Parameterization Process of the Maxwell Model to Describe the Transient Force Behavior of a Tire

Andreas Hackl, Wolfgang Hirschberg, Cornelia Lex, Georg Rill

Research output: Contribution to conferencePaperpeer-review


The present technical article deals with the modeling of dynamic tire
forces, which are relevant during interactions of safety relevant
Advanced Driver Assistance Systems (ADAS). Special attention has
been paid on simple but effective tire modeling of semi-physical type.
In previous investigations, experimental validation showed that the
well-known first-order Kelvin-Voigt model, described by a spring and
damper element, describes good suitability around fixed operation
points, but is limited for a wide working range. When aiming to run
vehicle dynamics models within a frequency band of excitation up to
8 Hz, these models deliver remarkable deviations from measured tire
characteristics. To overcome this limitation, a nonlinear Maxwell
spring-damper element was introduced which is qualified to model
the dynamic hardening of the elastomer materials of the tire.
However, the advantage of a more realistic description of the
transient behavior leads to a more complex parametrization process.
Therefore, in the proposed article attention is paid to describe the
identification process including defined maneuvers to parameterize
the tire model, where the accuracy of the parameter strongly depends
on the quality of the available input data from measurement. In order
to study this important aspect of parameterization, the reference data
from simulation of the full physical tire model FTire is applied like a
“virtual measurement” of specified testing maneuvers. The procedure
of simulation by means of the enhanced first order dynamics model is
implemented by the semi-physical tire model TMeasy. Finally, the
improvements of the extended model are discussed and an outlook
for future work is given.
Original languageEnglish
Number of pages10
Publication statusPublished - 28 Mar 2017
EventSAE 2017 World Congress Experience: WCX 2017 - Detroit, United States
Duration: 4 Apr 20176 Apr 2017


ConferenceSAE 2017 World Congress Experience
Abbreviated titleWCX17
Country/TerritoryUnited States
Internet address

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