Contact Patch Parameter Extraction

What is Altair's Simplified Durability Tire?

The Simplified Durability Tire model is a combination of the FIALA tire model and the 3D enveloping contact method. The 3D contact method captures the road surface using a series of parallel cams. The following characteristics of the road surface are captured:

Effective road height variation
Effective slope variation
Camber change

Based on the above variations, the forces are calculated using the FIALA algorithm. The 3D contact method allows you to predict the enveloping behavior of tire when rolling over an uneven surface.

Contact Patch Parameter Extraction from Testing

The following parameters are required to use the 3D enveloping contact with FIALA tire:


PA1	Coefficient of square root term in contact length equation
PA2	Coefficient of linear term in contact length equation
PAE	Half of ellipsoid length
PBE	Half of ellipsoid height
PCE	Order of ellipsoid
PLS	Scaling of distance between front and rear ellipsoid
ROAD_INCREMENT	Mesh Size for ellipsoid
N_WIDTH	Number of cams along contact width
N_LENGTH	Number of cams along contact length

PA1, PA2 show the variation of the contact patch length. The size of the contact patch increases with an increasing vertical load. The dimensions of the contact patch can be obtained by pressing a tire on carbon paper or by using ink.

Figure 2. Tire contact patch dimension 205/65 R16 at 4.7 KN and 2.5 bar

Contact Length Equation:

$a = r_{0} (P A 2 * F_{Z} / C_{Z} r_{0} + P A 1 \sqrt{F_{Z} / C_{Z} r_{0}}) \approx r_{0} (P A 2 * ρ / r_{0} + P A 1 \sqrt{ρ / r_{0}})$ $a = r_{0} (P A 2 * F_{Z} / C_{Z} r_{0} + P A 1 \sqrt{F_{Z} / C_{Z} r_{0}}) \approx r_{0} (P A 2 * ρ / r_{0} + P A 1 \sqrt{ρ / r_{0}})$

Contact Width Equation:

$b = w / 2$ $b = w / 2$


Parameters	Details
$a$ $a$	Half of the contact patch length
$b$ $b$	Half of the contact patch width
$r_{0}$ $r_{0}$	Unloaded tire radius
$ρ$ $ρ$	Tire deflection
$w$ $w$	Width of the tire
$C_{Z}$ $C_{Z}$	Radial stiffness of tire

Using the curve of contact patch dimensions versus vertical load or vertical deflection you can obtain PA1, PA2.

Important: The test matrix should have at least three different vertical loads and constant pressure, 0 camber.

Ellipse dimension: When a tire starts rolling over an obstacle, the shape of the tire circumference forms an elliptical contour. This is the basis of the elliptical cam contact model. A set of images of a tire rolling over an obstacle can be post-processed to extract the ellipse dimensions that are used in simplified durability tire. The image below presents the idea of extracting ellipse dimensions from test images:

The equation for the shape of cam can be written as:

PCE is the order of these ellipsoids and can be obtained using curve fitting.

For PLS a standard value of 0.8 is used.

Figure 4. Obstacle enveloping using elliptical cams

Tire parameter extraction from testing

For calculating the vertical load, the following parameters are needed:

Radial stiffness
Radial damping

These parameters can be obtained by simply pressing the tire and measuring the tire deflection. The damping can be obtained by measuring the response of tire to an impulse excitation.

For longitudinal force, the following parameters are needed:

Longitudinal slip stiffness
Relaxation length in longitudinal direction
Coefficient of friction between tire and road

For lateral force, the following parameters are needed:

Cornering stiffness
Relaxation length in lateral direction
Coefficient of friction between tire and road