Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 16 Dec 2024

A Study on Self-Sustained Vibrations of a Tire Operating above Peak Friction

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Page Range: 323 – 351
DOI: 10.2346/tire.23.22015
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ABSTRACT

When a tire operates at a side slip level above peak friction, large vibrations in the produced forces and moments are observed. In the lateral direction, these vibrations are typically centered at frequencies close to 50 Hz and significantly affect the force that is produced by the tire. As an example, high dynamics vehicle maneuvers with an electronic stability program control system in the loop can be affected by this behavior. To accurately reproduce the tire response in these operating conditions, it is important to employ a model that can capture this phenomenon.

Based on analysis of nonlinear, unstable systems and limit cycle phenomenon, a theory is presented that provides a physical background for the source of vibrations. The theory also gives insight in how the frequency and amplitude of the vibrations are influenced by the tire physical characteristics and the operating conditions. It is found that the most dominant characteristics are the shape of the steady-state force response of the tire around peak friction, the contact patch mass, the carcass damping and stiffness. Simulations with physical models of different complexity levels, as well as with the commercial Simcenter Tire MF-Tyre/MF-Swift tire software model, validate the theory and demonstrate how the vibrations can be reproduced in a simulation environment. The simulation results are compared with tire measurements in different operating conditions, validating the exposed theory and employed models.

Keywords: tire out-of-plane vibrations; limit cycle; tire modeling; tire testing; vehicle dynamics
Copyright: 2024
FIG. 1 —
FIG. 1 —

Standard side slip angle sweeping sequence for side slip test; wheel-forward speed Vx= 100 km/h, inclination angle 0 deg, time rate of side slip angle 3 deg = s.

FIG. 2 —
FIG. 2 —

Side slip angle holding test sequence; wheel-forward speed Vx= 50 km/h, inclination angle 0 deg.

FIG. 3 —
FIG. 3 —

Characteristics of the additional sequence overlay on the time response of the original sequence; wheel-forward speed Vx= 50 km/h, inclination angle 0 deg.

FIG. 4 —
FIG. 4 —

Wheel-forward speed effect on the amplitude of self-sustained vibrations; inclination angle 0 deg, time rate of side slip angle 3 deg/s.

FIG. 5 —
FIG. 5 —

Dynamic model, contact patch suspended on the rim.

FIG. 6 —
FIG. 6 —

Magic Formula reproduction of a tire steady-state response, with coefficients B = 12:22, C = 1:51, D = 6077 N, and E = –1:49.

FIG. 7 —
FIG. 7 —

Equivalent dynamic model, contact patch suspended on the rim.

FIG. 8 —
FIG. 8 —

Equivalent dynamic model, rigid ring suspended to the rim and contact patch suspended to the rigid ring.

FIG. 9 —
FIG. 9 —

Comparison of the frequency response between the 1DOF and 3DOF models.

FIG. 10 —
FIG. 10 —

Simulation results of the MF-1DOF and MF-3DOF models, time domain (a), phase plane (b).

FIG. 11 —
FIG. 11 —

Steady-state nonlinear response and polynomial approximation.

FIG. 12 —
FIG. 12 —

Parameters relationships and amplitude of the limit cycle.

FIG. 13 —
FIG. 13 —

Limit cycle from simulations and theoretical predictions.

FIG. 14 —
FIG. 14 —

Limit cycle from simulations on polynomial and theoretical predictions.

FIG. 15 —
FIG. 15 —

Lateral force produced during a side slip angle sweep, comparison between measurement and models.

FIG. 16 —
FIG. 16 —

Lateral force produced during a side slip angle sweep, comparison between measurement and models, detail.

FIG. 17 —
FIG. 17 —

Lateral force produced during a side slip angle sweep, comparison between different model features.

FIG. 18 —
FIG. 18 —

Measured lateral force produced by a tire in nominal conditions, comparison with different modeling approaches.

FIG. 19 —
FIG. 19 —

Measured lateral force produced by a tire, comparison with two forward speed levels.

Contributor Notes

1 Corresponding author. STS Simulations & Test Solutions, Siemens Digital Industries Software, Automotive Campus 10, 5708 JZ, Helmond, The Netherlands. Email: carlo.lugaro@siemens.com
2 GCAPS, 1020 Lotus Dr., Alton, VA 24520, USA. Email: yli@gcaps.net
3 STS Simulations & Test Solutions, Siemens Digital Industries Software, Automotive Campus 10, 5708 JZ, Helmond, The Netherlands. Email: mohsen.alirezaei@siemens.com
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