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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 赛车和车辆动力学介绍 汽车赛车的主要目的是实现一个整体的车辆配置,并且这种配置遵守一个指定的类型的规则,能够在一个驾驶员利用在他们能力范围内的技术的最少的时间内覆盖一个给定的赛道。在设计制造一个赛车时有许多因素要考虑,但是在这里我们只考虑悬架设置。 控制一个高速机动车辆的主要力量是由四个小补丁发展起来的,这就是四个轮胎与地面接触的 地方。对于轮胎产生的力量和时间在根源上有一个了解对于理解车辆动力学是非常有必要的 (Gillespie, 1992)。 为了最大化轮胎与地面的接触,对于手头上的任务建立正确的悬架几何以及选择正确的弹簧和休克吸收器是非常重要的。轮胎与地面的接触面越大,车辆就会有更多的抓地力和牵引力,反过来会使车更加安全的高速行驶。 什么阻碍了一个车辆在运行时的动力?接下来将要谈论一系列因素。第一个也是最明显的因素就是路况,凹凸不平的路面肯定车辆的驾驶。第二个因素是轮胎 /车轮总成。理性的情况下这个组装是柔软并且能够吸收小幅度的震动 和颠簸,这基本上意味着它不会添加任何震动给车辆,包括在车轮组装上的不平衡,空间的变化和刚度变化。 (Gillespie 1992)。 接下来要考虑的因素,也是在这个项目中需要考虑的最主要的因素,那就是动力传动系统励磁。也就是在这里,扭矩从发动机传送到传动轴通过变速箱,而后进入 差动器将会试图延其中心扭曲后桥总成线,称为轴风力,这使轴偏在其弹簧上,迫使整个车的后面上升,由于扭曲的轴也使整个车侧向。重新设计的悬架将努力保持这种传动系励磁降到最低 (Gillespie 1992)。 当为赛车建立悬架系统时,需要区 分提高汽车性能的变化和调整或平衡汽车的变化。第一类包括增加更多动力和更好轮胎的东西,而第二类包括诸如修改弹簧利率和轴中心的调整 (Milliken and Milliken 1995). 赛车就是在其限度内驾驶汽车。找到一个可以驱动产生这种期望的性能的车辆配置称为设置或底盘调优。这是一个艰巨的任务,需要适应每个电路和司机的能力和偏好。在参赛前在可用的时间内实现最优的设置往往是不可能的,司机将就着仍存在于车辆上的一些缺陷 (Milliken and Milliken 1995). III 设计汽车的主要目的是实现良好的 汽车转弯平衡(中性驾驶),找到转弯和高速电路以及消除特定控制盒稳定性问题上的折中,这些是司机所报道的在赛道任何一点上的情况 (Milliken and Milliken 1995)。当为一个赛车设计悬架设置的时候,需要考虑许多因素,因为每个组件和调整都会影响车辆的驾驶,同时也影响其他组件的操作方式。重量变化的影响,制动偏见,滚刚度,轴中心等许多因素都需要认真考虑以便实现一个理想的配置。 (Milliken and Milliken 1995). 这项设计的两个主要目的是实现最大反蹲和几何轴中心,这两种几何体是可 以调节的以便于小的调整,便于悬架系统在不同的情况下最大化的使用。 轴中心的高度部分决定了汽车在摇摆时的侧向力分布,在车轮的尾部降低轴中心的高度能够降低车尾部的摇摆程度,在转弯时,车尾的轮子也会比车前轮更加平稳。 (Milliken and Milliken 1995). 为了设计反蹲,需要清楚有效的点轴心或轮胎与地面的接触路径,用来计算实现这个几何体最大的角度。 (Bastow, Whitehead. 1993) 设计反蹲的目的是给车轮传递足够的力量,防止它们失去牵引力,其余的力量用来推动汽车前进。如果一个假象 的线通过下链接栏到汽车的前面,然后绘制另一条假想线通过上面的链接栏一直向前,直到它与那一条较低的线交叉,即时中心就被发现了。 (Bastow, Whitehead. 1993) 现在我们想象一下车辆的重心集中在集成电路所在的加速杆上。重心决定了力量是如何应用于悬架就像列车来驱动车辆前进一样。如果集成电路太高,那么就会有许多动力浪费在推动车尾向上。如果集成电路太低,那么就将没有足够的力量应用到后面的轮胎,结果会出现轮胎过度旋转的现象。无论集成电路在重心的前面或后面,都会有一些变量存在。某个地方会有一个位置,将把 足够的力量应用于车轮,会阻止车轮旋转,其余的力量将推动汽车前进,这个可以用反蹲来计算,为特定的汽车填写变量。 (Bastow, Whitehead. 1993) 一旦轴中心和反蹲几何被最大化,那么就是时候查看一下弹簧刚度了。弹簧刚度影响侧骑弹簧负载转移分布

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