The design of a Formula Student race car: a case study A Mihailidis*, Z Samaras, I Nerantzis, G Fontaras, and G Karaoglanidis Department of Mechanical Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece The manuscript was received on 28 November 2008 and was accepted after revision for publication on 5 March 2009. DOI: 10. 1243/09544070JAUTO1080 Abstract: This paper presents the procedure followed in order to design the first Formula Student race car of the Aristotle University of Thessaloniki, Greece.
Despite the restrictions imposed by the Formula SAE rules, the designer has a broad range of freedom in creativity and innovativeness. The design concept of the main vehicle parts, such as the frame and the suspension, is described and the design objectives and assumptions are analysed. The paper also focuses on several new features regarding the suspension adjustments, the steering system, and the engine modifications. Following this procedure, it was made possible to build a competitive and reliable car in a period of just 9 months.
Keywords: Formula Student, Formula SAE, tubular space frame, suspension design, drivetrain, engine 1 INTRODUCTION Formula Student (or Formula SAE (F-SAE)) is a worldwide university competition, organized by the Society of Automotive Engineers (SAE), which encourages university teams to design, build, and compete with a Formula-style race car. To participate in the competition the vehicles must comply with the F-SAE’s strict rules . The competition is split into static and dynamic events.Static events include vehicle presentation, cost, and design analysis, while dynamic events include four racing contests: acceleration, skid pad, autocross, and finally the endurance and fuel economy event. Common characteristics of all dynamic events are the very tight corners, the intense speed fluctuations, and the need for good vehicle handling. More information about the competition can be found in the F-SAE rules . This paper presents the design procedure that was followed in order to design and build a fully operational and high-performance single-seater race car.
It was decided that the car should not only fulfil the requirements set by SAE but also should be *Corresponding author: Department of Mechanical Engineering, Aristotle University of Thessaloniki, University Campus, Thessaloniki, 54124, Greece. email: [email protected] auth. gr JAUTO1080 F IMechE 2009 durable and easy to adjust over a wide range. This decision was based on the intention to use the car as a running test bench that should allow for on-track measurements as well as for suspension and motor set-up evaluation.Data from on-track experiments will serve as a valuable feedback for future similar efforts. In addition, the paper focuses on the new features introduced and the implementation of their design.
They include the fully adjustable suspension mechanism, the steering system, the spherical joint mounts, the fuel tank, and the intake manifold. Following this procedure the first Formula Student race car of the Aristotle University of Thessaloniki, Greece, was designed and built. The vehicle participated in two competitions and proved to be reliable, finishing all dynamic events with good scores.
In the following, the design of the frame is described first (section 2) because it is clearly one of the most important parts of a race vehicle, as it affects strongly its drivability and performance. Moreover, once manufactured, major modifications are usually difficult and expensive. However, it is not the first task of the overall design procedure shown in Fig. 1. Several decisions regarding the overall dimensions, the suspension, and steering system as well as the powertrain have to be met first, as outlined in sections 3 and 4 respectively.Further, it can be finalized only after the design of the subsystems. Proc. IMechE Vol.
223 Part D: J. Automobile Engineering 806 A Mihailidis, Z Samaras, I Nerantzis, G Fontaras, and G Karaoglanidis 2. The frame must be compact but should also allow for easy inspection, servicing, and replacement of all main parts of the vehicle. The first decision that has to be taken concerns the type of frame. It is known that monocoques made from carbon composites are lighter and stiffer than tubular space frames . However, space frames are easier to produce and less costly.Furthermore, they are easier to inspect, to modify, and even to repair in the case of an accident.
Therefore, it was decided to design the frame from steel tubes. Next, the cross-section of the tubes has to be chosen. Even though rectangular tubes are easier to join than circular ones, it was decided to use circular tubes because they offer a much higher stiffness-to-weight ratio. Besides the aforementioned design requirements, many parameters have to be determined and kept in mind in order to design a race frame successfully.The most important are as follows: (a) the overall vehicle dimensions as well as the suspension type and geometry, so that the points where loads act are known; they are determined according to the suspension design as described in section 3; (b) the engine and drivetrain components, which are going to be used; it is important to decide how they should be integrated in the frame and where the resulting forces and moments will act (see section 4); (c) human factors, regarding ergonomics and controls; particular attention should be given to the seat-belt attachment points, the pedals, and the head cushion; (d) the F-SAE rules , and especially those concerning the driver’s safety, i. e.
front and side impact protection as well as main and front hoop. Fig. 1 Overall design procedure 2 FRAME The frame design has to fulfil several contradicting design requirements. 1. The frame has to be light but also safe and stiff. High torsional stiffness has a great impact on the handling of the car [2, 3] because it affects unfavourably the vertical load distribution.
It also reduces the torsional springing. The torsional stiffness of the frame should be at least ten times greater than the roll stiffness of the suspension . Proc. IMechE Vol. 223 Part D: J. Automobile EngineeringIn the current case, the positions of the seat-belt attachment points were set according to the F-SAE rules ; the brake pedal was designed to withstand 1500 N, which is the maximum force that the driver can exert in panic situations; and finally the head cushion was made from Ethafoam and verified to withstand 1000 N applied rearwards.
Regarding the seating position of the driver the following dimensions were chosen: seat height, 80 mm; design seatback angle relative to vertical, 35u; steering wheel height, 440 mm; horizontal distance from the steering wheel to the ball of the foot, 560 mm; horizontal distance from the steering wheel to the H-point, 330 mm. These dimensions resulted in a comfortable driving position for drivers about 175 cm tall. In JAUTO1080 F IMechE 2009 The design of a Formula Student race car 807 order to obtain a comfortable driving position for taller drivers either the pedals or the steering wheel should be made adjustable.
All the above were embedded in a three-dimensional computer-aided design model, developed in Autodesk’s Inventor. The space frame was designed using the previously determined load-receiving points as nodes. This rule has been followed wherever possible in order to avoid bending of the frame members.
The nodes were then connected by tubes. Additional frame members were added in order to form triangles, since they are much stiffer than rectangles. In order to verify the strength and to choose the proper dimensions of the frame members, calculations were carried out using a simple finite element beam model (shown in Fig. 2(a)) that allows for easy and rapid design changes.It should be noted that suspension and powertrain elements such as wishbones, pushbars and springs, wheel uprights, and anti-roll bars as well as engine and differential elements were included in this model, in order to obtain the correct loads on the frame. Shell element models were used to approach parts with complicated geometries such as the suspension mounts (Fig. 2(b)).
Pre- and post-processing were carried out in BETA CAE System’s ANSA and mETA respectively, while MSC’s NASTRAN was used as the solver. The analysis included extreme load conditions to ensure that the space frame fulfils the main design goals: (a) cornering with 1. 5 g; (b) simultaneous cornering with 1. 5 g and braking with 2 g; (c) accelerating with 2 g; (d) braking with 2 g; (e) braking with 2 g and failure of one of the two available brake circuits.The above boundary conditions are not set by the F-SAE rules, but they were chosen on the basis of preliminary calculations assuming a tyre friction coefficient m 5 2 and sufficient engine torque to spin the tractive wheels. However, measurements carried out on the built car showed that the above values are rather overestimated. In particular, the maximum lateral acceleration was 1. 3 g, the longitudinal acceleration was 1 g, and the braking deceleration was 2 g.
The final space frame is shown in Fig. 3. The frame has a calculated torsional stiffness of about 3450 N m/deg, which is almost 14 times greater than the roll stiffness of the suspension.The durability of the frame must be sufficient to withstand the necessary tests and the races. Taking into account that Formula Student cars are allowed to participate in races that take place during 1 year, many of these are designed for a limited fatigue life, in order to save weight. However, the current frame was designed below the endurance limit, i. e.
for theoretically infinite life, since it was decided to use the car for tests and training of the drivers even after the racing Fig. 2 (a) The frame beam model; (b) shell element model, and finite element analysis results of suspension mounts Proc. IMechE Vol. 223 Part D: J. Automobile Engineering JAUTO1080 F IMechE 2009 808A Mihailidis, Z Samaras, I Nerantzis, G Fontaras, and G Karaoglanidis Fig.
3 The final space frame (for explanation of numbers, see text) period. This is the main reason for the relatively high net frame mass of 35 kg. Some details, which further increased the mass, are shown in Fig. 3. The front plate 1 is supported by two rectangular tubes and is shown in detail in view A. It completely isolates the impact attenuator (shown in Fig.
4) from the driver’s feet. The cross tube 2 with the seat-belt attachment points 3 and 4 is supported by the diagonal members 5 and 6. The side impact protection structure includes three more members 7, 8, and 9 per side than the obligatory 10, 11, and 12.Finally, it should be noted that the mounting plates 13 and 14 of the lower wishbones allow for the anti-dive and antisquat adjustment. Several compromises were required to keep the centre of gravity as low as possible, such as mounting the battery and the fuel tank as low as possible, reducing the size of the engine oil sump, and finally installing the driver’s seat to the alreadymentioned low position. The impact attenuator is interchangeable and mounted on the frame by eight screws.
They are positioned in the lateral direction as can be seen in Fig. 4(a) for safety reasons. If a mounting screw were in the longitudinal direction, then one of its fractures could enter the cockpit and injure the driver in case of an impact. According to the F-SAE rules, the Fig. 4 a) The impact attenuator and its mounting onto the frame; (b) detail of the shell element mesh; (c), (d) results of the finite element analysis JAUTO1080 F IMechE 2009 Proc. IMechE Vol. 223 Part D: J. Automobile Engineering The design of a Formula Student race car 809 impact attenuator must be designed so that, when a vehicle with a total mass of 300 kg runs into a solid non-yielding impact barrier with a velocity of 7 m/s, the average deceleration does not exceed 20 g.
The current design was evaluated by the finite element method with ANSA as the pre-processor and LSDYNA as the solver; the results are shown in Figs 4(b), (c), and (d). The mean deceleration at a crash with a velocity of 7 m/s was calculated as 15. 5 g. 3 SUSPENSIONThe main design requirements of the suspension design of a Formula Student race car are the following: (a) the ability to keep all four wheels in contact with the ground at the correct angles in order to exploit the maximum tractive force of the tyres; (b) the ability to have many adjustments, since different races often require alternative set-ups, and in this case it was decided that the suspension design should include the following adjustments: camber angles, anti-roll bar stiffness, front and rear anti-features, as well as steering angles; (c) optimal vehicle manoeuvrability; (d) compliance with F-SAE rules. The following sections describe how these objectives were met. and type.According to F-SAE rules, only 10 in and 13 in wheel sizes are allowed. Eventually, 13 in wheels were chosen because they provide more space for the brake discs and callipers.
Tyre behaviour is very complex and depends strongly on road surface, inflation pressure, operation temperature, speed, normal force, camber angle, and other parameters. Many analytical models have been developed in order to predict the tyre’s behaviour [6–10]. However, the implementation of these models requires the knowledge of numerous parameters, which are usually either not available or difficult to determine. For this reason, tyre data given by the Calspan Corp. were used .One of the most important characteristics of a tyre is the lateral force–slip angle diagram because it describes the way that the tyre will react in cornering.
In Fig. 5, diagrams of two typical Formula Student tyres are shown. Tyre D is a diagonal tyre, and tyre R a radial tyre. The need for a wide range of camber angle adjustments is evident, especially if tyre D is used. 3.
3 Type of suspension Unequal-length double wishbones with push rod actuators were chosen for the front and the rear suspension of the vehicle, as presented in Fig. 6. This type of independent suspension is typical for Formula-type race cars for the following reasons . 1.It allows for four-wheel independence. 2. The linkages are loaded just in tension or compression; there are no bending moments. 3.
The total unsprung mass is reduced. 4. Convenient adjustment of camber angle and antifeatures is possible. 5.
Progressive wheel rate can be achieved by properly designing the bell cranks. 3. 1 Overall dimensions The track and the wheelbase of the car are the first parameters to be defined. According to the F-SAE rules the wheelbase must be at least 1525 mm and the narrower track must be no less than 75 per cent of the wider track. In general, race cars with short wheelbase and wide tracks are less stable in straight line.
In contrast, they are more manoeuvrable and allow for higher cornering speeds . This type of handling performance is suitable for the Formula Student competition because the circuits consist of many small-radius (4. 5 m minimum) corners, while straight lines are limited in number and length. The front track width was chosen to be 1297 mm, the rear 1250 mm, and the wheelbase length 1650 mm, so as to ensure easy accessibility to all main car components and to improve space availability. 3. 4 Suspension geometry 3. 2 Wheels and tyres After the track width and wheelbase were defined, the next step was to choose the appropriate tyre size JAUTO1080 F IMechE 2009The placement of the roll centres plays an important role in the vehicle’s behaviour because it influences the way that the camber angle changes during cornering [5, 12, 13]. They also define the roll axis around which the frame pivots when it is laterally loaded.
If the roll centres are close to the ground, excessive roll occurs which may require too high wheel rates. Otherwise, if they are close to the centre of gravity, roll is minimized. This helps to reduce the anti-roll bar stiffness and the wheel rate but on the other side the frame receives jacking forces during cornering [5, 12–15].
When defining the attachment Proc. IMechE Vol. 223 Part D: J.
Automobile Engineering 810 A Mihailidis, Z Samaras, I Nerantzis, G Fontaras, and G Karaoglanidis Fig. 6 (a)Front and (b) rear suspension Fig. 5 a) Tyre D and (b) tyre R lateral force–slip angle diagrams points of the wishbones, care should be taken to avoid excessive roll centre migration. In the current case, the front and rear roll centres were set at 36 per cent and 40 per cent of the centre of gravity height above ground.
Their vertical migration is negligible and the lateral migration is about 80 mm. Pitching motion is even more disturbing than bounce motion . This is why an ideal suspension could be designed for 100 per cent anti-dive and anti-squat in order to eliminate pitch rotation during braking and accelerating. However, ‘anti’ features force the suspension to appear stiffer and less sensitive.
During high longitudinal accelerations the tyre forces are transmitted directly to the frame, bypassing the springs and the absorbers. Therefore, the suspension remains undeformed in contrast with Proc. IMechE Vol. 223 Part D: J. Automobile Engineering the tyres.
Their compliance becomes excessive and severe tramp may occur [5, 13]. In order to optimize the vehicle’s behaviour under acceleration alternations, adjustable anti-dive and anti-squat are implemented. Both front and rear lower wishbones have four tune-up positions varying from 20 per cent to 84 per cent anti-dive and from 30 per cent to 100 per cent anti-squat, which can be easily adjusted by altering the frame mounting positions, as shown in detail A in Fig. 7.The desirable range for the camber angle alternations was estimated from the tyre’s performance curves (Fig. 5) and it was used to determine the lower and upper wishbone lengths. Depending on the tyres used, the static camber can be easily changed by means of different spacers at the wishbone mountings, as shown in detail B in Fig.
7. As mentioned earlier, the bell crank geometry affects the wheel rates. By altering the angles q1 and q2 and radii l1 and l2 of the bell crank (Fig.
8(a)), the ride rates can be adapted to different tracks and driving styles. The bell cranks were designed to give a progressive wheel rate, as shown in Fig. 9, mainly at the front in order to react better in low road irregularities .The bell cranks are supported by JAUTO1080 F IMechE 2009 The design of a Formula Student race car 811 Fig. 7 View of suspension adjustments Fig. 9 Front- and rear-wheel rates driver preferences.
Therefore, they were designed to be easily interchangeable. The caster angle specifies the mechanical trail of the wheels and generates the self-steering effect. The caster and kingpin inclination influence the steercamber characteristics.
These angles were chosen so that, during cornering, the outside wheel has a more negative camber, while the inner has a more positive camber. In the current case these angles were chosen to be 6u and 14. 5u respectively.The steercamber characteristics are shown in Fig. 10 for two static camber adjustments. For example, if the static camber is set at 0u, when the car turns in a tight Fig. 8 (a) Top view of the front bell crank with the push rod and the shock; (b) section view of the bell crank mount two preloaded angular ball bearings in an O arrangement so as to be clearance free.
A section view of the mounting is shown in Fig. 8(b). The choice of the appropriate diameter of the antiroll bars depends on the circuit conditions and the JAUTO1080 F IMechE 2009 Fig. 10 Steer-camber characteristics for all anti-dive adjustments and for two static camber adjustments Proc.
IMechE Vol. 223 Part D: J.Automobile Engineering 812 A Mihailidis, Z Samaras, I Nerantzis, G Fontaras, and G Karaoglanidis corner the camber angle of the outer wheel is 21. 5u and that of the inner wheel is +5u. It should be noted that anti-dive has negligible effect on the camber angle change.
In all suspension joints, clearance-free spherical bearings were used. They have to be easy to replace and mounted clearance free. Figure 11 shows the design of a bearing mount which fulfils these requirements. It was proven to be compact, light, reliable, and cost effective . Figure 12 shows the design of the front uprights. They must be as light as possible, because their mass s unsprung, and stiff enough to hold the forces from the tyres without altering the suspension geometry.
The pushrod 2 is mounted straight on the upright 1 with a spherical bearing B and not at the lower wishbone 3, as is the common practice. In this way, bending of the lower wishbone is avoided and the suspension linkages are loaded only in tension or compression. The spherical joints A, B, and C lie on the kingpin axis. 3. 5 Steering geometry Fig. 11 Spherical bearing mount design: 1, carrying part; 2, carrying ring; 3, deformed lips; 4, outer ring; 5, inner ring; 6, spacers; 7, U-holder; A1, A2 and A3, A4, frictional-force-transmitting surfacesIn order to provide the proper steering angles while maintaining minimum bump steering and to gain adjustability, the steering mechanism shown in Fig.
13 was developed. It consists of a rocker 1 which transmits the axial motion of the rack 2 to the tie rod 3 via the auxiliary rod 4. During cornering, the outside wheels receive a much greater normal force than the inside because of the lateral weight transfer. Their slip angles define mainly the actual centre of the turn O. In the case of Ackermann steering the resulting slip angles afi and ari of the inner wheels will be greater than required (Fig.
14). The result is that the car could slow down because of the drag of the inner wheels.Moreover, their temperature and wear would rise. In order to avoid these phenomena the inner wheel should be steered at a smaller angle. Therefore, by mounting the rocker 1 in one of the alternative positions A, B, and C shown in Figs 13(a) and (b), the steering geometry can be adapted to the racing conditions. In Fig.
13(c) the steered wheel angles are presented for the three alternative adjustments. The position of the tie rod on the upright is defined so Fig. 12 (a) Front wheel upright; (b) finite element results when braking with 2 g (for explanation, see text) JAUTO1080 F IMechE 2009 Proc. IMechE Vol.
223 Part D: J. Automobile EngineeringThe design of a Formula Student race car 813 4 POWERTRAIN A 2005 Honda CBR 600RR motorcycle engine (engine type PC37E) was chosen. The original equipment manufacturer (OEM) configuration of the engine provides 61. 8 N m torque output at 11 000 r/min and 79.
6 kW power output at 13 000 r/min. In order to install this engine to a Formula-type car, several problems need to be addressed. The most important of these concern the following: (a) the mounting of the engine in the frame; (b) the engine lubrication during cornering; (c) the installation of a new fuel tank and fuelling system; (d) the new intake and exhaust manifold design according to F-SAE regulations.Starting from the mounting, there are two possibilities: the engine block can be used as part of the frame as is done in Formula-1 cars or, alternatively, the engine can be mounted in the frame in a way that does not allow the block to receive any forces or moments. The latter approach was followed in the current case, since it ensures that the deformations of the engine block remain in the range that its manufacturer has foreseen.
The engine is attached to the frame at eight points using rubber silent blocks. This ensures not only that the deformations of the frame do not load the engine block but also that vibrations are partially isolated from the frame. Regarding engine lubrication the following problem can be experienced owing to the original use of the engine in a motorcycle.During cornering, the engine of a car remains almost upright, unlike the engine of a motorcycle that leans. Therefore, the lubricant drifts towards the sides of the sump, and the lubricant flow in the pump may be disrupted.
In order to ensure proper lubrication, separators were added in the oil sump. Furthermore, its height was reduced in order to allow for a lower mounting of the engine. This design was chosen instead of a dry sump because it is cheaper, easier to manufacture, and lighter than the dry sump option since no additional mechanical parts are required. As concerns the fuelling system, selective laser sintering (SLS) technology was used for the production of the fuel tank. In Fig. 16 a detailed view of the fuel tank is presented.The overall weight and number of parts are significantly reduced because SLS provides the ability to create complex and compact geometric forms out of plastic material.
Several modifications had to be made to the engine intake manifold to meet the F-SAE reguProc. IMechE Vol. 223 Part D: J.
Automobile Engineering Fig. 13 Adjustable steering geometry in (a) full Ackermann and (b) parallel set-up. (c) Angles of steered wheels for the alternative steering geometries that the bump steering is minimized. In this case a bump steering of only 0. 03u was achieved. Anti-dive adjustments also affect the bump steering.
Therefore, the tie-rod mounting height on the rockers was designed to be djustable to ensure that bump steering remains low for every anti-dive setting as shown in detail C in Fig. 7. The rack and pinion steering was designed to provide zero clearance as shown in Fig. 15. The rack 1 is driven by the two helical pinions 2.
Elimination of clearance is achieved by axially preloading the Belleville springs 3 between the two pinions by means of the nut 4. In this way the left flanks of the first pinion and the right flanks of the other are pressed permanently on the rack. JAUTO1080 F IMechE 2009 814 A Mihailidis, Z Samaras, I Nerantzis, G Fontaras, and G Karaoglanidis Fig.
14 Steering angles Fig. 15 Rack and pinion steering (for explanation of numbers, see text) Fig. 16Fuel tank: 1, fuel pump mount; 2, main compartment; 3, secondary compartment used as overflow tank; 4, fuel inlet; 5, overflow inlet; 6, 7, air venting tubes lations. According to these regulations, a 20 mm restrictor must be placed in the intake manifold in a way that all intake airflow passes through it. In addition, a single throttle must be used and placed before the restrictor. These requirements significantly affect engine operation and performance. Furthermore, the engine was originally designed to deliver its nominal power and torque at relatively high speeds (above 11 000 r/min). The presence of a restrictor and the racing conditions of the F-SAE competitions call for lower-engine-speed driving.
Therefore, new intake and exhaust manifolds were designed, aimed at achieving the highest possible torque and power output in the 7000–9000 r/min operating range. The new intake manifold was manufactured by SLS, the exhaust manifold by welded stainless steel tubes. In order to compenJAUTO1080 F IMechE 2009 Proc. IMechE Vol. 223 Part D: J. Automobile Engineering The design of a Formula Student race car 815 sate for the new intake and exhaust systems and to achieve high engine performance, a new engine calibration was necessary. A programmable electronic control unit (ECU) by Motec was used in order to introduce the new engine control strategy in line with the aforementioned modifications.Finally, a new cooling system was designed in order to provide adequate cooling under low-average-speed, highpower-output conditions, similar to those encountered in Formula Student races, and to fit in the frame without compromising the vehicle weight balance.
It was decided that the engine should be configured with respect to the acceleration performance rather than the top speed, because the average race speed is limited to approximately 60–70 km/h. Since the restrictor causes a significant drop of the engine power output at high engine speeds (over 11 000 r/min), operation is optimized to the 7000–9000 r/min range. To save experimental time, the intake and exhaust manifolds were initially studied and optimized using computer simulation.The engine was modelled in Gamma Technologies’ GT-POWER, and the intake and exhaust runner lengths, the air-box volume, and the restrictor–diffuser system were studied to maximize the volumetric efficiency in the predetermined speed range. Figure 17 shows the intake manifold. Two sets of intake runners were foreseen, in order to provide a different maximum torque output curve according to the demands of each race track. The air filter is placed in the air box to assist the diffusion of the incoming air. Appropriate engine calibration was conducted for each intake configuration.
The resulting torque and power curves are shown in Fig. 18. The new ECU was programmed using an engine dynamometer to optimize the power output and fuel efficiency by tuning parameters such as the spark advance, fuel injection timing, and lambda value.The aim was not only to have an efficient and competitive engine but also to provide the ability of using different control strategies according to the requirements of each event. Thus, a leaner air–fuel mixture is used in the endurance and fuel economy event to minimize consumption, and a richer mixture for maximizing power during the autocross and the acceleration events. The self-contained gearbox of the engine was used. Engine power is transmitted to the rear wheels by a chain drive and a differential. The gears are shifted by an electropneumatic quick-shift mechanism mounted in the rear of the driver’s seat.
The quick shift contains an onboard air compressor and an adequate pressure accumulator so as to allow an unlimited number of gear shifts.Also, it is coupled with the engine ECU and cuts off the ignition for 40 ms during gear shifting. The driver can easily and rapidly shift the gears by pressing buttons mounted on the steering wheel.
The final transmission ratio of the chain drive is 43/12 5 3. 583 in order to enhance the acceleration performance of the car. Fig. 17 Intake manifold and runners Fig. 18 Output torque and power curves achieved JAUTO1080 F IMechE 2009 Proc. IMechE Vol. 223 Part D: J. Automobile Engineering 816 A Mihailidis, Z Samaras, I Nerantzis, G Fontaras, and G Karaoglanidis A Torsen type II differential (Fig.
19(a)) was chosen because it gives better drivability at the exit of the corner and better traction during straight-line acceleration.Its torque bias is affected by the initial preloading, the input torque, and the friction coefficient between the faces of the planetary gears and the cage of the differential [17, 18]. Regarding the mounting of the differential, it had to be decided whether to mount it on the engine or directly in the frame. In the first case the transmission forces do not load the frame. However, in the presented design it was chosen to mount the differential in the frame using two L-shaped arms 1, as shown in Fig. 19(b). In this way the engine and the differential can be dismounted or changed independently from each other.
5 RESULTS The design procedure described above can be summarized as follows.Given the F-SAE rules, the human factors regarding ergonomics and controls, and the required safety, the overall dimensions, and the engine are decided first. Then, the wheels and tyres, the type of the suspension and its geometry, and the steering geometry have to be chosen. An initial frame design may follow. It should be finalized after the design of the major car subsystems. It is important initially to set clearly the design objectives of each subsystem.
The bodywork is the last step to complete the design. This procedure includes of course much iteration because no explicit answers can be given to the complex questions that Fig. 19 (a) Magnified view of the differential. b), (c) Chain pre-tension and differential mount: 2, chain; 3, bolt; 4, Belleville springs JAUTO1080 F IMechE 2009 Proc.
IMechE Vol. 223 Part D: J. Automobile Engineering The design of a Formula Student race car 817 Fig.
20 View of the car arise during the development.Although Formula Student race cars and passenger cars are totally different, the presented design procedure can be adopted to speed up the development, especially in cases where the design of a completely new model is required. Figure 20 shows the completed car. It took part in two Formula Student contests, in Fiorano Mondenese, Italy, in September 2007, and in Silverstone, England, in July 2008, where it achieved the following results. In the acceleration event the car needed just 4. 05 s to cover 75 m, whereas the competitor finishing first needed 3.
997 s, and the competitor finishing last, 7. 5 s. In the skid pad the best time of the presented car was 5.
471 s, whereas the best time was 5. 02 s and the worst 10. 277 s. The tight course of the autocross event was covered in 61.
65 s, while the fastest car needed 9. 7 s less and the slowest 67. 66 s more. The 22 km of the endurance event was covered in 1465. 96 s. The fastest car needed 227. 41 s less and the slowest 456.
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