Longitudinal Force Distribution and Road Vehicle Handling
Doctoral thesis, 2010

The distribution of longitudinal forces has a large influence on vehicle handling characteristics such as the driver/vehicle interaction, road holding and yaw stability, in particular during combined traction/braking and cornering near the grip limit of the tires. In order to select and develop suitable driveline systems and associated active control that provide consistent driver/vehicle handling, maximum road holding and sufficient yaw stability margins, it is essential to understand the influence of a particular drive force distribution on these handling characteristics. Due to the highly non-linear interaction between the longitudinal and lateral forces near the grip limit, the studies in this area have thus far focused on prototype testing and/or simulations with sophisticated vehicle models. By developing simpler models and more informative graphical representations, the understanding of the fundamental interaction of the drive force distribution and vehicle handling can be further improved and thereby facilitate enhanced development of future driveline systems. In this thesis, improved graphical representations, simpler models and new approaches to optimization of longitudinal force distribution are presented. These new methods focus particularly on exploring and maximizing the road holding capability of the vehicle. Also, new indicators of a likely loss of yaw stability are presented for one particularly severe driving maneuver. One area of application of the presented optimization methods, is demonstrated for case when the entry speed is too high to track a particular curve due to friction limitations. For this scenario a new parabolic path recovery strategy is developed based on a particle representation. This strategy, when implemented in to the planar motion of a vehicle, is shown to exhibit considerably less deviation from the intended path than currently proposed methods based on yaw moment allocation. The results obtained in this work are applied for analysis of the performance of a wide range of driveline systems, and are expected to have applications also in the associated active control for these systems. Overall, the present work has expanded the fundamental framework of vehicle modeling, optimization formulations and graphical representations for analysis and optimization of a wide range of driveline system properties and vehicle level characteristics.

ehicle dynamics

quasi steady-state

drive force

combined grip

longitudinal force distribution

combined slip

vehicle handling


MB, Hörsalsvägen 5
Opponent: Prof. Christian Gerdes, Department of Mechanical Engineering, Stanford University, USA


Matthijs Klomp

Chalmers, Applied Mechanics, Vehicle Safety

Driver Warning Strategies for a Critical Cornering Maneuver

21st International Symposium on Dynamics of Vehicles on Roads and Tracks (IAVSD’09),; (2009)

Other conference contribution

Longitudinal Force Distribution Using Quadratically Constrained Linear Programming

Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility,; Vol. 49(2011)p. 1823-1836

Journal article

Subject Categories

Vehicle Engineering



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 3072

MB, Hörsalsvägen 5

Opponent: Prof. Christian Gerdes, Department of Mechanical Engineering, Stanford University, USA

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