Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 20 Mar 2024

An Exponential Decay Model for Decaying of Contact Patch Friction Steering Moment with Rolling Speed

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Page Range: 34 – 50
DOI: 10.2346/tire.23.21017
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ABSTRACT

Steering torque is a very important quantity for the driver's response. In fact, it gives the driver an idea of the road adherence condition during driving. Several models have been developed to simulate shear forces at the contact patch; most of them are based on semi-empirical tire models that account for slip and slip angles. They have good reliability when speed is high enough, but at very low speed, such as in parking, these models suffer from reliability and numerical issues. This paper presents a model to compute the steering moment due to contact patch friction at any longitudinal speed including pivot steering condition. In particular, it supplements the pivot steering model with a novel exponential decay of moment model to simulate steering moment for various wheel rolling speeds. The decay rate was found to be dependent upon contact patch geometry and rolling speed.

Keywords: pivot steering; steering resistance moment; steering torque at low speed
FIG. 1 —
FIG. 1 —

Torsion between contact patch and wheel hub.

FIG. 2 —
FIG. 2 —

Net steering torque. Reprinted from [22, p. 142].

FIG. 3 —
FIG. 3 —

Contact between tire and road surface. Modified and reprinted from [20].

FIG. 4 —
FIG. 4 —

Contact patch view: (a) contact patch approximation; (b) normal pressure distribution along longitudinal axis. Modified and reprinted from [20].

FIG. 5 —
FIG. 5 —

Shear stress at contact patch: (a) saturated twisting of bristles; (b) tire moved longitudinally considering free rolling; (c) remaining shear stress after the roll s.

FIG. 6 —
FIG. 6 —

Tire torsion during wheel steer.

FIG. 7 —
FIG. 7 —

Simulated and experimentally assessed variation of the moment vs steer angle for a non-rolling tire pressed against a flat plate at a load Fz= 4800 N. Reprinted from [21, p. 442].

FIG. 8 —
FIG. 8 —

Counter steering moment due to torsion for sinusoidal steering input at various speeds.

FIG. 9 —
FIG. 9 —

Counter torsion steering moment for sinusoidal steer input for pivot steering, acceleration, and constant non-zero rolling speed.

FIG. 10 —
FIG. 10 —

Counter torsion steering moment vs steer angle.

FIG. 11 —
FIG. 11 —

Comparison of net steering moment in simulations vs experiments.

FIG. 12 —
FIG. 12 —

Urban quadricycle.

Contributor Notes

1 Corresponding author. Mechanical Engineering, Politecnico di Milano, 20156 Milano MI, Italy. Email: jai.prakash@polimi.it
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