# Suspension Design Factors

When you build front or rear vehicle models using the Model Assembly Wizard you can add analyses using the Analysis Task Wizard that include output requests for Suspension Design Factors (SDFs) which are useful for assessing a suspension’s kinematic and compliance characteristics.

For example, one SDF is Ride Steer which is defined as the change in steer angle of a wheel for an incremental ride motion of both the left and right wheels. Another SDF is ride rate or the vertical stiffness of the suspension and tire as seen by the chassis. For a list of all the SDFs and their definitions see SDF Output.

The output requests for calculating SDFs use IDs in the range 50000000 to 50001000 and employ the user function "SDFREQUEST" in the "msautoutils" library. The first user parameter for the SDFREQUEST function 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. See the Interface to SDF Functions in msautotils topic to learn more about the inputs to the SDFREQUEST function in the MotionSolve input file.

## Important Definitions

Compliance Matrix
The primary input for SDF calculations is the compliance matrix for the suspension.
For non-steerable suspensions, the compliance matrix is the partial derivatives of the left and right wheel center displacements with respect to forces and moment forces at the wheel centers. To compute the first column of the compliance matrix, for example, MotionSolve applies a unit force in the global X direction to the left wheel center, performs a static analysis, and the resulting change in position and orientation of the left and right wheel centers becomes the first column of the 12 x 12 matrix. The process is repeated for the remaining 11 columns.
In the documentation for SDF parameters, terms in the compliance matrix are referenced using C(i,j):
• 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.

For steerable suspensions, the compliance matrix is expanded to include three additional markers to allow computation of the virtual kingpin (steer) axis and related characteristics like virtual caster angle and scrub radius. The three markers include one in the steering to determine the motion of the wheel centers due to a steering torque and markers where the left and right suspension springs attach to the un-sprung mass in order to lock the spring travel when computing steer motion using the compliance matrix.

Kingpin Axis
The assumed or ideal axis about which the wheel steers, which is the instantaneous axis of rotation of the knuckle due to steering input. This axis can be computed by two different methods, which is why measures that depend on this axis usually come in two flavors.
1. The geometric method: One or two markers can be used to compute the axis. The chosen method depends on the model. With one marker, the axis is assumed to be the z-axis of the marker. If two markers are given, the axis is the line passing through both markers. This can be the upper and lower ball joints of an SLA. It is important to note, that a system like a McPherson suspension needs the two marker method, because the upper and lower pivot do not share the same body. See the Interface to SDF Functions in msautotils topic for a description of the “Testrig Parameters Array” for indices 2, 3, 13 and 14, and how to pass the marker IDs for both cases.
2. The virtual method: For all suspension models, the compliance matrix may be used to compute the virtual kingpin axis. The virtual kingpin axis is the instant axis of rotation of the wheel center due to the steering input with the spring travel locked. The spring travel is locked manipulating the compliance matrix rather than applying a MOTION across the spring. The Locking Steering and Spring Travel topic describes how these locks are defined in the model.
Kingpin Ground Intersection Point
The point where the kingpin axis intersects the z = wcz - slr plane.

If the “Jack CP marker” is used, the implementation will use the actual Jack plane to compute the intersection. This intersection is used to compute scrub radius and caster trail.

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.
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

If the “Jack CP Marker” is provided, then the Tire Patch Point is determined as the intersection of the ground plane this marker defines, and the line, which is perpendicular on the plane and passes the wheel center.

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.