Forschung im Ingenieurwesen

, Volume 83, Issue 2, pp 105–118 | Cite as

Review and experimental evaluation of models for drivability simulation with focus on tire modeling

  • Korbinian J. FigelEmail author
  • Matthias Schultalbers
  • Ferdinand Svaricek


Recent research showed a significant role of the interaction between traction and torsional vibrations on control design in passenger cars. However, there is a large diversity in the proposed models for drivability control design and validation. This paper gives an overview of popular models in drivability simulation and addresses the quantitative evaluation of these models in a wide range of operating points. Experiments have been performed with diverse excitation signals. Based on these experiments, a number of popular models for control design and validation are identified and compared. A new model is proposed, which will be shown to be a good trade-off between model accuracy and complexity. The results give a guidance for control engineers during the model selection process for either controller concept design, parametrization or validation.



Derivative with respect to time


Estimated value


Normalized value


Physical parameter value


Median of a value


Average road elevation


Tire model parameter


Tire model parameter


Tire model parameter






Axle load ratio


Parameter set


Torsion of drivetrain


Relative angle of contact planes


Torsion of tire


Coefficient of traction


Air density


Approximate normalized position in backlash


Longitudinal relaxation length


Motor angle


Wheel angle


Natural Frequency


Rotational motor speed


Rotational tire speed


Rotational wheel speed


Cross sectional area of vehicle


Damping ratio


Climbing resistance


Aerodynamic drag force


Resistance acting on vehicle mass


Traction force


Rolling resistance at front/rear wheel


Vertical wheel force


Longitudinal Force


Motor-sided inertia


Inertia of two rims


Inertia of two tires


Tire-sided inertia


Inertia of two wheels


Wheel-sided intertia


Gain factors of LPV system


Number of samples


Length of chirp signal


Length of PRMS signal


Number of signals


Motor torque


Wheel resistance torque


Wheel torque


Root mean squared value of \(a_{wx}\)


Frequency weighted acceleration

\(a_{\tau x}\)

Running root mean square value of \(a_{x}\)


Longitudinal acceleration


Backlash angle


Fit of simplified backlash model to ideal model at contact


Drag coefficient


Coefficient of rolling resistance


Slip stiffness


Viscous damping factor of drivetrain


Viscous damping factor of chassis


Viscous damping factor of tyres


Cost function


Gravitational acceleration


Overall gear ratio


Stiffness coefficient of drivetrain


Stiffness coefficient of chassis


Stiffness coefficient of tires


Distance of center of front/rear wheel to COG in stand-still


Vehicle mass


Sampling instant


Sampling instant at peak


Fitting parameter of tanh2 backlash model


Wheel radius


Laplace variable


Relative inertial position of the chassis to the car body




Input vector in state-space system


Inertial vehicle speed


Inertial wheel and chassis speed


Weighting of chirp signal


State vector of state-space system


System output


Output vector from state-space system


Second order characteristics


Normalised root mean square fit


Normalised root mean square median fit


Relative root mean square median fit


Relative error of \(a_{\text{rms}}\)

Übersicht und experimentelle Bewertung von Modellen für die Fahrbarkeitssimulation mit Fokus auf der Modellierung des Reifens


Aktuelle Forschungsergebnisse haben einen wichtigen Einfluss der Wechselwirkung zwischen Traktions- und Drehschwingungen auf das Regelungsdesign in Personenkraftwagen gezeigt. Es gibt jedoch eine große Vielfalt an vorgeschlagenen Modellen für den Entwurf und die Validierung der Fahrbarkeitssteuerung und -regelung. Dieser Beitrag gibt einen Überblick über gängige Modelle in der Fahrbarkeitssimulation und befasst sich mit der quantitativen Bewertung dieser Modelle in einem breiten Bereich von Betriebspunkten. Es wurden Experimente mit verschiedenen Anregungssignalen durchgeführt. Basierend auf diesen Experimenten werden eine Reihe von gängigen Modellen für den Reglerentwurf und die Validierung identifiziert und verglichen. Es wird ein neues Modell vorgeschlagen, das sich als guter Kompromiss zwischen Modellgenauigkeit und Komplexität erweisen wird. Die Ergebnisse geben eine Orientierungshilfe für Regelungstechnikingenieure während des Modellauswahlprozesses für die Konzeption, Parametrierung oder Validierung von Fahrbarkeitsfunktionen.



Thanks to Florian Brunner for support in ECU-Bypass Coding, Sven Dannenberg for support in transmission control and Andreas Daasch and Dieter Schwarzmann for the provision of a test vehicle.


This research has been partly funded by IAV GmbH, Gifhorn, Germany


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Copyright information

© Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Control EngineeringBundeswehr University MunichNeubibergGermany
  2. 2.IAV GmbHGifhornGermany

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