Utilities to Calculate Tire Kinematics, Forces, and Moments
The following utilities to calculate tire kinematics, forces, and moments are available:
ACTCLC
- C Calling Sequence:
SUBROUTINE ACTCLC(TRAMAT, VEL, OMEGA, OMEGAR, RADIUS, RNORM,VLON, VCPLON, VCPLAT, VCPVRT,ALPHA, GAMMA, KAPPA,URAD, CPMTX)- Arguments
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Argument Type Description Symbol TRAMAT 3,3 array Input Transformation Matrix from ISO to Road Axis system 
VEL 3 array Input Velocity of Wheel Carrier in ISO 
OMEGA 3 array Input Angular Velocity of Wheel Carrier in ISO 
OMEGAR Double Precision Input Angular velocity of the Wheel 
RADIUS Double Precision Input Loaded Radius of the Wheel 
RNORM 3 array Input Road Normal Unit Vector in road axis system 
VLON Double Precision Output Longitudinal velocity of the tire in ISO 
VCPLON Double Precision Output Contact-patch longitudinal velocity in SAE 
VCPLAT Double Precision Output Contact-patch lateral velocity in SAE 
VCPRVT Double Precision Output Contact-patch vertical velocity in SAE 
ALPHA Double Precision Output Slip angle is SAE 
GAMMA Double Precision Output Inclination angle 
KAPPA Double Precision Output Slip Ratio in SAE 
URAD 3 array Output Unit vector from wheel centre to CP in road 
CPMTX 3,3 array Output Transformation Matrix from SAE to Road Axis system 
- Calculations
- Velocity of the Wheel Center in the Road reference frame is:
The Spin Axis (S) in the road reference frame is:
The coordinate system at the contact patch is defined by the transformation Matrix:
Here D represents unit vectors the directions corresponding to the Contact Patch:
The Longitudinal velocity of the Wheel center is given by:
Direction of the Unit Vector in the Direction of the CP from the wheel center:
The radius of the tire along the plane of the tire is:
Rigid body laws are applied to the tire to find the velocities at a different point on a rigid body in the road Frame of reference:
The Velocities in the Contact Patch Frame of reference is:
The SAE axis system is defined such that the Y and Z axis of the ISO axis system are flipped. This results in the following transformation matrix for moving any Vector from the ISO system to the SAE system:
The different components of the Contact patch velocities in the SAE axis system can be calculated from the following equation:
Since the Longitudinal velocity component is same in the SAE and the ISO system, they can be used interchangeably, which leads to the following SAE definition of Slip Angle and Slip Ratio:
The inclination angle is the angle between the road normal and the Wheel center to Contact Patch Vector:
XCP2HB
- C Calling Sequence:
SUBROUTINE XCP2HB(FCP, TCP, RAD, TRNMTX, FORCES, TORQUE)- Arguments
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Argument Type Description Symbol FCP 3 array Input Contact Patch Forces in SAE 
TCP 3 array Input Contact Patch Torques in SAE 
RAD 3 array Input Radius Vector from Wheel Centre to Contact Patch 
CPMTX 3,3 array Input Transformation Matrix from SAE to Road Axis system 
FORCE 3 array Output Hub Forces in road reference frame 
TORQUE 3 array Output Hub Torques in road reference frame 
- Calculations
- Force Translation to wheel center and move to road frame of reference:
Move to road reference frame followed by Torque translation to wheel center:
XCP2HB_ISO
- C Calling Sequence:
SUBROUTINE XCP2HB (FCP, TCP, RAD, TRAMAT, FORCE, TORQUE)- Arguments
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Argument Type Description Symbol FCP 3 array Input Contact Patch Forces in ISO 
TCP 3 array Input Contact Patch Torques in ISO 
RAD 3 array Input Radius Vector from Wheel Centre to Contact Patch 
TRAMAT 3,3 array Input Transformation Matrix from ISO to Road Axis system FORCE 3 array Output Hub Forces in road ISO 
TORQUE 3 array Output Hub Torques in road ISO 
- Calculations
- Force Translation to wheel center and move to road frame of reference:
Move to road reference frame followed by Torque translation to wheel center:
ACTFZ
- C Calling Sequence:
SUBROUTINE ACTFZ(VCPVRT, RADIUS, TIREK, TIREC, UNLRAD,FRCRAD, ERRMSG, IERR)- Arguments
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Argument Type Description Symbol VCPVRT Double Precision Input Vertical contact patch velocity (SAE co-ordinates) 
RADIUS Double Precision Input Loaded radius of the tire 
TIREK Double Precision Input Tire vertical stiffness 
TIREC Double Precision Input Tire vertical dampling 
UNLRAD Double Precision Input Unloaded Radius 
FRCRAD Double Precision Output Tire Vertical Force – Radial Direction 
ERRMSG Character Array Output Error Message IERR Integer Output Error Code - Calculations
