Design of a rear frame for a formula student race car CST 2010 › mate › pdfs › 11992.pdf ·...

Design of a rear frame for a formula student race car

CST 2010.051

Erik Stoltenborg

Eindhoven, July 9, 2010

Supervisor: P.C.J.N. RosieleTechnische Universiteit EindhovenDepartment of Mechanical EngineeringSection Control Systems Technology

Abstract

In the formula student race the competition is high, therefore improvements have to be madeevery year. For this years rear frame, it was demanded that it would be stiffer and lighter. Whichwas achieved by designing a compact tubular rear frame.

Contents

1 Introduction 2

2 Design Specification 32.1 Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Suspension lay-out and loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3.1 Lay out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3.2 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Design 93.1 Tubular frame lay-out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Suspension box mounting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3 Engine Mount . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.4 Pick up points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Analysis 144.1 Finite element analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.1.1 Pick up points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.1.2 Suspension mounting piramide . . . . . . . . . . . . . . . . . . . . . . . . . 20

5 Conclusion 22

1

Chapter 1

Introduction

Every year University Racing Eindhoven (URE) designs a car which they enter in a internationalcompetition; Formula student. This competition consist of 80+ university teams, who will competeon a design level as well as a racing level. It provides the students with a real-life exercise in designand manufacture and the business elements of automotive engineering. URE has been reasonablysuccessful (top ten) in the design contest, and are looking to improve every year. (herschrijf)Last years car, the URE05, preformed well but has room for improvement. In particular thesuspension and the rear frame, so these shall be redesigned. The rear frame will be redesignedalongside the suspension, making it possible to iterate to an optimal rear-frame and suspensionconfiguration. This rapport concerns the design of the rear frame.First the conditions on the race track will be discussed and its consequences for the frame. Thenthe requirements on performance will be discussed. After that the the design will be discussed.Finally the design will be analyzed using FEM analysis to evaluate the frames performance. Thisis followed by a conclusion and some recommendations for future designs.

2

Chapter 2

Design Specification

2.1 Rules

The car has to comply to some rules stated by the FSAE, these rules are made to keep thecompetition safe and fair. The rear frame has to comply to a couple of very restricting rules, whenthese are decisive for the design they will be mentioned throughout the report.

2.2 Stiffness

The rear frame will have to endure the forces of the suspension and engine as the car races alongthe track. The rear frame deals with forces of the rear suspension and the reactional forces onthe engine. The main goal is connecting all these parts in a structurally sound matter. The carsstiffness will be tested by a torsional test.The stiffness of the suspension called the anti-roll stiffness. This is a parameter used to tune howa car reacts in cornering. The overal car stiffness is calculated from 2.1. A car with a low anti-rollstiffness tends to understeer which is not desirable. A chassis’ stiffness needs to be as high aspossible, however it can not be at cost of the overal weight of the car.

1

koveral=

1

ksusp+

1

kchassis+

1

ksusp(2.1)

From 4 times the anti-roll stiffness(50 kn/rad) and higher, it will become less favorable to furtherstiffen a chassis for it has a small effect on the handeling of the car, with respect to the increasein weight [1]. Any increase in stiffness without a weight penalty is of course desirable. Thereforeit is demanded that the weight will not be higher than last years frame, yet the stiffness needs tobe higher than 200 kn/rad (4 times the roll stiffness).

2.3 Suspension lay-out and loads

In this section we will discuss the suspension lay-out and the forces it applies to the frame. Firstthe difference between the old and new suspension will be shown and then some demands arestated , made in cooperation with the suspension designer.

2.3.1 Lay out

Unlike last year, the suspension points will not all come together in one spot on the rear frame.The difference in layout is shown in figure 2.1.

3

Suspension lay-out and loads 4

New Suspension Lay-out Old Suspension Lay-out

Figure 2.1: The new and the old suspension lay-out

The main difference is that the control rods no longer all meet in the same point. This choice wasmade to keep the control rods as short and straight as possible, which results in a stiff and playfree suspension. To make discussing the separate control rods easier they are numbered in Figure2.2. First we discuss the demands on their placement/orientation. Then we will discuss the loadson these rods.

Upper A-arms

Push Rods

Tie Rods

Lower A-arms

3

2

15

64

Figure 2.2: The new suspension lay-out

Now, in cooperation with the suspension colleagues, the following demands were stated regardingthe control rod placement.

• Control rods 2 and 3, connect directly to the mainhoop/monoque.

• All control rods should be as short and straight as possible.

• Control rod 1 should be shorter than control rod 4*

• Control rod 1, 4, 5 (the lateral rods), should be arranged in an L-shape*. See Figure 2.3.


* these demands ensure good suspension characteristics on which we shall no further elaborate.This resulted in a limited space to vary the placement of the rods depicted in Figure 2.3. Thezones on which the control rod can be connected to the frame are shown by the translucent squarein their respective color.

Control Rod 2

Control Rod 4

Control Rod 5

4

1 5

Chain

Figure 2.3: A side view of the suspension lay-outs. The control rod placement zones are markedin their respected color

2.3.2 Loads

The loads on the wheels are transferred to the frame through the control rods. There are severaldifferent scenarios in which the loads are completely different: acceleration, braking, cornering,bump (symmetrical suspension travel due to a ’bump’) and static position.The forces on the rods in bump are shown in Figure 2.4, this graph shows the way force developsas suspension travel increases. These forces are also shown in a more graphic way in Figure 2.5.


��

��

��

��

��

�

��

��

��

��

��

vertical displacement [mm]

rod

forc

e [N

]

��4

6�

com

pres

sion

tens

ion

Figure 2.4: Forces in bump in each control rod

Bump

800 N800 N

1986 N 1986 N

330 N330 N

Figure 2.5: Bump Loadcase

This process was repeated for cornering, braking and acceleration in Figure 2.6, 2.7 and 2.8respectively. These forces will be used in chapter 4, and are obtained from the suspension designer.Do note that the forces the engine inflicts on the frame are not depicted here. These cars can reachup to 35ms−2 cornering and and bump, and up to 15ms−2 in acceleration and braking. This is avery significant force, since the engine weighs around a 100 kg, yielding a force of F = m·a = 3500.


Cornering

3400 N0 N

1500 N 1986 N

327 N45 N

Figure 2.6: Cornering Loadcase

Acceleration

226 N226 N

237 N 237 N

1136 N1136 N

Figure 2.7: Acceleration Loadcase


Braking

415 N415N

1287 N 1287 N

563 N563 N

Figure 2.8: Braking Loadcase

Chapter 3

Design

Before we start out the design it is useful to look to first draw out a couple of things that arefixed. In Figure 3.1 the layout of the URE06 can be seen, excluding the rear frame, drive shaftsand motor appendages.

Figure 3.1: Overview of the URE06 design

Last years rear frame was rather large and went around the differential. With this years designthe bulkhead will be in front of the differential. The engine and differential placement are given.Rules state the engine can not be a integral part of the frame unless a full FEM analyses of theengine is made, which in the time frame, does not seem achievable.

3.1 Tubular frame lay-out

In Figure 3.2, the region where the rear suspension pick-up points could placed is depicted incolor. These points should end up on a nodal point of the tubular rear frame.

9

Tubular frame lay-out 10

Control Rod 2

Control Rod 4

Control Rod 5

4

1 5

Chain

Figure 3.2: A side view of the suspension lay-outs. The control rod placement zones are markedin their respected color

The previous rear frame went over and around the differential assembly. The lowest configuration,is to place the highest pick-up point between the rear sprocket and the engine. This is a tightfit, but there is sufficient space for such a configuration. Keeping the center of mass low improvesthe cars’ handling. When this discission was made the other two optimum points for the rearsuspension were calculated, resulting in the placement depicted in Figure 3.2.Now we connect these parts so that control rod force lines meet exactly in the center of a tubeframe node. Which yields the following frame.

Figure 3.3: Sideview of the design

So a cross tube is placed behind the sprocket, inside chain and right behind engine. This isdepicted more clearly in figure 3.6

Suspension box mounting 11

Figure 3.4: ISO view of the bulkhead, the chain is depicted in purple.

This design choice made it possible to keep the frame very low and compact, which is favorablefor stiffness and ride characteristics. The bulkhead was triangulated this way to accommodatethe bottom control rod, which due to a demand of the suspension designer had to be at thatheight. The bottom part is fixed using a thin plate, also used to accommodate anti roll bar.The triangulation makes sure the tubes get loaded in the axial direction, avoiding bending. Theloads are transferred back to the monocoque. Unfortunately bulkhead still had to extend to thebottom/ride height of the car, for safety reasons, dictated by the rule:

• The lowest point of the rear must be the chassis itself i.e. not the engine.

To accommodate the tie rods, a small subframe is made to reach the desired point. This frame isrequired to be laterally stiff, hence the triangulation. This also serves as the quick jack, which incompetition is used to quickly jack up rear of the car. Hence this subframe has to be sufficientlyvertically stiff as well.The main roll hoop, is triangulated back to the monocoque.

• The Main Hoop must be supported by two braces extending in the forward or rearwarddirection on both the left and right sides of the Main Hoop.

• The attachment of the Main Hoop braces must be capable of transmitting all loads fromthe Main Hoop into the Major Structure of the Frame without failing. From the lower endof the braces there must be a properly triangulated structure back to the lowest part of theMain Hoop.

3.2 Suspension box mounting

To accommodate the suspension box a triangulated square piramid is put on top of the frame.The top of this piramide is exactly placed where the springs force lines cross. These meet in avirtual point in the middle.

Suspension box mounting 12

Figure 3.5: Suspension box mounting

The suspension needs to be precisely in the plane it was designed in, if we’d turn the dampertops they would be restricted to move. Since the plane in which the damper tops is so differentfrom the plane in which the piramide lies, a complex box was chosen to connect these parts. Thebottom has four pockets hollowed out to remove material where it’s not needed.

Front

Bottom

Side

Figure 3.6: The piramide cap

Engine Mount 13

3.3 Engine Mount

Figure 3.7: Engine mount

For engine mounting a basic tripod design was used, this is repeated twice in the front and in theback. These connect to either frame tube nodes or monocoque hard points. The tube sizing isdetermined by the simulations in chapter 4.

3.4 Pick up points

The pickup points are the points were the control rods are attached to the frame. These are locatedin the tube nodes, they are connected through the tubes, welded to both sides of the tube. Thisthrough-tube mounting allows the back of the tube to ’know’ that there is a force induced in thefront. The mount now gets more resistent to the moment developed about the tube center-axis.The improvement made by doing so is shown in chapter 4.1.1. The pick up points are hollowedout to keep the weight down. It is assumed control rods only move in the vertical plane i.e. thewheel does not move in the length direction of the car, therefor the control rods stay in a verticalplane.

Figure 3.8: Pick up point

Chapter 4

Analysis

Some of the frame tubes sizes are determined by the safety rules. To determine the other tubessizes a finite element analysis will be done on the rear frame using finite element analysis. Thiswill allow us to see forces which occur in different scenario’s. From these results we can dimensionthe tubes.Then other small components such as the pickup points and the suspension box mount will becalculated using unigraphics.

4.1 Finite element analysis

To analyse the tube forces in the main structure of the frame a finite element model is used. Themain hoop and its bracing was excluded because it does not significantly add to the stiffness ofthe frame. Also some triangulation differs from the actual frame: the plate in the bulkhead isreplaced by a beam, so are the front engine mounts. If the simulation yields high forces here thenmore attention will be payed to these parts.Simulations were run for the previously named scenarios: bump, cornering, braking and accelera-tion. The main forces which occur here come from the control rods and the engine.

Engine mount point

Monocoque hard point

Engine subframe tubes

Frame Tubes

Figure 4.1: The finite element model

14

Finite element analysis 15

To account for load that the engine transfers via the engine mounts, the engine will be representedin the simulation by a rigid frame connecting the engine mounts. Note that the engine takes awaythe frames last mechanism, of the top two tubes.

Engine representation

Figure 4.2: Engine representation

Figure 4.1 and 4.2 then put together in the finite element analysis, using the loadcases defined insection .The resulting finite element model then yields results as depicted in Figure 4.3.

-1.111e+003

-8.672e+002

-6.230e+002

-3.788e+002

-1.346e+002

1.096e+002

3.538e+002

5.980e+002

8.422e+002

1.086e+003

1.331e+003

job1Comp 11 of Stress

Inc: 0Time: 0.000e+000

Y X

Z

1

Figure 4.3: Axial tube forces in bump


-4.175e+003

-3.436e+003

-2.697e+003

-1.958e+003

-1.219e+003

-4.793e+002

2.599e+002

9.991e+002

1.738e+003

2.477e+003

3.217e+003


Inc: 0Time: 0.000e+000

Y X

Z

1

Figure 4.4: Axial tube forces in cornering

-1.108e+003

-8.802e+002

-6.523e+002

-4.244e+002

-1.965e+002

3.143e+001

2.593e+002

4.872e+002

7.152e+002

9.431e+002

1.171e+003


Inc: 0Time: 0.000e+000

Y X

Z

1

Figure 4.5: Axial tube forces in braking


-1.969e+002

-1.366e+002

-7.620e+001

-1.583e+001

4.454e+001

1.049e+002

1.653e+002

2.257e+002

2.860e+002

3.464e+002

4.068e+002


Inc: 0Time: 0.000e+000

Y X

Z

1

Figure 4.6: Axial tube forces in acceleration

Now we could determine all tube sizes, all tubes can be sized to the minimum stated by the rules.Tubes for which no minimum thickness was stated will have a wall thickness of 1mm. Outsidediameters(OD) are first chosen to take the load, making sure tubes never get deformed plastically,σtube <

23σy. In addition, since compressive forces are also present,σtube <

23σbuckling. In addition

a frame must be able to take a knock, therefore there needs to be a margin, or some other spikein load. Therefore the maximum load transfer the control rods can give, which is about 5.6 kNbefore failure, was used as load. This is used along with acceleration in any direction of 40ms−2.This along with practical considerations regarding welding and other construction points yieldedthe final tube sizing.Now to make a stiffness comparison a torsional simulation was done as well, this is done byapplying a load which ramps over time and plotting that against the angular deformation in thebulkhead. This was done to last years frame too for comparison. The result is depicted in Figure4.7.


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 105

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9Rotation of bulkhead versus aplied moment

Nm

Rot

atio

n of

bul

khea

d [ra

d]

URE06URE05

Figure 4.7: Frame torsional test

What can be learned from this is that last years frame was slightly under 200kNm/rad(theirdemand), however the new frame has a torsional stiffness of 660kNm/rad. If you compare thetwo frames, this does make sense. The difference is shown in Figure 4.8.

Figure 4.8: Frame torsional test

The new frame is a lot shorter and a lot more dense, which explains the higher resistance totorsion. In addition: new frame is also lighter, it weighs 10.3 kg, which is 2 kilo’s lighter than lastyears frame. This difference is due to last years long main hoop bracing and the big rear bulkhead.

4.1.1 Pick up points

The pickup points design was chosen to be simple, it can be easily made by turning and milling.However the mounting to see the effects of the mounting (see section 3.4) some simulations to test


the effects on stiffness. It is assumed dat forces remain in the control rods(vertical) plane. Forthis simulation, a force Fr of 500, at a 45◦ angle is applied, see figure 4.9.

Fr

Figure 4.9: Pick up point loadcase

56.1

51.4

42.1

46.8

37.4

32.7

28.0

23.4

18.7

14.0

9.4

4.7

0

Von mises stress in MPa

Figure 4.10: Through tube mounting stress

97.8

89.7

73.4

81.5

65.2

57.1

48.9

40.8

32.62

24.5

16.3

8.2

0

Von mises stress in MPa

Figure 4.11: Surface mountings stress


.23

.21

.17

.19

.16

.12

.10

.08

.06

.04

.02

0

Von mises strain in μm/mm

.14

Figure 4.12: Through tube mounting strain

.41

.37

.30

.34

.27

.20

.17

.13

.10

.07

.03

0

Von mises strain in μm/mm

.24

Figure 4.13: Surface mountings strain

As can be seen the stresses and strains the design depicted in Figure 4.10 and 4.12 are significantlylower than in the surface mounted pickup point. The rod through allows the rear of the tube tohelp cope with the vertical component of the force. As can be seen in Figure , the rear of thetube can not ’feel’ the forces applied in the front, which causes high stresses and deformation inde front of the tube. The maximum deformation (under the same load) in the tube is a factor twosmaller, the same goes for the stresses.

4.1.2 Suspension mounting piramide

The pyramid was made so that the suspension forces will end up exactly in the top, forces will beguided through the tubes neatly. For this a simulation was made also.

Figure 4.14: Piramide forces


-2.627e+002

-2.354e+002

-2.081e+002

-1.807e+002

-1.534e+002

-1.261e+002

-9.875e+001

-7.142e+001

-4.409e+001

-1.676e+001

1.057e+001


Inc: 0Time: 0.000e+000

Y X

Z

1

Figure 4.15: Forces on the piramide in bump

-6.529e+002

-5.497e+002

-4.464e+002

-3.432e+002

-2.399e+002

-1.367e+002

-3.342e+001

6.982e+001

1.731e+002

2.763e+002

3.796e+002


Inc: 0Time: 0.000e+000

Y X

Z

1

Figure 4.16: Forces on the piramide in bump

As can be seen the added stress the to the rest of the frame is low, forces do not exceed 650N.Therefore the tube size here is 20mmx1mm.

Chapter 5

Conclusion

In the formula student race the competition is high, therefore improvements have to be made everyyear. It is also a race with a strict set of safety rules which limit the design freedom.For this yearsrear frame, it was demanded that it would be stiffer and lighter. The design of the rear was donein collaboration with the suspension designers, iterating towards an optimum. A method whichtakes longer than working separately, but in the end yields a optimal result.The result is a small tubular frame, kept as compact as possible. Because of this the torsionalstiffness is 3 times higher than last year rear frame, but also 2 Kg lighter. By placing tube nodesat control rod pick up points, the need for a complex machined bulkhead was gone. Instead pickup points are simple turned/milled parts which can be welded in the frame nodes. The frame andall its components were analyzed using FEM software, which was used to dimension the tube size.

22

Bibliography

[1] J.D.G. van Kerkhoven. Design of a Formula student car (DCT 2008.154). Eindhoven Univer-sity of technology, 2008.

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