Suspension Design Factors

The REQUEST statements included in the model for calculating SDFs use IDs in the range 50000000 to 50001000. The first argument to the user subroutine is the "Branch ID" that identifies the specific SDF to be calculated. The subsequent arguments to the user subroutine vary from one SDF to another and include marker IDs, vehicle parameters and flags to control the output to the req file.

In MotionSolve, the SDFs are calculated by a C++ routine. In ADAMS, the SDFs are calculated using FORTRAN subroutines that are linked in with ADAMS as a REQSUB user subroutine to create a custom executable of ADAMS.

Important Definitions

Compliance Matrix

The compliance matrix for a system is the partial derivative of the marker displacements with respect to the applied forces to the markers. For SDF calculations a compliance matrix is returned for markers at the wheel centers giving the 12 X 12 matrix C(i,j) where:

i = 1-6 X Y Z RX RY RZ displacements of the left wheel center

i = 7-12 X Y Z RX RY RZ displacements of the right wheel center

j = 1-6 X Y Z RX RY RZ forces on the left wheel center

j = 7-12 X Y Z RX RY RZ forces on the right wheel center

When reading entries in the compliance matrix, i is the degree of freedom which is being displaced by a force in the j degree of freedom. For example, C(3,9) is the vertical displacement of the left wheel center due to a unit vertical force at the right wheel center.

Kingpin Axis

The assumed or ideal axis about which the wheel steers. Two points which are input by the user (for example the upper and lower ball joints) define the kingpin axis.

Kingpin Ground Intersection Point

The point where the kingpin axis intersects the z = wcz - slr plane.

Spindle Axis

The axis about which the wheel spins. Two points which are input by the user define the spindle axis. These points are the wheel center and the spindle alignment point.

Static Loaded Radius (slr)

The user-input vertical height (radius) of the tire under the current vehicle load.

Tire Patch Point

The estimated point where the tire contacts the ground. It is calculated with the following equations:

tpx = (spalignx*spalignz*slr)/(spalignx^2+spaligny^2)+wcx

tpy = (spalignz*slr+spalignx*wcs+spaligny*wcy)/spaligny - spalignx/spaligny*tpx

tpz = wcz - slr

Virtual Kingpin Axis

For front suspensions, the calculated instant axis of rotation of the knuckle with respect to the ground due to a lateral motion of the steering linkage. For rear suspensions, the calculated instant axis of rotation of the knuckle with respect to the ground due to in-phase aligning moments at each wheel.

Vehicle Orientation

Two orientation schemes are considered in the SDF calculations depending on whether the front end of the vehicle points to the positive or negative x-axis direction of the global coordinate system.

Orientation A

Vehicle front end points to the negative x-axis direction of the global coordinate system.

Orientation B

Vehicle front end points to the positive x-axis direction of the global coordinate system.

For those SDF items depending on orientation schemes, two sets of formulas are provided respectively for orientation A and B.