and P2. The
intersection of these two lines represents the roll center. The roll center can drift during
roll due to the movement of the wishbones. A roll moment can be formulated:
M roll = h2 ⋅ Fcg
(equation 4.3)
The roll moment in combination with the roll stiffness causes the chassis to roll.
Passenger car body roll is typically around 5o while race car chassis roll is 2o or less.
In Formula one body roll is minimized for aerodynamics. A large roll angle also affects
camber angles. Some roll is needed however to get a natural cornering feeling.
Therefore the FSRTE02 chassis roll will be 2o.
Constructing a roll center above the center of gravity CG will create a negative h2 and a
negative roll moment causing the chassis to roll into the curve like a motorcycle.
If the roll center is placed on the center of gravity CG the roll moment during cornering
will be zero. And no roll stiffness has to be added to suppress the chassis roll.
Creating a roll center below the center of gravity CG will create a positive h2 and a
positive roll moment causing the chassis to roll out of the curve, which is a natural
movement when driving the car. 2o Of chassis roll can be achieved using a small roll
moment with little roll stiffness or using a large roll moment with a large roll stiffness.
But what will happen when the roll center is placed below the road surface? Therefore
two lateral force equilibriums for static curving are drawn in figure 4.2.a and 4.2.b. In the
first situation the roll center lies above the road surface and in the second situation the
roll center lies below the road surface which means h1 is negative. The used forces are,
the lateral tire forces Flat, the tire normal forces FN and the so called load transfer force
FLT.
38
t
a)
CG
h2
+
+ + FLT
Flat-1
h1
t
b)
Fcf
Fg
RC
FLT
Flat-2
FN
+
+ + FLT
CG
h2
Flat-1
FN
FN
Figure 4.2 a: Force equilibrium RC above road
Fcf
Fg
FLT
-h1
Flat-2
FN
RC
b: Force equilibrium RC below road
The equilibrium of moments around RC:
FLT ⋅ 1 2 ⋅ t + FLT ⋅ 1 2 ⋅ t + FN ⋅ 1 2 ⋅ t − FN ⋅ 1 2 ⋅ t − ( Flat −1 + Flat −2 ) ⋅ h1 − Fcf ⋅ h2 = 0
Substituting Flat-1+Flat-2 by Flat result in equation 4.4:
FLT =
Flat ⋅ h1 Fcf ⋅ h2
+
t
t
(equation 4.4)
This function can be split in two parts, the so called geometric load transfer and the
elastic load transfer
FLT − geo =
Fcf ⋅ h2
Flat ⋅ h1
and FLT − elastic =
t
t
If a fast steering input (step) is given on t0 the front tires will make a drift angle and
lateral tire forces Flat-1 and Flat-2 build up immediately.
Initially the car will not make a curve, but Flat-1 and Flat-2 will be led through the A-arms
to the roll center where they act on the chassis. Due to the tire elasticity it takes till t1
before the car will be driving the curve statically and the centrifugal force Fcf has reached
its maximum. This can be seen in the force time graphs of figure 4.3.a and 4.3.b. These
graphs also show the FLT-geo, FLT-elastic and FLT as a function of time. When the roll center
lies below the road surface the load transfer will become negative first due to the FLT-geo
growing fast. This has a negative effect in fast steering situations like slaloming.
b)
a)
t0
Flat
Fcf
FLT-geo
FLT/elastic
FLT
force
force
Flat
Fcf
FLT-geo
FLT/elastic
FLT
time
t1
Figure 4.3 a: Time force graphs with RC above road
t0
t1
time
b: Time force graphs with RC below road
39
So the roll center has to be between the center of gravity and the road surface. Placing the
roll center close to the road surface enlarges the roll moment and more roll stiffness is
needed. Adding more roll stiffness will create a less independent suspension. An extreme
situation occurs when roll stiffness is set to infinity. If one wheel is lifted then, the
opposite wheel will travel the same distance too and unsprung mass is doubled.
So a high roll center is preferred to keep the suspension independent.
On the other hand there is the so called jacking effect. The jacking effect will cause the
chassis center of gravity to rise in a corner. This is unwanted because the load transfer
force FLT will enlarge and the maximum Flat will decrease.
The FSRTE02 suspension will have its roll center placed as low as possible, to prevent
the jacking effect. Furthermore the roll moments rear and front will be chosen equal to
minimize torque in the chassis.
The front roll center height is chosen h1-f = 10 mm above the road, h2-f then becomes
316-10 = 306 mm, using the front center of gravity height hcg-f from appendix A. The
front lateral centrifugal force during maximum cornering Fcg-f=2130 N (calculated in
paragraph 2.4.3). The front roll moment is 650 Nm during maximum lateral acceleration
(calculated using equation 4.3)
Using Mroll-f=Mroll-r the corresponding rear roll center height is determined; h1-r=97 mm.
4.2.2 Roll stiffness and damping
The roll angle front and rear consists of two parts;
The first part is the roll angle due to the tire stiffness. In appendix E the radial tire
stiffness front and rear are extracted from the Avon tire data at a tire pressure of 20 psi.
The front and rear stiffness’s are 200 N/mm and 210 N/mm respectively.
Combining this stiffness with the lateral load transfer force the tire compression can be
calculated. This results in a chassis roll of 0.3o front and 0.3o rear due to radial tire
compression.
The second part is caused by roll moment around the roll center. The maximum permitted
chassis roll angle is 2o. So 2o-0.3o=1.7o of roll is permitted on roll stiffness front and rear.
With the Mroll-f=Mroll-r= 650 Nm the required roll stiffness front and rear becomes:
650
Croll,f,r= o
= 22000 Nm/rad
1.7 ⋅ (π 180 )
So the total roll stiffness becomes Croll,f + Croll,r = Croll = 44000 Nm/rad
The roll damping is determined by setting the non-dimension damping ratio ξ to 0.5.
Unigraphics is used to calculate Jroll=9 kgm2. Equation 4.4 is used to calculate the roll
damping coefficient
d roll = 2 ⋅ ξ ⋅ C roll ⋅ J roll = 630 Nms/rad
This is the roll damping for the whole car. The roll damping is delivered by two dampers
one on the front and one on the rear. Therefore droll,f= droll,r= 630/2 = 315 Nms/rad.
40
4.2.3 Camber
Camber is defined as the angle between the tire and the road in rear view.
Figure 4.4 shows three situations for the outer wheel; in the left situation the wheel is not
cambered in other words the camber angle is zero. The middle situation shows a negative
camber angle. The right wheel is cambered positive.
_
0
+
Figure 4.4: Three different outer wheel camber situations in a left corner
The last situation is preferred, a positive cambered wheel can generate a higher friction
coefficient during cornering. Avon provides lateral tire force data for different camber
angles. Table 4.1 shows the lateral front tire force at a slip angle of -7o at camber angles
of 1o, 1.50 and 2o. It can be seen that the lateral front tire force rises as the camber angle
rises.
Camber angle
Avon 7.0/20.0-13 front tire
1
1.5
2
Lateral tire force [N]
At a slip angle of -7o
4460
4490
4520
Table 4.1: Camber angle and lateral tire force
Large camber angles are not useful. Because the contact patch starts to become smaller.
Avon tires were tested with camber angles of 1o, 1.50 and 2o, so that area is of interest.
Therefore the camber angle in cornering for the FSRTE02 is set on 2o.
41
Figure 4.5 shows a suspension geometry with parallel A-arms. When cornering at
maximum lateral acceleration resulting in 2o of body roll, the wheels will camber -2o too.
2°
2°
Figure 4.5: Parallel A-arm, body roll causes negative camber on both wheels
This is unwanted; it can partly be solved by using the wheel travel to create positive
camber in cornering. Figure 4.6 shows such a geometry; the right wheel pivots about the
imaginary pivoting point O1 causing this wheel to camber positive in a left curve.
The y-coordinate of point O1 determines the camber change rate, the closer point O1 lies
to the right wheel the more camber change will take place when the wheel travels
upwards. This is limited by line AB, placing point O1 between this line and the right
wheel will result in impracticable wishbone geometry.
right wheel
left wheel
B
D
O1
A
O2
C
rc
Z
Y
1225 mm (average track width rear and front)
Figure 4.6: Suspension lay-out with camber change rate
The largest possible camber change rate is reached with points O1 and O2 on lines AB
and CD. It will be arctan(1/1225)=0.0468 deg/mm
The suspension roll angle of 1.7o causes a wheel travel of tan(1.7)*1225=36 mm. This
means the inner wheel travels in 36/2=18 mm and the outer wheel travels out
36/2=18mm.
The positive camber change will be 18*0.0468=0.85o
This means that the wheels will camber -2o+0.85o= -1.15o during maximum lateral
acceleration.
By giving the wheel a static camber angle of 3.15o when driving straight, the camber
angle during maximum cornering becomes 3.15-1.15=2o.
42
2°
4.3 Longitudinal suspension design
The longitudinal suspension design affects the cars behavior during accelerating and
braking. Pitch angles occur when accelerating or braking. In figure 4.7 the different
causes of pitching are shown.
rise
lift
squat
dive
Figure 4.7: Pitching causes
The white arrows show the effects during acceleration; these are called lift and squat.
The black arrows indicate the effects of braking; these are called dive and rise.
These effects extend the time needed to reach a static accelerating or braking situation.
It takes longer to reach the equilibriums from figure 2.14 and 2.15.
Squat, dive and rise can be limited by applying anti-squat, anti- dive and anti-rise
respectively on the suspension design.
4.3.1 Acceleration; squat effect
To compensate for the squatting effect the traction forces are used.
Figure 4.8 shows the double wishbone suspension in side view, the rear suspension has a
pole C which can be considered as an imaginary pivoting point.
Figure 4.8 also shows the forces during accelerating.
The acceleration force is generated by the driveshaft torque. This means that acceleration
force is effectively applied on the car at hub height. The FN-f and FN-r have been split up
into the static part, FN-f-stat and FN-r-stat, and the load transfer part FLT-acc.
B
C
FLT-acc
A
Facc
Fcg
D
Fg
FLT-acc
FN-r-stat
FN-f-stat
Figure 4.8: Anti-squat geometry
43
If the pole of the rear suspension is placed on line A-B in figure 4.8, the combined force
of Facc and FLT-acc, points to point B which means no moment around B will be generated.
In other words the car will not squat, this is called 100% anti-squat.
Practically only 50 % anti-squat is applied due to the chassis shape, which means half of
the load transfer force FLT is compensated and the other half still causes the rear spring to
compress. This means distance CD is 50% of the distance BD as shown in figure 4.8.
Note: no anti-lift can be applied because there is no traction force on the front wheels to
compensate for the decreased normal force FN-f.
Finally the pitch effects can be calculated. In paragraph 2.4.2 FLT-acc for wet and dry
roads are determined. Combining these forces with the suspension stiffness front and rear,
the spring compression can be calculated. The results are in table 4.2
Dry road
Wet road
Wheel travel front [mm]
-21
-9
Wheel travel rear [mm]
+9
+4
Pitch angle [deg]
-1.1
-0.5
Table 4.2: Wheel travel and pitch angle during maximum acceleration.
44
4.3.2 Braking; dive and rise effect
Both the diving and rising can be decreased by applying an anti-dive and anti-rise
geometry. The force equilibrium during braking is drawn in figure 4.9
FB-r
F
100%
antidive
G
50% anti-d
ive
A
D
se
C 16 % anti-ri -rise
B
0
10
%
ti
an
FLT-brake
Fcg
Fg
FLT-brake
FN-r-stat
FN-f-stat
Figure 4.9: Anti-rise and ainti-dive geometry
Due to the use of inboard brakes on the rear of the car the rear braking force FB-r is
effectively applied at hub height. The load transfer FLT-brake has been moved along its line
of action to the rear hub center. Now line AB can be drawn, this is the so called 100%
anti-rise line. If the pole of the rear suspension would be on this line the rear braking
force exactly compensates rising of the car.
However the angles of the rear upper and lower A-arms in side view are already
determined in paragraph 4.3.1 by setting an anti-squat percentage of 50 percent. This
corresponds with line AC in figure 4.9 and 16% anti-rise. In other words the distance DC
is 16% of the distance DB. And 84% of the load transfer force FLT-brake is led through the
pushrod to the spring.
The front suspension side view is to be determined yet. The line EF shows the 100%
anti-dive line. The anti-dive percentage will be set 50 %, when using higher anti-dive
values, the front wheels tend to attack road irregularities. This means distance HG is 50%
of distance HF and 50% of the load transfer force FLT-brake is led through the pushrod to
the spring. Table 4.3 shows the wheel travel and pitch angle front and rear during
maximum braking.
Dry road
Wet road
Wheel travel front [mm]
+13
+7
Wheel travel rear [mm]
-17
-9
Pitch angle [deg]
+1.1
+0.6
Table 4.3: Wheel travel and pitch angle during maximum braking
45
4.4 Steering properties
Steering properties have large influence on the car’s road holding. Different properties
are considered: Ackermann, kingpin inclination, scrub radius, caster and bumpsteer.
4.4.1 Steering geometry
When using a “full Ackermann” steering geometry the steering arms are pointing inwards
when using a rearward placed rack. When making a curve the front axles intersection
point always lies on the rear axle. This intersection point corresponds with the actual
turning point when speed is zero. In this way no tire scrub occurs because all tires are
centered on the same point rolling on different radii. “Full Ackermann” is used on the
traditional London taxi, and the “Lunar Rover” which drove on the moon.
When centrifugal forces increase slip angles are needed to build up the necessary lateral
tire forces and the actual turning point moves forward. With “full Ackermann” steering
the slip angle of the inner wheel will always be larger than the outer wheel slip angle.
This is unwanted, the slip angles should be equal in case of zero load transfer to have the
highest total lateral force. In reality load transfer will take place and the outer wheel
normal force will be much higher than the inner wheel normal force causing a loss of
friction coefficient.
To counterbalance for this loss the slip angle on the outer wheel has to be larger than the
inner wheel slip angle. This can be reached by choosing a “negative Ackermann” steering
geometry.
Often a “parallel” steering system is used which means that the steering angles left and
right are always equal.
So at low speeds and sharp cornering an Ackermann geometry could be used to prevent
tire scrub which causes tire wear and rolling resistance.
At higher speeds and fast cornering on the tire’s performance limits, a “parallel” or
“negative Ackermann” steering geometry is needed.
The exact geometry is not calculated, the upright will be constructed with adjustable
linkage geometry. It can be adjusted from a “parallel” geometry with the steering arm
pointing rearwards to a “full Ackermann” steering system.
46
4.4.2 Kingpin inclination and scrub radius
The kingpin is constructed by connecting the upper and lower upright pivoting points.
Extending this line to the ground shows the scrub radius. The scrub radius causes steering
moment when riding a bump. When the kingpin is leaning inward in the frontview this is
called kingpin inclination or KPI. This can be used to change the scrub radius.
Figure 4.7 shows a schematic section of the front tire, the chosen rim has an offset of 21
mm from the rim midline, then the brake disk is placed with an inward offset of 9 mm.
The clearance between the rim’s inside and the brake disk is needed to mount the braking
caliper. The lower pivoting point is placed as close as possible to the brake disk (38 mm
from midline). If the upper pivoting point is placed straight above the lower pivoting
point the scrub radius would be 38 mm. KPI angle also introduces undesirable camber
changes. Some KPI is applied which has reduced the scrub radius to 24 mm.
The king pin inclination angle is arctan(23/240)=5.5o.
brake disk
upright
21
240
9
38
23
24 (scrub radius)
Figure 4.10: Front wheel in front view with king pin inclination and scrub radius
47
4.4.3 Caster and trail
Caster angle is defined as the angle of the king pin in side view. It influences mechanical
trail. Mechanical trail is used to create steering stability (just like a shopping trolley
wheel). Mechanical trail also causes steering moment. The tire lateral force is applied at
the tire contact patch, the mechanical trail functions as an arm rotating about the king pin
creating a moment on the king pin. This moment is felt by the driver through the steering
system. Besides the mechanical trail there is pneumatic trail, this trail is caused by the
tires. It reduces as the slip angle grows this is the feeling that one gets if the front tires
start sliding. The pneumatic trail can even become negative. To make the steering system
self centering, the mechanical trail has to be in the order of the pneumatic trail.
Furthermore caster can be used to counterbalance the camber changes due to the king pin
inclination angle.
The FSRTE02 front wheel side view is depicted in figure 4.8. The pneumatic trail lies in
the order of 35 mm, therefore the mechanical trail has been chosen 35 mm too.
The king pin intersects the front wheel axis. The caster angle is arctan(32/240)=7.6o.
V
240
32
35 (trail)
Figure 4.11: Front wheel in side view with caster angle and trail
48
4.4.4. Bump steer
Both the front and rear suspension have a tie rods which can be used to adjust toe in and
out. The front tie rods a coupled via the steering rack which enables us to steer the front
wheels. These tie rods can cause the wheels to make a steering angle when riding a bump.
This is referred to as bump steer.
By choosing the correct coordinate for tie rod connection point bump steer can be
prevented. This coordinate can be determined geometrically; this is done in figure 4.12.
F
D
α
-arm
upper A
G
α
C
lower A-arm
A
E
B
Figure 4.12: Graphical determination of anti-bump steer geometry
First points A and B are determined by extending the suspension lines. Then a line is
drawn from the steering arm connection point E to point C. Now a line from point B
through point E is drawn. The angle α in figure 4.12 between the lower A-arm and line
AC is used to determine point F, by drawing line CF. Then line AF is drawn which
intersects line CE in point G. If the steering rack-steering rod connection point is placed
in point G no bump steer occurs.
49
This is verified by using Matlab Simmechanics, which simulates the 3D model. The
result is plotted in figure 4.13.
Area of interest, + and – 25.5
mm variation on ride height
Figure 4.13: Toe characteristics of front and rear wheels
Although the anti bump steer geometry is applied some bump steer will still occur. This
is because the imaginary pivoting points (C, D and F) do not stay constant over the wheel
travel. But within this wheel travel of 51 mm in total, the toe in and out angles stay within
an acceptable range.
50
5 Chassis design
5.1 Main structure
The FSRTE02 chassis shape is tested with a FEM analysis. In that stage the materials and
the material thicknesses were already determined. Thereupon all the parts were designed
in detail using Unigraphics. In this paragraph the parts are shown and explained step by
step.
5.1.1 ALUCORE side panels
First the ALUCORE sidepanels were designed. The main thought has been to maximize
bent edges length thereby minimizing the glued edges. Unfortunately it was not possible
to fold the whole chassis from a single ALUCORE panel because the standard panel size
was not large enough. Therefore two chassis halfs are designed. They are joint using two
strips of aluminium to glue both (nearly) symmetrical parts together. Unigraphics sheet
metal has been used to create the layout of the ALUCORE panels.
This is depicted in figure 5.1a, b and c.
a
b
c
glue
Figure 5.1 a: Layout ALUCORE panels b: Joining both symmetrical half’s c: Gluing both half’s
51
5.1.2 ALUCORE front and seat panel
The front and seat panel also ALUCORE panels. Figure 5.2a shows the placement of
these panels. Figure 5.2b shows the detailed attachment cross sections in points 1, 2 and 3
from figure 5.2a.
a)
1
2
3
b 1)
b 2)
b 3)
seatpanel
sidepanel
bottompanel
sidepanel
seatpanel
Figure 5.2 a: Placement of front and seatpanel
frontpanel
b: Attachment details
Detail b3 shows the joint of the double layer ALUCORE frontpanel and the sidepanel.
The honeycomb structure will be locally removed on the edges and a milled rectangular
section tube will be glued in. Blind rivets are used every 100-150 mm to localize and
clamp the parts together for gluing. According to the glue manufacturer VIBA, the
optimal glue layer thickness is 0.05-0.1 mm. Depending on surface levelness and
roughness glue layers can be made as 0.01 mm.
52
5.1.3 Rearframe
The rearframe consists out of I-section profiles and will be milled out of a 25 mm thick
aluminium plate. The monolithic rearframe will have a mass of 1.87 kg.
The rearframe will be used to attach the rearward connection rods to the chassis. In
topview the connection rods meet the rearframe at different angles. The angles are
calculated using Unigraphics and assimilated in the rearframe by milling six flat faces.
The faces reach through slots in the sidepanels. These faces will later be used to bolt on
mounting points for the connection rods. In this way a universal mounting point type can
be used on all suspension connection points. The rules require a jacking point at the rear.
Therefore a round tube is bolted onto the two milled blocks reaching through slots in the
bottompanel. Figure 5.3 shows the rearframe and its placement in the chassis.
holes for M8
Allen bolts,
Rollhoop
bracing
A
flat faces for
connection rod
mounting points
with tapped M6
holes
countersunk
holes for M8
Allen bolts
milled blocks for jacking
point attachment
Figure 5.3: The rearframe and its placement in the chassis
The holes for the rollhoop bracing and the engine mounting plates are drilled. Figure 5.4
shows the attachment of the rearframe to the sidepanel and bottompanel in detail.
A milled rectangular tube is glued into the ALUCORE panel edges first. Then the
rearframe is glued and blind riveted into the chassis.
53
glued in
rectangular tube
sidepanel
Figure 5.4: Rearframe attachment
5.1.4 Suspension support beams
On eight places the suspension connection rods are mounted on an insert in the sidepanel.
To withstand the connection rod forces, support beams are placed on the inside of the
sidepanels. These are drawn in figure 5.5.
1
2
5
3
4
suspension support
beams
Figure 5.5: Suspension support beam placement with detailed attachment view
In the upper right of figure 5.5 an exploded view is drawn from the supportbeam
connection rod attachment. Part 1 is an aluminium bush with inner M8 thread, which is
welded into the standard 40x20x2 aluminium tube (part 2). Then an aluminium ring (part
3) is glued on tube (part 2). The tube with parts 1 and 3 is placed on the inside of the
chassis and the insert (part 4) is put through a corresponding hole in the sidepanel and
centered on part 1. Finally all is glued and secured by an Allen bolt. The insert is first
machined by lathe. Due to the axi-symmetrical shape after turning, it is easy to clamp it
54
onto the milling machine and mill on a flat face with the right angle. This face is used
later on for the attachment of the connection rod mounting points.
5.1.5 Torsion tubes
The torsion tubes are designed to have a maximum cross section area. Therefore a
traverse cross section is made at the driver’s elbows. This is depicted in appendix F.
The torsion tubes are made out of 5052 aluminium alloy plate of 1 mm thickness.
Figure 5.6 shows the layout and placement of the torsion tubes.
seam
seam
Figure 5.6: Torsion tube layout, placement and sub-parts
55
The torsion tube also has two flaps attached; these will be used for the mounting of the
front and rear cover plates. The flaps are made out of two layers of 1mm thick aluminum
plate. This is glued into the torsion tube seams this is depicted in figure 5.7a. Then the
torsion tube is glued onto the sidepanel. Figure 5.7b shows the cross-section of the
torsion tube attached to the sidepanel.
A
B
seam
rivnut m5
sidepanel
Figure 5.7 a: Glued in flaps
torsion tube
b: Sidepanel - torsion tube attachment
5.1.7 Front and rear roll hoop
The front and rear roll hoops have to extend from the lowest frame member on one side
of the chassis, up over and down to the lowest frame member on the other side of the
chassis. The top-most surface of the front hoop must extend above the top of the steering
wheel. Furthermore the roll hoops must be made out of 25x2.5mm round steel tube.
The roll hoops are placed outside the chassis. This makes it easy to attach and detach
them and it will also be used to mount the front wheel connection rods to the chassis.
Figure 5.8 shows the chassis with the roll hoops.
traverse beam
rear hoop braces
plane A
plane B
plane C
Figure 5.8: Front and rear roll hoop placement and rear hoop bracing
56
The roll hoop connection details are shown in the cross sections through plane a, b and c
in figure 5.9.a, b and c.
a)
M10 Allen bolt
rearframe
welded on endplate
M10 Nut
roll hoop brace
b)
rear roll hoop
aluminium
traverse beam
M8 Allen bolt
cylinder with
thread
welded in
steel bush
welded in
aluminium block
c)
M8
roll hoop
insert part 1
insert part 2
section nut
M8 Allen bolt
Figure 5.9 a: Cross section plane a
sidepanel
b: Cross section plane b
c: Cross section plane c
57
5.1.8 Dashboard
The dashboard will be part of the chassis structure. It will be a sandwich structure
consisting of two 1 mm thick aluminium plates with a 25 mm thick polyurethane core.
Figure 5.10 shows an exploded view of the dashboard.
large hole for steering
transmission
dashboard frontplate
dashboard PU-foam
core
dashboard rearplate
Figure 5.10: Exploded view of the dashboard
The top edge of the dashboard will be mounted onto the front roll hoop. The middle top
part of the front roll hoop will be sandwiched by the front and rear dashboard plates using
glue and blind rivets. The large round hole in the frontplate of the dashboard will later be
used to countersink the steering transmission onto the dashboard. The weakened
frontplate will be closed by adding a covering plate over the steering transmission, this
will be shown later. The large flange on the dashboard frontplate extending forward also
reinforces the frontplate around the large hole. Furthermore this flange is attached to the
suspension box and adds stiffness to the chassis structure. Figure 5.11 shows its
placement in the chassis.
glued and
blind riveted
Figure 5.11: Dashboard placement and attachment
58
5.1.9 Rear and front covering plates
The chassis is still a box without a cover. To finalize the structure covering plates are
added front and rear. Furthermore traverse beams are added front and rear to the structure
to distribute the connection rod forces into the covering plates. The traverse beams are
made out of standard 40x20x2 mm aluminium rectangular tube. They are attached on top
of the support beams and can easily be detached to reach the engine and pedalbox if
necessary. The front traversebeam are depicted in figure 5.12.
traverse beam
fitting bolts
welded
endplates
supportbeam
Figure 5.12: Attachment traverse beams onto support beam
Both the support beam and the traverse beam have a 4 mm thick welded endplate. The
support beam endplate has three 6 mm holes. Two holes are used for M6 fitting bolts.
The fitting bolts fit into tapered holes in the traverse beam endplate and are for
positioning the traverse beam. A long M6 bolt is used to tighten it all together.
At the rear suspension support beams a similar traverse beam is added.
The traverse beams will be used to mount on the rear and front covering plates. The
covering plates will be attached using rivnuts placed into the supporting edges.
A total of four plates will be used to close the structure; this is shown in figure 5.13.
space for the
suspension boxes
plates easy to detach
using M4 allen bolts in
rivnuts
Figure 5.13: Front and rear covering plates
59
5.2 Side impact and sloped floorpanel assembly
The rules require a side impact system. It should extend from the front to the rear roll
hoop. Furthermore it should reach at least up to 300 mm above ground. The FSRTE02
side impact will be made out of plate material glued into the chassis.
Figure 5.14 shows the cross section.
70.0
70.0
1.5
240.0
240.0
1.5
400.0
Figure 5.14: Side impact cross section
It should be equivalent to a side impact using tubular members stated in the rules
therefore the second moment of area is compared. The grey sections in figure 5.14 are
equivalent to the required tubular side impact structure.
To protect the steering rack and transmission a sloped floor panel is added. This
floorpanel also prevents the side impact tubes from crushing the driver’s legs in a side
impact. Figure 5.15 shows the folding of the sloped floorpanel. The floor panel will be
made out of 1 mm thick aluminium plate. The driver will enter the car by stepping onto
the sloped floorpanel, to reinforce the floorpanel a plate of ALUCORE panel is glued
underneath.
Figure 5.15: Sloped floorpanel layout and folded sloped floorpanel
The lay out of the side impact tubes is shown in figure 5.16. It also shows the chamfer
needed for the driver’s knees. Furthermore a hole is added to attach the seatbelt on the
60
side impact and the lower insert for the rear roll hoop attachment. There will be made two
side impact tubes, one for the left and one for the right.
hole for seat belt
mounting
chamfered corner for
knee support
Figure 5.16: Side impact tube lay out and folded joint
Figure 5.17 shows the assembly of the sloped floorpanel, the side impact, the side impact
traverse plates and the 25x25x1.5 mm tube. The traverse plates are glued into the side
impact tubes. These plates will prevent the tube from being crushed in a side impact. The
aluminium 25x25x1.5 mm tube is used to connect the side impact to the front rollhoop
through the inserts.
side impact traverse plates
25x25x1.5 aluminium
tube
glued
glued
Figure 5.17: Sloped floorpanel and side impact assembly
61
Figure 5.18 shows the sloped floorpanel and side impact assembly placed in the chassis.
welded
Figure 5.18: Sloped floorpanel and side impact placement
All is glued and blind riveted where necessary except for the square 25x25x1.5 mm tubes,
these are welded onto the inserts.
62
5.3 Steering system
The applied steering system is a pinion with a steering rack. This system is easy to use; it
can be built in everywhere. The transmission from the steering wheel to the steering rack
will must be free of play and must have a high stiffness for direct steering. This way the
driver can exactly feel the tire behavior though the vibrations on the steering wheel.
Therefore a system with four eccentric disks is used. Figure 5.19 shows the system.
Figure 5.19: Steering transmission with four eccentric disks
The steering wheel shaft and the steering rack shaft are parallel; on both shafts two
eccentric disks are mounted. Two opposite disks and one ring ended bar can be
considered as a “four bar system”. The disadvantage of a four bar system is that it can
only transmit a rotation angle<180o, larger angles will make the system to lock (all bars
are aligned). This can be solved by using two “four bar systems” with a phase difference
of 90o. If one system is in locking position, the other system is in its best position and
vice versa. The steering system uses eccentric disks instead of bars, the disks are made
out of aluminum and use special coating to minimize friction. The mechanism is mounted
into an aluminum housing made out of two symmetrical halfs. The mechanism is
over-determined with four parts determining the distance between the steering wheel
shaft and the steering rack shaft. Therefore the mechanism has to be manufactured very
accurate. By stacking up the parts that fix the shaft to shaft distance and bore through all
parts together, problems are prevented.
The steering transmission is very flat and will be placed in a flat 25 mm thick housing.
Then the steering transmission is placed into the chassis. This is shown in figure 5.20
63
traverse plate
Steering rack
mounting plates
Covering plate
blind riveted
Figure 5.20: Placement and attachment steering system
The order of placement is indicated by the arrows. First the transmission is tilted in.
Subsequently the transmission is sandwiched by a traverse plate mounted onto the
25x25x1.5 mm tubes with rivnuts for easy disassembling. The steering rack is placed
using two mounting plates glued onto the bottom panel. Then the steering rack shaft is
connected to the transmission. After they have been aligned the steering rack and the
transmission are fixed using bolts. Finally a covering plate is placed closing the hole in
the dashboard and the transmission is fixed completely using four bolts that go through
the covering plate, the transmission and the dashboard rear plate.
To protect the steering rack a second sloped floor panel is placed, shown in figure 5.21.
Figure 5.21: Second sloped floorpanel for steering rack protection
This panel will be attached using rivnuts, this way it is easy to remove the panel to reach
the steering rack and the transmission.
64
5.4 Power train and drive train
The engine is the heart of the powertrian. The Suzuki engine is accurately modeled using
Unigraphics. Therefore the mounting points have been measured exactly. Figure 5.22
shows the modeled engine.
M10 thread
Figure 5.22: Suzuki engine mounting points
The car will be driven using a chain, other final drives like a timing belt will be heavier.
The differential will be a Torsen type differential. Using a single brake disc mounted onto
the differential. When accelerating tensile force will be generated in the chain this force
should be lead through the rear sprocket, the differential and the differential bearings
back to the engine. Therefore two aluminium plates are used mounted onto the rearward
four engine mounting points. Figure 5.23 shows a topview of these plates together with
the differential, both sprockets and the brake disk. The actual design of the differential
housing and bearing, drive shafts, sprocket flange and braking system is done by formula
student team members and is therefore not discussed extensively.
65
260
12
25
7
11
3
6
4
151
1
2
3
5
8
17
9
10
y
8
12
x
1
2
3
4
5
6
Torsen differential
differential housing
differential covering plate
sprocket flange
brake disk flange
bearing mounting ring 1
7
8
9
10
11
12
bearing mounting ring 2
bearing mounting ring 3
connection tube
radial needle bearing
combined radial and axial bearing
oil seal
Figure 5.23: Topview of differential mounting plates with differential, sprocket and brake disk
The differential mounting plates are 25 mm thick. This way a deep pocket can be milled
into the plate to meet both engine mounting faces having an offset of 17 mm in
y-direction. If the 25 mm thick plates would be massive each plate would have a mass of
5.7 kg. By milling away 75 % of the material the plate will have a mass of 1.45 kg.
The right plate will also be used to mount the brake caliper. The drive shafts are chosen
hollow with an outer diameter of 26 mm. Furthermore flex-plates are used to transmit the
torque to the wheels over the whole suspension travel.
66
As the wheel travels there will be approximately 1 mm of axial shaft displacement, which
can also be absorbed by the flex-plates.
Figure 5.24 shows the exploded view and an assembled view of the complete drivetrain.
Figure 5.24: Drivetrain exploded view and assembly
To mount the drive train in the chassis, some brackets have been added bolted onto the
four frontward engine mounting points. Furthermore a brace is added to mount the
differential plates to the bottom panel in lateral direction, to prevent the plates from
working like a parallelogram due to lateral inertia forces. Figure 5.25 shows these
brackets and the placement of the engine in the chassis.
67
flange for
lateral forces
4 mm
4 mm
3 mm
Figure 5.25: Placement and attachment drivetrain and engine
The front engine brackets will be mounted onto the traverse beams behind the seatpanel.
The forces are transmitted to the rear roll hoop and to the seatpanel. The powertrain is
completed by adding the fuel tank, the battery and the radiator.
The battery is placed on the right as close a possible to the starter motor. This way cables
are kept short so little voltage is lost and weight is saved. The battery can be reached
through a hole in the sidepanel. The hole will be closed again by a cover, bringing back
the sidepanel stiffness. The fuel tank is chosen 6 liters and placed left.
68
Figure 5.26 shows the placement of the fuel tank and the battery.
heat shield
fuel
tank
battery
radiator
Figure 5.26: Placement of battery, fuel tank and radiator
69
6 Suspension design
The suspension properties were determined in chapter 4. In this chapter the suspension
with these properties will be designed fitted onto the chassis. First the suspension center
lines are determined.
6.1 Suspension center lines
The suspension center lines are drawn onto the chassis using AutoCAD coordinates in the
Unigraphics model. All properties are determined at ride height (ground clearance 50 mm)
therefore the suspension centerlines are given at ride height. Figure 6.1 shows the chassis
with the centerlines. The corresponding coordinates are given in appendix G.
3
1
2
1
Figure 6.1: Suspension center lines
The pushrod lines are pointing toward the empty spaces in the chassis. In these spaces the
suspension boxes will be placed.
6.2 Chassis connection points
Every wheel has six connection rods. Four rods have to be mounted to the chassis using
spherical joints fixing four degrees of freedom (d.o.f). One rod is connected to the chassis
by the bump stiffness fixing the 5th d.o.f. The last rod is the steering rod and can be
controlled by the driver, fixing the 6th d.o.f. At the rear the steering rod is called tie rod
and can be adjusted to align the wheels for toe in or toe out. The used spherical joints will
be standard INA rod ends. These rod end will be placed in vertical direction, as the wheel
travels the rod end will rotate in the right direction. The rod end specifications can be
found in appendix H. The numbers in figure 6.1 refer to the different mounting point
types. The different types will be show and explained in paragraph 6.2.1, 6.2.2 and 6.2.3.
70
6.2.1 Mounting point “type 1”
Mounting point “type 1” is used at the suspension support beams. Figure 6.2 shows a
cross section of this mounting point.
6
1
2
7
8
9
3
4
1
2
3
4
5
α1
5
welded in bush
M8x50 Allen bolt
suspension support beam
ring (glued to side panel and beam)
insert with angled face
6
7
8
9
bolted on U-profile
rod end
tapered offset washer
M8x35 Allen bolt
α2
Figure 6.2: “Type 1” mountingpoint
The flat face on the insert is determined by two angles, α1 and α2. α2 Is defined as the
angle between the indicated face and edge in figure 6.2. The angle is calculated by
Unigraphics, using the suspension centerlines, this can be seen in figure 6.3.
When suspension centerlines are changed Unigraphics automatically updates all angles.
The semi finished insert is made eight times on the turning lathe. Then four versions with
a different α1 are milled. Every version is used left and right. Angle α2 is determined
when gluing in the insert.
α1
α2
Figure 6.3: Suspension angles
71
6.2.2 Mounting point “type 2”
Mounting point type 2 is used at the front roll hoop. The inserts mounting the front hoop
are placed at the connection rod heights so the suspension forces will be directly
distributed into the chassis. To create a flat surface on the round roll hoop tube an
aluminium adapter plate is added with a rounded face, fitting on the roll hoop tube radius.
Figure 6.4 shows the mounting point on the front roll hoop.
aluminium
adapter plate
M8 section nut
α2 is definedα2 is defined
M6 Allen bolts
M8 Allen bolt
M6 section nut
Figure 6.4: Mounting point “type 2”
The roll hoop is tightened from the inside with and M8 Allen bolt using a section nut.
The u-profile and the adapter plate are fixed by two M6 Allen bolts that go through the
roll hoop into the M6 section nuts. The angle α2 is obtained by drilling the holes in the
U-profile off-centre.
6.3.3 Mounting point “type 3”
Mounting point “type 3”is applied at the rearframe (see figure 6.5). The flat faces are
already milled on the rearframe. The U-profiles have their attachment holes drilled offcentre to introduce the α2 angle.
Holes drilled offcentre w.r.t Uprofile
Figure 6.5 Mounting point “type 3”
72
6.3 Connection rods and uprights
The uprights were mainly designed by formula student team members as were the brake
disks and calipers. Therefore these parts are shown but not discussed. First a complete
overview of the connection rods and uprights is given in figure 6.6.
connection rod
A-arm
connector
steering rack
Figure 6.6: Overview of connection rods and uprights
Several parts will be discussed in detail starting with the connection rod. The rod will be
made out of an aluminium tube. On both ends a bush is welded, one with left and one
with right inner M8 thread. The bush has an 11 mm hole to improve the welding proces,
heat is conducted through the thin part of the bush to the thicker part. Also the stress
distribution will improve, there will be no stress concentration around the weld.
On the chassis side the rod end is screwed in, secured by a nut. The upright rod side is
connected to the A-arm connector by a stud. A cross section of the connection rod is
depicted in figure 6.7.
6
5
1
2
3
3
6
2
alumiunium tube Ø16 x 2
bush with M8 thread
left thread stud
1
4
5
6
2
4
rod end GAKR8-PW (INA)
A-arm connector
securing nut
Figure 6.7: Connection rod cross section
The connection rods can be marked with an arrow pointing out and a letter code for the
position. Markings must be made in the thicker end part.
Detailed information on the rod ends is given in appendix H.
73
The rear A-arm connector is a rather complex part. It has to join the lower A-arm
connection rods but also the pushrod is mounted on this part. Figure 6.8 shows a zoomed
view of the rear right upright. All the rod centerlines have to converge to the lower
upright pivoting point.
But the flexplate has a large diameter and conflicts with the pushrod centerline. Therefore
the A-arm connector needs a cut away and the pushrod force makes a small detour.
Figure 6.8: Flexplate intersects with the pushrod centerline, special A-arm connecter design
Furthermore the steering rack width is enlarged to prevent bump steer. This is done by
bolting on a steering rack extension. Figure 6.9 shows the aluminium extension.
M8 Allen bolt
aluminium steering rack
extension
Figure 6.9: Steering rack with extension
74
6.4 Suspension unit concepts
The FSRTE02 is equipped with pushrods. These pushrods will be attached to a rocker.
The rocker will pivot as the wheel travels. This is shown schematically in figure 6.10.
Figure 6.10: Schematic presentation of rocker in both utmost positions
Two situations are distinguished, pure bump and pure roll. Both corresponding stiffness’
were calculated in paragraph 4.1 and 4.2.2. A suspension system in which both can be
adjusted independently is therefore preferred.
Figure 6.11: Most common used system with two shocks
The most commonly used system is depicted in figure 6.11. This system has both bump
and roll stiffness and adjustments can not be made independently. If one installs shocks
with a higher stiffness, the roll stiffness also increases.
By using a single shock or monoshock instead of two, the system can be made
independent. This is depicted in figure 6.12.
Figure 6.12: Monoshock system
75
Another advantage is that the monoshock will be lighter than two single shocks.
Roll stiffness can be added in different ways. A simple solution is a classic
anti-roll bar. But there is little space at the upright to connect an anti-roll bar. The
uprights are coupled to the rockers through the pushrods, therefore the rocker rotation
will be used for the anti-roll system. Bump and roll can be identified using both rocker
rotation directions. Figure 6.13a shows the rocker rotation for pure bump and figure
6.13b shows the rotation direction for pure roll.
a)
b)
Figure 6.13 a: Rocker rotation in pure bump
b: Rocker rotation in pure roll
In the following paragraphs different concepts for the rocker activated anti-roll system
are discussed, starting with the original FSRTE01 design.
6.4.1 Original FSRTE01 design
The original design of the FSRTE01 is made by Wouter Berkhout. Figure 6.14 shows this
design
Figure 6.14: Original FSRTE01 anti-roll system design
76
Figure 6.15a shows a top view of the FSRTE01 anti-roll system in a pure bump situation.
Both rods move in opposite direction and the third rocker will rotate about point C.
Figure 6.15b shows a top view of the FSRTE01anti-roll system in a pure roll situation.
Both rods move in the same direction and the third rocker will translate in y-direction and
compress the Belleville spring washers. By changing the spring washer configuration the
roll stiffness can changed.
Belleville
spring
washers
a)
b)
belleville
spring
washers
C
C
x
third rocker
y
Figure 6.15 a: FSRTE01 anti-roll system in pure bump
x
third rocker
y
b: FSRTE01 anti-roll system in pure roll
In case of roll both rods are applying a force onto the third rocker. The y-components of
these forces are supported by the Belleville spring washers. The x-component is
supported by the guidance rail, causing friction.
The roll damping is provided by the friction between the Belleville spring washers, but
can not be adjusted independently.
The forces acting on the rockers in case of roll have an x-component which causes the
rockers to tumble in x direction.
Therefore other concepts have been looked at, in order to find an optimized system.
Some of them are based on the FSRTE01 principle, others are completely different.
77
6.4.2. Anti-roll concept 1
This paragraph actually shows two variations on one anti-roll concept based on
pneumatic and hydraulic. First the pneumatic version is discussed. Figure 6.16 shows this
concept. The system uses three concentric tubes. The inner tube (1) is connected to the
right rocker and has a piston on the other end. The second and middle tube (2) is
connected to the left rocker and acts like a cylinder. In a pure bump situation both tube
move in opposite direction over a distance x, compressing the large helical spring.
Meanwhile gas (air or nitrogen) is pumped out through radial holes in the cylinder wall
with a volume of A1*2*x. The outer tube (3) is a cylinder too in which the middle tube (2)
acts like a piston. The middle tube (2) is moving to the right over a distance x, area A2 is
chosen 2*A1 so the pumped in volume will cause the outer tube (3) to move over a
distance A1*2*x / 2*A1= x in respect to the middle tube (2). So in the end, the outer tube
(3) will not move in a bump situation. In a pure roll situation no gas is pumped and the
outer tube (3) is connected to the tube 1 and 2 with the gas stiffness.
The outer tube (3) is fixed on the chassis so the roll-stiffness is based on compressing the
gas. It can be adjusted by changing the gas volume.
gas
A2
A1
3
2
1
Figure 6.16: Pneumatic anti-roll concept
The pneumatic anti-roll concept is based on the same principle only the gas is replaced by
oil. This makes it possible to use the anti-roll system also for bump damping.
The oil stiffness is much too high to be used as the anti-roll stiffness. Therefore a relative
low stiffness is added between the outer tube (3) and the chassis. Roll damping should
also be added to this concept.
This concept needs a lot of development especially on the sealing of the parts.
78
6.4.3. Anti-roll concept 2
Figure 6.17 shows a schematic topview of the second anti-roll concept.
A
B
C
D
bump spring and damper (monoshock)
E
pushrod
pushrod
anti-roll spring and damper
rockers
x
rocker pivoting axis
y
Figure 6.17: Schematic topview of anti-roll concept 2
anti-roll spring compression[mm]
Two beams are pointing forward and have a pivoting point B. In a pure bump situation
point D and E move towards each other causing point B to move in a straight line in
forward direction. Point C will now describe an approximate radius about point A. This is
examined using SAM. The result is plotted in figure 6.18
wheel travel [mm]
Figure 6.18: Anti-roll spring compression in pure bump for concept 2
The anti-roll spring compression in pure bump is 0.033 mm max and is therefore
assumed to have no influence on the bump stiffness.
79
In a pure roll situation points D and E translate in the y-direction over an equal distance.
This means point B and C will also travel this distance in y-direction and the anti-roll
spring is actuated.
In reality points D and E will travel in z-direction too and spherical joints are needed in
all points. Furthermore this concept takes up a lot of chassis space.
6.4.4. Anti-roll concept 3
This concept is based on the original FSRTE01 design except that the third rocker is now
rotating about a horizontal axis. To keep it compact the third rocker is designed around
the monoshock. A schematic frontview of this concept is given in figure 6.19.
section A-A
C
monoshock
Figure 6.19: Anti-roll concept 3 in frontview
This is 2D system and all pivoting axes are parallel this means all forces are in one plane.
With the third rocker placed vertical, the system is not working symmetrically. To
examine this effect a SAM model is made. Three situation are depicted in figure 6.20,
together with the displacement of point C in y-direction
C
hard bump on both wheels,
maximum spring compression
y-displacement point C = +0.41 mm
C
ride height static
spring compression
y-displacement point C = 0 mm
C
z
wheels off the ground,
spring unloaded
y-displacement point C = +0.42 mm
y
Figure 6.20: SAM model results anti-roll concept 3
80
So the maximum y-displacement is approximately 0.4 mm in extreme bump situation.
This is acceptable so the asymmetric effect is neglected. The stiffness in y-direction of
point has not been worked out so that is a point of attention. Furthermore the rocker
connection points have to be detailed.
6.4.5. Anti-roll concept 4
This concept looks like the original FSRTE01 design. The main difference is that the
translating carriage is replaced by a rotating arm. The third rocker rotation point will now
describe a circular path instead of a linear path in a roll situation. This will solve the
friction problem of the FSRTE01 design. The rockers are not loaded in x direction.
Furthermore the monoshock is placed in front of the anti-roll system. A topview of this
concept is given in figure 6.21.
B
monoshock
roll stiffness
D
C
x
y
A
roll damping
Figure 6.21: Anti-roll concept 4
The rockers are made from a tube to transmit the torque. Welded on plates apply the
torque onto the tube. The stroke of point A is 25-30 mm in both directions depending on
the rocker ratio. Using an arm A-B of 200 mm this means the x-displacement of point A
will be 3.1-4.5 mm. This can be solved using revolute joints in points C and D.
The roll stiffness can be introduced using a helical spring. The roll-damping can be
applied using a motorcycle steering damper. Arm A-B intersects with the monoshock,
this is solved using a box shaped arm with a large hole for the monoshock
This system will take a lot of space in the chassis, therefore another concept is made.
81
6.4.6. Anti-roll concept 5
This concept uses a standard aluminum rectangular tube to mount in all suspension parts.
The idea is to build up and test a suspension box on the bench and place the whole
assembly in the car.
This way all accurate bearing alignments can be CNC machined on the aluminum tube.
The largest available aluminum tube of 120x80x2.5 is chosen. A monoshock with a
maximum outside diameter of 71 mm fits into this tube leaving 1.5 mm clearance with
the wall. In concept 4 the monoshock was placed in front of the anti-roll system.
In this system the monoshock is placed beneath the anti-roll system. For the linear
guidance of the third rocker pivoting point, a standard INA ball monorail guidance
system is used. Figure 6.22 shows a cross section of concept 5 in front view and a
topview.
ball monorail guidance
steering
damper
120
monoshock Ø71
rocker rotation tubes
80
Figure 6.22: Topview of anti-roll concept 5
This concept uses two parallelograms to be able to place the monoshock as low as
possible in the rectangular tube. The ball monorail guidance system reaches through a
hole in the top most face of the tube. On the ball monorail guidance system a block is
bolted which is used to mount the bearings for the third rocker rotation and to attach the
steering damper. The block is preloaded by two helical springs. The third rocker reaches
through two holes in the tube side faces. Outside the tube the third rocker is connected to
two rods using rod ends. The rods are also connected to a lever arm mounted onto the
rocker rotation tubes reaching through rectangular holes in the aluminum tube sidewalls.
This anti-roll system can be used front and rear. Furthermore the roll stiffness can be
adjusted by changing the lever arm length. The stiffness changes with the squared ratio.
An adjustable steering damper is used to adjust the roll damping.
82
6.5 Suspension unit design
Concept 5 will be used for the FSRTE02 suspension and will henceforth be called
suspension box. It has a lot of similarities with the FSTRE01 mechanism but it solves the
problems of friction, tumbling of the rockers and roll damping. Furthermore concept 5 is
the most compact one, it is the easiest to mount on the chassis and it can be applied front
and rear. It can also be bench tested prior to installation.
In this paragraph calculations will be made for the suspension ratios, the corresponding
monoshock specifications and the anti-roll springs and damper.
Finally the assembly is build up step by step.
6.5.1 Suspension ratios
The front and rear suspension box placement is shown in sideview in figure 6.23.
A
rear sprocket
17°
X0,r
90
A
section B-B
section A-A
38°
47°
Figure 6.23: Sideview of suspension box placement and pushrod plane sections
The rear pushrod is leaning 17o forward in sideview. The rear suspension box is aligned
with the pushrod. The largest rear sprocket of 260 mm and the engine determined the
position of the suspension box.
The torsion tubes have to extend forward as far as possible for high chassis torsion
stiffness. Therefore the front suspension box is placed horizontal in sideview. This means
the front pushrod is placed vertical in sideview.
Figure 6.23 also shows sections A-A and B-B through the rear and front pushrod planes
and the inclined angles of 47o and 38o rear and front.
83
Different ratios are calculated starting with the pushrod ratio “ip”. This is defined and
calculated using the displacements X0 and X1 and angles from figure 6.23:
X 1, r
i p ,r =
= cos(17 o ) ⋅ sin(47 o ) = 0.7
X 0, r
i p, f =
X 1, f
X 0, f
= cos(0 o ) ⋅ sin(38 o ) = 0.62
The next ratio is the monoshock ratio “im”. This ratio is defined as the monoshock travel
divided by the pushrod travel in pure bump.
Therefore the rocker and the parallelogram are depicted in figure 6.24:
rear system
55
2,r
2,r
front system
x
2,f
55
x
monoshock front
55
2,f
55
90°
On the front system all bar lengths are 55 mm this means X1-f = X2-f.
On the rear system all bar lengths are 60 mm this means X1-r = X2-r
In pure bump both pushrods travel an equal distance X1, this means that the monoshock is
compressed from both sides by a total distance of 2*X2.
Therefore the monoshock ratios im,r and im,f are 2 for the rear and front suspension
respectively.
Finally the anti-roll ratios ia,r and ia,f are determined; this ratio is defined as the ball
monorail guidance system displacement divided by the pushrod travel.
Therefore the length of the lever arm mounted onto the rocker rotation tubes outside the
rectangular tube is needed. This is depicted in figure 6.25.
90°
3,r
front system
x
x
3,f
1,f
55
60
1,r
x
b
a
rear system
x
90°
55
Figure 6.24: Rocker and parallelogram dimensions of front and rear suspension box
x
1,r
55
55
55
55
1,f
x
60
90°
55
55
x
x
monoshock rear
60
x
55
55
90°
60
60
1,r
60
60
x
55
90°
Figure 6.25: Rocker and lever arm dimensions of front and rear suspension box
84
1,f
Different ratios can chosen by changing the lever arm length. Then the anti-roll ratios
front and rear are:
X 3, r
a
i a ,r =
=
X 1,r 60
ia , f =
X 3, f
X 1, f
=
b
55
6.5.2 Anti-roll helical spring stiffness
The preferred roll stiffness Croll=22000 Nm/rad front and rear and the permitted roll angle
is 1.7 deg. The roll stiffness can also be expressed in a linear stiffness on the wheels by
equation 6.1:
C roll , wheel =
C roll
(equation 6.1)
( 1 2 t )2
With t, the track width. This results in a Croll,wheel,r of 61100 N/m and a Croll,wheel,f of
56300 N/m. By multiplying this value with the pushrod ratio and the anti-roll ratio, the
preferred anti-roll spring stiffness can be determined. But a reverse approach is used here.
First the anti-roll spring stiffness is determined, then the preferred anti-roll ratio is
calculated, and the anti-roll lever arm length is calculated. Figure 6.26 shows the helical
spring used front and rear, table 6.1 shows the corresponding spring properties.
d
Dm
Lo
Sn
Figure 6.26: Tevema helical spring for the anti-roll mechanism
Wire diameter
Mean diameter
Number of active coils
d [mm]
Dm [mm]
Nw [-]
5
32
5.5
Unloaded spring length
Spring stiffness
Maximum spring compression
Force at maximum compression
Order number at Tevema
Lo [mm]
Ctevema [N/mm]
Sn [mm]
Fn [N]
75
35.3
34.8
1226
D 13840
Table 6.1: Tevema helical spring for the anti-roll mechanism dimensions and specifications
85
The spring is used twice to preload the third rocker block, this is shown in figure 6.27
C
stiffness Ctevema
stiffness Ctevema
Figure 6.27: Third rocker block preloaded by two helical compression springs
So the stiffness in point C in horizontal direction equals 2*Ctevema=70.6 N/mm.
Both springs are preloaded over a distance of 17.4 mm, this is half of the maximum
allowable spring compression. The linear stiffness on the wheels caused by the anti-roll
system is given by equation 6.2.
C roll ,wheel = i p2 ⋅ ia2 ⋅ 2 ⋅ C tevema
(equation 6.2)
Ctevema, Croll,wheel and the ratio ip are already known. ia,r and ia,f are 1.33 and 1.44
respectively. The corresponding anti-roll lever lengths a and b in millimeters, are
calculated below:
a = i a ,r ⋅ 60 = 1.33 ⋅ 60 = 79.7
b = ia , f ⋅ 55 = 1.44 ⋅ 55 = 79.2
The roll stiffness front to rear ratio is very important for the road holding this can be used
to adjust over- or under steering properties. Therefore the roll stiffness should be
adjustable this is done by picking another connection hole on the lever arm changing
lengths a and b. The adjustment area is schematically shown in figure 6.28, furthermore
table 6.2 shows all corresponding roll stiffness and lever arm lengths a and b.
86
-6% +3%
rear roll stiffness
p
s t
front roll stiffness
Roll stiffness [Nm/rad]
20680
22000
22660
21340
22000
23320
Lever arm length [mm]
77.3
79.7
80.9
78
79.2
81.6
Table 6.2: Adjustments range for front and rear anti-roll stiffness and corresponding lever arm lengths
Table 6.3 shows all possible roll stiffness ratios.
Croll,r [Nm/rad]
Croll,f [Nm/rad]
Ratio Croll,r/Croll,f
20680
20680
20680
22000
22000
22000
22660
22660
22660
21340
22000
23320
21340
22000
23320
21340
22000
23320
0.97
0.94
0.87
1.03
1
0.94
1.06
1.03
0.97
u
-3% +6%
Figure 6.28: Schematic view of the absolute roll stiffness adjustments front and rear
Adjustment
p
q
r
s
t
u
q r
Table 6.3: Possible rear to front roll stiffness ratios
The front and rear levers can even be swapped, to double the number of possible front to
rear ratios.
87
6.5.3 Steering damper specifications
The used steering damper is shown in figure 6.29. The damper is designed and produced
by WP.
Figure 6.29: WP steering damper and mounting bracket
The steering damper has two concentric tubes. A piston is mounted onto the central rod.
If the piston travels oil is pumped from the inner tube to the space between the inner and
outer tube back to the inner tube on the other side of the piston. This way the damping
value is independent of the piston movement direction.
The oil is led along a resistance. This can be adjusted by a screw which uses 31 indication
clicks.
Damping properties are inquired at WP. Figure 6.30.a shows a measurement of damping
force on different speeds using a sinusoid speed signal. The measurement is done without
changing the oil resistance.
a
1000
b
900
5
800
This data
2
3
4
1
Force [N]
700
600
4
500
400
3
300
2
200
5
1
100
0
0
50
100
150
200
250
300
Speed [mm/s]
Figure 6.30. a: WP measurement data
b: Speed-force graph extracted from WP data
This graph is used to examine the damping properties. Therefore five data points are
picked, at which the current speed is plotted against the corresponding force in N.
The resulting graph is depicted in figure 6.30b. It is assumed to be a straight line so the
damping is proportional. This means the damping value and the speed are independent.
To find the relation between the resistance screw adjustment and the damping value a test
setup is build. The steering damper is placed vertical and a constant force is applied by a
mass of 12 kg. A digital camera is used to register the piston movement. Furthermore a
measuring tape is added to the test setup. The speed is determined by comparing the
distance traveled between two frames and the time between those frames. A schematic
drawing is shown in figure 6.31.
88
camera
mm
resistance adjustment
screw with 31 clicks
12 KG
Figure 6.31: Setup to determine WP damping coefficient
The graphs are shown in appendix L, a line is fitted through the measurement data
extracting equation 6.3. This equation can be used to calculate the damping coefficient
dwp for a certain number of resistance screw open clicks x.
d wp = 61 ⋅ e 0.19⋅ x
(equation 6.3)
The preferred roll damping was calculated in paragraph 4.2.2; droll,f= droll,r= 315
Nms/rad. This is translated to a linear damping at a single wheel by equation 6.4:
d roll , wheel , f ,r =
d roll , f ,r
(
1
t f ,r )
2
2
(equation 6.4)
The droll,wheel,f = 805 Ns/m and droll,wheel,r = 875 Ns/m. Now the preferred dwp can be
calculated depending using the pushrod and anti-roll ratio.
2
2
d wp , f = i p , f ⋅ ia , f ⋅ d roll , wheel , f = 0.62 2 ⋅ 1.44 2 ⋅ 805 = 640 Ns/m
2
2
d wp ,r = i p , r ⋅ ia ,r ⋅ d roll , wheel ,r = 0.7 2 ⋅ 1.33 2 ⋅ 875 = 760 Ns/m
The corresponding steering damper adjustment is calculated using equation 6.3. The front
damper has to be turned open 12.6 clicks and the rear damper resistance has to be opened
13.5 clicks.
89
6.5.4 Monoshock specifications
The required monoshock stiffness can be calculated using the pushrod and monoshock
ratios and the required wheel stiffness. When using a monoshock system,
a single shock has to supply stiffness to one axle instead of one wheel.
The needed axle stiffness is therefore 2*Cwheel. The wheel rates front and rear are
16800 N/m and 19600 N/m respectively. Equation 6.5 shows the relation between the
wheel stiffness and the monoshock stiffness.
2 ⋅ C wheel = I p2 ⋅ I m2 ⋅ C monoshock
(equation 6.5)
The monoshock stiffness’ front and rear are respectively 21900 N/m and 20000 N/m.
The corresponding maximum monoshock stroke sm can be calculated with equation 6.6,
using the maximum wheel travel sw of 51 mm.
sm = I p ⋅ I m ⋅ s w
(equation 6.6)
The monoshock strokes front and rear are respectively 63mm and 71 mm.
Furthermore the minimal required spring volume is calculated using equation 6.7:
Vspring =
C monoshock ⋅ s m2 ⋅ G steel
µ spring ⋅ τ steel
2
(equation 6.7)
Using Gsteel=8.0e10 N/m2 and τsteel=6.0e8 N/m2 and µspring=0.5 [-] the required front and
rear spring volumes become 3.86e-5 m3 and 4.48e-5 m3 respectively.
The helical spring stiffness can be expressed using the material properties and spring
dimensions. This is shown in equation 6.8.
C monoshock
∆F
G⋅d4
=
=
∆s 8 ⋅ Dm3 ⋅ N w
(equation 6.8)
With d the spring wire thickness, Dm the mean spring diameter and Nw the number of
active coils. The spring volume can also be expressing using the spring dimensions.
Vspring = π ⋅ Dm ⋅ N w ⋅ 1 4 ⋅ π ⋅ d 2
(equation 6.9)
Equations 6.8 and 6.9 can be combined. Filling in the minimal required volumes, enables
us to calculate the corresponding spring dimensions. Therefore one dimension variable
has to be chosen and the other two can be calculated. Table 6.4 shows three options that
comply for the front and rear monoshock spring.
90
option 1
option 2
option 3
Spring dimension variable
Front monoshock
Rear monoshock
d
[mm]
Nw
[-]
Dm [mm]
d
[mm]
Nw
[-]
Dm [mm]
d
[mm]
Nw
[-]
Dm [mm]
7.13
4.96
62
7
5.30
58
8
2.80
87.5
7.20
5.34
62
7
6.51
57
8
3.34
85
Table 6.4: Three different options for the monoshock spring front and rear
For “option 1”, Dm is chosen 62 mm, the spring just fits into the rectangular tube of
120x80x2.5 mm but the wire thickness is not standard. Options 2 and 3 show the
complying spring dimension with standard wire thickness’ of 7 and 8 mm. Using a d of
8 mm, Dm becomes too large and the spring does not fit into the tube.
Therefore option 2 is recommended, using a monoshock spring with a wire thickness d of
7 mm front and rear with a different number of active coils.
Finally the monoshock damping properties are determined. This is calculated using the
pushrod and monoshock ratios and the required wheel damping from paragraph 4.1.
2 ⋅ d wheel = I p2 ⋅ I m2 ⋅ d monoshock
(equation 6.10)
Using equation 6.10 the required front- and rear monoshock damping are respectively
1390 Ns/m and 1280 Ns/m.
91
6.5.5 Suspension box design
Finally the complete suspension box design can be made with the right ratios and
dimensions. The front suspension box design is showed step by step. Starting with the
front monoshock having an unloaded length of 330 mm in figure 6.32.
paralellogram link
330 mm
3 mm aluminium plates
10 mm shaft 2
offset
bushes
needle bearings
needle bearing
10 mm shaft 1
Figure 6.32: Exploded view of triangulalar plates, bearings and parallelogram links
First the aluminium triangular plates are welded onto the offset bushes, then the 10 mm
shaft and a needle bearing are pressed in. The subassembly is bolted onto the monoshock
using an M10 Allen bolt. Then needle bearings are pressed into the parallelogram links,
and placed on both sides of the triangular plates.
Figure 6.33 shows the rocker, the main shaft and the anti-roll levers.
3 mm aluminium anti-roll lever arm
alumium
ball bearings main shaft
bush 2
spline on
main shaft
rocker
bush 1
splined
hole
Figure 6.33: Placement of main shaft together with anti-roll lever arm and rocker
92
The anti-roll lever is made out of two 3 mm thick aluminum plates welded onto an
aluminum shaft. This shaft has a spline. The rocker is also made out of aluminum and has
a splined hole. Two ball bearings (appendix J) are pressed in the rectangular tube wall.
The shaft with the lever is placed in the rectangular tube through the rocker inside the
tube.
Figure 6.34 shows a detailed cross section of the main shaft placed in the rectangular tube.
1
6
7
8
9
2
3
4
5
1
2
3
4
5
rectangular tube
mounting ring ball bearing
filling bush 1
main shaft
ball bearing 61806-2z
6
7
8
9
rocker
filling bush 1
locking ring
anti-roll lever arms
Figure 6.34: Mainshaft cross section
Due to the use of filling bushes the main shaft spline can be made using wire-EDM (wire
electric discharge machining). When choosing another anti-roll lever arm length the
locking ring is released and the mainshaft is slid out partly, rotated one spline groove and
slid in again. The locking ring is placed and the rod is connected to the anti-roll lever arm
using another hole.
Ball bearings are pressed into the third rocker block. Ball bearing specifications can be
found in appendix I. Then the third rocker is put in the block using a 10 mm shaft and
two M5 Allen bolts. The block is bolted onto the ball monorail guidance with four M4
Allen bolts. The ball monorail guidance system specifications can be found in
appendix K. Figure 6.35 shows an exploded view of the sub assembly.
93
third rocker rotation shaft
M4 Allen bolts
ball bearings
M5 Allen bolts
third rocker
ball monorail guidance
Figure 6.35: Exploded view of the third rocker rotation an translation system
Subsequently the assembly from figure 6.35 is mounted upside down into the rectangular
tube of 120x80x2.5 using two brackets. This is depicted in figure 6.36
monorail mounting brackets
hole in rectangular tube
hole for the third rocker
small clearance with monoshock
Figure 6.36: Placement of ball monorail guidance system using brackets
94
Figure 6.37 shows the next assembling steps. First the helical anti-roll springs are added.
The springs are preloaded till half of their maximum compression and kept in place by
two square traverse tubes of 30x30x3 mm welded to the rectangular tube. The helical
spring ends are places on end caps preventing the spring from falling out by a small edge.
Then the WP steering damper is added. The steering damper rod en can be put through a
hole in the square 30x30x3 tube and through the helical anti-roll spring. It will be
attached to the third rocker block using an M8 Allen bolt. The steering damper itself is
fixed onto the rectangular tube using the original WP mounting bracket.
spring end caps
2
2
1
1
3
square aluminum
tube 30x30x3 mm
Figure 6.37: Spring and damper placement
Finally rods are added connecting the third rocker with the anti-roll lever arms using rod
ends and M8 bolts. This is shown in figure 6.38.
Holes in the rectangular tubes can be made to ease the assembling and save weight these
are not depicted.
Figure 6.38: Final design front suspension box
The rear suspension box has minor differences with the front suspension box and is
therefore not described separately.
95
7 FSRTE02 assembly
In this chapter the assembly is made by joining the suspension boxes and the chassis. In
paragraph 7.2 the construction process is described and illustrated using photographs.
7.1 Unigraphics assembly
To mount the suspension boxes into the chassis, bent mounting plates are welded onto the
rectangular tubes. Furthermore corner profiles of 2 mm thickness are glued and blind
riveted onto the suspension boxes. This is shown in figure 7.1 for the front suspension
box.
corner profiles
welded
bend mounting plates
Figure 7.1: Front suspension box with bend mounting plates and corner profiles
The suspension box is mounted on the chassis using six M8 Allen bolts. The bolts are put
in from the outside and reach through small inserts in the ALUCORE sidepanels. The
bump forces are guided into the sidepanels through these inserts. The roll forces are
guided into the front and rear covering plates through the corner profiles.
Figure 7.2 shows the placement of the suspension box rear and front.
96
Figure 7.2: Placement of the suspension boxes front and rear onto the FSRTE02 chassis
Figure 7.3 shows the final assembly with a driver seated.
Figure 7.3: Final FSRTE02 assembly with driver seated
97
7.2 FSRTE02 construction.
The FSRTE02 construction is performed by students. Machined parts are mainly made by
the GTD of the University. Appendix M shows the preferred sequence of the chassis
construction. It is important to work accurately to prevent later fitting problems.
Therefore the chassis has to be preassembled temporally as far as possible to see if all
parts fit before gluing it the together. This paragraph illustrates the building process till
thus far.
First the chassis halfs are watercutted and bent, this is shown in figure 7.4
Figure 7.4: Watercutted layouts and bending both halfs on the press brake
A table of 350 mm height has been built using a heavy steel frame with an MDF tabletop.
On this table a drawing is spread with the outlines of the bottom panels.
Furthermore sidepanel supports rigs are mounted onto the table.
Then both chassis halfs are placed onto the table and aligned onto the bottom outlines.
They are fixed using weights, pressing the bottom panel onto the table. The bottom seam
is joined by gluing on a strip pressed by weights. The rearframe is placed temporally to
ensure the rear chassis width will be correct. This is shown in figure 7.5a.
98
a
Figure 7.5 a: Gluing the bottom seam
b
b: Gluing in the rearframe
Then the rearframe is glued in using the milled rectangular tubes, this is depicted in
figure 7.5b. Then the bent ALUCORE edges are reinforced by gluing in a corner profile.
This can also be seen in figure 7.5.b.
The next step is to attach the frontpanel. Then the torsion tubes the side impact and the
sloped floorpanel are bent and glued in.
Figure 7.6 shows the bending of the torsion tube.
Figure 7.6: Bending of torsion tube
This is the chassis construction till thus far.
99
8 Conclusions and recommendations
In this chapter the final result will described in conclusions. Then recommendations are
made to help improve this design and give some ideas for the FSRTE03.
8.1 Conclusions
The conclusions are arranged per chapter.
General FSRTE02 properties
The wheelbase will be 1550 mm, the front and the rear track will be 1250 mm and 1200
mm respectively. The total car mass will be 295 kg including an 80 kg driver, the center
of gravity height is 317 mm. The front to rear weight distribution is 46/54, using 6 inch
wide front tires and and 8 inch wide rear tires, the contact pressures will be equal.
Maximum acceleration is 1.24 G, cornering can be done with a maximum lateral
acceleration of 1.6 G and maximum braking is done with 1.55 G.
Chassis properties
A box structure has a much higher specific stiffness than a tubular spaceframe structure
within the same volume. Therefore the chassis is mainly made out ALUCORE panels.
These prefabricated panels consist out of two 0.5 mm aluminium skins and a 9 mm
aluminium honeycomb core. The panels can be shaped using watercutting machine and a
press brake and the complete joint can be glued together. The FSRTE02 chassis shape is
based on the FSRTE01 shape but torsion stiffness is increased by 300%.
Suspension properties
The wheel rates front and rear are 16800 N/m and 19600 N/m respectively. The
maximum chassis roll will be 2o including the tire compression. The front roll center
height will be 10 mm and the rear roll center height will be 97 mm resulting in an equal
roll moment front and rear. Both the front and rear roll stiffness will be 22000 Nm/rad.
The static camber will be 3.15o. At the rear suspension 50% anti-squat is applied.
At the front suspension 50% anti-dive is applied. The steering geometry is adjustable
from parallel steering to a full Ackermann steering geometry.
Chassis design
The chassis consists out of two nearly symmetrical halfs, joined by two aluminum glued
on strips. The front- and seatpanel and the rearframe are glued in using corner profiles
and blind rivets. The torsion tubes are made out of 1 mm thick aluminium plates as well
as the sloped floorpanel and the rear and front covering panels. The side impact is made
out of 1.5 mm thick aluminum plate. All part layouts are optimized on minimum seam
length and are made using lasercutting. The front and rear roll hoops are placed around
the chassis and fixed from the inside. The dashboard is a sandwich structure of two 1 mm
thick aluminium outer layers and a 25 mm thick polyurethane core. The steering system
transmission is mounted in a 25 mm thick housing which is countersunk into the
dashboard. The suspension connection rods will be mounted onto the rearframe and onto
the front roll hoop. The remaining connection rod points are made using an insert that
100
reaches through the ALUCORE panel. The in-plane suspension force component is
guided into the ALUCORE panel. The perpendicular force component is distributed into
the chassis by a support beam on the inside. Space is reserved for the suspension boxes.
Suspension design
The different suspension mounting points are fully detailed. The A-arms are joined on the
upright side by a connector. The lower rear connector is enlarged to prevent it from
interfering with the flexplates. Different suspension unit concepts have been considered.
The best concept is the suspension box concept. The functioning is based on the
FSRTE01 design but all components are mounted into a standard aluminium rectangular
tube of 120x80x2.5. Needle- and ball bearings are used in the pivoting points and a ball
monorail guidance system is used for the third rocker translation. Roll stiffness can be
adjusted by changing the lever arm length and a motorcycle steering damper is added for
adjustable roll damping. The suspension box assembly can be bench built and tested prior
to installation.
FSRTE02 construction
The suspension box is placed into the chassis and mounted using M8 Allen bolts.
For the building of the chassis a building rig is made. A flat solid table of 350 mm height
is used. On this table both ALUCORE chassis halfs are aligned and joined together.
Then the frontpanel and the rearframe are glued in. Subsequently the side impact, the
sloped floorpanel and the torsion tubes are glued in. The roll hoops are placed using
special inserts and the dashboard is glued in. Finally the rear and front coverplates are
bolted on to reach full torsion stiffness.
8.2 Recommendations
First an enumeration has been made with specific FSRTE02 issues.
•
•
•
•
•
•
•
•
•
•
•
•
Too little attention is paid to the tire choice and the tire characteristics. Different tires
have to be compared. Therefore more tire data needs to be obtained from tire
manufacturers or by doing tire tests.
The scrub radius should be reduced.
The caster and trail have to be looked at in more detail.
FEM analysis has to be done on the rearframe to be able to see whether mass can be
saved or stiffness can be gained.
Mass could be saved on side impact using ALUCORE panels
The front left engine bracket has to be reinforced to be able to withstand lateral
engine inertia forces.
The radiator should be made smaller.
Flexplates need more optimization to reduce weight.
Adjusting the monoshock preload is difficult because it is placed inside the
rectangular tube so this should be solved.
The monoshock has to be choosen fast so the suspension box design can be fine tuned.
Weight can be saved on bolts, which are over dimensioned on some parts, either by
going to aluminium bolting or by redesigning for smaller size.
Air ducting in the engine compartment has to be examined.
101
Below a list of recommendations concerning the FSRTE03 design and some general
issues is made.
•
•
•
•
•
•
All team members should be able to work with Unigraphics. Parts should be designed
in such a way that they are easy to adapt by changing a single parameter which any
team members should be able to find in the part file.
Bottom up assembly in Unigraphics should be applied. This way holes or other
features can easily be made through different parts after assembling them.
The FSRTE03 design should be completely parametric. For example when the roll
center height changes, the complete assembly suspension geometry should change
along.
The Aprilia SXV 5.5 engine should be looked at seriously. The engine has a high
power to weight ratio and would therefore be very suitable for the FSRTE03.
Little mass can be saved on the FSRTE02 aluminium chassis structure (12% off car
weight). Mass saving must be done simultaneously on all parts.
The feasibility of a laminated carbon structure can therefore be examined.
The FSRTE02 suspension performance should be used to design the FSRTE03
suspension.
102
Bibliography
•
John C. Dixon, Tires suspension and handling, SAE, 1996
•
P.C.J.N. Rosielle E.A.G. Reker, Constructieprincipes 1, March 2000
•
W. Berkhout, Design for a formula student racecar, October 2004
•
D.O. de Kok, Optimal performance of a racing car on a circuit, March 9, 2001
•
Andries van Berkum Stijn Aben, Eindoverbrenging voor de FS racewagen,
March 12, 2004
•
Jasper Simons, Stuurinrichting voor formula student, December 2004
•
P. Brinkgreve R. Brinkgreve M.J.M. van der Velden, Wegligging van
automobielen, 1969-1972
•
F. Sass Ch. Bouché A. Leitner, DUBBEL Taschenbuch für den Maschinenbau,
Springer-Verlag, 1994
•
Racecar engineering, November 2003
•
Dr. Ir. I.J.M. Besselink, Vehicle Dynamics lecture notes, 2003
•
Dr. Ir. I.J.M. Besselink, Advanced Vehicle Dynamics lecture notes, 2004
103
Internet sites
http://www.avonracing.com/tyres
http://www.aluminium-info.nl
http://www.alucore.com
http://www.alcanairex.com
http://www.hexcel.com
http://www.favonius.com/soaring/foams/foams.htm
http://www.netcomposites.com/education.asp?sequence=53
http://www.suzuki.nl
http://www.aprilia.com
http://www.formulastudent.com
http://www.keizerwheels.com
http://www.safan.nl
http://www.wp.nl
http://www.tevema.com
http://www.ina.nl
http://fsae.utoronto.ca
104
Appendices
Appendix A: Static mass distribution
The static mass distribution on the wheels is calculated by taking into account all of the
cars parts heavier than 5kg. All mass centers are drawn below with their coordinates in
table A.1
3
1
2
z
x
Figure A.1: Car side view with all parts over 5 kg
Number
(fig A.1)
1
2
3
4
5
6
7
8
9
10
11
12
Part name
Chassis and small components
Engine (exhaust included)
Drivetrain
Suspension system front
Suspension system rear
Steering, dashboard and front rollhoop
Petrol tank and battery
Rear rollhoop
Radiator
Driver
Both front wheels
Both rear wheels
Total mass
Mass
[kg]
26.5
60
17
8
8
10
13
7.5
5
80
30
30
295
x-coordinate
[mm]
990
400
30
1550
90
1370
650
510
210
910
1550
0
z-coordinate
[mm]
300
275
260
400
460
350
140
670
720
345
261
282
Table A.2: Sprung and unsprung (front- and rear wheels) masses and positions
105
A matlab file is used to calculate the resulting center of gravity of the sprung + unsprung
mass. This determines the static weight distribution of the car.
Furthermore the sprung mass minimum moment of inertia J-axis is determined; this axis
is drawn in figure A.1. The results are plotted in table A.2 below:
Number
(fig A.1)
13
14
15
16
Point name
Combined center of gravity
sprung + unsprung mass
Center of gravity sprung mass
Acting point centrifugal force rear
Acting point centrifugal force front
x-coordinate
[mm]
z-coordinate
[mm]
713
317 (hcg)
697
0
1550
329
340 (hcg-r)
316 (hcg-f)
Table A.2: Combined centers of mass
The z-coordinates are used in the lateral load transfer calculation therefore they are called
centers of gravity rear and front, hcg-r and hcg-f respectively.
The moment of inertia Jroll about the roll axis is approximately 9 kgm2.
106
Appendix B: friction coefficients on dry and wet road
The friction coefficient is a linear function of the tire normal force, below the graphs and
the functions for the front and rear tires on dry and wet road are depicted.
1
♦
0.9
µlat-f Avon measurements
µlat-f and µlong-f
0.8
friction coefficient µ [-]
0.7
0.6
µlat-f = µlong-f= 0.87 – 0.64e-4*FN-f
0.5
0.4
0.3
0.2
0.1
0
0
500
1000
1500
2000
2500
3000
3500
4000
tire normal force Fn [N]
o
Figure B.1: µlat and µlong at a slip angle of 7 for the front tire on wet road
2.5
♦
µlat-r and µlong-r
2
friction coefficient µ [-]
µlat-r Avon measurements
1.5
µlat-r = µlong-r= 2.00 – 1.85e-4*FN-r
1
0.5
0
0
500
1000
1500
2000
2500
3000
3500
4000
tire normal force Fn [N]
Figure B.2: µlat and µlong at a slip angle of 7o for the rear tire on dry road
1.2
♦
friction coefficient µ [-]
1
µlat-r Avon measurements
µlat-r and µlong-r
0.8
0.6
µlat-r = µlong-r= 1.00 – 0.93e-4*FN-r
0.4
0.2
0
0
500
1000
1500
2000
2500
3000
3500
4000
tire normal force Fn [N]
Figure B.3: µlat and µlong at a slip angle of 7o for the rear tire on wet road
107
Appendic C: Sandwich material core table
108
Appendix D: FSRTE02 chassis FEM analysis results
The FSRTE02 chassis strength is analyzed by applying three different load cases,
accelerating (figure D.1), braking (figure D.2) and cornering (figure D.3).
Figure D.1: Stresses during maximum acceleration
Figure D.2: Stresses during maximum braking
Figure D.3: Stresses during maximum cornering
109
Appendix E: Radial tire stiffness
tire compression [mm]
The radial tire stiffness is calculated using the tire data and a trendline.
The trendline slope indicates the tire stiffness.
The results for the front and rear tire are plotted in figure E.1 and E.2.
20,0
18,0
16,0
14,0
12,0
10,0
8,0
6,0
Front tire stiffness
200 N/mm
4,0
2,0
0,0
0
500
1000
1500
2000
2500
3000
3500
4000
3500
4000
Normal force [N]
Figure E.1: Tire compression as a function of tire normal force for the front tire
tire compression [mm]
18,0
16,0
14,0
12,0
10,0
8,0
6,0
Rear tire stiffness
210 N/mm
4,0
2,0
0,0
0
500
1000
1500
2000
2500
3000
Normal force [N]
Figure E.2: Tire compression as a function of tire normal force for the front tire
110
Appendix F: Standard driver seated in FSRTE02 chassis
The rules prescribe a two dimensional driver template. It represents the 95th percentile
male. It is quoted below:
This has been used to create a sideview of the driver when seated in the FSRTE02 chassis.
Furthermore ergonomic data has been used to finish the legs of the driver and to create
the section A-A which.
50
R150
A
section A-A
280
450
R100
490
R100
400
Figure F.1: Sideview and cross section at the elbow of standard driver.
111
Appendix G: suspension coordinates
The suspension coordinates are determined using Autocad. They are given at ride height.
The origin is placed between the rear tires contact points on the road. Figure H1 shows
the suspension point naming and table H.1 shows the description and coordinates of each
point.
C3,r
C2,r
C8,r
C11,r
C9,r
C10,r C6,r
C7,r
C1,r
C4,r
C5,r
C11,f
C2,f C3,f
C6,f
C8,f
C10,f
C7,r
Figure G.1: Suspension points naming
point
C1,f
C2,f
C3,f
C4,f
C5,f
C6,f
C7,f
C8,f
C9,f
C10,f
C11,f
C1,r
C2,r
C3,r
C4,r
C5,r
C6,r
C7,r
C8,r
C9,r
C10,r
C11,r
C1,f
C9,f
C4,f
C5,f
description
connection upper A-arm front - chassis
connection upper A-arm upright
connection upper A-arm rear - chassis
connection lower A-arm front - chassis
connection lower A-arm upright
connection lower A-arm rear - chassis
connection upright - wheel centre
connection upright - steering rod
connection steering rod - steering rack
connection lower A-arm - pushrod
connection pushrod - rocker
connection upper A-arm front - chassis
connection upper A-arm upright
connection upper A-arm rear - chassis
connection lower A-arm front - chassis
connection lower A-arm upright
connection lower A-arm rear - chassis
connection upright - wheel centre
connection upright - tie rod
connection steering rod - steering rack
connection lower A-arm - pushrod
connection pushrod - rocker
coordinates x y and z in mm
1718, 277, 315
1523, 596, 363
1336, 296, 251
1717, 237, 117
1561, 627, 123
1335, 271, 127
1542, 611, 245
1478, 595, 157
1478, 231, 140
1561, 627, 123
1550, 294, 372
275, 313, 360
0,
566, 402
-144, 247, 310
275, 274, 215
0,
599, 162
-136 213, 147
0,
599, 282
-86, 570, 282
-149, 236, 238
0,
599, 162
93,
352, 424
Table G.1: description and coordinates of each suspension point
112
Appendix H: Rod end specification
This rod end is used for the connection rods, the pushrods and for the anti-roll system.
Specifications are stated in figure H.1
Figure H.1: Rod end specifications
113
Appendix I: Third rocker ballbearing specifications
For the third rocker in the front and rear suspension box INA 60002RS ball bearings are
used. Specifications from INA are stated in figure I.1.
Figure I.1: Suspension box third rocker ballbearing specifications
114
Appendix J: Suspension box mainshaft ball bearing
specifications
INA 61806-2Z ball bearings are used for the front and rear suspension box mainshaft.
Specifications from SKF which are equal to INA are stated in figure J.1.
Figure J.1: Suspension box mainshaft ball bearing specifications
115
Appendix K: Ball monorail guidance system specifications
A ball monorail guidance system will be used for the linear translation of the third rocker
in the suspension box front and rear. The monorail length is chosen minimal (100 mm).
Specifications are stated in figure K.1
Figure K.1: Ball monorail guidance system specifications
116
Appendix L: WP steering damper measurements
The damping has been measured with the test setup shown in paragraph 6.5.3 figure 6.31.
The measuring data is plotted in a graph and an exponential function is fitted through the
data points. This is shown in figure M.1
damping coefficient [Ns/m]
30000
25000
20000
15000
y = 60.93*e0.1868x
10000
5000
0
0
10
20
30
40
num ber of turned open resisance clicks [-]
Figure N.1: WP steering damper measuring data
117
Appendix M: Chassis construction sequence
Table M.1 shows an overview of the building operations in chronological order.
Action
1 Gluing the bottom seam
2 Glue in the milled rectangular tubes at the front and rear of the chassis on
the ALUCORE edges
3 Glue in the rearframe
4 Glue in the frontpanel
5 Glue in the corner profiles to reinforce the bend ALUCORE edge
6 Glue in the outer insert parts using the front hoop to align them
7 Weld the square 30x30x2 mm tubes onto the inner insert parts
8 Glue in the inner insert parts with the welded on square 30x30x2 mm tubes
9 Glue in the side impact and the sloped floorpanel assembly
10 Glue on the torsion tubes
11 Place the traverse beam behind the seatpanel
12 Glue in the seatpanel
13 Place the front roll hoop
14 Assemble the dashboard by gluing in the polyurethane core
15 Glue in the assembled dashboard
16 Glue in the milled rectangular tubes for the placement of the rear and front
cover plates on the ALUCORE edges.
Table M.1: Chassis construction sequence
118
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