MotionView User's Guide

Utilities to Calculate Tire Kinematics, Forces, and Moments

Utilities to Calculate Tire Kinematics, Forces, and Moments

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Utilities to Calculate Tire Kinematics, Forces, and Moments

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The following utilities to calculate tire kinematics, forces, and moments are available:

hmtoggle_plus1ACTCLC

C Calling Sequence:

SUBROUTINE ACTCLC(TRAMAT, VEL, OMEGA, OMEGAR, RADIUS, RNORM,VLON, VCPLON, VCPLAT, VCPVRT,ALPHA, GAMMA, KAPPA,URAD, CPMTX)

Arguments:

Argument

Type

 

Description

Symbol

TRAMAT

3,3 array

Input

Transformation Matrix from ISO to Road Axis system

tramat_equ

VEL

3 array

Input

Velocity of Wheel Carrier in ISO

vel_equ_mv

OMEGA

3 array

Input

Angular Velocity of Wheel Carrier in ISO

omega_equ_mv

OMEGAR

Double Precision

Input

Angular velocity of the Wheel

omegar_equ_mv

RADIUS

Double Precision

Input

Loaded Radius of the Wheel

radius_equ_mv

RNORM

3 array

Input

Road Normal Unit Vector in road axis system

rnorm_equ_mv

VLON

Double Precision

Output

Longitudinal velocity of the tire in ISO

vlon_equ_mv

VCPLON

Double Precision

Output

Contact-patch longitudinal velocity in SAE

vcplon_equ_mv

VCPLAT

Double Precision

Output

Contact-patch lateral velocity in SAE

vcplat_equ_mv

VCPRVT

Double Precision

Output

Contact-patch vertical velocity in SAE

vcprvt_equ_mv

ALPHA

Double Precision

Output

Slip angle is SAE

alpha_equ_mv

GAMMA

Double Precision

Output

Inclination angle

gamma_equ_mv

KAPPA

Double Precision

Output

Slip Ratio in SAE

kappa_equ_mv

URAD

3 array

Output

Unit vector from wheel centre to CP in road

urad_equ_mv

CPMTX

3,3 array

Output

Transformation Matrix from SAE to Road Axis system

cmptx_equ_mv

Calculations:

Velocity of the Wheel Center in the Road reference frame is:

vel_wh_ct_road_equ_mv

The Spin Axis (S) in the road reference frame is:

spin_axis_road_equ_mv

The coordinate system at the contact patch is defined by the transformation Matrix:

coord_sys_cntct_ptch_trnsfrm_mtrx_equ_mv

Here D represents unit vectors the directions corresponding to the Contact Patch:

d_vectors_cont_patch_equ_mv

The Longitudinal velocity of the Wheel center is given by:

long_vel_whl_cntr_equ_mv

Direction of the Unit Vector in the Direction of the CP from the wheel center:

dir_of_unit_vector_equ_mv

The radius of the tire along the plane of the tire is:

radius_of_tire_alng_plane_equ_mv

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:

rigid_body_velocity_equ_mv

The Velocities in the Contact Patch Frame of reference is:

velocities_contact_patch_equ_mv

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:

vector_from_iso_to_sae_equ_mv

The different components of the Contact patch velocities in the SAE axis system can be calculated from the following equation:

contact_patch_vel_sae_equ_mv

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:

slip_angle_equ_mv

slip_ratio_equ_mv

The inclination angle is the angle between the road normal and the Wheel center to Contact Patch Vector:

inclination_angle_equ_mv

contact_patch_vector_equ_mv
hmtoggle_plus1XCP2HB

C Calling Sequence:

SUBROUTINE XCP2HB(FCP, TCP, RAD, TRNMTX, FORCES, TORQUE)

Arguments:

Argument

Type

 

Description

Symbol

FCP

3 array

Input

Contact Patch Forces in SAE

fcp_equ_mv

TCP

3 array

Input

Contact Patch Torques in SAE

tcp_equ_mv

RAD

3 array

Input

Radius Vector from Wheel Centre to Contact Patch

rad_equ_mv

CPMTX

3,3 array

Input

Transformation Matrix from SAE to Road Axis system

cpmtx_equ_mv

FORCE

3 array

Output

Hub Forces in road reference frame

force_equ_mv

TORQUE

3 array

Output

Hub Torques in road reference frame

torque_equ_mv

Calculations:

Force Translation to wheel center and move to road frame of reference:

xcp2hb_force_trans_equ_mv

Move to road reference frame followed by Torque translation to wheel center:

xcp2hb_torque_trans_equ_mv
hmtoggle_plus1XCP2HB_ISO

C Calling Sequence:

SUBROUTINE XCP2HB (FCP, TCP, RAD, TRAMAT, FORCE, TORQUE)

Arguments:

Argument

Type

 

Description

Symbol

FCP

3 array

Input

Contact Patch Forces in ISO

fcp_equ_iso_mv

TCP

3 array

Input

Contact Patch Torques in ISO

tcp_equ_iso_mv

RAD

3 array

Input

Radius Vector from Wheel Center to Contact Patch

rad_equ_iso_mv

TRAMAT

3,3 array

Input

Transformation Matrix from ISO to Road Axis system

tramat_equ_iso_mv

FORCE

3 array

Output

Hub Forces in road ISO

force_equ_iso_mv

TORQUE

3 array

Output

Hub Torques in ISO

torque_equ_iso_mv

Calculations

Force Translation to wheel center and move to road frame of reference

xcp2hb_iso_force_trans_equ_mv

Move to road reference frame followed by Torque translation to wheel center

xcp2hb_iso_torque_trans_equ_mv
hmtoggle_plus1ACTFZ

C Calling Sequence:

SUBROUTINE ACTFZ(VCPVRT, RADIUS, TIREK, TIREC, UNLRAD,FRCRAD, ERRMSG, IERR)

Arguments:

Argument

Type

 

Description

Symbol

VCPVRT

Double Precision

Input

Vertical contact patch velocity (SAE co-ordinates)

vcpvrt_equ_mv

RADIUS

Double Precision

Input

Loaded radius of the tire

actfz_radius_equ_mv

TIREK

Double Precision

Input

Tire vertical stiffness

tirek_equ_mv

TIREC

Double Precision

Input

Tire vertical dampling

tirec_equ_mv

UNLRAD

Double Precision

Input

Unloaded Radius

unlrad_equ_mv

FRCRAD

Double Precision

Output

Tire Vertical Force – Radial Direction

frcrad_equ_mv

ERRMSG

Character Array

Output

Error Message

 

IERR

Integer

Output

Error Code

 

Calculations:

actfz_calc_equ_mv