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Research Article

Cornering stiffness estimation using Levenberg–Marquardt approach

ORCID Icon, ORCID Icon & ORCID Icon
Pages 2207-2238 | Received 08 Apr 2020, Accepted 08 Mar 2021, Published online: 04 May 2021
 

Abstract

Study of vehicle dynamics aggregates possibilities to enhance performance, safety and reliability, such as the integration of control systems, usually requiring knowledge on vehicle's states and parameters. However, some critical values are difficult to measure or are not disclosed. For this reason, dynamics and stability analysis of six-wheeled vehicles are compromised, and available information on this matter is limited. In this context, this paper proposes the estimation of the cornering stiffness of a 6x6 vehicle by an inverse problem approach applying the Levenberg–Marquardt (LM) method. The algorithm required data from field experiments and from simulations of a vehicle model during a double-lane change manoeuvre developed using Simulink®/MATLAB®. Experimental and theoretical values for the vehicle yaw rate were combined through LM method for cornering stiffness estimation. The excellent agreement between measured and simulated yaw rate indicates that the proposed model and the estimated parameters properly represent the vehicle dynamics response.

2010 Mathematics Subject Classifications:

Acknowledgments

The authors would like to thank Mr. Madson Ferrari Pereira, Head of LATAM Product Validation at IVECO Latin America, for providing technical support during the field experimental measurements, and the Brazilian Army for supporting research and scientific development in military equipment.

Nomenclature

α=

Slip angle

β=

Sideslip angle or attitude angle

δ=

Steer angle of a tyre

ωy=

Angular velocity of the vehicle in the y-axis

ωx=

Angular velocity of the vehicle in the x-axis

ωz=

Angular velocity of the vehicle in the z-axis

ψ=

Yaw angle or heading angle

θ=

Pitch angle

φ=

Roll angle

a1=

Distance of the front wheel to the centre of mass of a vehicle

a2=

Distance of the second wheel to the centre of mass of a vehicle

a3=

Distance of the third wheel to the centre of mass of a vehicle

ay=

Lateral acceleration

Cα=

Cornering stiffness

Fx=

Longitudinal force on a vehicle

Fy=

Lateral force on a vehicle

Fxi=

Longitudinal tyre force

Fyi=

tyre lateral force

g=

Gravitational acceleration

H=

Maximum height of the vehicle

Iz=

Moment of inertia of a vehicle along z-axis

L=

Total length of the vehicle

l=

Wheelbase of the vehicle

Mz=

Yaw Moment

m=

Total mass of the vehicle

p=

Roll rate of a vehicle

Ptyre=

tyre inflation pressure

q=

Pitch rate of a vehicle

r=

Yaw rate of a vehicle

vy=

Lateral velocity of a vehicle

vx=

Longitudinal velocity of a vehicle

wv=

Maximum width of the vehicle

w=

Track of the vehicle

Disclosure statement

No potential conflict of interest was reported by the author(s).

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