Co-ordinate axes
Forces are exerted on the chassis and therefore on the bodyshell when the vehicle is in motion. This gives rise to self-movements in the bodyshell which can be subdivided into and represented as three categories.
In design terms, a system of coordinates is used which possesses three spatial coordinate axes. Three main movement directions are derived from this system.
- Longitudinal dynamics
- Lateral dynamics
- Vertical dynamics
Longitudinal dynamics
The main movement direction or direction of travel is defined by the x or longitudinal axis of the coordinate system. Driving situations involving longitudinal dynamics, such as accelerating or braking, cause the vehicle to pitch and result in a movement about the y-axis.
Lateral dynamics
Lateral dynamics are said to occur when the direction of movement is along the y or lateral axis, as is the case with steering or swerving.
This causes the vehicle to move about the vertical axis (z-axis). This rotating motion about the vertical axis is called "yawing.
As a side effect of the lateral movement, a rotating motion is also introduced about the x-axis. This so-called "rolling", however, is described later in the section on vertical dynamics since, under these circumstances, the bodyshell moves in a vertical direction.
Vertical dynamics
In the body moves along the z or vertical axis, we speak of vertical dynamics and describe oscillating up and down movements of the body as kangarooing.
A rotating motion about the x-axis, or rolling, is also included in vertical dynamics. It is caused when the suspension of the left and right wheels is compressed to differing degrees.
A triggering factor for this may area of unevenness along one side of the road only. But it may also occur on bends where the centrifugal force created when cornering leads to a rolling movement of the bodyshell. The centrifugal force affects the vehicle's center of gravity thus creating a torque which rotates the bodyshell about x-axis.
Vehicle handling when cornering
A vehicle's handling when cornering is also referred to as its self-steering characteristics. This handling performance is considerably influenced by the changing ratio of lateral force to wheel load on the front and rear axles. Lateral force increases as centrifugal force increases.
Neutral handling
In order for the vehicle to remain stable when driven through bends, the sum of the lateral forces on the wheels must counteract the total centrifugal force exerted on the vehicle.
The slip angles arising as a result of lateral force are the same on the front and rear axles. Neutral cornering facilitates the best use of lateral forces and thereby the highest limit cornering speeds.
It also however, reduces the subjective perception of how close the vehicle already is to the physical limit. The limit referred to here is that of the maximum transferable force (or the sum of the forces). If this limit is exceeded, it is not possible for the driver to calculate in advance whether the vehicle :
- will exit the curve at a tangent
- will experience a front wheel slide out of the corner (understeer)
- lose traction at the rear axle (oversteer)
Understeer
The ratio of lateral force to wheel load is greater at the front axle than at the rear axle. The vehicle follows a larger cornering radius than that corresponding to the steering angle. The driver will have the impression that the vehicle is experiencing a front axle slide towards the outside of the bend. When designing the chassis, this road behavior is often the preferred option, because when the vehicle loses traction, this behavior will produce a straight ahead course which it is possible to calculate.
Take for example a vehicle which begins to break away via the front axle whilst being driven to the limits, if the steering angle is then reduced, the vehicle will recover to assume a straight line course.
Oversteer
The ratio of lateral force to wheel load is greater at the front axle than at the rear axle. The vehicle follows a smaller radius than that corresponding to the steering angle. The vehicle experiences a rear axle "slide" towards the outside of the bend.
Reference parameters
Before discussing the geometric values involved in describing wheel position, some reference values first need to be defined. A distinction is drawn between the values for the wheel and those for the entire vehicle.
Wheel reference values
Wheel center plane
The wheel center plane intersects the wheel's axis of rotation vertically in the center of the tire.
Wheel contact point
The wheel contact point is the intersection of a perpendicular line, going through the axis of rotation and the road surface plane. It is located in the wheel center plane.
Because the wheel deforms when subjected to force effects, It is possible that the wheel contact point will not correspond to the geometric center of the tire contact patch.
Pivot axis
The pivot axis is the effective axis about which the wheel being steered is turned. This doesn't actually have to correspond to the central axis of an axle component (spring strut). It lies on the line connecting the upper and the lower pivot point of the wheel suspension. The design dictates that the upper pivot point lies in the center of the spring strut support bearing. When determining the lower pivot point, the operating principle of the axle in question must be taken into account.
Wheelbase
The wheelbase is the distance between the center of the wheels on the front axle and the center of the wheels on the rear axle. In the case of multi-axles vehicles, the individual wheelbases are given in order, from front to rear. A large wheelbase means more useful space, better ride comfort and less tendency to pitch. By contrast, s short wheelbase makes tight cornering easier.
Track width
The track width is the distance from the center of one wheel to the center of the other wheel on the same axle. The track width considerably influences a vehicle's cornering performance. A wide track width allows the vehicle to take corners at higher speeds. In the case of independent wheel suspension, with control or semi-trailing arms, a change in track width occurs during wheel compression and rebound. Roll resistance and tire wear increase as a result. If the change in track width is too great, the vehicle's directional stability deteriorates.
Vehicle longitudinal center plane
The vehicle longitudinal center place is vertical to the road surface. This plane follows the same direction as the line joining the centers of the front and rear track width.
Geometrical axis
The geometrical axis is the angle bisector of the total toe-in angle of the rear axle. If this straight line deviates from the vehicle center plane, a driving axis angle is produced and the vehicle will "dog track".
Slip angle
The slip angle is the angle which the wheel plane forms with the direction of travel (wheel's direction of movement). When lateral forces (wind force, centrifugal force) act on a vehicle while it is in motion, the wheels change their direction of travel. They run at an angle to the original direction of travel.
Track
Total toe
The total track of an axle is the difference in the distance between the front of the wheels and the rear of the wheels on the same axle. The track is measured at the height of the wheel center at the rim flanges. An electronic axle alignment procedure measures the angle of the wheel center plane to the vehicle longitudinal center plane (when aligning the rear axle) and to the geometric axle (when aligning the front axle). A value is calculated in angular degrees and minutes.
The Toe is positive if the distance between the wheels of the axle in question is smaller at the front of the wheels than at the back. This is then referred to as toe-in.
If, on the other hand, the toe is given negative values, a toe out is then said to be present. It is characterized by a smaller distance between the rim flanges at the rear in comparison to the front.
Zero toe is characterized by the center planes of the wheels on the same axis being positioned parallel to each other. The toe-in or toe-out stabilizes the straight line running of the wheels by twisting the tire contact patch. By eliminating the play in the wheel suspension and in the steering transmission components, it is possible to reduce the tendency of the wheels to wobble.
The type of toe setting selected for a specific vehicle concept depends on the one hand on the type of driven axle. On the other hand, the required level of vehicle reaction to steering commands is also an important consideration. A vehicle with toe-in of the front axle conveys a significantly more immediate vehicle reaction to the steering wheel movements. Excessive toe-in, however, can easily cause jittery handling.
Toe-differential angle
For the straight-ahead position, it is certainly best for both individual toe values on the front axle to be not only within the specified tolerance range but also the same as each other.
When cornering, however, the two front wheels travel along arcs of circle which have differing radii. The wheel on the inside of a bend follows an arc of a smaller radius than that followed by the outside wheel. To obtain optimum transmission of forces, the inside wheel must be turned through a greater angle than the outside wheel in order to follow that tighter arc. Therefore, the steering angle of the inside wheel is greater than that of the outside wheel.
The difference between the two steering angles is called the toe-differential angle. The term toe-differential angle is therefore used to indicate that when cornering, the front wheels posses differently sized individual toe values. This does not, however, represent a shortcoming but rather an intended design feature. During cornering, the toe-differential angle ensures that the wheels travel on the road along their longitudinal direction instead of sliding sideways across the road. This allows an optimum transmission of power between vehicle and tires.
Camber
The camber is the angle between the wheel center plane and a perpendicular line in the wheel contact point with respect to the road plane.
It is positive (+)