Roll center
Encyclopedia
The roll center of a vehicle
is the notional point at which the cornering forces in the suspension are reacted to the vehicle body.
The location of the geometric roll center is solely dictated by the suspension
geometry, and can be found using principles of the instant centre of rotation
.
The SAE's definition of the force based roll center is, "The point in the transverse vertical plane
through any pair of wheel centers at which lateral forces may be applied to the sprung mass
without producing suspension roll".
The lateral location of the roll center is typically at the center-line of the vehicle when the suspension on the left and right sides of the car are mirror images of each other.
The significance of the roll center can only be appreciated when the vehicle's center of mass is also considered. If there is a difference between the position of the center of mass
and the roll center a moment arm is created. When the vehicle experiences angular acceleration
due to cornering, the size of the moment arm, combined with the stiffness of the springs and anti-roll bars (anti-sway bars in some parts of the world), dictates how much the vehicle will roll. This has other effects too, such as dynamic load transfer.
above the ground, the track width and the lateral acceleration. SUVs must shift their center of mass lower or decrease their lateral acceleration to avoid tipping. To keep them from tipping many auto manufacturer use tyres with lower grip to reduce the vehicles cornering capacity, or the roll stiffness balance front to rear can be altered to encourage understeer
or oversteer as necessary to limit the maximum lateral acceleration of the vehicle.
The geometric roll center of the vehicle can be found by following basic geometrical procedures when the vehicle is static. However, when the vehicle rolls the roll centers migrate. It is this movement of roll centers that vehicle dynamics seek to control and in most cases limit. The rapid movement of roll centers when the system experiences small displacements can lead to stability problems with the vehicle. The roll center height has been shown to affect behavior at the initiation of turns such as nimbleness and initial roll control.
The practical equivalent of the above is to push laterally at the tire contact patch and measure the ratio of the change in vertical load to the horizontal force.
Vehicle
A vehicle is a device that is designed or used to transport people or cargo. Most often vehicles are manufactured, such as bicycles, cars, motorcycles, trains, ships, boats, and aircraft....
is the notional point at which the cornering forces in the suspension are reacted to the vehicle body.
Theory
There are two definitions of roll center. The most commonly used is the geometric (or kinematic) roll center; the Society of Automotive Engineers uses a force-based definition.The location of the geometric roll center is solely dictated by the suspension
Suspension (vehicle)
Suspension is the term given to the system of springs, shock absorbers and linkages that connects a vehicle to its wheels. Suspension systems serve a dual purpose — contributing to the car's roadholding/handling and braking for good active safety and driving pleasure, and keeping vehicle occupants...
geometry, and can be found using principles of the instant centre of rotation
Instant centre of rotation
The instant centre of rotation, also called instantaneous centre and instant centre, is the point in a body undergoing planar movement that has zero velocity at a particular instant of time...
.
The SAE's definition of the force based roll center is, "The point in the transverse vertical plane
Transverse plane
The transverse plane is an imaginary plane that divides the body into superior and inferior parts. It is perpendicular to the coronal and sagittal planes....
through any pair of wheel centers at which lateral forces may be applied to the sprung mass
Sprung mass
In a vehicle with a suspension, such as an automobile, motorcycle or a tank, sprung mass is the portion of the vehicle's total mass that is supported above the suspension, including in most applications approximately half of the weight of the suspension itself...
without producing suspension roll".
The lateral location of the roll center is typically at the center-line of the vehicle when the suspension on the left and right sides of the car are mirror images of each other.
The significance of the roll center can only be appreciated when the vehicle's center of mass is also considered. If there is a difference between the position of the center of mass
Center of mass
In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body...
and the roll center a moment arm is created. When the vehicle experiences angular acceleration
Angular acceleration
Angular acceleration is the rate of change of angular velocity over time. In SI units, it is measured in radians per second squared , and is usually denoted by the Greek letter alpha .- Mathematical definition :...
due to cornering, the size of the moment arm, combined with the stiffness of the springs and anti-roll bars (anti-sway bars in some parts of the world), dictates how much the vehicle will roll. This has other effects too, such as dynamic load transfer.
Application
Load transfer is of critical importance for vehicle stability in vehicle such as SUVs. Ideally in high performance applications load transfer tends to be minimized as a tire's performance is directly affected by the amount of load that it has to transmit. In a steady state turn the final load transfer, summed across all the axles, is only related to the position of the center of massCenter of mass
In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body...
above the ground, the track width and the lateral acceleration. SUVs must shift their center of mass lower or decrease their lateral acceleration to avoid tipping. To keep them from tipping many auto manufacturer use tyres with lower grip to reduce the vehicles cornering capacity, or the roll stiffness balance front to rear can be altered to encourage understeer
Understeer
Understeer and oversteer are vehicle dynamics terms used to describe the sensitivity of a vehicle to steering. Simply put, oversteer is what occurs when a car turns by more than the amount commanded by the driver...
or oversteer as necessary to limit the maximum lateral acceleration of the vehicle.
The geometric roll center of the vehicle can be found by following basic geometrical procedures when the vehicle is static. However, when the vehicle rolls the roll centers migrate. It is this movement of roll centers that vehicle dynamics seek to control and in most cases limit. The rapid movement of roll centers when the system experiences small displacements can lead to stability problems with the vehicle. The roll center height has been shown to affect behavior at the initiation of turns such as nimbleness and initial roll control.
Testing Methods
Current methods of analyzing individual wheel instant centers have yielded more intuitive results of the effects of non-rolling weight transfer effects. This type of analysis is better known as the lateral-anti method. This is where one takes the individual instant center locations of each corner of the car and then calculates the resultant vertical reaction vector due to lateral force. This value then is taken into account in the calculation of a jacking force and lateral weight transfer. This method works particularly well in circumstances where there are asymmetries in left to right suspension geometry.The practical equivalent of the above is to push laterally at the tire contact patch and measure the ratio of the change in vertical load to the horizontal force.