Design of a tubular steel space frame for a Formula Student race car

Transcription

1 Design of a tubular steel space frame for a Formula Student race car A.J. Kemna CST CST report Eindhoven University of Technology Department of Mechanical Engineering Control Systems Technology Eindhoven, January 01, 2011

2 A chassis is nothing more than the car s largest bracket. Carrol Smith The race will start at 2 o clock. Prepare yourself for the race. Are you not ready? The race will start at 2 o clock. Known since humanity began racing By failing to prepare you are preparing to fail. Benjamin Franklin 2

3 1 Preface The goal of the rear frame was to make the best possible design and this report will summarize the design proces. However there are two additional goals of this report: (1) A good performance of the design event of the Formula Student competition and (2) The design of the successor of this rear frame. The reader is adopted to be the person who participate in one of the above points. To follow the red line of thinking of the design judges every part of the report is build up in three phases: What did you do? Why did you do it, including theoretical proof. Did the change work out, including practical evidence. To make sure that the conversation with the design judges can be optimized a few things have been added to the report. There are many different design concepts and layout concepts added, together with a large number of pictures and drawings. Also during the design itself a few things have been done to make sure that the judges will be well informed (and hopefully impressed): a mockup has been build after the first design to give practical prove to the theoretical design choices. Besides this a torsional stiffness test of the URE05e has been done to get an indication of the design goal. The same will be done with the URE06 to verify the design. 3

4 2 Abstract Formula Student Competition Formula Student is a project for technical students to design, build, test, and race a single seated formula style race-car. The project greatly improves knowledge and experience of the future engineer. Teams around the world gather on big international events to compete with their car against more then 450 different teams. Teams do not only get judged based on the race results, but also their technical design, costs, and business presentations. University Racing Eindhoven URE exists since 2003 and has participated in various Formula student competitions around Europe ever since. Every year a new race-car is developed in which improvements and new idea s are implemented. Last year the team built its first electric car: the URE05e, which can be seen in figure 1. In URE will build its successor: the URE06. The URE06 will have an electric powertrain that is an evolution of the URE05e powertrain. Besides this, improvements are made on the suspension and chassis design. Figure 1: A design impression of the URE05e Thesis Objective The objective of this thesis is to design the rear frame of the URE06 in such a way that it can mount the electric components. The URE06 will have a chassis consisting of a carbon fiber monocoque at the front and a tubular space frame at the rear. The design of the monocoque and the pickup points of the suspension have been finished and will thus be considered as a design constraint. This thesis consists of a design specification in which the working environment and the design targets are explained. The design of the rear frame itself will be explained after which it is supported by a structural calculation and analyzed using the Finite Element Method. Points of considerations that are taken into account during the design phase are the competition regulations, weight, stiffness, costs and manufacturability. This thesis will be concluded with the recommendations for the next rear frame. 4

5 Contents 1 Preface 3 2 Abstract 4 3 List of symbols 6 4 Design specification Working environment Rules Working coordinate system Design constraints Suspension Loads Design targets Overview Stiffness Serviceability Weight Weight distribution Production Design Design concepts Lay-out concepts First design Mockup Final design choices Analysis Finite element analysis Chassis Motor bracket Suspension brackets: Standard system Suspension brackets: Specific loadcases Tube P4 support Head restraint Torsional stiffness Recommendations 33 8 Bibliography 34 9 Appendix A - Important rules Appendix B - Weight analysis Appendix C - Suspension Load cases Appendix D - FEM results 42 5

6 3 List of symbols Symbol Quantity Unit k Safety factor [-] F Force [N] σ Stress [N/m 2 ] u Deflection [m] L Total length [m] a Length [m] E Young s modulus [N/m 2 ] I O Second moment of area [m 4 ] D O Outer diameter [m] D I Inner diameter [m] M Moment [Nm] α Angle [ ] z Difference in height [m] K Stiffness [Nm/ ] Table 1: List of symbols 6

7 4 Design specification The design specification consists of two parts, both describing the essence of the assignment. Every team has particular rules which it has to maintain during the design, without these rules and constraints the team will be unable to build a proper car. These are described in the working environment. In the design targets section the different targets of the rear frame will be discussed. These are the targets set to make sure that the rear frame of the URE06 is an improvement on the URE05 and URE05e. 4.1 Working environment In this section the working principles of University Racing Eindhoven and the Formula Student competition will be discussed. There are certain rules that must be maintained in order to be able to drive during the competition. The design constraints, systems that cannot be changed anymore, are then explained after which the suspension loads are given. The suspension loads are used for the loadcases on the rear frame in the FEM analysis Rules The first and most important thing that should be done prior to the designing is reading the rules. The rules are separated into three different articles. The first and most important one is the 2011 Formula SAE rules. Every Formula Student organization in the world uses these rules as a basic platform for their competition and apply additional rules if considered necessary. University Racing Eindhoven will participate in Formula Student England Class 1A, Formula Student Germany Electric and Formula Student Austria Electric. The different rules are stated in the list below, this means that the rear frame will have to satisfy four different rule books Formula SAE rules[6] Formula Student England Class 1A[7] Formula Student Germany Electric[8] Formula Student Austria Electric (These rules are not known yet.) The additional 2011 rules for Formula Student Germany and Austria were not known at the time of writing, therefore the rules of 2010 were used. The most important rules necessary for the rear frame are stated in chapter Working coordinate system In order to eliminate any misunderstandings, a sign convention is provided in figure 2 which is based on the international norm ISO 8855[9]. The point (x,y,z) = (0,0,0) is located on the road, directly under and between the rear wheel center points Design constraints Beside the rules there are a number of design constraints which should be taken into account. There are five systems which are fixed in both size and position. The global size and position are referred to in figure 3. The carbon fibre monocoque (orange) The drivetrain, fixed in z and x direction (green) The suspension geometry (pink) The spring-damper system (blue) 7

8 Figure 2: Sign convention used by University Racing Eindhoven The chain, primary sprocket fixed in y plane of the drivetrain (red), (The primary sprocket on the motor side can be repositioned) (a) Isometric view (b) Topview Figure 3: The five different systems which are fixed in size and position. In the beginning of the design phase for the rear frame there was an additional design constraint which involved a backup motor, controller and batterybox. This plan was rejected during the design phase and will therefore not be treated in this report. The design constraints which are fixed in size but can be changed in their position in the rear frame are shown in figure 4. Two AGNI motors (light red) The battery box (light green) Two controllers (gray) 8

9 The wiring loom (not shown) (a) Isometric view (b) Topview Figure 4: The three systems which can be repositioned, now shown in the final position Suspension Loads The loads going trough the connection rods of the suspension are depicted in table??. Beside the sign convention used by University Racing Eindhoven there is also a naming convention for the suspension. This can be seen in figure 5. This figure will further explain table??. The suspension loads are used for the FEM analysis done in chapter 6. Figure 5: The naming convention for the suspension rods used by University Racing Eindhoven, the names on the left size are the same on the right. URE06 forces Static position [N] Acceleration [N] Braking [N] Cornering [N] Bump [N] P P P P P5 (Tie rod) P6 (Pull rod) Table 2: Suspension forces for worst case scenario s on the URE06 [4]. Negative values are compressive forces. 9

10 4.2 Design targets In this chapter the design targets of the rear frame of the URE06 will be discussed. A summary is given beforehand in chapter after which each subsection will go into detail about their specific target Overview In table?? an overview of the design targets can be seen. Stiffness Battery removal time Motor removal time Weight Production time > 4000 Nm/ < 5 minutes < 5 extra minutes < 13 kg < 1 week Table 3: A summary of the design targets of the rear frame of the URE Stiffness To get an indication of the chassis stiffness Helder [15] has measured the previous cars of University Racing Eindhoven. The results have been summarized in table??. Car Chassis stiffness Car mass Specific Stiffness [Nm/ ] [kg] [Nm/ /kg] URE URE * URE * URE05e URE06 target Table 4: Measured stiffness and mass of the cars troughout the years. estimates. Numbers with a * are Although the chassis stiffness does not need to be more than 2200 Nm/, according to William B. Riley (Cornell Formula Student Team) [16], it is necessary that the stiffness of the chassis should at least exceed its predecessor. The suspension geometry of the URE06 has been changed, to make sure that these changes can be verified, other variables of the car needs to be as constant as possible. The stiffness of the URE06 should therefore be at least 4000 Nm/ (the real predecessor of the URE06 is the URE05), and the specific stiffness should be higher than the previous car, as the decrease of weight is one of the important design goals of the management Serviceability The main focus of attention for the rear frame is the serviceability for the mechanics. Opposite to the design and manufacturing phase, losing time during testing is an absolute killer for the team and must be avoided at all times. The second and third quote found at the front page perfectly explains this main focus. The designers have to put in their ultimate effort to make sure the mechanics have an easy job servicing the vehicle. Three targets have been set that will improve the predecessors chassis: Remove the battery within 5 minutes and with less than 8 bolts. Remove the motors within 5 extra minutes and with less than 5 extra bolts. The brush holders of the motors must be easily accessible. 10

11 4.2.4 Weight To determine the maximum weight of the rear frame a weight analysis has been made, this can be seen in the appendix, chapter 10. This weight analysis of the URE05e resulted in a weight budget for the URE06. To make sure the weight of the URE06 is not excessively larger than its competitors it needed a weight reduction of at least 30kg compared to the URE05e. In the appendix it can be seen how this reduction can be achieved. A weight reduction of the rear frame by 5.5kg is needed which gives the new frame a weight budget of 13kg Weight distribution Different studies have been done on the perfect weight distribution of a Formula Student car. Four were conducted by team members of University Racing Eindhoven during the last years (Lamers [10], Hopmans [11], Spierings [12] and Janssen [13]). Even though they all succeeded in finding the perfect weight distribution, the results were spreaded around the 50/50 percent range with a variation of 8 percent. This means that the perfect distribution could be 42 percent or 58 percent to the front. Although the placement of heavy objects as the battery box and motors are a very good tool to change the weight distribution, the time and place needed to do this is very limited. Because the results of "a perfect weight distribution" are - as of today - not proven, the possible advantages do not weigh up against the extra design time needed. The weight distribution will therefore be neglected Production To make sure that the car will be ready in April, it is necessary that the different components do not have excessively long production times. In the past it has been proven that a rear frame could be cut and welded within one week. The goal for the URE06 frame will be the same. The fabrication time of the rear frame should not exceed one week. The use of exotic material (i.e. titanium) needs to be as little as possible to make sure that repairs can be easily done on track. 11

12 5 Design This section will have a chronological time line which is maintained during the assignment. First a design begins with concepts where different types of designs are discussed. When one concept is chosen various layout concepts of the different subsystems are shown. These are then worked out in the first design after which a mockup will be build to verify the first design. When an early simplified FEM analysis shows that the design is feasible the final design is discussed. 5.1 Design concepts In this section a comparison will be made between a steel tubular rear frame and a full Carbon Fiber Reinforced Plastic (CFRP) monocoque. The (dis)advantages of both concepts will be explained and weighted against each other to form a viable conclusion. In the comparison in table?? the key design targets will be compared. In addition several secondary targets as cost, design time and present design knowledge are added. Steel space frame Full CFRP Stiffness in bending 0 + Stiffness in tension 0 + Stiffness in torsion 0 ++ Weight 0 + Serviceability ++ 0 Fabrication + - Manufacturing time ++ Cost ++ Design time 0 0 Present design knowledge + 0 Total nr. of Table 5: Comparing steel rear frame vs. full CFRP Stiffness In the report of Andries van Berkum [1] can be seen that a plate construction is stiffer than a tubular spaceframe. A full CFRP monocoque will be 2 times stiffer in bending, 1.6 times in tension and 2.6 times in torsion. This comparison is done with a maximum outside dimension and having identical material volume. Weight A empirical comparison has been done between the weights of the best cars in the FSAE competition [3][2]. It can be concluded that the difference between a full CFRP monocoque and full steal space frame remains within the 10kg. Although a CFRP monocoque can be made slightly lighter, this is normally not achieved in the first year of implementation where the CFRP monocoques are heavier than the steel spaceframes. Looking only at the rear frame the difference would be smaller than 5kg. This is nearly negligible for a team that focuses more on serviceability and time efficiency. Fabrication and Manufacturing time When taking a closer look at the time between the final design and final product, the steel spaceframe comes out as an absolute winner. A steel spaceframe takes around 1 to 2 weeks to fabricate in the past years at URE. The monocoque of the URE05 took around 7/8 weeks. This was mainly due to the long manufacturing time of the positive and negative molds. The molds are also the reason why the amount of actions needed to complete the product is much greater for a CFRP product. Design time and knowledge 12

13 Although the time needed to design the two chassis do not differ that much, it is especially the analysis that makes the difference. A spaceframe requires basic mechanical knowledge and this is widely known in the team. This can also be analyzed using Marc Mentat which is offered by the Eindhoven University of Technology. The knowledge needed to analyse a CFRP chassis is still very new in the team and not readily accessible to implement it. Conclusion As can be seen in table?? it can be concluded that a steel rear spaceframe is favorable, mainly due to the better serviceability. Besides this the manufacturing time and total cost is much lower than the CFRP chassis. 5.2 Lay-out concepts Multiple layout concepts have been analyzed to make sure the best suitable solution is found for the URE06. In the concept phase it is important to look for every possible solution as it is easier to make changes and it will cost less money and time, opposite to the fabrication/testing phase. Five different options are shown in figures 6, 7, 8, 9 and 10. The explanation of the layouts are described in each caption. The golden rule in University Racing Eindhoven is that changes should not be made to things that work. This means that gearing systems as a planetary set, direct gearing and the bevel are ruled out. To make the choice between the two chain geared layouts (figures 8 and 9), two extended designs have been made. It was discovered that the motors would collide with the suspension system in concept 4. Another problem with this concept was the chain which would collide with the battery box. It was therefore chosen to use concept 3 where the motors will reside between the battery box and the drivetrain. (a) Topview (b) Sideview Figure 6: Concept 1. The motors are located underneath the drivetrain and connected through direct gearing. The battery box is lying on its back. 13

14 (a) Topview (b) Sideview Figure 7: Concept 2. The motors are located next to the drivetrain and connected with a planetary set. The battery box is lying on its back. (a) Topview (b) Sideview Figure 8: Concept 3. Chain reduction, the motors are located between the standing battery box and the drivetrain. (a) Topview (b) Sideview Figure 9: Concept 4. Chain reduction, the motors are located on top of the battery box which is on its back. 14

15 (a) Topview (b) Sideview Figure 10: Concept 5. The motors are located underneath the drivetrain, connected via a bevel or hypoid. The battery box is lying on its back. 5.3 First design The first design is the design in which every component fits properly and which was ready for FEM analysis, see figures 11 and 12. The mockup, described in subsection 5.4, was made with this design. This chapter will shortly describe the design choices for the different subsystems of the rear frame. A very important point of notice is that the chassis complies to rule B8.14 of the FSUK Class rules 2010 [7]. This rule makes it mandatory that the the motor, battery and controllers are protected by a side impact structure. Figure 11: The first design of the rear frame in which only the left motor bracket is shown. Motor bracket Figure 13 shows the motor bracket. It is statically determinate supported by a spring leaf and two rod aerials. A major problem with this design is that the chain is going straight through the upper tube. This first design indicates a bracket of 300g and each motor can be removed with 4 bolts after when the battery is removed. 15

16 (a) Top view (b) Side view Figure 12: The first design of the rear frame, including the different subsystems. Notice that the motors are placed with the brush holders facing outside. (a) Isometric view (b) Side view Figure 13: Section view of the motor bracket shown in green, with the (x,z) plane as cutting plane. Battery mounting At the time of writing the design of the battery box itself was not started. A mounting of the box was therefore not designed and will not be discussed. Damper mounting The mounting for the dampers is shown in figure 14. The placement of the dampers is chosen to make sure that the mechanics can reach it very easily. To make sure that the damper forces are redirected correctly a pyramid shape is needed. A force parallel to the plane of a cross is very weak but as soon as the pyramid is heightened it is a statically determined system. 5.4 Mockup As soon as the first design has been made a mockup can be made. For a designer this is necessary as it gives them a much better insight and feeling of the structure. Beside for the visualization of the designer there are a number of things that can be checked: The designer will get a better feeling whether or not it is possible to remove the battery and motors. The designer will get a better insight which of the diagonals are really necessary and which are less important. The wiring loom can be made more accurately using a mockup. 16

17 (a) Isometric view (b) Rear view (c) Side view Figure 14: The first design of the damper mounting. The spring/damper system are in blue, the supports are shown in green. The "reachability" and serviceability for the mechanics can be checked (the brushes of the electric motor, cooling ducts, bolts and nuts, etc.). The fabrication of the mockup is very simple. The materials used cost around 40 euro s and it took 5 hours to manufacture it. This particular mockup is a 1:1 model made out of PVC tubes and duct-tape with an accuracy estimated to be around 1 cm (see figure 15). The following was discovered: The diagonal under the battery box is needed. This diagonal fills up one of the largest open squares in the frame, thus creating torsional weakness. The diagonal under the motors is needed for the same reason as stated above. The diagonal can be made out of a plate steel cross. This adds, roughly measured, the same stiffness as a diagonal tube. Figure 15: The mockup made out of PVC tubes and duck-tape. 17

18 (a) The diagonal under the battery tested as a plate cross.(b) The arrow is pointing towards the diagonal under the motors. Figure 16: The diagonal under the motors and the battery were found to be crucial for the torsional stiffness. 18

19 5.5 Final design choices After the first design and the mockup were analyzed, a few things were changed in the final design. The most important changes are listed below, see figures 17, 18 and 19. The different sub systems will be explained more thoroughly further down this chapter in the caption of figures 20 and 21., The position of the motors were mirrored such that the brush holders face each other. This is done for three reasons: Throughout the year the management decided to use another type of controller. The dimensions of this type was bigger than the regular one. This meant it could not fit between the battery and monocoque anymore, as can be seen in figure 12. Rule B8.14 [7] made it mandatory that the controller is protected with a side impact structure. The controllers are therefore moved to the back of the vehicle between the two drive trains. To make room for this the sprocket (and thus the motors) needed to move sideways, the motors were mirrored for this purpose. The mounting points of the motors were located on the inside of the frame (almost directly on the (y,z) plane), the brackets would therefore be loaded in the middle of the tube. Mirroring the motors made it possible that the brackets could be supported near stiff nodes of the chassis. With the chains on the inside of the frame it was very inconvenient to make a proper bracket for the suspension rods P1 and P4, the replacement of the motors made this easier. The damper support pyramid has been made higher to increase the systems stiffness, see figure 18. The mounting strips are therefore horizontally instead of vertically in order to make it fit. The motor bracket has an extra flange attached to withstand the torsion moment. The tube on which P1, P4 and the damper rocker mount support on, has been made thicker to accommodate the bracket for the damper rocker. It now measures 25.4mm outer diameter and 20mm inner diameter. The FEM analysis showed that the P1 mount wasn t possible in the first version. The mounting point has been changed that it can accommodate the forces. The battery box was not ready on the time of writing this report, the final design of this bracket will therefore not be included. Figure 17: Isometric view. The controllers are placed between the drive trains which needed the motors to be rotated 180 in the z direction to make it fit. 19

20 Figure 18: Side view. Notice that the battery box has been moved forward and nearly touches the monocoque to create more space for the motor. The side impact structure is now protecting all the high voltage components. Figure 19: Top view. There is still room near the motors and controllers for a cooling system. Notice that the bracket for the controllers are not designed yet as the placement is not determined at the time of writing. 20

21 (a) Isometric view (b) Side view Figure 20: The bracket of the motor is shown in green. It can be removed with just 3 bolts after the battery box has been removed. (a) Isometric view (b) Rear view (c) Side view Figure 21: The final design of the damper changed in two ways: The pyramid has been heightened to withstand the forces better and the bracket itself is horizontally oriented instead of vertically. The black cylinder shows the maximum clearance the damper needs. There are however two design targets that did not make it into the final design: The brush holders are not easily reachable. This is due to the fact that the motors had to be rotated, see above for the explanation. However because of the short removal time of the motors (within 10 minutes) the brush holders can be reached easily after the motors have been removed. This is a very big progression compared to the URE05e in which the brush holders were not easily reachable plus it took more than 45 minutes to remove the motor. The weight will probably exceed 13 kg. At the moment of writing this is not sure yet as the rear frame has not been manufactured. The theoretic design showed a weight of around 12.6kg (excluding the main roll hoop) but in practice the weight will probably exceed the target because of the welds and paint. The excess in weight is due to the fact that the battery, motor and controllers have to be protected by a side impact structure. These tubes are twice the weight of the physically required tubes and covers nearly the entire rear frame. The rear frame is therefore over dimensioned with nearly a factor two. 21

22 6 Analysis In this section the chassis will be analyzed on both the maximum stress during operations and the torsional stiffness. It is therefore divided in two subsections. In section 6.1 the FEM analysis of the different parts of the chassis is given, this includes the chassis itself as well as the subsystems as the motor bracket and suspension brackets. In 6.2 an analysis of the torsional stiffness is shown. 6.1 Finite element analysis This section is divided in 6 different subsections, each describing the FEM analysis of a particular subsystem of/in the frame. The first section will describe the analysis of the chassis itself using Marc Mentat. The second subsection describes the FEM analysis of the motor bracket. The third and fourth section provides a standardized system for respectively the suspension brackets and the analysis of each suspension bracket itself. The latter two sections describe "vergeetmenietjes" for the suspension forces Chassis This section will give information about the FEM analysis of the entire chassis. The Finite Element Method package used to analyze this rear frame is Marc Mentat. This is due to the fact that the normal package used by University Racing Eindhoven (Unigraphics 5) is having trouble with meshing tubes in large quantities. Marc Mentat gives the opportunity to easily analyze a truss and beam system, without having to calculate the entire 3D system as Unigraphics does. The safety factor of the system has chosen to be the normal system of University Racing Eindhoven: Forces acted on the chassis: k chassis = 1.2 Maximum yield stress: k stress = 0.8 (Which results in a smaller yield stress.) There are four basic loadcases, as described in the design chapter 4.1.4, and an extra cornering loadcase with the forces on the other side of the chassis. For an indication of the boundary conditions see figure 22 which shows the bump loadcase. Bump Left cornering Right cornering Braking Acceleration With the safety factor and loadcase in mind the plan shown below is followed: 1. Model the rear frame using trusses and choose the surface A to be 1 mm 2, this makes the stresses similar to the forces. 2. Choose the material of the tubes and get an indication of the available tube dimensions in the market. 3. Choose the tube sizes according to the following steps. Also see chapter 12 for the excel file. (a) Run the model to get the maximum forces going through each tube. See figure 23. (b) Give all tubes minimum wall thickness of 1 mm for welding purposes. (c) Choose outer diameter depending on the maximum force reached. (d) Make sure the tubes do not buckle due to compressive forces. (e) Give the tubes the minimum sizes due to rules. 4. Assign the dimensions to the trusses and run the analysis to get the maximum stresses in the rear frame. See figure

23 Figure 22: The boundary conditions used in the model. It is assumed that the monocoque is infinitely stiff and the forces are going trough the connection rods to the brackets at their respective angle. 23

24 Figure 23: Acceleration loadcase. This is step 3a of the plan. The numbers indicate the forces going trough each tube. This is done for every loadcase in order to get the maximum force going trough the chassis in every possible loadcase. 24

25 Figure 24: Bump loadcase, including the area, this is the loadcase in which the chassis undergoes the maximum forces. This is step 4 of the plan, notice that the maximum stress does not exceed 84 MPa (three times lower than the yield stress of steel). 25

26 6.1.2 Motor bracket The safety factor for the motor bracket is different compared to the regular safety factor. University Racing Eindhoven uses a system for the drivetrain that makes sure that the chain is the first thing to break during driving. This means that instead of the maximum load on the part itself the loadcase is the maximum load until the chain breaks, this means a chain force of 15000N. See figure 25 for the FEM results. The flanges that were added in the final design are not taken into account for simplicity reasons, the flanges do not add strength in the radial direction. (a) Isometric view (b) Side view Figure 25: The maximum stress is given in MPa, black indicates a value above the yield stress of 300 MPa. Notice that this is only reached in the holes for the bolts where the tension force of the washers have not been taken into account Suspension brackets: Standard system The suspension brackets will be chosen to be as simple as possible and the manufacturing time as short as possible, a standardized system would therefore be convenient. In order to make this system for the brackets, four designs are analyzed on their strength. These four designs can be seen in figures 27, 28, 29 and 30. The first design (case 1) is the ultimate design from last years car, the URE06 combustion [5]. This design is optimized for the lowest stress, but the manufacturing time is long and expensive and the weight is enormous. Case 2, 3 and 4 are therefore designed as a substitute for the original system. They are analyzed to show which of the three substitute designs are stronger and lighter than case 1. Case 2 is lighter than case 1 but the forces go perpendicular into the tube, creating a lot of deformation. This problem is solved in case 3. The idea behind case 4 is that the welding spot will not go trough the tube, which will happen in case 3. For this simulation, a tensile force F r = 3500N is applied at an angle of 45 s to the bracket, see figure 26. Case 1 Case 2 Case 3 Case 4 Maximum stress [MPa] Mass [g] Deformation of tube [mm] Table 6: Results of the FEM cases for the pick up points, normalized to the maximum value respectively. The normalized results are given in table??. The standard system for the brackets is chosen to be case 4 because the maximum stress is the lowest while the weight and maximum deformation of the tube are nearly the same. With this basic system in mind the suspension brackets are analyzed on their specific design and loadcase in section

27 Figure 26: Pick up point loadcase (a) View in zx plane. (b) View in zy plane. Figure 27: Case 1, maximum stress given in MPa, black indicates a value above the yield stress of 300 MPa (a) View in zx plane. (b) View in zy plane. Figure 28: Case 2, maximum stress given in MPa, black indicates a value above the yield stress of 300 MPa 27

28 (a) View in zx plane. (b) View in zy plane. Figure 29: Case 3, maximum stress given in MPa, black indicates a value above the yield stress of 300 MPa (a) View in zx plane. (b) View in zy plane. Figure 30: Case 4, maximum stress given in MPa, black indicates a value above the yield stress of 300 MPa 28

29 6.1.4 Suspension brackets: Specific loadcases In this section the specific loadcases on the suspension brackets are analyzed to make sure that all the systems will never fail during driving. The figures each show a different bracket and will give an indication of the maximum stress in the part. All the forces have a total safety factor of k = 1.5. It is assumed that the dynamical loading is calculated with this safety factor thus the maximum stress is σ max = 300 [MPa]. The load cases can be seen in the appendix, chapter 11. The results of the FEM analysis have been summarized in table??. Suspension point number Description P1 See figure 32 P4 P5 See figure 31 Damper rocker mount See figure 33 Damper bracket See figure 34 The loads on the P4 suspension rod is more than 4 times lower then other suspension brackets. It is therefore assumed that the bracket will hold under the load. Table 7: Results of the FEM cases for the specific mounting brackets of the suspension rods (a) Side view. (b) Close up of the stressed parts. Figure 31: P5 suspension bracket. Results of the FEM analyis: the gray area is where the stress is higher than 300 MPa. This can be neglected as the clamping of the ring and bolts were not taken into account. 29

30 (a) Side view. (b) Close up of the stressed parts. Figure 32: P1 suspension bracket. Results of the FEM analyis: There are no areas where the stress is higher than 300 MPa. (a) Side view. (b) Close up of the stressed parts. Figure 33: Damper rocker mount. Results of the FEM analyis: the black area is where the stress is higher than 300 MPa. This can be neglected as the welding of the tubes is unpredictable. (a) Top view. (b) Close up of the stressed parts. Figure 34: Damper bracket. Results of the FEM analyis: the black area is where the stress is higher than 300 MPa. This can be neglected as the clamping of the ring and bolts were not taken into account. 30

31 6.1.5 Tube P4 support The loads on the P4 suspension rod is more than 4 times lower then other suspension brackets. It is therefore assumed that the bracket will hold under the load. However the attachment point of the bracket is in the middle of the tube (a few centimeters away from the fixed end), which makes it necessary to calculate whether the tube will not deflect too much (see figure 35). Equation 1 gives the solution for a built-in beam with a concentrated force, according to Fenner[14]. u a = F (L a)3 a 3 3EI o L 3 (1) With u a the deflection of the beam directly under the force F = 2000N at a distance a = 45mm from its end. Equation 2 gives the polar second moment of area of a thin hollow tube. I o = π 64 (D4 O D 4 I) (2) These equations give a deflection u a of 0.012mm which can be neglected. Figure 35: Close up of the rear frame, the tube is shown in green and the P4 bracket in red Head restraint According to the rules [6] the head restraint should be capable of holding a force of F r = 900N. Equation 3 gives the maximum stress of a tube under a force F. σ max = F 1/4π(D 2 O D2 I ) (3) A tube with outer and inner diameter of 8 and 6 mm respectively results in a maximum stress σ max = 40.1MPa. This is done in the ultimate case where the helmet is resting on only one tube (The head restraint consist of two tubes as the drivers heights differ, see figure 36). The yield stress of rolled steel is σ yield = 300MPa which therefore makes the head restraint correct according to the rules. 31

32 Figure 36: Isometric view of the rear frame, the head rest is shown in gray. 32

33 6.2 Torsional stiffness When the area s of the tubes are chosen the torsional stiffness can be calculated. A vertical load is applied to both rear wheel centers in opposite direction to simulate the torsional load while the monocoque is assumed to be infinitely stiff. The vertical load is recalculated in the force vectors going trough the suspension rod with help of Cadesh [4]. This is to make sure that the suspension stiffness is not added to the chassis stiffness. The torsional stiffness K of the chassis can then be calculated by measuring the angular deformation in the rear bulkhead. K = M α (4) M = 2F l (5) α = sin 1 ( z quickjack L quickjack ) (6) gives a torsional stiffness K = Nm/. This is in the same range as Erik Stoltenborg calculated his rear frame for the (never build) URE06 [5], we therefore assume that the model is correct. This is much higher as anticipated but can be related to the fact that the entire chassis is over dimensioned due to the Side Impact rules. 7 Recommendations Try to reposition the dampers in such a way that the three major components can be repositioned where they are protected by just 1 side impact structure (SI structure). In this design there are three separate SI systems which makes the rear frame over-dimensioned in weight( and stiffness). It is absolutely necessary to measure the (chassis)stiffness of the URE06 in order to evaluate the theoretical torsion stiffness calculations. When designing the rear frame of the URE06 it is advised to make a full monocoque instead of a hybrid. This will reduce the weight while increasing stiffness (no transition between carbon and steel). Plus the problem with the positioning of systems due to the side impact structure is decreased. However this mean that the mold need to be redesigned and manufactured which takes time and money. In the past few years a torsional stiffness test has not been a high priority activity, in order to keep improving on the chassis (and the suspension) it is very much recommended to do the torsional stiffness test of the URE06 as soon as it is built. 33

34 8 Bibliography References [1] van Berkum, A., Chassis and suspension design FSRTE02, pp , March [2] Website Rennteam Stuttgart, [3] Website Joanneum Racing, [4] Ozturk, C., Design and development of the URE06 rear suspension, pp , Nov [5] Erik Stoltenborg, Design of a rear frame for a formula student race car, CST , pp , Jul [6] Formula SAE International, 2011 Formula SAE rules, [7] Formula Student England, 2011 Formula Student Class 1A Rules, [8] Formula Student Germany Electric, 2010 Formula Student Electric Rules, [9] Internation Organisation for Standardization, Road vehicles - Vehicle dynamics and road-holding ability - Vocabulary, [10] Lamers, W., Development and analysis of a multi-link suspension for racing applications, pp , May [11] Hopmans, J.A.M., Analysis and development of Formula Student racing tyres, pp , Feb [12] Spierings, J.T., Performance analysis of a Formula Student racing car, pp.??-??, Dec [13] Janssen, M.,???, pp.??-??, Nov [14] Fenner, R.T., Mechanics of Solids, pp , 1999, CRC Press LLC. [15] Helder, R Project Report: Torsional test bench, pp , year unkown [16] Riley, W.B. and George, A.R. Design, Analysis and Testing of a Formula SAE Car Chassis, pp. 17, Dec 2002 [17] Rosielle, P.C.J.N. Constructieprincipes, Hfd. 1, Maart

35 9 Appendix A - Important rules 2010 FSAE Rules (Also see 2010 FSAE rules explained PDF.) B3.3 Minimum Material Requirements B3.4 Alternative Tubing and Material - General B3.5 Alternative Steel tubing B3.6 Aluminium Tubing Requirements B3.8 SEF B3.9 Main and Front Roll Hoops - General Requirements B3.10 Main Hoop B3.12 Main Hoop Bracing (Especially B3.12.7) B3.14 Other Bracing Requirements B3.15 Other Side Tube Requirements B3.16 Mechanically Attached Roll Hoop Bracing B3.24 Side impact structure for tube cars B4.5 Firewall B5.4 Shoulder Harness B5.6 Head Restraint B6.2 Ground Clearance B6.6 Jacking Point B8.13 Drive Train Shields and Guards B11.1 Master switches B11.2 Primary master switch B11.4 Batteries FSUK Class 1A rules 2010 B4.5 Firewall B8.14 Powertrain System location FSE Germany Rules Drive Train 35

36 10 Appendix B - Weight analysis 36

37 37

38 38

39 39

40 40

41 11 Appendix C - Suspension Load cases Bump Cornering Braking Acceleration Vector componenten Normaal Kracht Kracht Kracht Kracht P1 A 325, tension 7125 tension 3505 tension 915 tension Ax 95 0, , , , ,3186 Ay , , , ,89-866,675 Az -43-0, , , , ,997 P4 A 277, comp 1987 tension 95 comp 744 comp Ax 120 0, , , , ,0566 Ay , , , , ,694 Az -85-0, , , , ,123 P5 A 305, comp 6543 comp 2677 comp 716 tension Ax Ay , , , ,16-707,483 Az -47-0, , , , ,105 P6 A 269, comp 3704 comp 945 comp 2174 comp Ax 83,2127 0, , , , ,3671 Ay -162,8143-0, , , , ,6 Az 197,9245 0, , , , ,872 Damper A 209, ,739 comp 5368,11594 comp 1369,565 comp 3150,725 comp Ax 38,9655 0, , , , ,1188 Ay -205,7925-0, , , , ,53 Az -2,3288-0, , , , ,0298 Rocker mount A 434, ,442 comp 8252,49106 comp 2105,455 comp 4843,66 comp Ax 122, , , , ,486 Ay -368, , , , ,13 Az 195, , , , ,842 41

42 12 Appendix D - FEM results On the next page the excel file of the FEM results is added. 42