汽车转向系统外文原文及翻译

本文摘于《Race Car Vehicle Dynamics》

作者：William F. Miliken and Douglas L. Miliken

Steering systems

Introduction

This chapter begins with a discussion of steering geometry—caster

angle ,trail ,kingpin inclination ,and scrub radius .The next section discuss Ackermann geometry followed by steering racks and gears .Ride steer (bump steer ) and roll steer are closely related to each other ;without compliance they would be the

same .Finally ,wheel alignment is discussed .this chapter is tied to chapter 17 on suspension geometry –when designing a new chassis ,steering and suspension geometry considerations are high priorities . 19.1 steering geometry

The kingpin in a solid front axle is the steering pivot .In modern independent

suspensions , introduced by Maurice olley at Cadillac in 1932,the kingpin is replaced by two (or more ) ball joints that define the steering axis .This axis is not vertical or centered on the tire contact patch for a number of reason .see figure 19.1 to clarify how kingpin location is measured .

In front view ,the angle is called kingpin inclination and the offset of the steering axis from the center of the tire print measured along the ground is called scrub (or scrub radius ). The distance from the kingpin axis to the wheel center plane , measured horizontally at axle height ,is the spindle length .

In side view the kingpin angle is called caster angle ; if the kingpin axis does not pass through the wheel center then side view kingpin offset is present ,as in most motorcycle front ends .The distance measured on the ground from the steering axis to the center of the tire print is the trail (called caster offset in ref .1 )

Kingpin front view geometry

As mentioned in chapter 17, kingpin inclination ,spindle length ,and scrub are usually a compromise between packaging and performance requirements .Some factors to consider include :

1.With a positive spindle length (virtually every car is positive as shown in figure 19.1) the car will be raised up as the wheels are steered away from center .

The more the kingpin inclination is tilted from vertical the more the car will be raised when the front wheels are steered .This effect always raises the car , regardless of which direction the wheel is steered ,unless the kingpin inclination is true

vertical .the effect is symmetric side to side only if there is no caster angle .See the following section on caster angle .

For a given kingpin inclination ,a longer positive spindle length will increase the amount of lift with steer .

2.The effect of kingpin inclination and spindle length in raising the front end ,by itself ,is to aid centering of the steering at low speed .At high speed any trail will probably swamp out the effect that raise ad fall have on centering .

3. Kingpin inclination affects the steer –camber characteristic .when a wheel is steered ,it will lean out at the top ,toward positive camber ,if the kingpin is inclined in the normal direction (toward the center of the car at the upper end ). Positive camber results for both left– and right-hand steer .the amount of this effect is small ,but significant if the track includes tight turns.

4. When a wheel is rolling over a bumpy road ,the rolling radius is constantly changing ,resulting in changes of wheel rotation speed . This gives rise to longitudinal forces at the wheel center .The reaction of these forces will introduce kickback into the steering in proportion to the spindle length .If the spindle length is zero then there will be no kick from this source .Design changes made in the last model of the GM ―P ‖car (fiero ) shortened the spindle length and this resulted in less wheel kickback on rough roads when compared to early model ―P ‖cars.

5. The scrub radius shown in figure 19.1 is negative ,as used on front-wheel –drive cars (see below ) . driving or braking forces (at the ground ) introduce steer torques proportional to the scrub radius . If the driving or braking force is different on left and right wheels then there will be a net steering torque felt by the driver

(assuming that the steering gear has good enough rev erse efficiency ).The only time that this is not true is with zero scrub (centerpoint steering ) because there is no moment arm for the drive (or brake ) force to generate torque about the kingpin .

With very wide tires the tire forces often are not centered in the wheel center plane due to slight changes in camber ,road surface irregularities ,tire nonuniformity (conicity ),or other asymmetric effects .These asymmetries can cause steering kickback regardless of the front view geometry .Packaging requirements often conflict with centerpoint steering and many race cars operate more or less okay on smooth tracks with large amounts of scrub .

6. For front drive ,a negative scrub radius has two strong stabilizing

effects :first ,fixed steering wheel –if one drive wheel loses traction ,the opposing

wheel will toe –out an amount determined by the steer compliance in the system .This will tend to steer the car in a straight line ,even though the tractive force is not equal side-to –side and the unequal tractive force is applying a yaw moment to the vehicle .

Second ,with good reverse efficiency the driver’s hands never truly fix the

steering wheel . In this case the steering wheel may be turned by the effect of uneven longitudinal tractive forces ,increasing the stabilizing effect of the negative scrub radius .

Under braking the same is true .Negative scrub radius tends to keep the car traveling straight even when the braking force is not equal on the left and right side front tiresome (due to differences in the roadway or the brakes).

Caster angle and trail

With mechanical trail ,shown in figure 19.1,the tire print follows behind the steering axis in side view .Perhaps the simplest example is on an office chair caster –with any distance of travel ,the wheel aligns itself behind the point .More trail means that the tire side force has a large moment arm to act on the kingpin axis .This produces more self-centering effect and is the primary source of self-centering

moment about the kingpin axis at speed .Some considerations for choosing the caster angle and trail are :

1.More trail will give higher steering force .with all cars ,less trail will lower the steering force .In some cases ,manual steering can be used on heavy sedans (instead of power steering ) if the trail is reduced to almost zero .

2.Caster angle ,like kingpin inclination ,cause the wheel to rise and fall with steer .unlike kingpin inclination ,the effect is opposite from side to side .With

symmetric geometry (including equal positive caster on left and right wheels ) ,the effect of left steer is to roll the car to the right ,causing a diagonal weight shift .In this case ,more load will be carried on the LF –RR diagonal ,an oversteer effect in a left-hand turn .

The diagonal weight shift will be larger if stiffer springing is used because this is a geometric effect .The distance each wheel rises (or falls ) is constant but the weight jacking and chassis roll angle are functions of the front and rear roll stiffness. This diagonal load change can be measured with the car on scales and alignment ( weaver ) plates .

Keep in mind that the front wheels are not steered very much in actual racing , except on the very tightest hairpin turns . For example , on a 100-ft .radius (a 40-50 mph turn ), a 10-ft. wheelbase neutral steer car needs only about 0.1rad .(5.7)of steer at the front wheels (with a 16:1steering ratio this is about 90degree at the steering wheel ).

For cars that turn in one direction only , caster stagger (differences in left and right caster ) is used to cause the car to pull to one side due to the car seeking the lowest ride height . caster stagger will also affect the diagonal weight jacking effect mentioned above .

If the caster is opposite (positive on one side and negative the same number of degrees on the other side ) then the front of the car will only rise and fall with steer ,

no diagonal weight jacking will occur .

3. Caster angle affects steer-camber but ,unlike kingpin inclination ,the effect is favorable . With positive caster angle the outside wheel will camber in a negative direction (top of the wheel toward the center of the car ) while the inside wheel cambers in a positive direction , again learning into the turn .

In skid recovery , ―opposite lock ‖ (steer out of the turn ) is used and in this case the steer–camber resulting from caster angle is in the ―wrong ‖ direction for increased front tire grip . conveniently ,this condition results from very low lateral force at the rear so large amounts of front grip are not needed .

4. As discussed in chapter 2, tires have pneumatic trail which effectively adds to (and at high slip Angles subtracts from ) the mechanical trail . This tire effect is nonlinear with lateral force and affects steering torque and driver feel .In particular , the fact that pneumatic trail approaches zero as the tire reaches the limit will result in lowering the self-centering torque and can be s signal to the driver that the tire is near breakaway .

The pneumatic trail ―breakaway signal‖ will be swamped out by mechanical trail if the mechanical trail is large compared to the pneumatic trail .

5.Sometimes the trail is measured in a direction perpendicular to the steering axis (rather than horizontal as shown in figure 19.1) because this more accurately

describes the lever (moment ) arm that connects the tire lateral forces to the kingpin .

Tie rod location

Note that in figure 19.1 a shaded area is shown for the steering tie rod location . Camber compliance under lateral force is unavoidable and if the tie rod is located as noted ,the effect on the steering will be in the understeer ( steer out of the turn ) direction becomes much more complex than can be covered here . 19.2 Ackerman steering geometry

As the front wheels of a vehicle are steered away from the straight-ahead

position ,the design of the steering linkage will determine if the wheels stay parallel or if one wheel steers more than the other .This difference in steer Angles on the left and right wheels should not be confused with toe-in or toe-out which are adjustments and add to ( or subtract from ) Ackerman geometric effects .

For low lateral acceleration usage (street cars) it is common to use Ackerman geometry . as seen on the left of figure 19.2, this geometry ensures that all the wheels roll freely with no slip Angles because the wheels are steered to track a common turn center . Note that at low speed all wheels are on a significantly different radius , the inside front wheel must steer more than the outer front wheel . A reasonable approximation to this geometry may be as shown in figure 19.3.

According to ref .99, Rudolf Ackerman patented the double pivot steering system in 1817 and in 1878, Charles Jeantaud added the concept mentioned above to eliminate wheel scrubbing when cornering . Another reason for Ackermann

geometry ,mentioned by Maurice olley , was to keep carriage wheels from upsetting smooth gravel driveways .

High lateral accelerations change the picture considerably . Now the tires all

operate at significant slip Angles and the loads on the inside track are less than on the outside track . Looking back to the tire performance curves ,it is seen that less slip angle is required at lighter loads to reach the peak of the cornering force to a higher slip angle than required for maximum side force . Dragging the inside tire along at high slip Angles ( above for peak lateral force ) raise the tire temperature and slows the car down due to slip angle ( induced ) drag .For racing , it is common to use parallel steering or even reverse Ackermann as shown on the center and right side of figure 19.2.

It is possible to calculate the correct amount of reverse Ackermann if the tire properties and loads are known . In most cases the resulting geometry is found to be too extreme because the car must also be driven (or pushed ) at low speeds , for example in the pits .

Another point to remember is that most turns in racing have a fairly large radius and the Ackermann effect is very small . In fact , unless the steering system and

suspension are very stiff ,compliance (deflection ) under cornering loads may steer the wheels more than any Ackermann (or reverse Ackermann ) built into the geometry .

The simplest construction that generates Ackermannn geometry is shown in figure 19.3 for ―rear steer ‖ . Here ,the rack (cross link or relay rod in steering box systems ) is located behind the front axle and lines staring at the kingpin axis ,

extended through the outer tie rod ends , intersect in the center of the rear axle . The angularity of the steering knuckle will cause the inner wheel to steer more than the outer (toe-out on turning ) and a good approximation of ―perfect Ackermann ‖ will be achieved .

The second way to design-in differences between inner and outer steer Angles is by moving the rack (or cross link ) forward or backward so that it is no longer on a line directly connecting the two outer tie rod ball joints .This is shown in figure 19.4. with ―rear steer ‖ , as shown in the figure ,moving the rack forward will tend more toward parallel steer (and eventually reverse Ackermann ), and moving it toward the rear of the car will increase the toe-out on turning .

A third way to generate toe with steering is simply to make the steering arms different lengths . A shorter steering arm (as measured from the kingpin axis to the outer tie rod end ) will be steered through a larger angle than one with a longer knuckle. Of course this effect is asymmetric and applies only to cars turning in one direction—oval track cars . Recommendation

With the conflicting requirements mentioned above , the authors feel that parallel steer or a bit of reverse Ackermann is a reasonable compromise . With parallel steer , the car will be somewhat difficult to push through the pits because the front wheels will be fighting each other . at racing speeds , on large-radius turns , the front wheels are steered very little , thus any ackermann effects will not have a large effect on the individual wheel slip angles , relative to a reference steer angle , measured at the centerline of the car .

文献翻译 摘自《Race Car Vehicle Dynamics》

第19章 转向系统

序言：

本章以转向几何参数的讨论为开始，包括主销后倾角，后倾拖距，主销内倾角，主销偏置量。接下来的部分讨论了转向齿轮齿条以及阿克曼转向几何关系。跳动转向和侧倾转向之间是紧密相关的，如果没有柔性这两种情况是等同的。最后讨论了车轮的调整。这一章与第17章的悬架几何形状密切相关，在设计新的底盘系统时，转向和悬架几何参数是优先考虑的因素。

19.1 转向几何关系（定位参数）

在整体式车桥上转向节主销是转向时的枢轴。1932年Maurice Olley在Cadillac首次提出了现在的非独立悬架，主销因此而被两个球绞连接定义的转向轴线代替。因为各种原因这根轴并不是垂直的也不在轮胎接地中心处。主销的位置表示见图19.1。

·在前视图中，主销偏转的角度被称为主销内倾角，转向主销与地面的交点至车轮中心平面与地面相交处的距离称之为主销偏置量。在前轴所在水平面内，从主销轴心到车轮中心平面的距离称为主销偏距（spindle length）。

·在侧视图中，主销偏转角度称为主销后倾角。如果主销轴线没有通过车轮中心那么就有了侧视的主销偏距（side view kingpin offset），就像大部分的摩托车前轮一样。在地平面内测量从主销到轮胎接地点中心的距离称为主销后倾拖距。 前视图中的主销定位参数

正如在17章中提到，主销内倾角，主销偏距还有主销偏置量在装配以及性能满足时往往是互相妥协的。一些需要考虑的因素包括以下：

1. 当主销偏距是正的时（一般的车都是正主销偏距，如图19.1中一样）那车轮转离中心位置的时候车会有一个抬升效果。主销内倾角偏离竖直平面越大前轮转向时车被抬起的效果越明显。不管车轮往哪个方向转都会是一个抬升的效果，除非主销是完全垂直的。这个效果只有在主销后倾角为零时才是两边对称的。见后面关于主销后倾角部分。对于一个给定的主销内倾角来说，主销偏距越大转向时的抬升量也越大。

2. 主销内倾角和主销偏距将车子前端抬起的效果对于自身来说是有助于低速转向的。在高速转向时，只要有主销后倾拖距就可能会掩盖掉转向时抬升和下落的效果。 3. 主销内倾角影响转向时车轮的外倾角特性。如果主销向内倾斜（主销上端倾向车辆

中心）当车轮转向的时候，车轮上端将会向外倾斜，趋向正的车轮外倾角。左右转向都会导致正的车轮外倾。如果跑道有比较紧的弯这个作用效果是比较小但却是有重要意义的。

4. 当车轮滚过颠簸不平的路面时，滚动半径是不断变化的，将会导致轮速的改变。这将会增加车轮中心的纵向力。这些力的反作用与主销偏距的大小成比例，成为反冲效果进入转向系统。如果主销偏距为零，那么将不会有由此引起的反冲。在前面提到的一辆通用“P”型车（菲罗车）中做出设计改动，与较早的一辆“P”型车模型相比，减小了主销偏距，因此而减少了不平路面上的反冲。

5. 如图19.1中所示的主销偏置量是负的，正如下面这辆前轮驱动车用的一样。来自地面的驱动和制动力与主销偏置量成比例的转化成转向力矩。如果左右轮的制动或者驱动力是不等的，那么驾驶者将会感受到的到这个转向力矩（假设转向器有较高的逆效率）。只有在主销偏置量为零时才不会有这个力矩产生因为此时制动力或驱动力对主销的作用力臂为零。

如果轮胎比较宽的话轮胎力通常并不是作用在轮胎中心平面内的，因为轻微的外倾角变化、路面不平、轮胎有一定圆锥度、或者其他的不对称因素存在。这些不对称因素可能导致转向反冲，即使没有前轮的各个定位参数作用。装配要求通常会与中心点转向要求冲突因而很多赛车在较平整的赛道上是采用较大的主销偏置量也是可以的。 6.

对于前轮驱动来说，一个负的主销偏置量有两个重要的稳定作用：

第一， 固定方向盘，如果一个驱动轮打滑，另外一个轮将会外张一定角度，因为 转向系统内有变形。即使两侧的牵引力不等，不同的牵引力使车辆产生一个偏航角，这个负的主销偏置量作用也会使车辆回复到直线行驶。

第二， 有良好的反馈作用情况下驾驶员从来不会真正的固定住方向盘。在这种情况下方向盘可能在不等的车轮纵向牵引力作用下而转动，因此而增加了负主销偏置量的稳定效果。

制动的情况同样适用。负的主销偏置量能使车子回正，即使是在左右轮制动力不等的情况下（左右轮的制动情况或者路面情况不同时）。(fsae没人用吧)

主销后倾角和后倾拖距

如图19.1中所示，在有后倾拖距时，侧视图中轮胎接地点是在主销之后的。或许最简单的例子就是办公室座椅上的小脚轮（？）——不管移动多远，轮子总会校正使其自身在枢轴之后。主销拖距越大意味着轮胎侧向力在主销轴上作用有更大的力臂。这会产生更明显的

回正作用，并且是作用在主销上最主要的回正力矩。在选择主销后倾角和主销拖距时需要考虑的因素如下：

1. 主销后倾拖距越大转向力也越大。对于所有的车来说，小的后倾拖距都将会减小转向力。在某些情况下，如果后倾拖距减小接近零的话，人力转向也可能被用于重型轿车（代替助力转向）。

2. 像主销内倾角一样，主销后倾角伴随着转向过程也会引起车轮的抬起和回落。与内倾角不同的是，后倾角对两侧的影响是相反的。在有对称定位参数时（包括左右轮有相等的正的主销后倾角），左转的效应是使车向右侧倾，导致一个对角线的重量转移。在这种情况下，左前——右后对角线会承受更大的载荷，有一个左转时的过度转向效应。

使用的弹簧越硬对角线的重量转移效果也会越明显因为这个是几何效应。每个车轮被抬起（或者下落）的距离是恒定的但是重量抬起量和底盘侧倾角是前后侧倾刚度的作用结果。这个对角线的载荷转移可以通过把车放在秤上和定位板上来测量。

记住在实际比赛中前轮并没有转过很大的角度，除非是非常紧的发夹弯。例如，在一个半径是100英尺（时速在40-50英里）的弯，一个10英尺的轴距的中性转向车辆转弯时前轮只需要转过0.1rad（5.7°）（转向传动比是16：1时方向盘的转角大概在90°）。

对于只往一个方向转的车来说，因为整车为了寻求最低的最小离地间隙，可以使主销后倾角交错（左右主销后倾角不同）来把车拉到一边。主销后倾角的交错也会影响上面提到的对角线重量抬升效应。

如果两侧主销后倾角是相反的（一侧为正一侧为负且两侧角度大小相等）那么在转向时车的前端只会抬升和下落，而不会有对角线的重量抬升。

3. 主销后倾角也会影响转向外倾角，但是不像内倾角一样，这个效应是有利的。当有正的后倾角时将会导致外侧车轮内倾（车轮的上部指向车的中心）同时内测轮外倾角为正，两轮都向弯内倾。

在侧滑恢复的时候，反打方向（出弯），后倾角引起的外倾角变化会使前轮抓地力减小。而此时后轮抓地力也很小并不需要很大的前轮抓地力。

4. 如第2章提到，轮胎本身的轮胎拖距会使实际主销后倾拖距明显增加（有大的侧偏角时会减小）。这个效应并不是随着侧向力变化而线性变化的，并且会影响转向力矩和驾驶感。特别是轮胎到极限时轮胎拖距会接近零，这时回正力矩会减小，并给车手一个信号轮胎就要侧滑了。

如果主销后倾拖距相对轮胎拖距很大的话，轮胎拖距给出的这个信号会被掩盖。 5. 有时主销后倾拖距是在垂直于主销轴心的方向上进行测量的（而不是像19.1中在水平面内测量的），因为这能更准确的描述轮胎侧向力对主销作用的力臂。 拉杆位置

注意在19.1中的阴影部分就是转向拉杆的合适位置。侧向力引起的外倾角是不可避免的，如果拉杆的位置如图中示，会有不足转向效应。如果悬架和齿条安装在一些柔性的副车架上，情况要比现在的更加复杂。

19.2 阿克曼转向几何关系

当汽车前轮转向时，转向传动机构的设计将会决定车轮是保持平行还是一个轮比另一轮转过更多的角度。左右轮转向的角度差不应该被车轮前束值混淆，前束值是静态调整时的值，他是在阿克曼几何效应的基础上增减的。

对于横向加速度较小的车（街车）一般使用阿克曼几何关系。正如图19.2左图所示，这个几何关系保证了所有轮子在没有滑动的情况下自由滚动，因为所有轮子只有一个滚动中心。需注意的是在低速时所有车轮的转弯半径都不同，前内侧轮必须比前外轮转过更大的角度。一个合理的近似几何关系可见图19.3。

根据Ref.99中Rudolf所说，阿克曼在1817年获得双枢轴转向系统的专利，1878年，Charles Jeantaud 又提出了上段中的概念，消除了转向时车轮的滑动。Maurice Olley 又提出了阿克曼转向几何关系的推导以使车轮免于镦粗平滑的砾石车道。

在高侧向加速度下要对这个几何模型做明显的修改。实际轮胎都会有一个侧偏角，内侧轮的载荷也要比外侧轮小。回顾轮胎性能曲线可以看出负载较轻的时候获得峰值侧向力所需的侧偏角较小。使用低速几何结构（阿克曼关系），前内侧轮会被迫超过对应最大侧向力时

的侧偏角，这样，拖动内轮会使轮胎升温并降低车速。对于赛车来说，通常使用平行转向甚至反阿克曼结构如图19.2中（b）（c）所示。

如果知道轮胎参数通常可以计算出正确的反阿克曼量。大部分情况下计算得到的几何关系是比较极端的因为车肯定会有低速行驶的情况，如进站加油等。

另外值得注意的一点是比赛时大部分弯道半径都比较大阿克曼影响是非常小的。实际上，除非悬架、转向系统结构刚度很大，转向载荷作用下产生的变形也可能使车轮转向，会超过几何关系上的阿克曼转角关系（或者反阿克曼）。

能产生阿克曼几何关系的最简单模型见图19.3，为后置转向。这里，齿条（以及转向器系统内的横拉杆连接）是在前轴之后的，从主销轴心开始画线，延伸到横拉杆外端，并交于后轴中心。转向节的这个角度使内轮转向角度大于外轮（转向时外张）可以获得一个较好的近似的100%阿克曼关系。

第二种获得内外轮转角差的方法是通过前移或后移齿条（或拉杆）的位置，这时两个拉杆外端球头间的连接不再是直线连接。如图19.4所示。图中后置梯形将齿条前移时将倾向

于平行转向（最后至反阿克曼），齿条后移将增加转向时的前轮外张量（内外轮转角差更大）。

第三种获得转角差的方法是使两边转向节臂不等长。节臂（从主销轴至拉杆外端的距离）越短转向时转角越大。当然这种不对称结构仅会用于只向一个方向转向的车辆——椭圆形赛道赛车。

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虽然上文提到的一些要求间会有冲突，笔者认为平行转向或者反阿克曼是一个较合理的折中方法。虽然平行转向时进站会有一点困难因为前轮会互相干涉。在高速时，弯道较大，转向角较小，相对参考的转向角度，阿克曼效应对于车轮的侧偏角影响不大。

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