The important elements of a steering system consist not only of the visible linkages just described, but also the geometry associated with the steer rotation axis at the road wheel. The geometry determines the force and moment reaction in the steering system, affecting its overall performance. The important features of the geometry are shown in Figure2.2.
The steer angle is achieved by rotation of the wheel about a steer rotation axis. Historically, this axis has the name “kingpin” axis, although it may be established by ball joint or the upper mounting bearing on a strut. The axis is normally not vertical, but may be tipped outward at the bottom, producing a lateral inclination angle (kingpin inclination angle; K.P.I.) in the range of 10-15degrees on passenger cars.
It is common for the wheel to be offset laterally from the point where the steer rotation axis intersects the ground. The lateral distance from the ground intercept to the wheel centerline is the offset at the ground and is considered positive when the wheel is outboard of the ground intercept. Offset may be necessary to obtain packaging space for brakes, suspension, and steering components. At the same time, it adds “feel of the road” and reduces static steering efforts by allowing the tire to roll around an arc when it is turned [12].
Caster angle result when the steer rotation axis is inclined in the
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longitudinal plane. Positive caster places the ground intercept of the steer axis ahead of the center of tire contact. A similar effect is created by including a longitudinal offset between the steer axis and the spin axis of the wheel, although this is only infrequently used. Caster angle normally ranges from 0 to 5 degrees and may vary with suspension deflection.
2.2.2. Camber angle
Camber angle is the angle made by the wheel of an automobile; specifically, it is the angle between the vertical axis of the wheel and the vertical axis of the vehicle when viewed from the front or rear. It is used in the design of steering and suspension. If the top of the wheel is farther out than the bottom (that is, away from the axle), it is called positive camber; if the bottom of the wheel is farther out than the top, it is called negative camber. The camber angle can be recognized better in a front view, as shown in Figure2.3.
The different camber angle change the touch point and the pivot point of tire with ground, direct effect the traction and abrasion of tire. Then change the achieve force distribute on axle from vehicle weight, avoid axle produces exceptionally abrasion.
Besides, the camber can be cancel the angels change from vehicle weight on suspension system to become deformed and the gap of active surfaces.
Camber also effects the car drive direction, like the motorcycle incline the body to corner. So the camber of the right and left wheels must equivalent can‟t affect the cars straight-line after the balance of force. And combine toe angle, greater straight-line stability and avoid tire exceptionally abrasion. Increase the negative
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camber needs combine increase toe-out. Increase the positive camber needs combine increase toe-in.
2.2.3. Kingpin inclination angle(Lateral inclination angle)
The angle is in front elevation between the steering axis and the vertical.
The K.P.I. angle can be recognized better in a front view, as shown in Figure2.4.
The K.P.I. can make the vehicle weight uniform distribution on the axis; protect the bearing to impair to hard. The angle can make the cornering force uniform and steering easily. Otherwise, if the angle is zero, then the vehicle weight and reacting force from ground will produce more lateral shear force, make the bearing to impair to easy and hard to cornering. Besides, the angle is the source of the aligning torque after the front wheel corning. The angle usually can‟t change from the vehicle suspension design started.
2.2.4. Toe angle
Toe is the symmetric angle that each wheel makes with the longitudinal axis of the vehicle, as a function of static geometry, and kinematic and compliant effects. The toe angle can be recognized better in a top view, as shown in Figure2.5. This can be contrasted with steer, which is the ant symmetric angle, i.e. both wheels point to the left or right, in parallel (roughly). Positive toe, or toe in, is the front of the wheel pointing in towards the centerline of the vehicle.
Negative toe, or toe out, is the front of the wheel pointing away from the centerline of the vehicle. Toe can be measured in linear units, at the front of the tire, or as an angular deflection.
In a rear wheel drive car, increased front toe in (i.e. the fronts of the front
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wheels are closer together than the backs of the front wheels) provides greater straight-line stability at the cost of some sluggishness of turning response, as well as a little more tire wear as they are now driving a bit sideways. On front wheel drive cars, the situation is more complex.
Toe is always adjustable in production automobiles, even though caster angle and camber angle are often not adjustable. Maintenance of front end alignment, which used to involve all three adjustments, currently involves only setting the toe ; in most cases, even for a car in which caster or camber are adjustable, only the toe will need adjustment.
One related concept is that the proper toe for straight line travel of a vehicle will not be correct while turning, since the inside wheel must travel around a smaller radius than the outside wheel; to compensate for this, the steering linkage typically conforms more or less to Ackermann steering geometry, modified to suit the characteristics of the individual vehicle.
It should be noted that individuals who decide to adjust their car's static ride height, either by raising or lowering, should immediately have the car properly aligned. The common misconception is that Camber angle causes an increased rate of tire wear, when in fact camber's contribution to tire wear is usually only visible over the entire life of the tire.
2.2.5. Caster angle
Caster angle is the angular displacement from the vertical axis of the suspension of a steered wheel in a car, bicycle or other vehicle, measured in the longitudinal direction. It is the angle between the pivot line (in a car - an
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imaginary line that runs through the center of the upper ball joint to the center of the lower ball joint) and vertical. The caster angle can be recognized better in a lateral view, as shown in Figure2.6. Car racers sometimes adjust caster angle to optimize their car's handling characteristics in particular driving situations.
The pivot points of the steering are angled such that a line drawn through them intersects the road surface slightly ahead of the contact point of the wheel.
The purpose of this is to provide a degree of self-centering for the steering - the wheel casters around so as to trail behind the axis of steering. This makes a car easier to drive and improves its straight line stability (reducing its tendency to wander). Excessive caster angle will make the steering heavier and less responsive, although, in racing, large caster angles are used to improve camber gain in cornering. Caster angles over 10 degrees with radial tires are common.
Power steering is usually necessary to overcome the jacking effect from the high caster angle.
The steering axis (the dotted line in the diagram above) does not have to pass through the center of the wheel, so the caster can be set independently of the mechanical trail, which is the distance between where the steering axis hits the ground, in side view, and the point directly below the axle. The interaction between caster angle and trail is complex, but roughly speaking they both aid steering, caster tends to add damping, while trail adds 'feel', and return ability. In the extreme case of the shopping trolley (shopping cart in the US) wheel, the system is undammed but stable, as the wheel oscillates around the 'correct' path.
The shopping trolley/cart setup has a great deal of trail, but no caster.
Complicating this still further is that the lateral forces at the tire do not act at the
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center of the contact patch, but at a distance behind the nominal contact patch.
This distance is called the pneumatic trail and varies with speed, load, steer angle, surface, tire type, tire pressure and time. A good starting point for this is 30 mm behind the nominal contact patch
2.2.6. Slip angle
Slip angle is the angle between a rolling wheel's actual direction of travel and the direction towards which it is pointing. This slip angle results in a force perpendicular to the wheel's direction of travel (the cornering force). This cornering force increases approximately linearly for the first few degrees of slip angle, and then increases non-linearly to a maximum before beginning to decrease.
A non-zero slip angle arises because of deformation in the tire carcass and tread. As the tire rotates, the friction between the contact patch and the road result in individual tread 'elements' ( infinitely small sections of tread ) remaining stationary with respect to the road. If a side-slip velocity u is introduced, the contact patch will be deformed. As a tread element enters the contact patch the friction between road and tire means that the tread element remains stationary, yet the tire continues to move laterally. This means that the tread element will be „deflected‟ sideways. In reality it is the tire/wheel that is being deflected away from the stationary tread element, but convention is for the co-ordinate system to be fixed around the wheel mid-plane. The slip angle can be recognized better in a top view, as shown in Figure2.7.
Because the forces exerted on the wheels by the weight of the vehicle are
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not distributed equally, the slip angles of each tire will be different. The ratios between the slip angles will determine the vehicle's behavior in a given turn. If the ratio of front to rear slip angles is greater than 1:1, the vehicle will tend to understeer, while a ratio of less than 1:1 will produce oversteer. Actual instantaneous slip angles depend on many factors, including the condition of the road surface, but a vehicle's suspension can be designed to promote specific dynamic characteristics. A principal means of adjusting developed slip angles is to alter the relative roll couple (the rate at which weight transfers from the inside to the outside wheel in a turn) front to rear by varying the relative amount of front and rear lateral load transfer. This can be achieved by modifying the height of the Roll centers, or by adjusting roll stiffness, either through suspension changes or the addition of an anti-roll bar.
Because of asymmetries in the side-slip along the length of the contact patch. The resultant force of this side-slip occurs behind the geometric center of the contact patch, a distance described as the pneumatic trail, and so creates a torque on the tire.
2.2.7. Formulation of geometry
Before we analyze the geometry, we define the geometry meaning of each term in fundamental dynamics equation.
Nomenclature
d : Kingpin offset at the ground
Fxr : Traction force on right-front wheel Fxl : Tractive force on left-front wheel
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Fyr : Lateral force on right-front wheel Fyl : Lateral force on left-front wheel Fzr : Vertical force on right-front wheel Fzl : Vertical force on left-front wheel Mzr : Aligning torque on right-front wheel Mzl : Aligning torque on left-front wheel MT : Moment produced by traction force ML : Moment produced by lateral force MV : Moment produced by vertical force
MV,KPI : Moment produced by vertical force acting on kingpin inclination angle
MV,caster : Moment produced by vertical force acting on caster angle
MAT : Moment produced by aligning torque Ts : The feedback torque of steering system Th : The torque of driver steering
r : Tire radius
Rw : Steering wheel radius λ : Kingpin inclination angle υ : Caster angle
δ : Tire steer angle
: Steering wheel angle
: Slip angle
Is : Moment of inertia of steering shaft Cs : Damping coefficient of steering shaft
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Ks : Elasticity coefficient of steering system Ih : Moment of inertia of steering wheel Ch : Damping coefficient of steering wheel