I An introduction to racing and vehicle dynamics The main aim in motor vehicle racing is to achieve an overall vehicle configuration, which abides by the rules of a given class, which can cover a given race track in a minimal time, when piloted by a driver utilizing techniques within their capabilities. There are many factors to be considered when designing and building a race vehicle, but for this case we will only be looking into the rear suspension setup. The primary forces by which a high speed motor vehicle is controlled is developed in four small patches, this is where the four tyres make contact with the road surface. A knowledge of the forces and moments generated by the tyres at the ground is essential to understanding vehicle dynamics (Gillespie, 1992). To maximize the tyre contact with the road at all times it is important to set up the suspension geometry correctly and select the correct springs and shock absorbers for the task at hand as evidently the more contact the tyres have with the road surface, the more grip or traction the vehicle will have which in turn will allow the car to travel at higher speeds more safely. What upsets the dynamics of a vehicle whilst in motion? There are a number of factors which will now be discussed. The first and most obvious is the quality of road surface, as bumps and dips most certainly upset the handling of the vehicle. The second factor is the tire/ wheel assembly. Ideally the assembly is soft and accommodating to absorb small vibrations and bumps to some extent as well as running true, which essentially means it isnt adding any vibrations to the vehicle in the form of unbalance in the wheel assembly, dimensional variations and stiffness variations (Gillespie 1992). The next factor to be considered, which is a major factor that is being considered in this project in particular is driveline excitation. This is where the torque transmitted from the engine through the gearbox on to the driveshaft and into it. II differential will try to twist the rear axle assembly along its centre line which is referred to as axle wind up, this causes the axle to skew on its springs forcing the whole rear of the car to hop or tramp, this also tends to force the car sideways due to the skewing of the axle. The redesigned rear suspension will strive to keep this drive train excitation to a minimum (Gillespie 1992). When setting up a suspension system for a race car it is necessary to make the distinction between changes that will always improve the performance of the car and changes that will tune or balance the car. The first category consists of things like adding more power or getting better tyres, where as the second category consists of things such as making changes to spring rates and roll centre adjustments (Milliken and Milliken 1995). Racing is all about driving a car at its limits. Finding a vehicle configuration which can be driven to produce this desired performance is referred to as setting up or chassis tuning. It is a difficult task requiring many compromises to fit each circuit and the drivers capabilities and preferences. Often it will not be possible to achieve the optimum setup in the available time for testing prior to a race event and the driver will have to make do with any deficiencies that remain in the vehicle (Milliken and Milliken 1995). The principal objectives in setting up the car are achieving a good cornering balance (neutral steer), finding a compromise between cornering and drag on high speed circuits and eliminating specific control and stability problems at any points on the race circuit as reported by the driver (Milliken and Milliken 1995). There are many factors to be considered when designing the suspension set up of a race car, as each component and adjustment will have an effect on the way the vehicle handles and will also have an effect on the manner in which the other related components will operate. The effects of weight shifts, brake bias, roll stiffness, roll centre, anti dive, camber are all factors that need to be carefully looked into to achieve a desirable set up (Milliken and Milliken 1995). Two of the major objectives of this project are to achieve optimum anti squat and roll centre geometrys, both of these geometrys will be adjustable to III allow for minor tweaks to optimize the use of the rear suspension system in different circumstances. Roll centre heights partially determine the way the roll moment on the car from lateral force is distributed. Lowering the roll centre on the rear of the vehicle will lower the roll moment resisted by that end; the wheels on that end will be more evenly loaded in cornering compared to the front of the car (Milliken and Milliken 1995). To set up anti squat, the effective point pivots or suspension travel paths of the tyre to road contact need to be known to calculate the optimum angles for this geometry to be achieved. (Bastow, Whitehead. 1993) The goal in setting up anti squat is to transfer just enough force to the tyres to keep them from loosing traction and then allow the rest of the force to push the car forward. If an imaginary line is drawn through the lower link bar in a forward direction toward the front of the car and another imaginary line is then drawn through the upper link bar forward until it intersects with the lower line, the Instant Centre (IC) is found. (Bastow, Whitehead. 1993) Now imagine that the Centre of Gravity (CG) of the vehicle is concentrated at the gearstick. Where the IC is located when compared with the CG is what determines how the force applied to the rear suspension from the dri ve train acts on the vehicle to get it moving. If the IC is too high then there will be too much energy wasted pushing the rear of the car skyward. If the IC is set too low then there will not be enough force applied to the rear tires and as a result there will be excessive wheel spin. There are also variables if the IC is in front of the CG or behind the CG. Somewhere there is going to be a position that will apply just enough force to the tires to keep them from spinning and the rest of the force will push the car forward, this can be determined using anti squat calculations, filling in the variables for the particular car in question. (Bastow, Whitehead. 1993) Once the roll centre and anti squat geometry is optimised is it then time to look at spring rates. Ride spring rates affect the lateral load transfer distribution. Lowering the spring rate on one end of the vehicle will even out the loads on that particular end and this will raise the lateral force available IV from that end. The fitment of stiffer spri ngs than what is found on a production car will generally limit the amount of body motion in pitch and roll, this is desirable for a race car. Race cars generally wind up with the un-driven end of the car very stiffly sprung relative to the driven end, this keeps drive wheels more evenly loaded for traction (Milliken and Milliken 1995). The differential (commonly referred to as the diff) basically transmits the torque transmitted from the driveshaft on to the wheels. There are three main types of differential to be discussed here, the open differential, the locked type (known as a spool) and the Limited slip differential (LSD). The type of diff chosen will greatly affect the amount of traction a car will have. Most factory road going cars are fitted with open differentials. An open differential works in the following manner. Refer to the figure below and while reading the following. A pinion gear which is rotated by the drive shaft engages with the much larger ring gear or crown wheel. The ring gear drives a small set of three planetary gears which are designed so that the two side gears can turn in opposite directions to one another. These two side gears turn the axle half shafts, which in turn drive the wheels (Wikipedia, 2007). The reason for the two outer planetary gears being able to rotate against one another is so that the right and left wheels can rotate at different speeds when the car is negotiating a corner, although the same torque is supplied to each of the axle shafts under all conditions. Figure 2.1 Open differential http:/www.offroa ders .c om/info/tech -c orner/proj ec t-cj7/i ma ges /loc ker/open -di fferential-pa rtsid. The torque on each wheel is a result of the engine and transmission applying torsion against the resistance of the traction at that wheel. Unless the load is exceptionally high, the engine and transmission can usually supply as much torque as necessary, so the limiting factor is usually the traction under each wheel. It is therefore convenient to define traction as the amount of torque that can be generated between the tyre and the ground before the wheel starts to slip. If the total traction under all the driven wheels exceeds the V torque required to push the car forward at any particular instant, the vehicle will be driven forward; if not, then one or more wheels will simply spin (Wikipedia, 2007). The limitation of the open differential is due to the fact that it will always allow the wheel of lesser resistance to spin faster relative to the other wheel. For example in a left hand turn the weight of the unsprung mass will tend to shift to the right hand side of the car in roll therefore applying a greater force into the road to the right wheel and effectively a lesser force into the road on the left wheel, this will generally to cause the lef t driven wheel to spin or loose traction. In this process the planetary gears inside the diff will start to rotate against each other as the loaded wheel (right) has a greater resistance from spinning than the left wheel. The open differential will allow the left wheel to spin faster, with the right wheel maintaining its current speed. Note that the open differential supplies the same amount of torque to both wheels, so both wheels are striving to push the car forward the same amount, although due to the force required for the left wheel to break traction being much less than the right wheel it will effectively spin much faster relative to the right wheel (Wikipedia, 2007). This has led many to believe that the open differential is only one wheel drive, although this type of differential always provides equal torque to both driven wheels. Due to varying levels of traction at each of the driven wheels as a result of variances in road surface, weight shifts and twisting torques from the engine and driveline etc the open differential is not desirable for racing conditions. Enter the Limited slip differential. The most commonly used form of LSD is the clutch type LSD. This differential uses clutch plates which are used to limit the speed difference between the side gears and thus the two wheels. By restricting the speed difference between the two driven wheels, useful torque can be transmitted to both wheels as long as there is some friction available on at least one of the wheels. The LSD is the most commonly use d form of differential in circuit racing cars (Wikipedia, 2007). The locked differential or spool does not contain planetary gears and the VI speed of the two wheels will always be the same. The major limitation of the spool is that due to not allowing the wheels to rotate at different speeds, the car is harder to turn into corners as front end understeer is heavily promoted due to the fact that the two driven wheels will always be trying to push the car in a straight line. Spools are most commonly used in dra g racing and low budget circuit race cars as they are much less expensive than LSDs. II 賽車和車輛動(dòng)力學(xué)介紹 汽車賽車的主要目的是實(shí)現(xiàn)一個(gè)整體的車輛配置，并且這種配置遵守一個(gè)指定的類型的規(guī)則，能夠在一個(gè)駕駛員利用在他們能力范圍內(nèi)的技術(shù)的最少的時(shí)間內(nèi)覆蓋一個(gè)給定的賽道。在設(shè)計(jì)制造一個(gè)賽車時(shí)有許多因素要考慮，但是在這里我們只考慮懸架設(shè)置。 控制一個(gè)高速機(jī)動(dòng)車輛的主要力量是由四個(gè)小補(bǔ)丁發(fā)展起來的，這就是四個(gè)輪胎與地面接觸的 地方。對(duì)于輪胎產(chǎn)生的力量和時(shí)間在根源上有一個(gè)了解對(duì)于理解車輛動(dòng)力學(xué)是非常有必要的 (Gillespie, 1992)。 為了最大化輪胎與地面的接觸，對(duì)于手頭上的任務(wù)建立正確的懸架幾何以及選擇正確的彈簧和休克吸收器是非常重要的。輪胎與地面的接觸面越大，車輛就會(huì)有更多的抓地力和牽引力，反過來會(huì)使車更加安全的高速行駛。 什么阻礙了一個(gè)車輛在運(yùn)行時(shí)的動(dòng)力？接下來將要談?wù)撘幌盗幸蛩亍５谝粋€(gè)也是最明顯的因素就是路況，凹凸不平的路面肯定車輛的駕駛。第二個(gè)因素是輪胎 /車輪總成。理性的情況下這個(gè)組裝是柔軟并且能夠吸收小幅度的震動(dòng) 和顛簸，這基本上意味著它不會(huì)添加任何震動(dòng)給車輛，包括在車輪組裝上的不平衡，空間的變化和剛度變化。 (Gillespie 1992)。 接下來要考慮的因素，也是在這個(gè)項(xiàng)目中需要考慮的最主要的因素，那就是動(dòng)力傳動(dòng)系統(tǒng)勵(lì)磁。也就是在這里，扭矩從發(fā)動(dòng)機(jī)傳送到傳動(dòng)軸通過變速箱，而后進(jìn)入 差動(dòng)器將會(huì)試圖延其中心扭曲后橋總成線，稱為軸風(fēng)力，這使軸偏在其彈簧上，迫使整個(gè)車的后面上升，由于扭曲的軸也使整個(gè)車側(cè)向。重新設(shè)計(jì)的懸架將努力保持這種傳動(dòng)系勵(lì)磁降到最低 (Gillespie 1992)。 當(dāng)為賽車建立懸架系統(tǒng)時(shí)，需要區(qū) 分提高汽車性能的變化和調(diào)整或平衡汽車的變化。第一類包括增加更多動(dòng)力和更好輪胎的東西，而第二類包括諸如修改彈簧利率和軸中心的調(diào)整 (Milliken and Milliken 1995). 賽車就是在其限度內(nèi)駕駛汽車。找到一個(gè)可以驅(qū)動(dòng)產(chǎn)生這種期望的性能的車輛配置稱為設(shè)置或底盤調(diào)優(yōu)。這是一個(gè)艱巨的任務(wù)，需要適應(yīng)每個(gè)電路和司機(jī)的能力和偏好。在參賽前在可用的時(shí)間內(nèi)實(shí)現(xiàn)最優(yōu)的設(shè)置往往是不可能的，司機(jī)將就著仍存在于車輛上的一些缺陷 (Milliken and Milliken 1995). III 設(shè)計(jì)汽車的主要目的是實(shí)現(xiàn)良好的 汽車轉(zhuǎn)彎平衡（中性駕駛），找到轉(zhuǎn)彎和高速電路以及消除特定控制盒穩(wěn)定性問題上的折中，這些是司機(jī)所報(bào)道的在賽道任何一點(diǎn)上的情況 (Milliken and Milliken 1995)。當(dāng)為一個(gè)賽車設(shè)計(jì)懸架設(shè)置的時(shí)候，需要考慮許多因素，因?yàn)槊總€(gè)組件和調(diào)整都會(huì)影響車輛的駕駛，同時(shí)也影響其他組件的操作方式。重量變化的影響，制動(dòng)偏見，滾剛度，軸中心等許多因素都需要認(rèn)真考慮以便實(shí)現(xiàn)一個(gè)理想的配置。 (Milliken and Milliken 1995). 這項(xiàng)設(shè)計(jì)的兩個(gè)主要目的是實(shí)現(xiàn)最大反蹲和幾何軸中心，這兩種幾何體是可 以調(diào)節(jié)的以便于小的調(diào)整，便于懸架系統(tǒng)在不同的情況下最大化的使用。 軸中心的高度部分決定了汽車在搖擺時(shí)的側(cè)向力分布，在車輪的尾部降低軸中心的高度能夠降低車尾部的搖擺程度，在轉(zhuǎn)彎時(shí)，車尾的輪子也會(huì)比車前輪更加平穩(wěn)。 (Milliken and Milliken 1995). 為了設(shè)計(jì)反蹲，需要清楚有效的點(diǎn)軸心或輪胎與地面的接觸路徑，用來計(jì)算實(shí)現(xiàn)這個(gè)幾何體最大的角度。 (Bastow, Whitehead. 1993) 設(shè)計(jì)反蹲的目的是給車輪傳遞足夠的力量，防止它們失去牽引力，其余的力量用來推動(dòng)汽車前進(jìn)。如果一個(gè)假象 的線通過下鏈接欄到汽車的前面，然后繪制另一條假想線通過上面的鏈接欄一直向前，直到它與那一條較低的線交叉，即時(shí)中心就被發(fā)現(xiàn)了。 (Bastow, Whitehead. 1993) 現(xiàn)在我們想象一下車輛的重心集中在集成電路所在的加速桿上。重心決定了力量是如何應(yīng)用于懸架就像列車來驅(qū)動(dòng)車輛前進(jìn)一樣。如果集成電路太高，那么就會(huì)有許多動(dòng)力浪費(fèi)在推動(dòng)車尾向上。如果集成電路太低，那么就將沒有足夠的力量應(yīng)用到后面的輪胎，結(jié)果會(huì)出現(xiàn)輪胎過度旋轉(zhuǎn)的現(xiàn)象。無論集成電路在重心的前面或后面，都會(huì)有一些變量存在。某個(gè)地方會(huì)有一個(gè)位置，將把 足夠的力量應(yīng)用于車輪，會(huì)阻止車輪旋轉(zhuǎn)，其余的力量將推動(dòng)汽車前進(jìn)，這個(gè)可以用反蹲來計(jì)算，為特定的汽車填寫變量。 (Bastow, Whitehead. 1993) 一旦軸中心和反蹲幾何被最大化，那么就是時(shí)候查看一下彈簧剛度了。彈簧剛度影響側(cè)騎彈簧負(fù)載轉(zhuǎn)移分布