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Formula Student challenges teams of University students to design, build, and race a high-performance open wheel sports car as part of an annual competition. The project aimed to design a chassis for the next generation Leeds car, F14, to be entered into the 2010/11 competition. The chassis was to be constructed as a spaceframe model as a Monocoque chassis is not only complicated but also expensive to be fabricated.
A key criterion for chassis performance was identified to be torsional stiffness, with a target value for an FSAE car of 1000Nm/Â°. Two methods of measuring torsional stiffness were chosen and compared; one independent of suspension geometry and one which simulated loading from the suspension system.
A test method in which suspension load locations were considered gave a stiffness of 2524Nm/0 for a chassis of projected mass of 31Kg.
The author would like to thank Prof. D.C. Barton for his help and support throughout the project. He offered invaluable guidance and insight into many aspects of the chassis development. Additional thanks go to the 2009/2010 Level 4 FSAE team for their feedback and thoughts of F14, and overall moral support.
The Formula Student is a competition that is organized the Institution of Mechanical Engineers (IMechE) in association with the Society of Automotive Engineering (SAE) between teams of students from different universities to design, build and market a single seater sprint race car. University of Leeds is now in its 13th year of participation with the F12 to race in California this year and the F14 that will be developed by the end of the current academic term. The F14 is being designed to incorporate a four stroke, single cylinder Yamaha KTM engine as compared to the 4 stroke engine that is used in the F12.
The F10 was the last car that had incorporated monocoque chassis and the F11 was the first to be designed with a full space frame chassis. But due to design flaws the F11 did not make it to competition. F12 is the second car to be designed using a space frame chassis and it mainly addressed the flaws in the F11 design with similar handling characteristics as F10. Presently the F12 is being optimized for its performance for the race this year and F14 is in its initial design stages.
AS on date the F14 chassis stands nearly complete as per the initial designs without the rear end because the orientation of engine mounting was not finalized by the Level 4 team. Thus it is still yet to be decided. This report provides information regarding the design and computational testing of the F14 chassis with a view of what may possibly be the final version of the chassis.
It is to be noted that the chassis is one of the last components of a car that is decided since the individual components that go into the car are decided initially. The design of the suspension of the car is something that is also done hand in hand with the chassis design because one may have a very good chassis but probably not very good suspension geometry to go with it and vice versa. The best combination is achieved when they are modelled simultaneously.
It is also noteworthy that the project progresses from the Level 3 to Level 4 when the knowledge of chassis structures, suspension geometry is furthered some aspects of the current chassis are subject to modification. This might involve inclusion or exclusion of certain members, relocation of certain members etc.
Aims & Objectives
The project aims to computationally design, analyze, and test a new chassis for the Leeds Formula Student Car F14. These include gaining useful insight into the previously done work and organize that knowledge to be implemented into the new car to be developed and effectively transfer all the knowledge for the students to work on the future versions of the vehicle.
The bigger picture for the university is to finish with be one of the top and best competitors in the competition in the various events within the overall competition.
To conduct the necessary literature review.
To research the Level 4 reports of the 2005-06 Chassis Team and the Level 3 and 4 reports of the 2007-10 F12 team.
To pick up information from various SAE technical publications by various competing universities including Leeds University
To develop basic the basic understanding of the design of race car chassis and implementation for the Leeds Formula Student Car.
Determine the specific Torsional stiffness of the Leeds Formula Car F12 for having a bench mark or a target value of Torsional stiffness for the car F14.
Torsional stiffness data from the 2007-08 level 4 report to be used as a bench mark of the actual experimental data
Torsional stiffness data from the 2007-08 Level 3 report to be used as a reference for the computational result.
To design computer models to suit requirements.
Use an iterative design process to maximize the specific torsional stiffness.
To take into account the suspension mounting locations, engine mounting points whilst adhering to the FSAE rules and ergonomics.
To measure the Torsional Stiffness of the computational models.
To optimize the chassis structure and pass recommendations for the next generation vehicles
Theory & Literature Review
Automotive racing is one of the world favourite sports. With millions of fans across the globe this is one of the most widely followed sports. Among the various categories of car races the general favourite is Sprint Type racing as it involves competitions ranging from the local to the national level. The most popular among this being the Formula 1 racing in which the teams generally comprise of the various car manufacturers. To promote the sport and design and manufacture of such vehicles and racing them amongst students, the IMechE in association with the SAE organizes the Formula Student competition.
In this competition, teams of students from various universities spend roughly a year to develop race cars as per the rules that are laid down by the IMechE and SAE for the various categories of competition, namely class 1, 1A and 2. Leeds University is participating in the class 1 competition which involves, "This is for a fully constructed and running vehicle as defined by the FSAE rules ("first year vehicles"). Points are awarded for design, presentation, cost, acceleration, skid pad, sprint ("Autocross" in FSAE rules), endurance and fuel economy."
The chassis developed by the 2009/10 Level 4 team for the F12 is a full space frame chassis that provides "a platform to connect the engine, drive train, and suspension, and offers driver protection in the event of a collision or roll-over." The chassis of the car is the most important feature present in it as it is the one that determines how well the vehicle can be handled during its usage.
The current work focuses on the development of a chassis for the Leeds Formula car F14, under the guidance and recommendations passed by the 2009/10 Level 4 team. Chassis design mainly involves the knowledge of the type of car that is being built with the basic knowledge of the type of structure that is to be incorporated. The most important constraints in this design procedure are the overall bending and Torsional stiffness and the strength required to deal with the maximum loads encountered due to the various factors such as side forces, braking, engine torque etc., which are taken in to consideration as the specifications for it.
Milliken and Milliken in their book, Race Car Vehicle Dynamics also add that "good vision, adequate cockpit size, comfortable seating etc." are necessary for the best performance of the vehicle.
Once the chassis is designed, the other features such as weigh distribution, Aerodynamics suspensions etc, may be designed as the required setup for the various situations would be different. The following literature reviews attempt to discuss the ideas and principles involved in designing the chassis for F14.
The current work is closely associated with the work done by James Thompson, whose work is being used as the base for the development of the chassis for the F14. As discussed in his report, Leeds University has used two chassis configurations as of now namely, the Monocoque and the Space frame. A monocoque design combines chassis and bodywork into one load bearing structure and offers a higher stiffness to weight ratio compared to an equivalent tubular space frame. However it is not adopted for the F12 as it is more complicated and expensive to fabricate and the individual mouldings must be manufactured for each part of the structure. The lack of bracing around the cockpit also makes it less suitable for an open top car. Previous Leeds FS cars have used this construction and have shown that there is a considerable amount of weight added to this type of car in the form of bolts and fixtures; this owes to the fact that mounting tabs cannot be directly welded to the composite panels.
The main advantage of incorporating a space frame chassis is that it is easy to make requiring a skill welder to ensure the chassis remains durable throughout its life. This design makes accessibility to the engine easier because obstructive tubing can be designed to be removable. This configuration is used for F12 because of the potential weight savings obtainable by welding ancillary parts such as the dashboard, harness mounts, and suspension pickups directly to frame. And a similar design is being incorporated for the F14 as well.
In order to manufacture a chassis that is durable a wide range of materials that are acceptable as chassis deign materials, their material and welding properties are the most important. It is by inputting this data into the computer generated models that we can get the various test data for the particular material in consideration. In this context, the account of the various materials that are used in race car manufacture and selection and usage of materials is described very well by Carroll Smith.
Finding a vehicle configuration which can be driven to produce the maximum desirable performance is referred to as setting up or chassis tuning. It is a difficult task requiring many compromises to fit each circuit and the driver's capabilities and preferences. Often it will not be possible to achieve the optimum set-up in the available testing and practise time and the driver will have to allow for the vehicle deficiencies that remain. To meet FSAE rules the chassis is required to accommodate drivers ranging from the 5th percentile female to the 95th percentile male to preserve safety, driver comfort, and prevent fatigue.
Of all the types of loadings a car chassis can be generally subjected to mainly four different types of loadings that go into it.
Vertical bending caused by the weight of the driver and the other components that go into the car such as the engine, mountings, etc.
Lateral bending caused by the cornering forces and the camber angle
Horizontal loading that caused by the forces induced in the axle
Longitudinal torsion that causes twisting about the length of the chassis
It is the torsion that causes the maximum effect on the handling and is also one of the largest forces that a chassis frame experiences. (1)
Equation - 1: Torsional Stiffness calculation equation
Where = torsional stiffness, = applied torque, and = angle of twist
Equation 1 gives a general formula for the ability of a body to resist a torsional load.
Figure 1 shows a front view of a vehicle body.
Figure 1: Torsional stiffness calculation reference diagram (1)
Applied torque, T at a point, is the product of the force F acting at that point, and the perpendicular distance, L, from the point of application. The deflection, y, can be measured and converted to an angle of twist, Î¸. Averaging the deflection at the ends gives a more accurate result. Equation 2 gives the relation between torsional stiffness and chassis deflection.
Equation 2: Relation between torsional stiffness and chassis deflection (1)
3.4 Chassis Configuration
A spaceframe chassis consists of several tubular members welded together with bodywork fixed over it. It has the advantage of being well suited to low volume production because of small tooling costs, but requires a skilled welder to ensure the chassis remains durable throughout its life. This design makes accessibility to the engine easier because obstructive tubing can be designed to be removable (1).
3.5 Design considerations
Spaceframes remain rigid even if the welded joints in the structure are replaced by pinned joints. It was found that bending loads should never be fed into a welded joint if this condition is to be upheld; they should only be loaded in tension or compression (1). Although it may be necessary to compromise this principle, for example to allow more convenient positioning of the steering wheel, it is a very important design consideration for a chassis. It was found that a low mass and centre of gravity are factors which can improve handling performance, critical factors for F14 (2). Front to rear weight distribution also influences handling; the chassis should contribute toward a roughly 45:55 distribution (3). To meet FSAE rules the chassis is required to accommodate drivers ranging from the 5th percentile female to the 95th percentile male to preserve safety, driver comfort, and prevent fatigue (4).
Closed structures are usually more rigid than open structures. In a single seater race car the cock pit cannot be closed or triangulated as it obstructs the driver's entry into the vehicle. A solution to the problem is to build diagonally braced beams onto either side of the cockpit (5), an approach taken in the design of the Mercedes-Benz 300SL, Spaceframe Lister-Jaguar, and the Cornell University FS car (6).
3.6 Test methods
There are several methods employed by people when it comes to the measure ment of torsional stiffness of a chassis. The most popular among them being usage of commercial CAD and FEA software packages like, SolidWorks, ANSYS FEA, ABAQUS, etc.
Computational modelling is generally preferred before undertaking any other testing as it not only saves time but also money and the various other resources that are utilised otherwise for the testing methods.
3.7 Revisiting the F12 chassis - The Big Picture
As a usual practice, the previously done work at Leeds University was reviewed as a part of the take off point in the project work and the following key observations regarding the F12 chassis were noted:
Front suspension units mounted beneath the vehicle (Figure 2). The level 4 team commented that the decision to go for this arrangement was to enhance the handling characteristics of the vehicle. In addition to this they also spoke of the difficulty in adjusting them and mentioned that the sub-frame that supports it adds another 0.5kg to the mass of the chassis.
Figure - F12 front suspension beneath the chassis
Non-structural sidepods (Figure 3). They house the cooling unit of the vehicle in addition to adding to the overall stiffness of the chassis.
Figure 3: [a] Geometrical Model (1) [b] Actual structure built on the chassis [c] The cooling unit
Extra Bulkhead (Figure 4). It holds the impact attenuator in position and offers some additional stiffness to the chassis at the cost of another 2.2Kg being added to the chassis structure.
Figure - [a] The Geometry of the extra bulkhead (1) [b] the bulkhead with the impact attenuator
Unevenly chassis floor (Figure 5). The chassis rises up from the driver's seated position and then lowers at the pedal box near the front suspensions.
Figure - Chassis with an uneven floor
For the design of the chassis of F14, initial computational methods were chosen as it is very easy to manipulate them as per desire, to explore the various situations without actually wasting raw materials. Since the maximum expense is some time and computational space on a computer, it is very cost effective.
Modelling Software- SolidWorks 2009 SP4.0 (Educational Version)
Computer Aided Design computer programme called SolidWorks was used to create computational models of the chassis through the course of the project. The software provided was the Educational Version of SolidWorks 2009 with Service Pack 4.0
FEA Software- Solidworks Simulation
Solidworks Simulation is the inbuilt Finite Element Analysis package provided along with SolidWorks. It was formerly known as COSMOSWORKs.
The best performance from a car is obtained when the chassis and suspension are made for each other and not individually.
One of the methods for measuring torsional stiffness is to constrain the rear suspension uprights and applying equal forces at the front uprights(r). This method was used by the F10 team and is also recommended by the F12 team.
The first of the two approaches used to determine the torsional stiffness was to apply two equal and opposite loads in the front bulkhead of the chassis while constraining the rear bulkhead. This induces twisting torque throughout the length of the chassis. This method is useful when one is just interested in the stiffness of the chassis.
Figure 6- F14 restraints and loads located at extremities of vehicle
The rear bulkhead of the chassis was restrained using fixed boundary conditions, shown in green in Figure 6.
In such cases of designing a chassis, care must be taken to place the members at appropriate positions and use of shear panels but use of excessive members not only increases the torsional stiffness but also increases the weight of the chassis.
Torsional Test Method 2
In this approach, the forces are input into the chassis through the front suspension mounting location whilst clamping at the rear (Figure 7). This method has been known to eliminate the problem of compliance within the suspension system and preserve accurate loading of the structure (1). This method can be recreated experimentally.
Figure 7- F14 restraints and loads at wishbone mounting locations
A maximum experimental torque of 316.27Nm was applied to the first spaceframe built at Leeds, F11. Computational testing of F12 followed this value to maintain comparative results between the two designs (12). Since the F14 chassis has not been manufactured and tested, this experimental value of the force was used in the computational model as a reference for comparing the computational result with the actual experimental data.
The selection of suitable materials for chassis construction is very important. Considerations for common chassis materials are shown in Table - Typical properties of chassis materials .
Table - Typical properties of chassis materials (1)
Aluminium 6082 T6
Grade 5 Titanium
Plain carbon steel
The key criterion for the successful performance of a chassis is its torsional stiffness. As shown in the table above, plain carbon steel has higher specific stiffness and is also easy to work with during manufacturing process. Hence it is the obvious choice.
Mass properties of F14
Output coordinate System: -- default --
Density = 7.8e+003 kilograms per cubic meter
Mass = 31 kilograms
Volume = 3.97e+006 cubic millimeters
Surface area = 3.96e+006 millimeters^2
Center of mass: ( millimeters )
X = -0.0115
Y = 411
Z = 454
Principal axes of inertia and principal moments of inertia: ( kilograms * square millimeters )
Taken at the center of mass.
Ix = (-1.97e-005, -0.0798, 0.997) Px = 2.69e+006
Iy = (-0.000265, -0.997, -0.0798) Py = 1.43e+007
Iz = (1, -0.000265, -1.44e-006) Pz = 1.45e+007
Moments of inertia: ( kilograms * square millimeters )
Taken at the center of mass and aligned with the output coordinate system.
Lxx = 1.45e+007 Lxy = 81.4 Lxz = -228
Lyx = 81.4 Lyy = 1.42e+007 Lyz = -9.24e+005
Lzx = -228 Lzy = -9.24e+005 Lzz = 2.76e+006
Moments of inertia: ( kilograms * square millimeters )
Taken at the output coordinate system.
Ixx = 2.62e+007 Ixy = -65.5 Ixz = -391
Iyx = -65.5 Iyy = 2.06e+007 Iyz = 4.85e+006
Izx = -391 Izy = 4.85e+006 Izz = 7.99e+006
Torsional Test Method 1
The angle of twist was calculated at 12 points along the length of the chassis. They are labelled 1 to 6 from left to right along the length of the chassis. The deflections at all the blue marked locations were utilised for the calculation of the deflection angle in the structure.(Figure 8)
Figure 8- Deflection measurement locations along the chassis
AS we can see, the high stress concentrations are in the front bulkhead region. And the stresses reduce in the regions along the length of the chassis. This simulates a sudden bump during the cornering of the vehicle. (Figures 9 and 10)
Maximum stress plot.jpg
Figure 9- F14 method 1 high stress areas
Figure 10- F14 maximum stress location
This method yields a torsional stiffness value of 2451Nm/0. And the specific torsional stiffness is calculated to be 79.1Nm/0Kg fir the 31Kg chassis of F14.
Torsional Test Method 2
This method yields a torsional stiffness value of 2530N/0 which is 1.5 times the calculated value of F12. The specific torsional stiffness value is calculated to be 81.1 Nm/0Kg which is 2% higher than the previously calculated result.
As reported previously in the Level 3 report of the Design of Chassis, the method of feeding the forces into the suspension points gives a more accurate picture of the torsional stiffness.
The value of torsional stiff that we obtain is largely dependent on the type of method that we use to calculate it. In this case two different methods were considered for the calculation of torsional stiffness and clearly one of them shows high value of 2530Nm/0 with a specific value of 81.1Nm/0kg while the other gives a value of 2451 Nm/0 with a specific stiffness of 79.1 Nm/0Kg.
Clearly we can see a difference of 2.4% in the values. So we can conclude that any of the above two methods is a good one for calculating the torsional stiffness of the chassis.
It was not really possible for accurate comparisons of the previous year's data and the present computational results since there was no decisive decision regarding the model that was studied. And also due to the lack of some of the information that was needed for the successful completion was not available the current report could not reach an apt comparison to the results obtained.
The current study could not decide exactly the accurate methods for the determination of torsional stiffness. The computationally calculated value of the torsional stiffness in the present study is 2530Nm/0 with a specific torsional stiffness value of 81.1Nm/0Kg.
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