ftire: high-end tire model for vehicle simulation in · pdf filein ftire, simpack’s...

3RD PARTY PRODUCT | Michael Gipser, Gerald Hofmann, cosin scientific software

10 | SIMPACK News | March 2014

FTire: High-End Tire Model for Vehicle Simulation in SIMPACK

IDEAS DRIVING FTIRE DEVELOPMENTA modern tire simulation model is expected to be a virtual reproduction of the true tire, covering all of its vehicle dynamics-relevant aspects and their respective cross-correla-tion, and providing reliable insight into the dynamic behavior of the tire.Such an accurate tire model has to take into account many different kinds of external or internal excitations, for example:

• short-waved road irregularities (Fig. 1)• sharp-edged and/or high obstacles with

small extensions like cleats and stones• location- and time-dependent road fric-

tion properties and water film depth• high-frequency rim oscillations induced

by active suspension control systems• variable inflation pressure• variable tire and road surface temperature• actual tread wear state• tire imbalance, non-uniformity, run-out

and other imperfections

• rim flexibility• road surface flexibility and/or plasticity

Due to the nonlinear and high-frequency nature of most of the tire dynamics aspects, a physics-based model appears to be the only option. The intrinsic benefit of physics-based models is that there is no need to find and ‘build in’ the tire behavior for every single combination of tire input signals, tire states and operating conditions. Rather, as with the real tire, the behavior is a consequence of fewer but more reliable physical principles. The art of tire modeling is no longer the Si-syphean task of implementing ever more ar-tificial influencing factors, trying to take into account every new observed phenomenon. Rather, it comes down to deciding which physical effects may be neglected or simpli-fied under certain conditions. The remaining

Fig. 1: Tire structure distortion on Belgian block road

simplified model still observes all related physical principles. To a certain extent, and in clear contrast to pure mathematical ap-proximations, such models are able to ex-trapolate conditions not completely covered by a respective experiment. For example, consider the real tire’s main structure. This structure is composed of a ‘nearly’ axisymmetric placement of carcass,

belt, and bead, ar-ranged in layers and embedded into dif-ferent types of rubber compound as matrix

material. In FTire, SIMPACK’s high-end tire model, this structure is replaced by a closed chain of small nonlinearly flexible bodies. Despite this obvious simplification, the fol-lowing are automatically observed:

• well-known relationships between differ-ent modes and mode-shapes, and their dependency on load and rolling speed

“A modern tire simulation model is expected to be a virtual reproduction of the true tire...”

The tire is undoubtedly both the most important and the most complex vehicle suspension component.With this in mind, tire simulation today requires more than the mathematical approximation of a hand full of steady-state, deflection- and slip-based force/moment characteristics on ideally flat or con-stantly curved surfaces. And it requires more than

sensing the road below the tire at a single point, or an ‘equivalent volume’ ap-proach, which condenses the complex

geometrical road surface shape into one value.

Neglecting this would result in over-simplified tire dynamics and rough road

influence. This is what 'classical' tire models have done since the earliest vehicle dynamics

simulations.Instead, the increasing complexity of state-

of-the-art vehicle models requires a versatile, robust and multi-purpose tire model that can be

used not only in 'classical' handling application scenarios, but also with highly dynamic road excita-tions, misuse scenarios, and any component test rig application, simultaneously.

Ready for Print - 20.12.2013

Michael Gipser, Gerald Hofmann, cosin scientific software | 3RD PARTY PRODUCT

➡ 500 to 2500 DOFs, assigned to a ring of belt segments:

translation along x/ y / z rotation about longitudinal axis bending with 3 to 9 shape functions

➡ Belt segments coupled to each other and to rim by a large set of nonlinear spring/damper elements, reflecting the tire's structural stiffness properties

hysteresis by dry friction

Ffriction ddyn

dradial

cfriction cdyn

belt node

dynamic stiffening by Maxwell elements

force/deflection progressivity run-on-flat bottoming

by nonlinear radial springs

rim

Ffriction

belt node

c radial

progression

d radial

c dyn

F friction d dyn

ddyn

cdyn

cfriction

belt node

cradial

progression

SIMPACK News | March 2014 | 11

• impulse and energy conservation• structure distortion under different kinds

of static loads• relationships between local and global

stiffness• symmetry and defined of linearized mass

and stiffness matrix, etc.

FTire arranges the physics-based tire de-scription into subsystems, well-defined sys-tem boundaries and interface signals which have clear physical meaning. This allows easy activation and deactivation of certain tire model extensions, without replacing the data-file or changing the model interfacing. To complete this 'model scope on demand' approach, two more aspects have to be mentioned:

• FTire is scalable with respect to timely and spatial resolution of structural dis-cretization and road surface sensing. This is achieved by strictly decoupling physical data and numerical settings. Whatever internal time step, segment number or tread block number is chosen, the pre-scribed static, modal and steady-state properties used to determine internal physical parameters will be precisely matched by FTire. This is achieved in a fully automated way, during the so-called data pre-processing phase, which is re-peated if numerical settings are changed.

• Several of the subsystem models were introduced to extend FTire’s scope of ap-plication, e.g., road surface description,

soft-soil model and rim flexibility model, which may be replaced with user-written versions using standardized C-code interfaces.

By the means listed above, the tire model variant actually used is tailored to the ap-plication, saving computing time without the need to maintain different tire models or tire model data files.

The most important development aspect of FTire is the design and implementation of feasible, reliable, and affordable methods to determine the parameters of the physical submodels.After this, the inherent numerical complex-ity of some of the models requires the de-velopment of optimized ODE and PDE solv-ers, running in co-simulation with the MBS, FEM, or system dynamics solver. Today, it is expected that tire models run in real-time, for HiL and driving simulator applications. FTire does so, after some internal tuning, but with the original core model.

CORE MECHANICAL MODELFTire’s core model is a special, MBS-like ar-rangement of nonlinear elasticity, dissipative and inertia elements which replace the real tire structure (Fig. 2a/b). Selection of these elements and their parameterization is such that belt distortion under a wide range of relevant external loads on flat or non-flat surface matches that of the real tire in a de-tailed way. Lower-order eigenfrequencies, mode shapes (including bending modes), and modal damping values are matched sufficiently well at the same time. Stiffness parameters and internal belt normal forces are influenced by actual inflation pressure (Fig. 2c).The related parameterization takes respec-tive measurements of the global tire stiff-ness under different conditions, as well as eigenfrequencies and related mode shapes, for use in a parameter identification (PI) pro-

Fig. 2b: Structure model: radial force elements

Fig. 2a: Structure model: belt segments



pressure forces:

Fpressure = F (p) • n

stiffness:c = c (p)

> 0.800.70 .. 0.800.60 .. 0.700.50 .. 0.600.40 .. 0.500.30 .. 0.400.20 .. 0.300.10 .. 0.20< 0.01

t= 0.152ss= 0.84hgrid-line dist. 20mm

ground pressure [MPa]


Fig. 2c: Inflation pressure influence

Fig. 3: Tread model

cess. Alternatively, comparable static load cases or modal analyses of a FEM tire model may serve as 'virtual measurements'. In or-der to compare modal data, FTire provides linearized system matrices at any arbitrary operating point.The second component of the core model is the tread description, comprised of an arbitrary number (typically between 3.000 and 10.000) of massless 'contact ele-ments' (Fig. 3). These contact sensors, with extensions in the range of millimeters, are attached to the structure model elements and potentially come into contact with the road. If so, radial deflection (and thus local ground pressure), local sliding velocity, indi-vidual temperature, and local road contact tangent planes are used to compute sensor-individual normal and friction forces. These forces constitute the distributed external load of the structure model.By setting the unloaded lengths of the contact sensors in an appropriate way, it is possible to take into account grooves, lugs, and other tread patterns (Fig. 3).FTire’s road evaluation supports all quasi-industry-standard road data formats, and in addition, has a simple interface for user-defined road models. The complete decoupling of road evaluation from SIM-PACK allows SIMPACK to be connected to all FTire-supported road models, without any extra provisions within SIMPACK.

SUBSYSTEMSNext to the core model, FTire optionally pro-vides several extensions, most of which are

implemented in internal, switchable subsystems (Fig. 4):

• Extra contact elements for tire misuse simulations, like belt-to-rim contact (bot-toming), sidewall-to-curb contact, and rim-to-curb contact• Several modifications of the core mode parameters, to take into account differ-ent types of tire imperfec-tions such as imbalance, non-uniformity, tread gauge variations, conicity, ply-steer

and more• A thermal model, predicting

the filling gas temperature as well as the tread surface temperature field.

It is driven by heat generated in all dis-sipative and friction elements of the me-chanical core model, as well as by cooling through convec-tion, radiation and a transfer of heat into the environment. In turn, the temperatures influence both inflation pressure (and by this indirectly

structural stiffness), and tread friction characteristics

• A tread wear prediction model, driven by local friction power and tread tempera-ture (Fig. 5)

• A flexible and visco-elastic rim model, which can be replaced by a user-provided model

• A soft soil model, based on the Bekker-Wong soil equation [7] which can be replaced by a user-provided terra-me-chanical soil model (Fig. 6)

• A fluid-dynamics-based filling gas vibra-tion model, driven mainly by time- and location-dependent variations of the tire cross section, to predict excitation and influence of 'cavity modes'

PARAMETERIZATIONIn FTire's parameterization procedure, a clear distinction is made between data

used internally in the model equations ('pre-processed' data), and data to be supplied by the user ('basic' data). Basic data are obtained

by standard laboratory measurements, or by equivalent simulations with an FEM model, if available.

“A clear distinction is made between data used internally in the model equations, and

data to be supplied by the user.”



internal stiff roads

user defined

stiff road

interface

internal soil model

user defined

soil model

interface

FTire core

stiff rim

internal flexible rim model

user defined

flex. rim

model interface

internal MBS susp. model

3rd Party MBS solver

3rd Party system

simulator

CTI

CTI


Fig. 5: Tread wear model activated

Fig. 4: FTire: subsystems, system borders, interfaces, plug-ins

These standard measurements are selected to be as inexpensive, repeatable, signifi-cant, and as reliable as possible. Observing this, a standardized measurement proce-dure — which was recently defined by a working group of German car manufactur-ers — has been recommended.Comprehensive software (FTire/fit, Fig. 7) is available to automate the parameterization and validation process (Fig. 8a/b), based upon these measurements. However, such methods require significant training and expertise in tire dynamics. Certain test labo-ratories provide 'turn-key' FTire data files.

INTERFACING AND NUMERICSFTire is run in co-simulation, thus completely decoupling the integration of its huge number of internal state variables from SIMPACK’s DAE solver. As with all other supported simulation environments, the in-terface between SIMPACK and FTire is real-ized by an easy to apply, but comprehensive application programming interface. This API, called CTI (cosin tire interface), handles:

• exchange of system signals between ve-hicle and tire model

• loading of tire and road data files• specification of operating conditions• requests for extra output

• control of FTire’s animation• provision of TYDEX/STI output• provision of key tire data, as required by

the calling vehicle model

• selection of user-defined submodels• specification of FTire’s ‘speed mode’, a

collection of settings to influence FTire’s speed of computation (up to real-time


Directly Measured Data

size & geometry, mass vertical stiffnes....

Traction / Braking

tread stiffness...

In-Plane Statics

belt in-plane and lateral bending stiffness, belt longitudinal stiffness...

In-Plane Cleat Tests

belt extensibility, in-plane damping, more tread rubber properties...

Handling small slip values

belt-out-of-plane bending stiffness...

Out-Of-Plane Statics

belt lateral and torsional stiffness...

Out-Of-Plane Cleat Tests

out-of-plane damping, belt out-of-plane flexibility kinematics...

Friction Characteristics large slip values

sliding friction coefficients

> 0.800.70 .. 0.800.60 .. 0.700.50 .. 0.600.40 .. 0.500.30 .. 0.400.20 .. 0.300.10 .. 0.20< 0.01

t = 0.091ss = 1.63hgrid-line dist. 20mm

ground pressure [MPa]



capability for simultaneous computation of all tires of a vehicle)

and much more. The use of these capa-bilities is under sole control of the calling solver. CTI and FTire are packed into a single dynamic library (cti.dll in Windows systems and libcti.so in Linux systems), without any extra dependencies.

Fig. 6: FTire on soft soil model: pressure distribution and road surface deformation

Fig. 7: Sequential parameter identification, using direct data, static properties, steady-state measurements, and dynamic cleat tests for in-plane and out-of-plane excitation

FTire’s specialized ODE/PDE solver updates tens of thousands of state variables (includ-ing 3D displacements, temperature, friction and wear state of all contact elements) once per internal time step. The duration of this time step can be cho-sen, but is typically around 0.2 ms.

The integrator deals with potentially extremely large non-linear structure defor-mations, locally unstable friction character-istics, and high numerical stiffness of the structure’s equations of motion.The integrator takes full advantage of FTire’s numerical properties, like the nearly axisym-metric tire structure and clear discrimination between stiff and non-stiff system com-ponents. It guarantees certain static and modal properties of the discretized model, independent of actual numerical settings like internal step-size and mesh resolution.Although using a constant internal step-size is preferable, CTI and FTire can be connect-ed to any step-size- and order-controlling external solver. However, FTire’s perfor-mance is best if the solver step size does not change too often.

CONCLUSIONNearly 15 years of intense development, preceded by 15 years of experience in tire modeling, have made FTire the most

comprehensive and frequently used physi-cal tire model today. Providing the complete tool chain to create,

analyze, and process data for both tire and road surface properties, it is available

“A modern tire simulation model is expected to be a virtual reproduction of the true tire...”


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Wheel Load 2.3 kN Wheel Load 3.5 kN Wheel Load 4.7 kN

Wheel Load 2.3 kN Wheel Load 3.5 kN Wheel Load 4.7 kN

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Fig. 8b: Cleat test validation, v = 40 km/h (blue = measurement, red = FTire)

Fig. 8a: Cleat test validation, v = 5 km/h (blue = measurement, red = FTire)

in all important vehicle simulation environ-ments. FTire is used by several dozen OEMs, tire manufacturers, tier-1-suppliers, and research institutes world-wide and can be applied to almost all types of ground vehicle and aircraft tires. It has become the first choice for ride comfort, handling, durability, and mobility applications.

REFERENCES[1] FTire documentation and more material: www.cosin.eu[2] Gipser, M.: FTire — the Tire Simulation Model for all Applications Related to Vehicle Dynamics. Vehicle System Dynamics, Vol. 45:1, pp. 217–225, 2007[3] Gipser, M.: RGR Road Models for FTire. Proc. SAE World Congress 08M-54, Detroit 2008[4] Gipser, M.: The FTire Tire Model. In: Pacejka,H. B.:

Tyre and Vehicle Dynamics (3rd ed.), pp. 582–586. SAE International 2012[5] Gipser, M.: Pneumatic Tire Models: the Detailed Mechanical Approach. In: Road and Off-Road Vehicle System Dynamics Handbook. Mastinu, Plöchl (eds), CRC Press, to appear in November 2013[6] Wong, J.Y.: Terramechanics and Off-Road Vehicle Engineering (2nd ed.). Butterworth-Heinemann, Oxford 2010


ftire: high-end tire model for vehicle simulation in · pdf filein ftire, simpack’s...

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