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Description and design of the steering system for a Formula Student car Descripción y diseño del sistema de dirección para un coche de formula student Autor: Daniel Nuviala Civera Supervisor: D. Francisco Javier Martínez Gómez Escuela Universitaria Técnica Industrial d Zaragoza Departamento: Ingeniería mecánica Convocatoria: Septiembre 2011 Final Project: steering system design 2009-2010 Pg 1 Summary Our Project has as aim the description and design the elements of the steering system for a formula S.A.E. The steering system is one of the most important parts of the car because has the task to control the car and guide by the desirable trajectory. The action starts on the hands of the pilot and is transmitted through several elements that have different tasks until turn the wheels. A failure on this mechanism can be fatal to the health of the pilot. Before start to design the elements of the steering system car, we will study different aspects that have influence on the design of the steering system. First of all we report to the reader all about the Formula S.A.E. The aim, where take place the race the rules and the history of the competition. We will discover the main objective of the competition the development of young engineers because they have to manufacture the cars themselves. Then we study the formula S.A.E. rules and we will put on our project the rules the more general rules and the rules directly related with the steering system in order to design our system bear in mind these restrictions that are established by the competition. We will do a compilation of the general characteristics of a formula S.A.E. in order to know more about this kind of cars comparing with a formula one car that is known for the most of the people. Subsequently we will study the theoretical knowledge and the technical fundamentals and general comments about the steering in general in order to understand better this system and applied on our formula S.A.E. In this chapter we will find out the characteristics that must has a steering system and the geometry (Ackerman and Jeantaud) of some elements of the system that produce the car has a different performance on the road. Also we will study the different angles that we can give to the Final Project: steering system design 2009-2010 Pg 2 wheel and we will see the different qualities that the vehicle has depending on these angles. Continually we will start with the design of our steering system. We will start this task separating the elements of the car that have influence on the design of the steering and the elements that really make up the system. As regards the elements of the car to take in consideration to design our system we will study the measures of the cockpit because will be important in order to situate the elements of the steering system. Then we will be able to start to design the elements. We begin giving a description of the mechanism and continually we will describe the function and the characteristics of each element. We will focus on the steering column, the rack and pinion and the steering arms because we do the difference between the elements that we can manufacture and design and the elements that we will buy to the manufacturers. In order to design the elements that we will design ourselves we will use the Solid works program which we can to draw the elements and to calculate the stress that can support. To finish we will calculate the budget of the project. Final Project: steering system design 2009-2010 Pg 3 Acknowledgements. TO: - My family because without them I could not study a career in Zaragoza and now I could not make this project and anything. - The teachers: Phil Storrow, Nick Burdon by his help that it has been fundamental. - My mates who are studing here with me and have been a great help for me: Fco.Javier Ruiz de Erenchun, Ricardo Oltra, Pablo Tris, Ivan Ruiz, Enrique Patiño, Tomas Vallés. - My friends from Spain whit which I have study and I life together: Ignacio Balet, Daniel Repollés, Diego Embid, Antonio Plaza, Jorge Leciñena, Guillermo Grande, Ruben Cortés, Javier Roche, Iciar Miguel, Patricia Rodriguez, Elena Garriga, Alberto Polo. - Somo, Boulevard, Cai, Filosofia, Sinués - Glyndwr, Wrexham. Final Project: steering system design 2009-2010 Pg 4 Contents 1. Introduction 6 1.1. Project aim 7 1.2. Importance of the steering system on a car. 8 1.3. The steering system on a common car 9 2. Aims of project 10-11 3. Review of literature 12 3.1. The competition: Formula Student 13-15 3.1.1. Formula student rules that have influence on the steering system 15-19 3.1.2. Differences between a S.A.E. car and a formula one. 19-20 3.2. General comments about the steering 20-27 3.3. Technical fundamentals 28-37 4. Design process, results and discussions 38 4.1. Introduction. 39 4.2. Elements of the car that have influence on the steering system design. 40 4.2.1. The cockpit and seat 40-46 4.3. Calculation of the force to turn the wheels. 47-52 4.4. Description of the steering system elements 52-90 4.5. Budget 91 5. Conclusions 92-94 Final Project: steering system design 2009-2010 Pg 5 6. Recommendations 95-96 7. References 97-99 8. Figures 100-103 9. Tables 104-105 10. Appendices 106-108 10.1. Glossary 10.2. Planos Final Project: steering system design 2009-2010 Pg 6 1. Introduction. 1.1. Project aim 1.2. Importance of the steering system on a car. 1.3. The steering system on a common car Final Project: steering system design 2009-2010 Pg 7 1.1. Project aim. In this project we are going to carry out the study and the design of the steering system for a car used on competition races in circuits. Along the project we will focus in the steering system but also we will watch the steering in a car that we can find travelling in one street in order to understand better the performance of the steering elements in order to after focus in a formula S.A.E. which is a car that requires a steering system more exigent due to is used on races. By other hand we must know that we are manufacturing a steering system for a car so we will bear in mind different elements of the car which have influence at the time to manufacture the steering system. In this project we will do reference to the characteristics to these parts of the car and the measures, the weight or the design. The project will be carry out bearing in mind a lot of very different aspects as the total cost of the project, the analysis stress and the materials to manufacture the steering components and the design of the car carefully since there are some technical rules which must be taken in consideration With regards to the budget, the Formula Student stipulates that there is no a maximum cost so I will make my project and finally I will calculate the total cost. Once finished the single-seater will have as objective compete in the race of the Formula S.A.E competition that/which it will celebrate in Silverstone circuit the dates from 15th until 18th de Julio 2010. Final Project: steering system design 2009-2010 Pg 8 1.2. Importance of the steering system on a common car. The steering system is one of the most important parts of any car. Whether this element is vital to the safety driver of the vehicle in question concern. While the steering, as we have said, is important in a common car which we can drive daily in our life, obviously is even more significant in a formula S.A.E. car since this kind of vehicles are designed to compete in races and the objective of the team and the pilot is always to bring the car to the limit to try to win. A failure of this mechanism during operation of the vehicle could lead to fatal circumstances to the driver who is at the expense of a car without control and with high velocity. As we have seen along the history, a lot of the most serious accidents have been caused due to a failure on the steering system with different fates for the drivers. Although in this project we will start talking and explaining the elements of a common car to know more about the steering in general in any car, then we focus on the steering system for a competition car which is a little bit different that in a common car. Final Project: steering system design 2009-2010 Pg 15 It is possible calculate the score with the follow equation: - 1 Skid pad score = 47.5 x + 2.5 - 1 Where: Tyour: is the average of the left and the right time laps on your best lap including penalties Tmin: is the elapsed time of the faster car Due to the growth and success that this event had teams eligible to participle in formula S.A.E. American, European Formula Student, Formula S.A.E. Australia, in Italian or Brazilian. We focus on the European formula of students and to build the guidance system for a student of the formula that will compete in this kind of competition, in which the race will held at Silverstone circuit (England) for provisional dates 15 to 18 July. 3.1.1. Formula student rules that have influence on the steering system. We will base our design of the steering system according to the rules and restrictions that impose the Formula Student. There are a lot of articles about all the aspects of the car as the fuel, the noise caused by the car, the different parts of the vehicle: cockpit, aerodynamic elements, the fuel tank etc, different safety measures as the belt or the cockpit padding etc. But the most general and important for our project are the next: Final Project: steering system design 2009-2010 Pg 16 - The vehicle must be open-wheeled and open-cockpit (a formula style body) with four wheels that are not in a straight line - The cars normally have a measure around 3 meters but the car must have a wheelbase of at least 1525 mm. The wheelbase is measured from the center of ground contact of the front rear tyres with the wheels pointed straight ahead DIMENSIONS FRONT REAR Overall length, width, height 2815mm, 1310mm, 1025mm 2815mm, 1310mm, 1025mm Wheelbase 1525mm 1525mm Track 1200mm 1100mm Table 1. Fsae rules - The smaller track of the vehicle (front or rear) must be no less than 75 % of the larger track - There must be no openings through the bodywork into the driver compartment from the front of the vehicle back to the roll bar main hoop or firewall other than that required for the cockpit opening. Minimal openings around the front suspension components are allowed - Among other requirements, the vehicle´s structure must include two roll hoops that are braced, a front bulkhead with support system and impact attenuator, and side impact structures. Note: the main hoop and the front hoop are classified as ``roll hoops´´. Main hoop: a roll bar located alongside or just behind the driver´s torso Front hoop: a roll bar located above the driver´s legs, in proximity to the steering wheel. - The engine can have a maximum of 610cc. Must be only one round air intake of 20 mm. Final Project: steering system design 2009-2010 Pg 17 - The fuel must be of 100 octane or a maximum of bi-ethanol E-85 - It is possible to use turbo or compressor only if is an own design - The car must be equipped with a breaking system that acts on all four wheels and is operated by a single control - The perimeter shear strength of the monocoque laminate should be at least 7.5 KN for a section with a diameter of 25 mm. this must be proven by physical test by measuring the force required to pull or push a 25 mm diameter object through a sample of laminate and the results include in the SEF. Figure 4. Fsae rules As regards of the steering restrictions: - The steering system must be affect at least two wheels - The steering system must have positive steering stops that prevent the steering linkages from locking up (the inversion of a four-bar linkage at one of the pivots). The stops may be placed on the uprights or on the rack and must prevent the tyres from contacting suspension, body, or frame members during the track events. - Allowable steering system free play is limited to seven degrees total measure at the steering wheel - Real wheel steering is permitted only if mechanical stops limit the turn angle of the rear wheels to (+-3) degrees from the straight ahead position Final Project: steering system design 2009-2010 Pg 18 - The steering wheel must be mechanically connected to the front wheels, i.e. ``steer-by-wire´´ of the front wheels is prohibited - The steering wheel must be attached to the column with a quick disconnect. The driver must be able operate the quick disconnect while in the normal driving position with gloves on - The steering wheel must have a continuous perimeter that is near circular or near oval, i.e. the outer perimeter profile can have some straight sections, but not concave sections, or cutout wheels are not allowed. - In any angular position, the top of the steering wheel must be no higher than the top-most surface of the front hoop Figure 5. Fsae rules - The wheels of the car must be 203.2 mm or more in diameter - Vehicles may have two types of tyres as follows: • Dry tyres: the tyres on the vehicle when it is presented for technical inspection are defined as its ``Dry tyres´´. The dry tyres may be any size or type. They may be slicks or treaded. Figure 6. Dry tire Final Project: steering system design 2009-2010 Pg 19 • Rain tyres: Rain tyres may be any size or type of treaded or grooved tyre provided: 1. the tread pattern or grooves were molded in by the tyre manufacturer or his appointed agent. Any grooves that have been cut must have documentary proof that it was done in accordance with these rules. 2. there is a minimum tread depth of 2.4 mm Figure 7. rain tire 3.1.2. Differences between a common car, formula S.A.E. car and a formula one. In order to know how is the system which we are going to design, we must to know the characteristics of the car. We know that the car will be a vehicle to compete in close circuits so the features must be high quality. However this car is made for students, young engineers which manufacture the car themselves so it is not a competition for professionals so the aim of the Formula S.A.E. is that the engineers learn about this world. So we can conclude that the car, will be a vehicle for a competition but with a not very advanced features due to it is not a professional competition and with a reduce budget. Final Project: steering system design 2009-2010 Pg 20 We will do a comparison with a formula one, the highest competition car. The usually measures of a S.A.E. car are the followings: Wheelbase: 1500 to 1650 mm Track: 1200 to 1300 mm Engine: maximum of 610 cc Weight: around 300 kg As regards a formula one the difference clearest difference that we can see is the engine since a formula one has a engine of 2400 cc and reach a velocity of 340 km/h. With this parameter we are going the difference between the two kinds of cars analyzing the velocities that reach the two cars in the Silverstone circuit where will be the race of formula S.A.E. SILVERSTONE Curva velocidad de entradaFormula SAE velocidad entrada Formula 1 1 91.67 235,00 2 94.83 270,00 3 66.33 210,00 4 96.17 175,00 5 84.50 235,00 6 89.17 190,00 7 77.33 105,00 8 74.17 130,00 9 67.67 125,00 10 54.6 90,00 Table 2. Comparison between Fsae F1 Final Project: steering system design 2009-2010 Pg 21 3.2. General comments about the steering. As we can say before in this project the steering system is the mechanism which has the task to turn the wheels in order the driver can guide the vehicle along the desirable trajectory. All steering system must satisfy the following characteristics: Safety: the most important. Depend on the reliability of the mechanism and this one depends directly on the quality of used materials. Gentleness: it achieves with a precise assembly and a perfect greasing. The hardness in the driving it make difficult and tiring drive the car along the desirable trajectory. It might be caused to badly position the tyres or because there is more friction due to the tyres are flat Accuracy: it takes doing a neither very hard nor gentle steering. The lack of the steering it might be caused by the next causes: - Caused by here is too much play in the steering elements - Caused by a differently debilitate of the right and left tyres - Caused by the imbalance of the tyres that is the main responsible of the shimmy - Caused by different pressures of the right and left tyres Irreversibility: The steering must be semi-reversible. It consists of the steering wheel has to transmit the motion to the wheels, but these, in spite of the land irregularities, don´t must transmit the oscillations to the steering wheel. The semi-reversibility allows that the wheels recover their normal position with a small effort done by the driver after turn the steering wheel. Final Project: steering system design 2009-2010 Pg 22 Kinematic conditions. If we observe a car covering a curve, in order to do the turn correctly, the wheel that is in the interior of the curve must turn more than the other wheel. On the contrary the rear wheels in any time of the turn are parallels. The problem about the difference of the distance covering by the two rear wheels it is solved thanks to a device called differential. However in spite of the differential, always the rear wheels skid overall in sharp curves taken fast. In order to the car do the curve with precision it is necessary come up with a geometric condition, known as the Ackerman principle which explain that when a vehicle is turning he axis of all the wheels must meet in the same point which it is called instant rotation center. Figure 8. Ackerman principle We can see in this picture not only the instant rotation center, also the different angle of the right and left wheel. The wheel that is in the interior of the curve describe an α angle bigger than the β angle described by the other wheel. It must be on this way because on the contrary if the front wheels will be parallels will finish broken. To obtain these angles it is used an articulated trapezium called Jeantaud trapezium which we can show in the next picture. Final Project: steering system design 2009-2010 Pg 23 This trapezium has two parallel sides, one is the tie rod is shorter than the other which is the front axle which is fixed and two sides whit the same length but no parallels (the extension of the steering arms). In the next pictures we can see clearly in a real steering system. Figure 9. Jeantaud trapezium The studies executes by Jeantaud established that for the turn center of the all he wheels it will be the same, the extension of the steering arms must join with the center of the rear axle as we can show in the next picture. Final Project: steering system design 2009-2010 Pg 24 Figure 10 Jeantaud trapezium With all of this, we can determinate the relationship between the wheelbase, the track and the angles of the interior and exterior wheels in a curve. So if we have the next picture: Figure 11. Turn radius of the wheels Final Project: steering system design 2009-2010 Pg 31 used a low value of divergence but always applied on the front wheel assembly because we applied on the rear wheel assembly the car will be very difficult to drive. By other hand the election of convergence or divergence it depends on the circuit because on curves the convergence does not facilitate the turn as the divergence but on a straight line the divergence is the bad factor. In our case the circuit where the competition take place on Silverstone circuit. This circuit has a first part very fast with straight lines and fast curves and a final part with slow curves where the divergence will help to the pilot. As the most part of the circuit is fast we will choose between 0º and 1º degrees of divergence. Figure 14. Silverstone circuit Final Project: steering system design 2009-2010 Pg 32 Camber angle. Caster is a line drawn through the steering axis, compared to vertical. If the axis is tilted back at the top, the angle is positive, tilted forward is negative. Camber improves stability, steering wheel return and cornering. Figure 15. Camber angle If the wheel has a inclination in the outside direction of the car the angle is positive and on the contrary the angle is negative Nowadays the majority of vehicles have a camber angle around 1º on their front wheels. Final Project: steering system design 2009-2010 Pg 33 The upright supports flexure efforts equivalent to the momentum M = W*L Where: W: weight L: distance The fact to change the camber has influence on the toe angle because if the camber angle increases the toe angle decreases and vice versa. Also this angle has a lot of influence on the tyres because an excessive value of the camber angle produces a high wear down of the tyres. If the camber angle is positive the wear is produced on the exterior of the tyre and with a negative angle the wear is produced on the interior of the tyre. The camber angle equal to the caster angle provides the steering to keep the straight line by the cone effect. The external and internal circumferences turn in different velocities since have different diameters and this is the same movement that a cone will have if go round over a plane surface. As this movement is produced on both guidelines wheels so the same force appears on each wheel doing the vehicle improve the steering stability. Final Project: steering system design 2009-2010 Pg 34 Finally the suspension has a very important role regard the camber angle. Suspension configuration Wheel displacement Camber angle Roll center Body 0º Negative Positive Body Only negative Body Only positive Body Only positive Body Mainly positive Body Mainly negative Body Mainly negative Table 3. Camber angle Final Project: steering system design 2009-2010 Pg 35 Caster angle. Caster is a line drawn through the steering axis, compared to vertical. If the axis is tilted back at the top, the angle is positive, tilted forward is negative. Caster improves stability, steering wheel return and cornering. Figure 16. Caster angle In a formula S.A.E. the propulsion is produced by the rear wheels so the front axle moves on back direction a little producing instability on the steering. We can solve this problem given a certain camber to the pivot doing the extension line of the axis pivot cut with the displacement line in front of the wheel. With this appears an action on the wheel that provides stability to the steering. The caster angle can also obtain situating the pivot in front of the vertical of the wheel axis. On both process the wheel is dragged and then it produces stability on the front wheels. We will bear in mind in this system the effects of the direction radius and the toe angle. In this case only act the backward movement forces produced by the toe angle of the pivots. The caster angle also depends of the camber angle. If the camber is of a considerable importance, even the caster may be negative in order to reduce the Final Project: steering system design 2009-2010 Pg 36 re-position effect. In fact a lot of modern vehicles when are stopped have a negative caster. The caster effect must not be very important since increase the turn effort. In other hand if the caster is very intense the return of the wheel is made a very high velocity and can produce an abnormal position of the wheel and appear oscillations. On cars that has the engine on the back and also has a rack inside the steering box, as in our case, the caster has a higher value being always no very high. Normally on this kind of cars the caster angle has a value between 5º and 10º degrees in order to avoid the instability when the car suffer an acceleration produce by the fact to has the engine on the back. Drift effect When a car is in a curve, the vehicle does not continue exactly by the trajectory that guide the guidelines wheels since due to the effect of the transversal forces which appear on the tyres the car is displaced guiding a trajectory that form an angle with the rim. This angle is denominated as drift angle. So the tyre drift is the change of the trajectory produced by the out of shape of the tyre. It cannot confuse the drift with alost of grip or with a skid. The lost of grip can produce the skid but it has not influence on the drift. The drift depends on the velocity, the weight of the car, the pressure and the width of the tyre and the width of the rim. Figure 17. Drift angle Final Project: steering system design 2009-2010 Pg 37 Figure 17´. Drift angle vs transversal force Final Project: steering system design 2009-2010 Pg 38 4. Design process results and discussions. 4.1. Introduction. 4.2. Elements of the car that have influence on the steering system design. 4.2.1. The cockpit and seat 4.3. Calculation of the force to turn the wheels 4.4. Description of the steering system elements. 4.5. Budget Final Project: steering system design 2009-2010 Pg 39 4.1. Introduction. In this part of the project we will start to explain the different functions of the steering system elements. Once finish, we will investigate the different possible solves to the design of each element explaining the reason of each one. We are going to do all of this, taking in consideration the Formula S.A.E. rules and the theoretical fundaments that we have shown in the previous chapters. On this way in the next chapter the best solution for each element will be choose in order to a possible manufacture of the vehicle in a future. We have the problem that we don´t have the measures of the chassis so we are going to do our steering system with a supposedly measures Final Project: steering system design 2009-2010 Pg 40 4.2. Elements of the car that have influence on the steering system design. 4.2.1. The cockpit. The criterion to design a cockpit is to create a comfortable place to the driver. The cockpit must be sufficiently spacious to allow the necessary movements of the pilot to have a good control of the car. By other hand the cockpit must not be excessively big because this fact decreases the aerodynamics capacities and the acceleration due to the car is heavier. Figure 18. Cockpit In our project we design the steering system so the design of the cockpit is not our responsibility, being a task of a project in which the chassis of the car is designed. However this part of the single-seater has influence on the steering system design so we will do a study of a rough estimate measures that could have a Formula S.A.E. car based on a possible pilot measures, without give much details of the cockpit design. Final Project: steering system design 2009-2010 Pg 47 4.3. Calculation of the force to turn the wheels Once we have done the design the total elements of the steering arms we are going to calculate the force that must to do the driver to turn the wheels. We will study the highest value of the force to turn the wheels. This force appears when the car is stopped and it starts the movement of the wheel. Fr = friction force mg = weight FL = lateral force N = normal Final Project: steering system design 2009-2010 Pg 48 The wheel rest on the floor in a surface not in a point so it appears two friction forces as we can show in the next picture. In the picture the big black square is a sketch of the steering arm, the red point is the application point of the lateral force, the distance between the red point and the middle in horizontal direction is Rs (steering arm length), the small black square is the contact surface between wheel and floor and Fr1 and Fr2 are the friction forces that appears in the contact surface of the wheel which are an a distance r1 and r2 of the middle. Fr1 and Fr2 but in different direction are equals and r1 and r2 are equals to so: r1 = r2 = r Now we can do the Calculations: Σ Fx = 0; FL – Fr = 0 (1) Σ Fy = 0; N – mg = 0 (2) Σ My = 0; FL*Rs – 2*Fr*r = 0 (3) Final Project: steering system design 2009-2010 Pg 49 From equation (1) we calculate: FL = Fr From (2) we have: N = mg This kind of vehicles have a weight around 250 kg without the weight of the driver. We take a weight of 300 kg that is an excessive weight for these cars but on this way we establish a safety coefficient. The weight of the pilot will be 71 kg (show on chapter 4 measures of pilot model) so we take 80 kg for the same reason that before. By other hand the 45 per cent of the car weight is on the front wheel assembly on these cars. So the weight will be: (300 kg + 80 kg)*45/100 = 171 kg And now each wheel supports the half of this weight: 171/2 = 85.5 kg 85.5 kg*9.81 = 838.755 N N = 838.755 N Now we are going to calculate the Fr. Fr = µ*N; Where µ is the friction coefficient. On the same way than before we are going to take a high value of µ in order to establish a safety coefficient. So we take µ = 1. Now we calculate the friction force: Fr = µ*N = 838.755 Final Project: steering system design 2009-2010 Pg 50 And from equation (1) Fr = FL so: FL = 838.755 N It is the force that the rack has to transmit to the tie rods and these to the steering arms to move the wheel. Now we can calculate the torque on the pinion. To calculate the torque we use the following equation: T = F * rpinion In our case we have a pinion with a diameter of 24 mm (show in chapter 4.3) so: T = 838.755*24 = 20130 N*mm This is the torque in the pinion and it is transmitted through the steering column until the steering wheel. Finally we will to calculate the necessary tangential force that must be made in the steering wheel by the driver to turn the wheels. T = F * Rsteering wheel Firstly we have to calculate the steering wheel radius because our steering wheel is not a perfect circle it has 200mm in the vertical direction and 250mm in the horizontal direction (show in chapter 4.3). Final Project: steering system design 2009-2010 Pg 51 By other hand the hands of the driver will be making an angle of 30º degrees with the horizontal direction, in the same position that ten to past in a clock. The red point represents the position of left hand of the driver. We have to calculate x, being r = 250/2 = 125 mm. x = cos 30º * r = cos30º * 125 = 108.25 mm And finally we calculate the necessary tangential force that the driver must produce to turn the wheels: T = F * Rsteering wheel F = T / Rsteering wheel F = F = 185.95 N It is the force when the car is stopped, the moment when the force to turn the wheels has the highest value. Also We have to bear in mind the high values of the weight and the that we have taken in order to put a safety coefficient in the calculations. Final Project: steering system design 2009-2010 Pg 52 With this force we can calculate if the material for the steering column is adequate for the torque that is transmitted by the force on the steering wheel. The steering column support torsion efforts so: τmax = Where: T: torque in the steering column R: radio columna J: Inertia for hollow columns Π * ( ) Where: D = 18mm; d = 16 mm (show in chapter 4.3) τmax = = 93.58 MPa The SAE 1015 steel with which we have made the steering column supports 386.1 Mpa and we have a value of around 100 MPa so the design is correct Final Project: steering system design 2009-2010 Pg 53 4.4. Description of the steering system elements In this chapter we be able to see the elements which to made up the steering system of one car and more in detail which are used in a competition vehicle. The weight of the car has importance on the performance of the car since depending of the weight the car has a different performance on the road. So we can distinguish in two parts different elements of the car: The elements which belong to the hang weight and the other that belong to the not hang weight. The not hang weight: is the part of the total weight of the car which is not support by the suspension. This weight support all the disruptions of the road so we try to reduce this weight the much as possible - Rims - Upright - Brakes - The bearings, springs and shocks absorbers (elements of the suspension) The hang weight: Is the weight that is supported by the suspension. This part is the heavier part of the car. - Steering box - Steering column - Steering wheel - Chassis, engine, driver, fuel, bodywork and one part of the suspension. Final Project: steering system design 2009-2010 Pg 54 Now we are going to start with the design of the elements. We can difference between the elements that we will design ourselves and the elements which we will buy to the manufacturers. Elements to design Elements to buy Steering column Steering wheel Rack and pinion Quick disconnect device Tie rods Universal joint Steering arms Ball-and-socket joint Upright Pivot Steering wheel Is the element that joins the driver with the steering system in order to control of the car. The steering wheels change according with the manufacturer since the steering wheels can have different radius. Important characteristics on the steering wheel are the feel and the thickness that must be comfortable to the driver. Also the shape of the exterior radio can has different shapes trying to achieve the most comfort to the pilot. The steering wheel joins with the steering column through a device that is called quick disconnect device which has the function to separate the steering wheel of the steering column in a few seconds. On the competition world the same that on the common car the purpose of the steering wheel is transmit a tangential force to the steering column with the most possible accuracy. The steering wheel is inside the cockpit and it will be situated on a correct position according with the driver. Final Project: steering system design 2009-2010 Pg 55 The steering wheel has three important points according with the design: the interior diameter, the cover and the diameter. The interior diameter is on where the pilot puts their hands and if the driver can grab the steering wheel without problems, he will be able to do the necessary tangential force along the curve. As Eastman Kodak studied on 1983 the value recommended for this diameter ranges between 18 and 53 mm, however the manufacturers normally make designs about 30 mm and usually are oval shape to improve the hold making the driving more comfortable. So we choose this thickness for our steering wheel. The steering wheel cover is also important because decrease the tiredness of the driver if the friction with the gloves is high preventing the slide between the steering wheel with the gloves of the pilot when he is turning. A good election for the cover is suede because is hardwearing and have good friction properties when joins with the gloves of the pilot which usually also are made of suede. The diameter of the steering wheel determine the easily to drive the car. The tangential force applied over the steering wheel is between 20 and 200 N (according the studies of the Eastman Kodak 1983). This force depends on the position of the wheels according with the pilot. The pilot applied the force on the exterior diameter of the steering wheel so the momentum applied on the steering column will increase if we increase the radio of the steering wheel although the applied force have the same value. But by other a big exterior diameter will cause problems at the time to turn it inside a cockpit that has a limited size. In order to adapt the steering wheel to the cockpit on a correct position the most of the manufacturers create the steering wheels with the down part horizontal in order to achieve more distance between the legs of the pilot and the steering wheel. We will chose this kind of design because is a perfect model for the position of the pilot in a competition car where the pilot is with their legs full-length save. Final Project: steering system design 2009-2010 Pg 56 Once we have established the kind of design of the steering wheel, finally we are going to choose it. We have three possibilities to choose the steering wheel: Possible solution 1: The first possibility is Sparco 015P260F: Diameter: 260 mm Price: 289 $ Grip: a good grip of suede Figure 24. Sparco steering wheeel Possible solution 2: The second possibility is Sparco 015P310: Dimensions: 310 * 260 mm Price: 239 $ Grip: a good grip of suede Figure 25. Sparco steering wheeel Final Project: steering system design 2009-2010 Pg 63 Steering column This torsion bar joins the steering wheel with steering box through the quick disconnect mechanism. This bar only support the torsion effect produced by the turn of the steering wheel so it is not necessary a high quality steel. Also appears short compression efforts when the pilot leaning on the steering wheel, but are insignificant. In order to do the design of the steering column we will see the Formula S.A.E. rules and the effort analysis. According with the Formula S.A.E. rules the steering column cannot be one bar with only one direction due to different aspects. One of this is the safety of the driver since in case of accident, on a front crash, if the steering column only has on direction it will be easy that go out in direction to the pilot being very dangerous. The other aspects depend on the design for the comfort of the driver. Using a universal joint we can join two parts of the steering column making an angle allowing increase the distance between this element and the legs of the pilot and also increase the entry pinion angle into the steering box. Our design Measures: we will design a steering column with a diameter of 18 mm a very normal measure in this kind of cars and which will be fit with our steering box perfectly. The thickness will be 2 mm since the steering column is a hollow bar. Final Project: steering system design 2009-2010 Pg 64 Material: The steering column support torsion efforts so we do not need a high quality steel. We will use SAE 1015. Figure 34. AISI 1015 steel Situation: the steering column will start on the steering wheel until the universal joint that is fixed with the chassis. Here it is produced the change of angle on the steering column and starts the second part of the element that join the universal joint with the steering box. The angle between the two parts of the steering column will be δ < 180º. When we fixe the steering box and with the exact measures of the cockpit, we will be able to calculate the angle that it always will be δ < 180 and the difference with the horizontal between γ φ around 15º and 20º degrees being the value of φ between 15º and 20º. Final Project: steering system design 2009-2010 Pg 65 φ + (15º or 20º) = γ . Figure 35. Steering wheel situation Figure 35’. Assembly steering wheel-quick disconnect-steering column Universal joint This kind of joint is very utilized on the self-propulsion industry in order to manufacture the steering columns, keeping the torque between bars with different angles Final Project: steering system design 2009-2010 Pg 66 The most common kind of these devices for short angles between bars is the pin and block which works efficiently with angles bigger than 35º degrees. Figure 36. Universal joint The most of the universal joints for the competition require a bar of ¾ inches with a plane final in order to transmit the torque through the join. We will choose the Fr1820 UNIVERSAL JOINT STEEL N which cost 59.95 $ Steering box Is the part of the steering system defining as the joint of gear assemblies that convert the torque transmitting by the steering column on a horizontal force. In other words in the steering box the rotational movement transmitted by the steering column is converted on a rectilinear movement. At the same time the rack and pinion produces a decrease on the effort executed by the pilot from the turn of the steering wheel until the turn of the wheels avoiding on this way the extreme tiredness of the driver. The effort necessary to turn the wheels is higher when the vehicle is stopped and decrease in accordance with the increase of the velocity. However we can say that this effort depends mainly on the resistance made between the wheels and the floor due to the friction which is function of the velocity and the weight of the vehicle. Final Project: steering system design 2009-2010 Pg 67 Exist different kinds of steering box with their respective characteristics, although in general in the competition world is used the rack and pinion. We are going to do a brief description of the other kinds of steering box. WORM AND SECTOR WORM AND ROLLER Figure 37. Worm and sector Figure 38. Worm and roller WORM AND NUT OR RECIRCULATING BALL CAM AND LEVER Figure 39. Worm and nut Figure 40. Cam and lever The location on the car is very significantly since the geometry formed by the steering box, tie rods and the end of the steering arms will form the Jeantaud trapezium which will have a lot of influence on the performance of the car at the time to drive it. Worm and sector In this type of steering box, the end of the shaft from the steering wheel has a worm gear attached to it. It meshes directly with a sector gear (so called because it is a section of a full gear wheel). When the steering wheel is turned, the shaft turns the Final Project: steering system design 2009-2010 Pg 68 worm gear, and the sector gear pivots around its axis as its teeth are moved along the worm gear. The sector gear is mounted on the cross shaft which passes through the steering box and out the bottom where it is splined, and the pitman arm is attached to the splines. When the sector gear turns, it turns the cross shaft, which turns the pitman arm, giving the output motion that is fed into the mechanical linkage on the track rod. The following diagram shows the active components that the present inside the worm and sector steering box. The box itself is sealed and filled with grease. 1. Sector shaft seal 2. Input worm gear and rack 3. Worm ball 4. Ball return guide 5. Worm thrust bearing adjuster 6. Locknut 7. Worm thrust bearing Figure 41. Worm and roller 8. Sector shaft 9. Input worm gear and rack Worm and roller The worm and roller steering box is similar in design to the worm and sector box. The difference here is that instead of having a sector gear that meshes with the worm gear, there is a roller instead. The roller is mounted on a roller bearing shaft and is held captive on the end of the cross shaft. As the worm gear turns, the roller is forced to move along it but because it is held captive on the cross shaft, it twists the cross shaft. Typically in these designs, the worm gear is actually an hourglass shape so that it is wider at the ends. Without the hourglass shape, the roller might disengage from it at the extends of its travel. Final Project: steering system design 2009-2010 Pg 69 Figure 42. Worm and roller parts Worm and nut or recirculating ball This is by far the most common type of steering box for pitman arm systems. In a recirculating ball steering box, the worm drive has many more turns on it with a finer pitch. A box or nut is clamped over the worm drive that contains dozens of ball bearings. These loop around the worm drive and then out into a recirculating channel within the nut where they are fed back into the worm drive again. Hence recirculating. As the steering wheel is turned, the worm drive turns and forces the ball bearings to press against the channel inside the nut. This forces the nut to move along the worm drive. The nut itself has a couple of gear teeth cast into the outside of it and these mesh with the teeth on a sector gear mechanism. This system has much less free play or slack in it than the other designs, hence why it is used the most. Final Project: steering system design 2009-2010 Pg 70 The example below shows a recirculating ball mechanism with the nut shown in cutaway so you can see the ball bearings and the recirculation channel. Figure 43. Worm and nut parts Cam and lever Cam and lever steering boxes are very similar to worm and sector steering boxes. The worm drive is known as a cam and has a much shallower pitch and the sector gear is replaced with two studs that sit in the cam channels. As the worm gear is turned, the studs slide along the cam channels which forces the cross shaft to rotate, turning the pitman arm. Final Project: steering system design 2009-2010 Pg 71 One of the design features of this style is that it turns the cross shaft 90ºdegrees to the normal so it exists through the side of the steering box instead of the bottom. This can result in a very compact design when necessary. Figure 44. Cam and lever The rack and pinion In general Before the appearance of the car the use of the rack and pinion was limited only to small vehicles because the steering proved too heavy and the improvements were not sufficiently suitable so it was necessary to make a lot of turns with the steering wheel in order to guide the wheels on the desirable trajectory. Nowadays this problem has been solved with the power-assisted steering. Final Project: steering system design 2009-2010 Pg 72 Actually the rack and pinion is very used by the fact that is cheap and the assembly is simply allowing the incorporation system that help on the driving as the power-assisted steering. Figure 45. Rack and pinion The system is connected directly with the tie rod and this one with the wheels having a high mechanical output. It is a great accuracy system, particularly in cars with the motor on the front part and with front-wheel-drive since decrease enormously the effort to do, is very smooth, and has a good recuperation and is safe. The steering column ends with a pinion (generally helicoids) that engages constantly with a bar that is a rack. The rack moves inside a framework that is used as a guide and as protection of the outside agents. The rack is directly jointed with the tie rods with the ball-socket-joints transmitting the movement to the wheels. There are steering systems that have a power-assisted steering. This mechanism has the task of decrease the necessary effort at the time to drive the car. On the common cars the most used is the hydraulic system although is also used the pneumatic system or with an electrical system in the steering column. But in our case of a formula S.A.E. we will not use a power-assisted steering. Final Project: steering system design 2009-2010 Pg 79 Design 4: Pinion 2 with rack 1 Now we calculate the displacement of the rack advance: d = = = 83.9 cm Now we are going to do a graphical representation: Table 7. Graph designs As regards the velocity with the rack is moved , we can calculate as we can say before with the following equation: v = N ( ) But in this case we are not going to do the calculations because we are looking for the best design, and now we are interested in achieve a greater velocity of the rack not a determined velocity only which design produce the highest value on the velocity 0 10 20 30 40 50 60 70 80 90 0 0.25 0.50 0.75 1 disatance cm number of turns pinion distance rack vs turns of pinion diseño 1 diseño 2 diseño 3 diseño 4 Final Project: steering system design 2009-2010 Pg 80 of the rack. So if we take any value for the velocity of pinion turn and the same for all the designs we obtain the same result because the velocity multiply to the lateral displacement of the rack (d = z/n) so the design with the highest value of ``d´´ also will be the highest value of ``v´´. Finally we can conclude that our design will be the pinion 2 with the rack 1. Pinion2 Modulus 2 Z 12 D 28 C 24 E 20 Material SAE 1045 Rack 1 Modulus 2 n 14 Total length 98 B 20 C 25 D 23 Material SAE 1045 Table 8. The design chosen Position: The position of the steering box will be determinate with the dimensions of the wheel. For Formula S.A.E. we will choose a wheel for the competition with the followings dimensions: 20.0 x 7.0 – 13 inches If we translate to cm, we have an exterior diameter of 20 x 2.5 = 50 cm. Bearing in mind that the steering box is joined with the wheel through the tie rods and the steering arms at the middle of the wheel. So we can obtain the distance of the steering box with the road and if we had the exacts measures of the cockpit we could calculate the distance of the steering box with the cockpit floor but the project of the chassis is studied in other project. Finally the distance of the steering box to the road is: 50 / 2 = 25 cm Final Project: steering system design 2009-2010 Pg 81 Tie rod In our case in which we have chosen the rack and pinion for our steering box the tie rods are the bars which join the rack with the steering arms. The join is made through ball-and-socket joint. The connection between the ball-and-socket join and the steering arms is thread, making possible the variation of the distance from the end of the rack to the end of the steering arms. Then the joint secures through with nuts and locknuts. This is used to adjust the parallelism between the wheels. The tie rods must be made of alloyed steel since must be support the knocks to come from the wheels through the upright and the steering arms. Figure 50. Tie rod Our design Material: The tie rods support compression and traction efforts so for this element we will use AISI/SAE 1023 steel with a treatment of the surface in order to protect against the corrosion. Final Project: steering system design 2009-2010 Pg 82 Measures: The formula S.A.E. stipulates that the front track must be a minimum of 1200 mm so the distance of the tie rods will define with the measure of the rack the front track of the formula S.A.E. Track = rack measure + tie rod measure * 2 = We will determinate the measure of the tie rods with the team which carry out the suspension design because they have to do the task of the design the suspension arms and springs that will join with upright. Now we will join the tie rod with the steering arm through a ball-and-socket joint. Ball-and-socket joint The ball-and- socket joint allows the oscillations produced by the movement of the steering (the movement of the rack and he steering arms are in different plane) and the effect of the suspension (the wheels and the steering arms oscillate with the suspension whereas the rack is joined rigidly to the chassis). These elements consist of three parts: one ball, one bearing situated behind the ball in order to Figure 51. Ball socket joint reduce the friction and the framework that contains them. The ball is connected with a thread rod in where is connected one of the elements to articulate. The other element is connected with another thread rod that comes from the framework. Final Project: steering system design 2009-2010 Pg 83 Figure 52. Ball socket joint measures Steering arms The steering arms are the last part of the Ackerman quadrilateral. In his movement, through the ball-and-socket joints, push or pull from the steering arms which transmit the movement to the upright that is element that fix the wheel causing finally the turn of the wheels. As we can explain in a previous chapter and as we also can show in the pictures we will situated the steering arms with an angle that in the stop position the extensions of the lines that join the ends of the steering arms coincide on the center of the rear axle according with the Jeantaud trapezium Figure 53. Jeantaud trapezium Final Project: steering system design 2009-2010 Pg 84 Our design We thought firstly to design a upright with the steering arm include. However we do not choose this option because with a separate steering arm the efforts are not so concentrate in the upright. We are going to see the stress analysis for the steering arm when the driver turns the wheel and the tie rods transmit a force to the steering arms. The force applied in the steering arm is the force calculated previously in the chapter 4.3. Figure 54. Steering arm in solid works Final Project: steering system design 2009-2010 Pg 85 Figure 55. Stress analysis in solid works of the steering arm As we can see in the picture the deformation is produced in the joint with the tie rod and with the force that we have applied the steering arm support the effort correctly because have a maximum deformation of 2.031e-002 mm Upright There are two kinds of uprights: the front and the rear uprights. Both are quite different since have different tasks on the car. The front uprights turn around the pivot and move the wheel due to the force that has transmitted the steering wheel. Furthermore the upright have two more functions: to fix the wheel and join the wheel with the suspension arms. Final Project: steering system design 2009-2010 Pg 86 These elements must be very stiff in order to support the knocks that in frequently occasions will be very violent but at the same time they must be sufficiently tough in order to do not finish braked. Our design We have designed, as we have said before, the upright separately of the steering arm in order to decrease the efforts on this element. By other hand we have designed the upright in order to be light. Finally the last parameter, we are going to design the upright inside a rim of 13 inches . Figure 56. Upright in solid works Final Project: steering system design 2009-2010 Pg 87 Now we are going to see the stress analysis hen we apply the force. Front upright Figure 57. Stress analysis of the upright Back upright Figure 58. Stress analysis of the upright Final Project: steering system design 2009-2010 Pg 88 The displacement Figure 59. Displacemnet When we apply the force on the steering arm this one transmit the force to the upright and as we can show in the picture the maximum deflection is 8.154e-002 mm. The assembly: Figure 60. Assembly Final Project: steering system design 2009-2010 Pg 95 6. Recommendations. Final Project: steering system design 2009-2010 Pg 96 From my point of view it will be interesting to continue with the design of the upright and the steering arms in order to improve these elements trying to decrease the weight of these elements maintaining the features and that the design of the element is no too expensive. By other hand this kind of cars has not power-assisted steering but it will be interesting to decrease the force made by the driver to turn the wheels. Final Project: steering system design 2009-2010 Pg 97 7. References. Final Project: steering system design 2009-2010 Pg 98 In this chapter we are going to write the web pages which have been used to make this project: WEB PAGES: www.Librospdf.net/ingenieria-automovil www.thef1.com/protagonistas/circuitos/silverstone www.squadracorse-polito.com/en/sc-events/venueevents/1-silverstone-circuit.html http://www.slideshare.net/gatox99x/seleccion-de-material-para-el-sistema-de-direccion- por-cremallera www.students.sae.org/competitions/formulaseries www.fsae.com www.circulaseguro.com http://www.tecnun.es/fstudent http://www.formulastudent.com/ http://www.motorweb-es.com/ formulaSAE.htm http://www.mimecanicapopular.com/ http://www.autocity.com/ http://www.imeche.org http://www.auto-publitest.com/SP1/FamProd_Geometria.htm http://grupos.emagister.com/debate/formula_sae/6745-304276 www.khkgears.co.jp http://www.scribd.com/doc/2561082/Tema8Torsion www.beldenuniversal.com www.streetsideauto.com www.sparcousa.com Final Project: steering system design 2009-2010 Pg 99 www.ompracing.it www.tarsa.biz/pagina_nueva_13.htm www.efunda.com www.scribd.com www.antonio-Ida.blogspot.com/2009/05/pinion-cremallera.html www.truechoice.com www.substech.com www.carbible.com/steering_bibles.html www.km77.com http://www.hoosiertire.com/Fsaeinfo.htm http://www.racegoodyear.com/tires/sae.html BOOKS: José Duran Abarca, 2001, La dirección. Ceac J.N. Alonso, 1998, Técnicas del automóvil. Paraninfo P.Luque, D.Alvarez, C.Vera. Ingeniería del automóvil. Thomson Simon McBeath, 1999, Competition car preparation. Haynes publishing Hans B. Pacejka, 2002, Tyre and vehicle dynamics. BH. Carroll Smith, 1984, Engineer to win. Motorbikes international J. Rempell, H. Stoll, J.W. Betzler, 1986, Theautomative chassis. BH. Catalogue Demontweeke Final Project: steering system design 2009-2010 Pg 100 8. Figures. Final Project: steering system design 2009-2010 Pg 101 Figure 1. Fsae logo 13 Figure 2. Formula Student logo 13 Figure 3. Formula Student logo 14 Figure 4. Fsae rules 17 Figure 5. Fsae rules 18 Figure 6. Fsae rules 18 Figure 7. rain tire 19 Figure 8. Ackerman principle 22 Figure 9. Jeantaud trapezium 23 Figure 10. Jeantaud trapezium 24 Figure 11. turn radius of the wheels 24 Figure 12. Wheels angles 28 Figure 13. Toe rod 29 Figure 14. Silverstone circuit 31 Figure 15. Camber angle 32 Figure 16. Caster angle 35 Figure 17. Drift angle 36 Figure 17’ Drift angle vs transversal force 37 Figure 18. Cockpit 40 Figure 19. arms movement for a seated man 41 Figure 20. Pilot model 43 Figure 21. Pilot model 43 Figure 22. Measures cockpit 44 Figure 23. Seat 46 Figure 24. Sparco steering wheeel 56 Final Project: steering system design 2009-2010 Pg 102 Figure 25. Sparco steering wheeel 56 Figure 26. Sparco steering wheeel 57 Figure 27. Ssteering wheel angle 58 Figure 28. Measures Calculus 58 Figure 29. Fsae rules 59 Figure 30. Hex drive 60 Figure 31. Quick disconnect device 61 Figure 32. quick disconnect device 62 Figure 33. quick disconnect device 62 Figure 34. AISI 1015 steel 64 Figure 35. Steering wheel situation 65 Figure 35’. Assembly steering wheel-quick disconnect-steering column 65 Figure 36. Universal joint 66 Figure 37, worm and sector 67 Figure 38. worm and roller 67 Figure 39. Worm and nut 67 Figure 40, Cam and lever 67 Figure 41. Worm and roller 68 Figure 42. Worm and roller parts 69 Figure 43. Worm and nut parts 70 Figure 44. Cam and lever 71 Figure 45. Rack and pinion 72 Figure 46. Rack and pinion lateral 73 Figure 47. Rack and pinion front 73 Figure 48, Rack and pinion SAE 1045 74 Final Project: steering system design 2009-2010 Pg 103 Figure 49. Rack and pinion parameters 75 Figure 50, Tie rod 81 Figure 51. Ball socket joint 82 Figure 52. Ball socket joint measures 83 Figure 53. Jeantaud trapezium 83 Figure 54. Steering arm in solid works 84 Figure 55. Stress analysis in solid works of the steering arm 85 Figure 56. Upright in solid works 86 Figure 57. Stress analysis of the upright 87 Figure 58. Stress analysis of the upright 87 Figure 59. Displacement 88 Figure 60. Assembly 88 Figure 61. The pivot 89 Figure 62, Slick tyre 90 Figure 63, Rain tyre 90 Final Project: steering system design 2009-2010 Pg 104 9. Tables. UNLESS OTHERWISE SPECIFIED: DIMENSIONS ARE IN MILLIMETERS SURFACE FINISH: TOLERANCES: LINEAR: ANGULAR: DEBUR AND BREAK SHARP EDGES B C D 1 2 A 321 4 B A 5 6 DRAWN CHK'D APPV'D MFG Q.A FINISH: NAME SIGNATURE DATE MATERIAL: DO NOT SCALE DRAWING REVISION TITLE: DWG NO. SCALE:1:1 SHEET 1 OF 1 A4 C WEIGHT: 3 Daniel Nuviala Civera Phil Storrow Rack 98.0 25.0 23.0 20.5 UNLESS OTHERWISE SPECIFIED: DIMENSIONS ARE IN MILLIMETERS SURFACE FINISH: TOLERANCES: LINEAR: ANGULAR: DEBUR AND BREAK SHARP EDGES B C D 1 2 A 321 4 B A 5 6 DRAWN CHK'D APPV'D MFG Q.A FINISH: NAME SIGNATURE DATE MATERIAL: DO NOT SCALE DRAWING REVISION TITLE: DWG NO. SCALE:1:1 SHEET 1 OF 1 A4 C WEIGHT: 4 Daniel Nuviala Civera Phil Storrow Pinion 18.2 29.5 20.0 28.0 24.0 Final Project: steering system design 2009-2010 Pg 109 ``If you have the control, you are not in the limit´´ Ayrton Senna