Implementation of the Rigid Ring Tyre Model and Accompanying Soil Model in a Complete Vehicle

82 Pages·2016·8.38 MB·English

Implementation of the Rigid Ring Tyre
Model and Accompanying Soil Model in a
Complete Vehicle Simulation Tool for
Trucks
Master’s thesis in Applied Mechanics
ALBIN BRANTIN
´
OSCAR GRUNDEN
Department of Applied Mechanics
CHALMERS UNIVERSITY OF TECHNOLOGY
G¨oteborg, Sweden 2016

MASTER’S THESIS IN APPLIED MECHANICS
Implementation of the Rigid Ring Tyre Model and Accompanying Soil Model
in a Complete Vehicle Simulation Tool for Trucks
ALBIN BRANTIN
OSCAR GRUNDE´N
Department of Applied Mechanics
Vehicle Dynamics
CHALMERS UNIVERSITY OF TECHNOLOGY
G¨oteborg, Sweden 2016
Implementation of the Rigid Ring Tyre Model and Accompanying Soil Model in a Complete Vehicle
Simulation Tool for Trucks
ALBIN BRANTIN
OSCAR GRUNDE´N
(cid:13)c ALBIN BRANTIN, OSCAR GRUNDE´N, 2016
Master’s thesis 2016:58
ISSN 1652-8557
Department of Applied Mechanics
Vehicle Dynamics
Chalmers University of Technology
SE-412 96 G¨oteborg
Sweden
Telephone: [phone]
Examiner: Bengt Jacobson
Supervisors: Artem Kusachov, Fredrik ijer
Cover:
A representation of the wheel plane and out of plane rigid ring model with soil model included.
Chalmers Reproservice
Go¨teborg, Sweden 2016
Implementation of the Rigid Ring Tyre Model and Accompanying Soil Model in a Complete Vehicle
Simulation Tool for Trucks
Master’s thesis in Applied Mechanics
ALBIN BRANTIN
OSCAR GRUNDE´N
Department of Applied Mechanics
Vehicle Dynamics
Chalmers University of Technology
Abstract
Volvo got a library of Virtual Transport Models of their trucks (VTM). These models cannot simulate
soft soil roads due to the currently implemented tyre model. A new tyre/soil model is being developed
in conjunction with the University of Ontario Institute of Technology, which is to be implemented to
work with the models in the VTM library.
The university model the tyre and soil using finite element method (FEM) and smoothed particle
hydrodynamics (SPH), which is too computationally demanding to implement in VTM. The model
that was to be implemented was instead a simplification comprising of springs, dampers and masses.
The parameters of these elements are estimated from different FE-simulations done by the university.
Once the tyre model is implemented it will be verified against the FE-model by comparing simulation
results. In addition, the model will be compared to the currently implemented model to ensure an
overall similarity between the models.
The overall results shows promise in the new tyre model. All of the single tyre simulations have given
satisfactory results after some of the parameters were corrected. The soil model is however not able
to completely capture the results of the FE-simulations but is considered acceptable. The full vehicle
model has given good results even though the vertical soil model and the rolling resistance in the soil
needs further investigation to capture an even more realistic dynamic response.
The rigid ring model on rigid ground is deemed to work properly and gives good results. The soil
model has given acceptable results but it does not capture the full soil behaviour. Additionally the
soil model has been non-physically altered to get good results. This warrants further studying of the
model and its parameters in order to further refine the model. The rolling resistance in the soil also
needs further investigation since the model is crude and uncertain. The implemented tyre model
requires the same order of magnitude in simulation time as the original magic formula rigid ground
model.
Keywords: Rigid Ring Tyre Model, Soft Soil Model, Tyre Modeling, Vehicle Dynamics
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Preface
This project acts as a continuation of an ongoing collaboration between Volvo Trucks, the University
of Ontario Institute of Technology and the Pennsylvania State University. Volvo wants to implement
a new tyre model into their full vehicle dynamic simulator, VTM. By adopting this tyre model into
VTM the same tyre model will be used as in their FEM tool. In addition a soil model compatible
with this model will be investigated and implemented.
Acknowledgements
We want to give a huge thank you to our supervisor, at Volvo GTT, Fredrik O¨ijer who has helped us
tremendously throughout the project. We would also like to thank Sachin Janardhanan and Inge
Johansson and all the other people at the Chassis Strategy and Vehicle Analysis department at Volvo
GTT who has been very helpful. Finally we would like to thank our examiner, Bengt Jacobson, and
our supervisor, at Chalmers, Artem Kusachov, for their help in this project.
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Nomenclature
SI-units and radians are used.
C(v ) slope compensation factor [∼]
x
ca first slope compensation constant [1/(m/s)cb]
c second slope compensation constant [∼]
b
c third slope compensation constant [∼]
c
c lateral tyre stiffness [N/rad]
l
c longitudinal sidewall damping
bx
c lateral sidewall damping
by
c vertical sidewall damping
bz
c wheel plane rotational damping of the sidewall
bθ
c out of plane rotational damping of the sidewall
bγ
c vertical soil damping
soil
c(cid:48) equivalent vertical soil damping
soil
c(cid:48) approximate equivalent damping of the soil
soil,app
c total vertical damping of the tyre
tot
c vertical residual damping
vr
F bulldozing resistance force
B
F rolling resistance force
r
F rut rolling resistance force
R
F longitudinal slip force
sx
F lateral slip force
sy
F longitudinal force acting on tyre belt
wx
F lateral force acting on tyre belt
wy
F longitudinal force acting on wheel rim
x
F longitudinal slip force saturation for rigid ground
x,max
F longitudinal slip force saturation for soft soil ground
x,max,soil
F lateral force acting on wheel rim
y
F lateral slip force saturation for rigid ground
y,max
F vertical force acting on wheel rim
z
F static load
z0
I wheel plane rotational inertia of wheel rim, with or without inertia of wheel axle
1y
I out of plane rotational inertia of tyre belt
2x
I wheel plane rotational inertia of tyre belt
2y
k lateral tyre tread stiffness
l
k longitudinal sidewall stiffness
bx
k lateral sidewall stiffness
by
k vertical sidewall stiffness
bz
k out of plane rotational stiffness of the sidewall
bγ
k wheel plane rotational stiffness of the sidewall
bθ
k longitudinal tyre tread stiffness
cx
k cornering stiffness
f
k longitudinal tyre stiffness
k
v
k vertical soil stiffness
soil
k(cid:48) equivalent vertical component of soil stiffness
soil
k additional vertical soil stiffness
soil,2
k total vertical stiffness of the tyre
tot
k vertical residual stiffness
vr
M driving moment
in
M reaction moment acting on wheel rim
y,r
M reaction moment acting on tyre belt
y,b
M moment used as output from the model
y,out
m tyre rim mass, with or without wheel axle mass
1
m tyre belt mass
2
m fictive mass of the soil
soil
m fictive mass of soil + mass of tyre
tot,soil
R undeformed tyre radius
0
R effective radius
e
rrc rolling resistance coefficient [∼]
r first rolling resistance constant [∼]
a
r second rolling resistance constant [∼]
b
r third rolling resistance constant [∼]
c
u tyre tread deformation
x
u˙ tyre tread deformation speed
x
V velocity at the contact point
c
v longitudinal velocity of wheel rim
x
v lateral velocity of wheel rim
y
v vertical velocity of wheel rim
z
x longitudinal position of wheel rim
1
x longitudinal position of where the sidewall meets the tyre tread
2
y lateral position of wheel rim
1
y lateral position of where the sidewall meets the tyre tread
2
z vertical position of wheel rim
1
z vertical position of where the sidewall meets the tyre tread
2
z vertical position of tyre/soil interaction point
3
z vertical position of the road
r
α longitudinal slip [∼]
x
α lateral slip [rad]
y
β average local slope angle
β(cid:48) equivalent local slope angle
γ out of plane angle of tyre belt
2
δ logarithmic decrement of oscillations [∼]
ζ dimensionless damping constant [∼]
θ wheel plane angle of wheel rim
1
θ wheel plane angle of tyre belt
2
σ relaxation length of tyre
ϕ lateral road slope
x
ϕ longitudinal road slope
y
ω tyre frequency, soil frequency
ω nominal frequency
0
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