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MF-Tyre/MF-Swift
Copyright TNO, 2013
Copyright TNO, 2013
MF-Tyre/MF-Swift
Dr. Antoine Schmeitz
Copyright TNO, 2013
Introduction
TNO’s tyre modelling toolchain
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Identification Simulation
parameter fitting+
database
MF-Tool
TYDEX files
tyre propertyfile
tyre modelMF-TyreMF-Swift
MBSsolver
tyre (virtual) testing
signalprocessing
Measurement
2
MF-Tyre/MF-Swift
Copyright TNO, 2013
Copyright TNO, 2013
Introduction
What is MF-Tyre/MF-Swift?
MF-Tyre/MF-Swift is an all-encompassing tyre model
for use in vehicle dynamics simulations
This means:
emphasis on an accurate representation of the generated (spindle) forces
tyre model is relatively fast
can handle continuously varying inputs
model is robust for extreme inputs
model the tyre as simple as possible, but not simpler for the intended
vehicle dynamics applications
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Copyright TNO, 2013
Introduction
Model usage and intended range of application
All kind of vehicle handling simulations:
e.g. ISO tests like steady-state cornering, lane changes, J-turn, braking, etc.
Sine with Dwell, mu split, low mu, rollover, fishhook, etc.
Vehicle behaviour on uneven roads:
ride comfort analyses
durability load calculations (fatigue spectra and load cases)
Simulations with control systems, e.g. ABS, ESP, etc.
Analysis of drive line vibrations
Analysis of (aircraft) shimmy vibrations; typically about 10-25 Hz
Used for passenger car, truck, motorcycle and aircraft tyres
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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MF-Tyre/MF-Swift
Copyright TNO, 2013
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Modelling aspects and contents (1)
1. Basic tyre properties and constitutive relations
for tyre radii, contact patch size, stiffness, rolling resistance
nonlinear, effects of loads, velocity, inflation pressure
2. Inclusion of measured tyre steady-state slip char acteristics
described by load and inflation pressure dependent Magic Formula
responses to sideslip, longitudinal slip, camber and turn slip
3. Tyre transients / relaxation length properties
carcass compliance
proper contact transient properties due to finite contact length
4. Inclusion of belt dynamics
primary natural frequencies (rigid ring modes) and gyroscopic effects
5. Tyre rolling over uneven road surface
tyre deformation on obstacles, arbitrary uneven roads
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Modelling aspects and contents (2)
6. Model usage and availability
selection of complexity level
road definition
7. Model parameterisation
measurement requirements
MF-Tool
8. Concluding remarks
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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MF-Tyre/MF-Swift
Copyright TNO, 2013
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1. Basic tyre properties and constitutive relations
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Some definitions
• free tyre radius RΩ
• loaded radius Rl
• effective rolling radius Re
• tyre deflection ρ• forward velocity Vx
• wheel spin velocity Ω• longitudinal slip velocity Vsx
• lateral slip velocity Vsy
• longitudinal force Fx
• lateral force Fy
• vertical force Fz
• overturning moment Mx
• rolling resistance moment My
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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• self aligning moment Mz
• inclination angle γ
FxMx
FyMy
Mz
FzVx
normal to the road
Vsx Vsy
ReRl
γ
C
S
RΩΩ
ρ
For a freelyrolling wheel:
Ω= x
e
VR
lRR −= Ωρ
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MF-Tyre/MF-Swift
Copyright TNO, 2013
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Constitutive relations
Tyre radii, stiffness, contact patch dimensions, rolling resistance, etc. are non-
constant for different operating conditions (load, velocity, etc.)
In MF-Swift nonlinear empirical relations are used to describe these basic tyre
properties
Examples:
vertical force
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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( )iyxz pFFfF ,,,,Ω= ρ
( ) 01
2
02
01
2
0
2
00
02
1
1
ziFzFzFz
z
yFcy
z
xFcxvz
FdppR
qR
q
F
Fq
F
Fq
V
RqF
+
+
⋅
−
−Ω+=
ρρ
coefficient from curve fitting
Fz
Copyright TNO, 2013
Constitutive relations
effective rolling radius
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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+
−= Ω
00
0 arctanz
zreff
z
zreffreff
z
ze F
FF
F
FBD
c
FRR
Ω+=Ω
2
0
0100 V
RqqRR vre
Fz
coefficient from curve fitting
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MF-Tyre/MF-Swift
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2. Inclusion of measured tyre steady-state slip characteristics ( magic formula)
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Magic Formula
Descriptions are available for the three steady-state modes of slip
Equations depend on vertical load Fz, inclination angle γ and inflation
pressure pi ; [Fx, Fy, Mx, My, Mz] = MF (Fz, κ, α, γ, ϕ, pi, V)
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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side slip
α
Mz
V
Fy
α0 0.1 0.2 0.3
0
Mz
Fy
t
turn slip+ camber
R
V Mz Fy
aϕ = a/R
spin
0 0.1 0.2 0.3
Mz
Fy
κ0 0.1 0.2 0.3
Fx
longitudinal slip
FxVsx
+ combinations
x
ex
x
rx
x
sx
V
RV
V
VV
V
V
Ω−−=
−−=−=κ
=
x
sy
V
Varctanα Vt
ψϕ &−=
Vx
Vsy
ψ&
VxΩ
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MF-Tyre/MF-Swift
Copyright TNO, 2013
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Magic Formula
Notion: the base tyre characteristics Fx=f(κ), Fy=f(α) and Mz=f(α) have a
sinusoidal shape, with a “stretched” horizontal axis for large values of slip
This consideration is the basis for a tyre model known as “Magic Formula ”
Some notes:
First versions developed by Egbert Bakker (Volvo) and prof. Pacejka (TU
Delft, TNO)
MF-Tyre software developed and distributed by TNO since 1996
Probably the most popular tyre model for vehicle handling simulations
(worldwide!)
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Copyright TNO, 2013
Base Magic Formula
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Note:
• C determines the limit value when x→∞
• BCD determines the slope near the origin
• B, E & C determine the location of the peak
H
f
x
F
D
SV
S
arctan(BCD) X
X : input, e.g.α or κF : output, e.g.F or Fxy
D : peak factor
C : shape factor
B : stiffness factor
E : curvature factor
SH,V : hor./vert. shift
f = D sin[ C arctan Bx – E( Bx – arctan(Bx) ) ]
F(x) = f(x) + SV
x = X + SH
f∞
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MF-Tyre/MF-Swift
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Stretching the sine…
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parameters in this example:
B=8, C=1.5, D=5500, E=-2
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Example: pure longitudinal slip characteristics
where:
note:
• Kx = Cfκ: longitudinal slip stiffness
• Bx is calculated from Cx, Dx and Kx
• equations simplified for educational reasons…
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• coefficients p are determined in curve fitting process
• scaling coefficients λ:• equal 1 during fitting
process• may be used to adjust
tyre characteristics• vertical load increment:
• Fz0 is nominal load0
0
z
zzz F
FFdf
−=
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MF-Tyre/MF-Swift
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Example: pure longitudinal slip characteristics
result after fitting coefficients: ⇒
data reduction:
495 measurement points ⇒ 11 coefficients
interpolation/extrapolation (load, braking/driving):
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Copyright TNO, 2013
Magic Formula
Similar equations exist for Fx, Fy, Mx, My and Mz
Combined slip: reduction of Fx and Fy by applying a
weighting function G to the ‘pure’ characteristics
Example:
In total 144 parameters that are curve fitted
using an automated process;
typical fit errors of a few percent
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0xxx FGF ⋅= α
Fz
Fx
Fy
Mx
My
Mz
κ
pi
Vx
ϕt
α
γ
vertical force
longitudinal slip
side slip angle
inclination angle
forward velocity
inflation pressure
longitudinal force
lateral force
overturning moment
rolling resistance moment
self aligning moment
turn slip
MagicFormula
parameters: general (4), Fx (29), Fy (50), Mx (15), My (8), Mz (38)
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MF-Tyre/MF-Swift
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3. Tyre transients / relaxation length properties
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Tyre transients
Measure step response to
side slip angle
Procedure:
1. Apply steering angle of 1 deg.
2. Load the tyre
3. Start rolling the track at low
velocity (e.g. 0.05 m/s)
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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MF-Tyre/MF-Swift
Copyright TNO, 2013
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Tyre transients
• Tyre cannot instantaneously react to changes in slip
• Travelled distance required to build up forces
• Relaxation effects exist for all modes of slip
This is due to:
1. carcass compliance
2. finite contact length
In MF-Swift both are considered:
1. carcass stiffness → springs
2. contact patch slip model
(Magic Formula (MF) slip model and
contact patch transients)
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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*V_
α*
belt
wheel plane
ϕ*
ϕ γ
αV_
c
C
ψ.-
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Simplified example carcass stiffness
• Assume linear tyre model for small slip angles:
• Create dynamic tyre model by accounting for tyre sidewall stiffness:
• Dynamic side slip angle:
• Introducing the relaxation length σ (=C/k) and V≈u:
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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αCFy =
uv−=α
εα kCFy =′= . .εα kC =′
.
u
v εα +−=′
.ααασ =′+′
V α ′= CFy
ααα =−=+′u
v
uk
C&
1 ′contact patch
wheel plane
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MF-Tyre/MF-Swift
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Simplified example carcass stiffness
• First order dynamics between lateral force and side slip angle input, transfer
function:
• Relaxation length σ does not depend on forward velocity V:
• response time reduces when increasing V;
• travelled distance required to build up the lateral force remains the same.
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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1)(,
+=
sV
CsH
yF σα time constant:
Vσ
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Simplified example carcass stiffness
step response (α = 1 deg, C = 1000 N/deg, σ = 0.5 m)
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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MF-Tyre/MF-Swift
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Tyre relaxation effects
• Experiments show that relaxation length
depends on:
• vertical load Fz
• slip level
• inflation pressure
• Thus also relaxation effects when Fz is
changed at e.g. constant side slip
Modelling
Slip and vertical load dependency can be
included by using nonlinear slip characteristics
(MF) and load and inflation pressure
dependent carcass stiffness
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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processed measurements:relaxation lengths σ
αfrom
small changes in side slip angle (∆α = 0.5°)
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Contact patch slip model
• For shorter wavelengths λ (0.1 < λ < 5 m) of e.g. side slip, the finite length of
the contact patch needs to be considered
• Important for aligning torque response to sideslip and for turn slip
MF-Swift contact patch slip model:
• Contact patch has stiffness (stiffness of tread elements)
• From physical brush model derived differential equations for contact patch
transients (relaxation lengths depend on slip and tread stiffness)
• Nonlinear slip characteristics from Magic Formula model
(basically the brush model slip characteristics are replaced by the more
accurate Magic Formula characteristics)
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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MF-Tyre/MF-Swift
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Contact patch slip model
In total 7 nonlinear 1st-order differential equations (derived from brush model):
• one 1st-order differential equation for κc’
• two 1st-order differential equations for αc’ and αt’
• four 1st-order differential equations for ϕc’
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κc’, αc’, αt’, ϕc’inputs into
Magic Formula
s
Fy
s0
0s
Fx
s0
0
κ α
s
-Mz
s0
0
α
s
Fy
s0
0
ϕ
s
Mz
s0
0
ϕ
κ α ϕcontact patch step responses
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Contact patch slip model
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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carcass forces, moments
contactpatchdynamics
slip forces and moments
first-ordercontacttransientslipequations
deflection angle
transient slipquantities
tyre carcass compliance
MagicFormula
-βst
+
αc
contact patchslip quantitiesκ
c
α'
κ'c
F
My
z
Fx
-βα
Fy
αc
V
-Mz
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MF-Tyre/MF-Swift
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Wheel load oscillations at constant side slip
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V = 0.6 m/sα = 5oFzo= 4000N Fzv= 2000NF = F +F sin(2π s/λ)zvzoz
0.2 0.4 0.6 0.8 12
3
4
5
6
[kN]
00.2 0.4 0.6 0.8 10
150
[Nm]
100
50
0
test
2
3
4
5
6
[kN]
150
Fy -Mz
yF -Mz
[Nm]
100
50
0
model
s/λ s/λ
moment
1.20.60.3
2.4m
λ =side force
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4. Inclusion of belt dynamics
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MF-Tyre/MF-Swift
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MF-Swift: inclusion of belt dynamics
• First mode shapes are rigid belt vibrational modes
• Below about 100 Hz we can suffice considering these modes
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Rigid ring / tread band
Road surface (flat)
Sidewall stiffness &damping (6 DOF)
Rim
Residualstiffness &damping
Magic Formulaslip model
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Residual stiffness
Residual stiffness elements ( ccz, ccy, ccΨ, ccx) between belt and contact patch
• assure correct overall tyre stiffness resulting in correct loaded radius vs.
vertical force and correct relaxation lengths
• describe the effects of the modes that lie above the maximum frequency of
interest (high-frequency modes, i.e. non rigid belt modes)
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vertical
ccz
beltrim
-zcr
ccx
belt
xcr
Msx
Fsy FsxMsy
FNMsz
rim
tangentiallateral and yaw
ycr
ψcr
ccyccψ
belt
wheelplane
contactpatch
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MF-Tyre/MF-Swift
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In-plane modes and natural frequencies
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vertical 80Hzin-phase 33Hz anti-phase 76Hz longitudinal 100Hz
longitudinal 74Hzrotational 0Hz vertical 74Hz torsional 78Hz
free
loaded
featured by model at stand-stillafter having fitted parameters from tests on loaded and rolling tyre
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Out-of-plane modes and natural frequencies
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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yaw 46Hz camber 46Hz
free
loaded
lateral 42Hz
camber 44Hz yaw 46Hz lateral 103Hz
featured by model at stand-stillafter having fitted parameters from tests on loaded and rolling tyre
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MF-Tyre/MF-Swift
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Validation: dynamic braking
longitudinal force response
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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0 20 40 60 80 100 0 20 40 60 80 100
200
0
180
0
-180
90
-90
0
180
0
-180
90
-90
30belt
dynamicsslip stiffness
relaxation length
experimentmodel
V = 25 km/hFz = 4000 N
Fxκ
Fx
MB
[1/m] [N]
n [Hz] n [Hz]
to brake torque variations to wheel slip variations
φ φ
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Validation: yaw oscillation
side force and moment
response to yaw
oscillations at
different speeds
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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100 101
105
106
104
Frequency [Hz]100 101
Frequency [Hz]
102
103
104
105
106
amplitude ratio F ψy amplitude ratio M ψz
V = 110 km/h
V = 20 km/h
V = 110 km/h
V = 20 km/h
ExperimentSimulation
Note: splitting of single peak at low velocity into two peaks (camber and yaw mode) due to gyroscopic action
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MF-Tyre/MF-Swift
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Validation: yaw oscillation
side force and moment response to yaw
oscillations at different speeds
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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experiments
φ ψF
[ ]o
Fyψ
φ ψM
Mzψ
106
105
104
180
90
0
-90
-180
106
104
102
180
90
0
-90
-180
Nrad
Nmrad
100 101 100 101n [Hz] n [Hz]
[ ]o
side force moment
φ ψF
[ ]o
Fyψ
φ ψM
Mzψ
106
105
104
180
90
0
-90
-180
106
104
102
180
90
0
-90
-180
Nrad
Nmrad
100 101 100 101n [Hz] n [Hz]
[ ]o
side force moment
simulations
25 km/h59 km/h92 km/h
V =xα = 0o
Note: splitting of single peak at low velocity into two peaks (camber and yaw mode) due to gyroscopic action
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Validation: yaw oscillation
side force and moment response to yaw
oscillations at different slip angles
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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V =59km/hx
φ ψF
[ ]o
Fyψ
φ ψM
Mzψ
106
105
104
180
90
0
-90
-180
106
104
102
180
90
0
-90
-180
Nrad
Nmrad
100 101 100 101n [Hz] n [Hz]
[ ]o
side force moment
φ ψF
[ ]o
Fyψ
φ ψM
Mzψ
106
105
104
180
90
0
-90
-180
106
104
102
180
90
0
-90
-180
Nrad
Nmrad
100 101 100 101n [Hz] n [Hz]
[ ]o
side force moment
0
31
5
oooo
α = 0
experiments simulations
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MF-Tyre/MF-Swift
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Validation: step changes in brake pressure
responses to
successive step
changes in brake
pressure versus time
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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[rad/s]
20
23
22
21
0
1000
2000
3000simulation
time [s] time [s]0 2.5 0 2.5
simulation
experiment
0 20
23
22
21
20
Ω
experiment
[N]
-Fx
zF xV= 4000N, = 25km/h
brake force wheel speed of rev.
Note:• steps in brake pressure
up to wheel lock; then brake released
• vibrations (about 28 Hz) attributed to the in-phase rotational mode of the system with the brake and axle inertia included
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Validation: step changes in brake pressure
responses to successive step changes in brake pressure versus longitudinal
wheel slip
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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experimentsimulation
0 2 4 6-κ [%] 8 10
3000
2000
1000
012
[N]
-Fx
brake force
wheel slip
zF xV= 4000N, = 25km/h
Note:• similarity with longitudinal slip characteristics• maximum friction in experiment earlier reached
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MF-Tyre/MF-Swift
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Validation: step changes in steering angle
side force response to
successive step changes in
steer angle versus time
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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[N]
4000
3000
1000
0
Fyexperiment
z =3700N, =25km/hF xV
2000
[N]
4000
3000
1000
0
Fy
2000simulation
=0ψ
1
2
3
45
6 7 8
o
o
o
o
oo o o
0 1 2 3 4time [s]
1 2 3 4time [s]0
o
sideforce
Note:• vibrations attributed to
yaw/camber mode with frequency of about 40 Hz
• decrease overall relaxation length at larger sideslip angles
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Validation: step changes in steering angle
aligning moment response to
successive step changes in steer
angle versus time
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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0
[Nm]
200
100
0
-100
-200
-Mz
0 1 2 3 4time [s]
1 2 3 4time [s]
[Nm]
200
100
0
-100
-200
-Mz
simulationmoment
experiment
z =3700N, =25km/hF xV
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MF-Tyre/MF-Swift
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5. Tyre rolling over uneven road surface
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Summarising
So far:
excitation of the tyre via axle motions or braking/steering on a flat road
surface
Next:
tyre dynamics can also be excited via the road;
for short wavelength unevenness (e.g. short obstacles/cleats) the tyre
enveloping behaviour is important:
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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MF-Tyre/MF-Swift
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Enveloping example: rolling over short obstacle
Constant axle height experiment
Three distinct responses:
• variations in vertical force
• variations in longitudinal force
• variations in wheel spin velocity
Note:
• tyre touches obstacle before and after
wheel centre is above the obstacle!
• shape of the response is totally
different from obstacle shape
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Phenomena enveloping behaviour
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lengtheningresponse
swallowingobstacles
filtered responseat axle
road profile
filteringunevenness
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MF-Tyre/MF-Swift
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The effective road surface
Assumptions
• The tyre contact zone, where the large deformations due to envelopment of
the unevenness occur, dynamically deforms mainly in the same way as it
does quasi-statically
• Local dynamic effects can be neglected
• Rigid ring model takes care of the tyre dynamics
Approach
• A special road filter has been developed to take care of the enveloping
properties
• This filtered road surface is called the effective road surface
• Instead of the actual road surface, this effective road surface is the input of
the rigid ring model
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Copyright TNO, 2013
The effective road surface
The concept of the effective road surface
is that for each axle position an
effective road plane can be defined the position
and orientation of which is governed by the
resulting tyre force.
Definition
• Vertical position w of eff. road plane
varies according to vertical axle movement zaxle
at constant vertical load FV.
• Slopes βy (and βx for 3D) of the eff. road plane
according to orientation of the resulting tyre force
FN when moving over frictionless surface (µ = 0).
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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w FN
β y
FV
2-D
= ∆ zaxle
constant
z axle
FH
µ = 0
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MF-Tyre/MF-Swift
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Tandem-cam enveloping model
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cam
cam
ls
wheelcentre
w-βy
F
cam
cam
ls
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3D Tandem-cam enveloping model
Four effective road input quantities
Road curvature dβy /dx used for extra variation of the eff. rolling radius
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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−βx−βy
w
z
xy
xβd
d+ y
ISO
contact patch width
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MF-Tyre/MF-Swift
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3D Tandem-cam enveloping model
For higher accuracy on short obstacles one might introduce:
• for w and βy:
• more parallel
tandems
(multi-track)
• for βx:
• intermediate
cams at the
side edges
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'6x5' cams= 18 cams
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Example of validation result
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MF-Tyre/MF-Swift
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Example of validation result
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Low speed perpendicular and inclined cleat tests
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MF-Tyre/MF-Swift
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Copyright TNO, 2013
MF-Swift: 3D road unevenness
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Rigid ring (6 DOF)
Enveloping model with elliptical cams
Effective road plane
Sidewall stiffness& dampingRim
Residualstiffness &damping
Slip model
Cleat
ff
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Validation: various obstacle shapes
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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MF-Tyre/MF-Swift
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Validation:
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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-0.05 0 0.05 0.1 0.15 0.2 0.25-4000
-2000
0
2000
4000
∆Fz
[N]
0 50 100 1500
50
100
150
200
PS
D √
(SF
zFz)
-0.05 0 0.05 0.1 0.15 0.2 0.25-1
-0.5
0
0.5
1x 10
4
∆Fx
[N]
0 50 100 1500
100
200
300
400
500
PS
D √
(SFx
Fx)
-0.05 0 0.05 0.1 0.15 0.2 0.25-10
-5
0
5
10
Time [s]
∆Ω [r
ad/s
]
0 50 100 1500
0.2
0.4
0.6
0.8
Frequency [Hz]
PS
D √
(SΩ
Ω)
vertical mode
in-phase rotational mode
in-phase rotational mode
10 15
100 290 105mm 237 120 221 50
15 10
∆Fz
∆Fx
∆Ω
time [s] frequency [Hz]Fz0 = 4000 N, V = 39 km/h
simulationsmeasurements
Copyright TNO, 2013
Validation: Strip 10x50 mm, 34 °, Fz0 = 4 kN
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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measurement model
0 20 40 60 80 100 120 140 160 180 2000
0.05
0.1
0.15
0.2
Frequency [Hz]
√(S
ΩΩ
)
-0.05 0 0.05 0.1 0.15 0.2 -4
-2
0
2
4
Time [s]
Ω [
rad/s
]
0 20 40 60 80 100 120 140 160 180 2000
50
100
150
√(S
KxK
x)
-0.05 0 0.05 0.1 0.15 0.2 -4000
-2000
0
2000
4000
∆ Kx [
N]
0 20 40 60 80 100 120 140 160 180 2000
10
20
30
40
√(S
KzK
z)
-0.05 0 0.05 0.1 0.15 0.2 -500
0
500
1000
1500
∆ Kz
[N]
∆Fz
∆Fx
∆Ω
rotational mode
rotational mode
Vdrum= 39 km/h
time [s] frequency [Hz]
30
MF-Tyre/MF-Swift
Copyright TNO, 2013
Copyright TNO, 2013
Validation: Strip 10x50 mm, 34 °, Fz0 = 4 kN
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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measurement model
0 20 40 60 80 100 120 140 160 180 2000
2
4
6
Frequency [Hz]
√(S
TxT
x)
-0.05 0 0.05 0.1 0.15 0.2 -100
-50
0
50
100
Time [s]
∆ Tx [
Nm
]
0 20 40 60 80 100 120 140 160 180 2000
1
2
3
√(S
TzT
z)
-0.05 0 0.05 0.1 0.15 0.2 -100
-50
0
50
100
∆ Tz
[Nm
]
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
√(S
KyK
y)
-0.05 0 0.05 0.1 0.15 0.2 -500
0
500
∆ Ky [
N]
camber mode
yaw mode
camber mode
camber
∆Fy
∆Mz
∆Mx
time [s] frequency [Hz]
Copyright TNO, 2013
Validation: running over pothole while braking
constant axle height
constant speed
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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free rolling medium brake torque
large brake torque
-4
-3
-1
0
1
2
3
0.0 0.20.1 0.0 0.20.1 0.0 0.20.1time [s]
[kN]
∆FX
-2
500mm15mm
F = 4000NVo
V = 35km/h
measurements simulations
31
MF-Tyre/MF-Swift
Copyright TNO, 2013
Copyright TNO, 2013
Road load simulation example
Durability load calculation at Nissan, Japan
SAE paper 2011-01-0190
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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OpenCRG file4x4 mm grid sizebinary, 273 MB
Adams modelflexible bodyrigid suspensionMF-Swift 6.1.2
durability roaddigitised 4x4 mm grid9.7 GB
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Road load simulation example
Validation: front left shock absorber force
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MF-Tyre/MF-Swift
Copyright TNO, 2013
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Road load simulation example
Validation: lower link ball joint forces
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6. Model usage and availability
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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33
MF-Tyre/MF-Swift
Copyright TNO, 2013
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Using the tyre model
Tyre model parameters
Tyre property file (*.tir)
Result of MF-Tool
Road surface definition
Road data file (*.rdf, *.crg)
Select model complexity
Operating or use mode
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Copyright TNO, 2013
Complexity level of the model can be changed
The most complex model is not always needed (dynamics mode)
Within validity range simulation results are identical
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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< 1 Hz < 10 Hz, linear < 10 Hz, nonlinear < 60-100 Hz, nonlinear
massless tyre model tyre model includes mass of the belt
34
MF-Tyre/MF-Swift
Copyright TNO, 2013
Copyright TNO, 2013
Complexity level of the model can be changed
The most complex contact model is not always needed
• Depending on the wavelength of the obstacles/unevenness a contact method
can be selected
• For enveloping the number of contact points and cams can be chosen
• 2D/3D enveloping is generally combined with rigid ring dynamics because of
the high frequency excitation
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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single point 2D enveloping 3D enveloping
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Road definition
• Road definitions inside the tyre model
• predefined road profiles with limited set of parameters
(e.g. flat, plank, sine, polyline, drum + cleat)
• 3D measured road profiles (OpenCRG®)
• In many packages it is also possible to use the native road definition, coming
along with the simulation package.
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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OpenCRG® is on:http://www.opencrg.org
35
MF-Tyre/MF-Swift
Copyright TNO, 2013
Copyright TNO, 2013
Model availability
MF-Tyre/MF-Swift is available for all major simulation packages used in
vehicle dynamics
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Copyright TNO, 2013
7. Model parameterisation
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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MF-Tyre/MF-Swift
Copyright TNO, 2013
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Tire modelling toolchain
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measurement parameteridentification
simulation
cost $savings $
Virtual Prototyping
accumulating error determines accuracy
Copyright TNO, 2013
Measurement requirements
MF-Tyre can be parameterised using the following tests:
Geometry, mass and inertia measurements
Force and moment measurements (Magic Formula dataset)
Loaded radius and rolling radius measurements
Footprint measurements
Stiffness measurements
Additionally for MF-Swift
(enveloping and rigid ring components)
Cleat experiments
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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37
MF-Tyre/MF-Swift
Copyright TNO, 2013
Copyright TNO, 2013
Measurement requirements
Source:
German OEM
AK 3.5.1
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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geometrical data,stiffnesses,cleat tests, inertias
specific data forcomplex tire models. e.g. belt angle, cord stiffness ...
force & momentand transient tests
Copyright TNO, 2013
MF-Tool
Fitting of current and
historical tyre models
(including MF 5.2)
Database and
plotting functionality
Software is able to
make estimates
Available at all major
tyre manufacturers
Due to the model’s semi-empirical nature different aspects of the tyre
behaviour can be handled separately in (relatively) small optimisation steps
and represented with maximum accuracy
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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MF-Tyre/MF-Swift
Copyright TNO, 2013
Copyright TNO, 2013
8. Concluding remarks
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
75
Copyright TNO, 2013
Concluding remarks
The TNO Delft-Tyre toolchain (MF-Tyre/MF-Swift and MF-Tool) offers a
versatile, high quality and cost efficient solution for tyre modelling:
MF-Tyre leading Magic Formula implementation and unique features
MF-Swift extension of MF-Tyre (rigid ring, enveloping, turn slip)
MF-Tool provides independent parameter identification possibilities
MF-Tyre/MF-Swift is one model for many applications
implementations for all main simulation packages
little measurements required
computationally efficient
MF-Tyre (Magic Formula) part is free of charge for many packages
TNO provides parameter identification, training and consultancy
well validated and open/accessible theory (many scientific publications)
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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MF-Tyre/MF-Swift
Copyright TNO, 2013
Copyright TNO, 2013
Roles & responsibilities and contact information
• Model development is done by TNO (large independent research and
technology organisation in The Netherlands)
• Worldwide sales and distribution of Delft-Tyre products (MF-Tyre/MF-Swift
and MF-Tool) is done by TASS (TNO Automotive Safety Solutions), which is a
TNO subsidiary
Website:
http://www.tassinternational.com/delft-tyre
TNO, Delft-Tyre, P.O. Box 756, Helmond, The Netherlands
Willem Versteden (product manager) [email protected]
Dr. Antoine Schmeitz (technical leader) [email protected]
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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Copyright TNO, 2013
Further reading
MF-Swift theory extensively described in book:
Hans Pacejka , Tire and Vehicle Dynamics ,
third edition, Butterworth-Heinemann, 2012
Dr. Antoine SchmeitzMF-Tyre/MF-Swift
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