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

Transcription

3RD PARTY PRODUCT | Michael Gipser, Gerald Hofmann, cosin scientific software
FTire: High-End Tire Model
for Vehicle Simulation in SIMPACK
Fig. 1: Tire structure distortion on Belgian block road
IDEAS DRIVING FTIRE DEVELOPMENT
A 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-correlation, 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 friction 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
10 | SIMPACK News | March 2014
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 constantly curved surfaces. And it requires more than
sensing the road below the tire at a single
point, or an ‘equivalent volume’ approach, which condenses the complex
geometrical road surface shape into
one value.
Neglecting this would result in oversimplified 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 stateof-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 excitations, misuse scenarios, and any component test rig
application, simultaneously.
• rim flexibility
• road surface flexibility and/or plasticity
simplified model still observes all related
physical principles. To a certain extent, and
in clear contrast to pure mathematical apDue to the nonlinear and high-frequency
proximations, such models are able to exnature of most of the tire dynamics aspects,
trapolate conditions not completely covered
a physics-based model appears to be the
by a respective experiment.
only option. The intrinsic benefit of physicsFor example, consider the real tire’s main
based models is that there is no need to
structure. This structure is composed of a
find and ‘build in’ the tire behavior for every
‘nearly’ axisymmetric placement of carcass,
single combination of
belt, and bead, artire input signals, tire
“A modern tire simulation
ranged in layers and
states and operating
model is expected to be a virtual
embedded into difconditions. Rather, as
reproduction of the true tire...”
ferent types of rubber
with the real tire, the
compound as matrix
behavior is a consequence of fewer but
material. In FTire, SIMPACK’s high-end tire
more reliable physical principles.
model, this structure is replaced by a closed
The art of tire modeling is no longer the Sichain of small nonlinearly flexible bodies.
syphean task of implementing ever more arDespite this obvious simplification, the foltificial influencing factors, trying to take into
lowing are automatically observed:
account every new observed phenomenon.
Rather, it comes down to deciding which
• well-known relationships between differphysical effects may be neglected or simplient modes and mode-shapes, and their
fied under certain conditions. The remaining
dependency on load and rolling speed
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
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 complexity of some of the models requires the development of optimized ODE and PDE solvers, 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.
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
CORE MECHANICAL MODEL
FTire’s core model is a special, MBS-like arrangement 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 detailed 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 respective measurements of the global tire stiffness under different conditions, as well as
eigenfrequencies and related mode shapes,
for use in a parameter identification (PI) pro-
Fig. 2a: Structure model: belt segments
• 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 description into subsystems, well-defined system 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 discretization 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 prescribed 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 repeated if numerical settings are changed.
•Several of the subsystem models were
introduced to extend FTire’s scope of application, 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 application, saving computing time without
the need to maintain different tire models
or tire model data files.
rim
Ffr
ictio
n
dd
yn
cfr
Ffriction
ddyn
d dyn
d radial
c radial ssion
gre
ictio
n
pro
cd
dradial
yn
cfriction
belt
hysteresis
by dry friction
F friction
nod
c dyn
cradial
cdyn
progression
belt
e
nod
belt node
e
dynamic stiffening
by Maxwell elements
force/deflection progressivity
run-on-flat bottoming
by nonlinear radial springs
Fig. 2b: Structure model: radial force elements
SIMPACK News | March 2014 | 11
implemented in internal, switchable
subsystems (Fig. 4):
stiffness:
c = c (p)
pressure forces:
Fpressure = F (p) • n
Fig. 2c: Inflation pressure influence
cess. Alternatively, comparable static load
cases or modal analyses of a FEM tire model
may serve as 'virtual measurements'. In order 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 elements' (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, individual temperature, and local road contact
tangent planes are used to compute sensorindividual 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 quasiindustry-standard road data formats, and
in addition, has a simple interface for
user-defined road models. The complete
decoupling of road evaluation from SIMPACK allows SIMPACK to be connected to
all FTire-supported road models, without
any extra provisions within SIMPACK.
SUBSYSTEMS
Next to the core model, FTire optionally provides several extensions, most of which are
structural stiffness), and tread friction
characteristics
• A tread wear prediction model, driven by
local friction power and tread temperature (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 BekkerWong soil equation [7] which can be
replaced by a user-provided terra-mechanical soil model (Fig. 6)
• A fluid-dynamics-based filling gas vibration model, driven mainly by time- and
location-dependent variations of the tire
cross section, to predict excitation and
influence of 'cavity modes'
• Extra contact elements for
tire misuse simulations, like
belt-to-rim contact (bottoming), sidewall-to-curb
contact, and rim-to-curb
contact
• Several modifications of
the core mode parameters,
to take into account different types of tire imperfections such as imbalance,
non-uniformity, tread gauge
variations, conicity, ply-steer
and more
• A thermal model, predicting
the filling gas temperature as well
PARAMETERIZATION
as the tread surface temperature field.
In FTire's parameterization procedure, a
It is driven by heat generated in all disclear distinction is made between data
sipative and friction
used internally in the
elements of the me“A clear distinction is made
model equations ('prechanical core model,
between data used internally
processed' data), and
as well as by cooling
in the model equations, and
data to be supplied by
through
convecdata to be supplied by the user.”
the user ('basic' data).
tion, radiation and a
Basic data are obtained
transfer of heat into the environment.
by standard laboratory measurements, or by
In turn, the temperatures influence both
equivalent simulations with an FEM model,
inflation pressure (and by this indirectly
if available.
3rd Party
MBS solver
user
defined
stiff
road
interface
> 0.80
0.70 .. 0.80
0.60 .. 0.70
0.50 .. 0.60
0.40 .. 0.50
0.30 .. 0.40
0.20 .. 0.30
0.10 .. 0.20
< 0.01
grid-line dist. 20mm
Fig. 3: Tread model
t= 0.152s
s= 0.84h
stiff rim
CTI
internal MBS
susp. model
FTire core
3rd Party
system
simulator
internal flexible
rim model
internal
soil model
user
defined
flex.
rim
model
interface
user
defined
soil
model
interface
Fig. 4: FTire: subsystems, system borders, interfaces, plug-ins
These standard measurements are selected
to be as inexpensive, repeatable, significant, and as reliable as possible. Observing
this, a standardized measurement procedure — which was recently defined by a
working group of German car manufacturers — 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 laboratories provide 'turn-key' FTire data files.
ground pressure [MPa]
CTI
internal
stiff roads
• 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
INTERFACING AND NUMERICS
FTire 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 interface between SIMPACK and FTire is realized by an easy to apply, but comprehensive
application programming interface. This
API, called CTI (cosin tire interface), handles:
• exchange of system signals between vehicle and tire model
• loading of tire and road data files
• specification of operating conditions
• requests for extra output
Fig. 5: Tread wear model activated
The integrator deals with potentially
extremely large non-linear structure deformations, locally unstable friction characteristics, and high numerical stiffness of the
structure’s equations of motion.
The integrator takes full advantage of FTire’s
numerical properties, like the nearly axisymmetric tire structure and clear discrimination
between stiff and non-stiff system components. 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 connected to any step-size- and order-controlling
external solver. However, FTire’s performance is best if the solver step size does not
change too often.
ground pressure [MPa]
> 0.80
0.70 .. 0.80
0.60 .. 0.70
0.50 .. 0.60
0.40 .. 0.50
0.30 .. 0.40
0.20 .. 0.30
0.10 .. 0.20
< 0.01
t = 0.091s
s = 1.63h
grid-line dist. 20mm
Fig. 6: FTire on soft soil model: pressure distribution and road surface deformation
capability for simultaneous computation
of all tires of a vehicle)
and much more. The use of these capabilities 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.
in all important vehicle simulation environments. 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.
longitudial force
size & geometry,
mass
vertical stiffnes....
belt in-plane and lateral
bending stiffness,
belt longitudinal stiffness...
Out-Of-Plane Statics
belt lateral and torsional
stiffness...
tread stiffness...
Handling
small slip values
belt-out-of-plane bending
stiffness...
longitudial force
600
400
200
200
0
0
-400
0.000.050.100.150.200.250.300.350.40
time [s]
[N]
3600
vertical force
3400
0
-200
-200
-400
-400
-600
-600
0.000.050.100.150.200.250.300.350.40
0.000.050.100.150.200.250.300.350.40
time [s]
time [s]
[N]
4400
vertical force
[N]
5600
4200
5400
4000
5200
3800
5000
3600
4800
3400
4600
vertical force
3200
3000
2800
2600
2400
Fig. 8a: Cleat test validation, v = 5 km/h (blue = measurement, red = FTire)
Wheel Load 2.3 kN
In-Plane Cleat Tests
belt extensibility,
in-plane damping,
more tread rubber properties...
Out-Of-Plane Cleat Tests
out-of-plane damping,
belt out-of-plane flexibility
kinematics...
Friction Characteristics
large slip values
sliding friction coefficients
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
Wheel Load 4.7 kN
[N]
800
2000
3200
4400
0.000.050.100.150.200.250.300.350.40
0.000.050.100.150.200.250.300.350.40
0.000.050.100.150.200.250.300.350.40
time [s]
time [s]
time [s]
Directly Measured Data
Traction / Braking
longitudial force
400
200
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.). ButterworthHeinemann, Oxford 2010
Wheel Load 3.5 kN
[N]
600
400
2200
In-Plane Statics
[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.:
Wheel Load 2.3 kN
[N]
-200
CONCLUSION
Nearly 15 years of intense development,
FTire’s specialized ODE/PDE solver updates
preceded by 
15 years of experience in
tens of thousands of state variables (includtire modeling, have made FTire the most
ing 3D displacements,
comprehensive
and
temperature, friction
“A modern tire simulation
frequently used physiand wear state of all
model is expected to be a virtual
cal tire model today.
contact elements) once
reproduction of the true tire...”
Providing the complete
per internal time step.
tool chain to create,
The duration of this time step can be choanalyze, and process data for both tire
sen, but is typically around 0.2 ms.
and road surface properties, it is available
REFERENCES
[N]
1500
longitudial force
Wheel Load 3.5 kN
[N]
1500
1000
1000
500
500
0
0
-500
-500
longitudial force
Wheel Load 4.7 kN
[N]
1500
longitudial force
1000
500
0
-500
-1000
-1500
-1000
-1000
0.000.02 0.040.06 0.080.10
0.000.02 0.040.06 0.080.10
0.000.02 0.040.06 0.080.10
time [s]
time [s]
time [s]
[N]
4000
vertical force
[N]
5000
vertical force
[N]
6000
vertical force
3500
4500
5500
3000
4000
5000
2500
3500
4500
2000
3000
4000
1500
2500
3500
1000
0.000.02 0.040.06 0.080.10
time [s]
3000
2000
0.000.02 0.040.06 0.080.10
0.000.02 0.040.06 0.080.10
time [s]
time [s]
Fig. 8b: Cleat test validation, v = 40 km/h (blue = measurement, red = FTire)

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

Transcription

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