553 Kd1080型載貨汽車后橋總成設(shè)計（有exb圖）
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英文資料翻譯
Introduction
This chapter begins with a discussion of steering geometry-caster angle,trail, kingpin inclination, and scrub radius. The next section discusses Ackemann 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.
19.1Steering Geometry
The kingpin in a solid front axle is the steering pivot.In modern independent suspensions,introduced by Maurice Olly at Cadillac in 1932,the kingpin is replaced by two (or more) ball joints that that define the steering axis.This axis is not vertical or centered on the tire contact patch for a number of reasons.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 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 nocaster angle.See the following sectiong on Caster Angle.
For a given kingpin inclination,a lenger 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 rise and fall have on centering.
3. Kingpin inclination affects the steer-camber characteristics.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 beft and right-band steer.The amount of this effect is small, but significant if the track includes tight turns.
4. When a wheel in 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 is different on left and ringht wheels then there will be a net steering torque felt by the driver (assuming that the steering gear has good enough reverse 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) forces 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 driv,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 delermined by the steer compliance in the system.This wll 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 tires(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 asis in side view.Perhaps the simplest example is on an office chair caster-with any distance of travel,the wheel aligns itself behind the pivot.More trail means that the tire side force has a larger 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,causes 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 carride 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 stiff-ness.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 40-50mph turn),a 10-ft.wheelbase neutral steer car needs only about 0.1 rad.(5.7)of steer at the front wheels(with a 16:1 steering ratio this is about 90 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 leaning 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 a 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 19.1a shaded area is shown for the steering tie rod location.Camber comploance under lateral force is unavoidable and if the tie rod is locater as noted ,the effect on the steering will be in the understeer(steer out of the turn)direction.If the suspension and rack are mounted on som sort of flesible subframe,the situation becomes much more complex than can be covered here.
19.2Ackermann 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 static adjustments and add to (or subtract from)Ackermann geometric effects.
For low lateral acceleration usage (street cars)it is common to use Ackermann geometry.As seen on the left of Figure 19.2,this geometry ensures that allthe 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 made as shown in Figure 19.3.
According to Ref.99,Rudolf Ackermann patented the double pivot steering system in 1817 62and,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 considerable.Now the tires all operate at significant slip angles and the loads on the inside track are much 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 curve.If the car has lowspeed geometry (Ackermann),the inside front tire is forcee to a higher slip angle than required for maximum side force.Dragging the inside tire along at high slip angles (above the peak lateral force )raises 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 Ackernann 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 Ackermann 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 starting 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 turing.
A third way to generate toe with steering is simply to make the steering arms different lengths.A shorter 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,this 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.
19.3Steering gears
The steering rack or steering box translates rotary motion of the steering wheel to linear motion at the tie rods.In turn, the tie rods translate this linear motion back to rotary motion about the kingpin axis (steering axis)resulting in steer of the front wheels.
The first thing that should be obvious is that there are a lot of connection in the steering system.All of these connections are a source of compliance (bending or deflecting)or lost motion (looseness or slop),any of which will make the steering imprecise-the driver will not know exactly in which direction the front wheels are aimed.The steering system components must all be tight and mounted securely for both safety and control.
Steering ratio
The overall steering ratio is defined as degrees of steering wheel angle divided by corresponding front wheel angle.For race cars it varies from over 20:1(slow)for Superspeedway cars to less than 10:1(very fast)for Formula One cars on tight street circuits,Of course, the ultimate in fast steering is the go-kart with nearly1:1.Common values in road racing are 16:1to 18:1.With Ackermann(or reverse Ackermann)geometry,the steering ratio will be different side to side.Depending on the linkage configuration the steering may be nonlinear,that is ,the ratio may vary with wheel angle.
Steer-steer test
A straightforward way to measure the overall steering ratio is to set the front end on slignment tables(Weaver plates)with a steering scale.A circular protractor is mounted(centered) on the steering wheel and a suitable pointer is attached so that the steering wheel angle can be measured.This test is called steer-steer and should be performed with the car at known load and ride height.The steering wheel is turned to the right in even intervals,perhaps 45,90,etc,and the steer angles of both front wheels are noted.The test continues by rotating the steering wheel back to center,stopping at each angle,and checking the front wheel steer angles again to look for any slop (or hysteresis).Continue past center, steering to the left, and finally return to center.
Data and a plot of the results of this test are shown in Figure 19.5.From the plot,the average slope of the data points is called the overall steering ratio.Note that the data plots make loops;this is called hysteresis and means that there is some compliance and/or lost motion in this steering system.Also note that the plot is not straight;this nonlinear characteristic indicates that the linkage is not”perfect”,common in many steering systems.For racing, it is appropriate to take data points only in the range of steering wheel angles that are normally used.Steering ratio data near full lock will reflect performance only during low speed mancuvers.
Steering ratio partialIy determines the steering effort that is required for a manual steering system in conjunction with the kingpin geometry (trail and scrub). Higher (20: 1) ratios will require less effort than lower (quicker) ratios. When interpreting driver comments，be aware that a quick steering ratio can often be confused with a fast vehicle transient response time, as discussed in the chapters on vehicle dynamics.
Steering ratio can be calculated as described in the following sections
Rack-and-Pinion Steering Box Ratio.
Rack -and-pinion gearsets convert rotary motion at the steering wheel to linear motion at the inner tie rod ball joint. The steering ratio is calculated using the rack c-factor and the
steering arm 1ength(as measured from the outer ball joint to the kingpin axis).
c-factor = travel (in. )/3600 pinion rotation
Often, a steering rack will be described as a "1-7/8-inch rack" or a "2-inch rack"; this dimension
is the amount the rack moves for one rotation of the steering wheel-the c-factor.
Once the c-factor is known for the rack, the steering ratio can be calculated approximately by
Steer ratio = sín-1(c-factor/steering arm length)/360
where dimensions are in in.
angles are in deg.
Sin-1 is the same as "the angle with sin of," or arcsin
The approximation will be good as long as the angularity in the. system is minimal, that is, the tie rod is nearly perpendicular to the steering arm in top and front view. For designs with high angularity ， a layout is required to determine the steering ratio.
序言：
本章以轉(zhuǎn)向幾何參數(shù)的討論為開始，包括主銷后傾角，后傾拖距，主銷內(nèi)傾角，主銷偏置量。接下來的部分討論了轉(zhuǎn)向齒輪齒條以及阿克曼轉(zhuǎn)向幾何關(guān)系。跳動轉(zhuǎn)向和側(cè)傾轉(zhuǎn)向之間是緊密相關(guān)的，如果沒有柔性這兩種情況是等同的。最后討論了車輪的調(diào)整。這一章與第17章的懸架幾何形狀密切相關(guān)，在設(shè)計新的底盤系統(tǒng)時，轉(zhuǎn)向和懸架幾何參數(shù)是優(yōu)先考慮的因素。
19.1 轉(zhuǎn)向幾何關(guān)系（定位參數(shù)）
在整體式車橋上轉(zhuǎn)向節(jié)主銷是轉(zhuǎn)向時的樞軸。1932年Maurice Olley在Cadillac首次提出了現(xiàn)在的非獨立懸架，主銷因此而被兩個球絞連接定義的轉(zhuǎn)向軸線代替。因為各種原因這根軸并不是垂直的也不在輪胎接地中心處。主銷的位置表示見圖19.1。
·在前視圖中，主銷偏轉(zhuǎn)的角度被稱為主銷內(nèi)傾角，轉(zhuǎn)向主銷與地面的交點至車輪中心平面與地面相交處的距離稱之為主銷偏置量。在前軸所在水平面內(nèi)，從主銷軸心到車輪中心平面的距離稱為主銷偏距（spindle length）。
·在側(cè)視圖中，主銷偏轉(zhuǎn)角度稱為主銷后傾角。如果主銷軸線沒有通過車輪中心那么就有了側(cè)視的主銷偏距（side view kingpin offset），就像大部分的摩托車前輪一樣。在地平面內(nèi)測量從主銷到輪胎接地點中心的距離稱為主銷后傾拖距。
前視圖中的主銷定位參數(shù)
正如在17章中提到，主銷內(nèi)傾角，主銷偏距還有主銷偏置量在裝配以及性能滿足時往往是互相妥協(xié)的。一些需要考慮的因素包括以下：
1. 當主銷偏距是正的時（一般的車都是正主銷偏距，如圖19.1中一樣）那車輪轉(zhuǎn)離中心位置的時候車會有一個抬升效果。主銷內(nèi)傾角偏離豎直平面越大前輪轉(zhuǎn)向時車被抬起的效果越明顯。不管車輪往哪個方向轉(zhuǎn)都會是一個抬升的效果，除非主銷是完全垂直的。這個效果只有在主銷后傾角為零時才是兩邊對稱的。見后面關(guān)于主銷后傾角部分。對于一個給定的主銷內(nèi)傾角來說，主銷偏距越大轉(zhuǎn)向時的抬升量也越大。
2. 主銷內(nèi)傾角和主銷偏距將車子前端抬起的效果對于自身來說是有助于低速轉(zhuǎn)向的。在高速轉(zhuǎn)向時，只要有主銷后傾拖距就可能會掩蓋掉轉(zhuǎn)向時抬升和下落的效果。
3. 主銷內(nèi)傾角影響轉(zhuǎn)向時車輪的外傾角特性。如果主銷向內(nèi)傾斜（主銷上端傾向車輛中心）當車輪轉(zhuǎn)向的時候，車輪上端將會向外傾斜，趨向正的車輪外傾角。左右轉(zhuǎn)向都會導(dǎo)致正的車輪外傾。如果跑道有比較緊的彎這個作用效果是比較小但卻是有重要意義的。
4. 當車輪滾過顛簸不平的路面時，滾動半徑是不斷變化的，將會導(dǎo)致輪速的改變。這將會增加車輪中心的縱向力。這些力的反作用與主銷偏距的大小成比例，成為反沖效果進入轉(zhuǎn)向系統(tǒng)。如果主銷偏距為零，那么將不會有由此引起的反沖。在前面提到的一輛通用“P”型車（菲羅車）中做出設(shè)計改動，與較早的一輛“P”型車模型相比，減小了主銷偏距，因此而減少了不平路面上的反沖。
5. 如圖19.1中所示的主銷偏置量是負的，正如下面這輛前輪驅(qū)動車用的一樣。來自地面的驅(qū)動和制動力與主銷偏置量成比例的轉(zhuǎn)化成轉(zhuǎn)向力矩。如果左右輪的制動或者驅(qū)動力是不等的，那么駕駛者將會感受到的到這個轉(zhuǎn)向力矩（假設(shè)轉(zhuǎn)向器有較高的逆效率）。只有在主銷偏置量為零時才不會有這個力矩產(chǎn)生因為此時制動力或驅(qū)動力對主銷的作用力臂為零。
如果輪胎比較寬的話輪胎力通常并不是作用在輪胎中心平面內(nèi)的，因為輕微的外傾角變化、路面不平、輪胎有一定圓錐度、或者其他的不對稱因素存在。這些不對稱因素可能導(dǎo)致轉(zhuǎn)向反沖，即使沒有前輪的各個定位參數(shù)作用。裝配要求通常會與中
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