Tire Kinematics - MapleSim Help

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Tire Kinematics

Description

Variables associated with the tire kinematics as well as the contact patch forces/moments are shown in the figure below.

Tire kinematics and force/moment calculations are performed with respect to ISO coordinates. The origin of the ISO coordinate system is the tire-surface contact point, C. The unit vector for the z-axis, e^zISO, aligns with the surface normal vector which in turn is a result of defined surface geometry as explained in Surface. The unit vectors for the x and y axes, e^xISO and e^yISO, are calculated using the following vector algebra equations:

e^xISO=e^spin×e^zISO

e^yISO=e^zISO×e^xISO

where e^spin is the unit vector for the tire spin axis.

The inclination angle or camber, γ is

γ=sin−1e^yISO×e^spin·e^xISO

Tire revolution speed or spin rate Ω, which is needed for slip calculations, is derived using the following equation

Ω=ω&conjugate0;·e^spinω&conjugate0;·e^zISOsinγ

where ω&conjugate0; is the angular velocity vector of the tire.