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Special Issue Modeling, Analysis and Control Methods for Improving Vehicle 1
Dynamic Behavior
Modeling, Analysis and Control Methods for Improving Vehicle
Review Dynamic Behavior (Overview)
Toshimichi Takahashi
Abstract
So-called vehicle dynamics (or controllability behavior, the vehicle dynamics control and state
and stability) refer to the "running, cornering and estimation, and the analysis of driver-vehicle
stopping" of automobiles, which are the most system, are briefly summarized. Also, the
important and basic performance of automobiles. purpose and background of these studies are
Therefore, many studies have been undertaken mentioned. Moreover, a brief introduction to the
from several points of view all over the world. In three technical papers included in this special
this paper, our former studies, which focused on issue is presented.
the analysis and modeling of vehicle and tire
Keywords Vehicle dynamics, Modeling, Simulation, Control system, State estimation, Tire model,
Optimum control, Driver-vehicle system
R&D Review of Toyota CRDL Vol. 38 No. 4
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1. Introduction Chapter 5.
Among the many points of view and stages in Finally, the purpose and outline of the three
research and development in the vehicle dynamics technical papers included in this special issue are
field, we have been studying fundamental subjects briefly explained.
focusing on the following concepts and purposes, 2. Tire modeling
mainly in the three following categories for In addition to the analysis and modeling of tire
improving vehicle dynamic behavior and safety. 1, 2)
Here, it should be also noted that the "tire" is one of transient properties, we have also been
the key factors influencing our research activities, developing a software system to model a tire steady
state characteristics using the so-called Magic
either directly or indirectly, because the tire plays an 3-5)
essential role in all aspects of vehicle behavior. This Formula which has frequently been employed in
paper provides a brief summary and background of vehicle dynamics simulation in recent years. The
our studies. The layout of this paper is as follows. goal is to describe the tire force and moment
(1) Analysis and modeling of vehicle and tire behavior properties very accurately over wide ranges of input
Considering the importance of the tire to vehicle variables including combined slip cases, this being
maneuvering, we have been studying and modeling very important to the analysis of vehicle dynamic
tire characteristics, especially from the viewpoint of behavior with multi-body dynamics simulation
developing accurate tire models for use in vehicle software like ADAMS or DADS, as well as by in-
simulation calculations. In Chapter 2, we house development.
summarize the models we have developed to To establish the Magic Formula (abbreviated to
describe the tire steady state characteristics. MF) tire model, the optimum values for many MF
In the analysis of vehicle dynamic behavior, the parameters and coefficients have to be decided by
using measured data for each tire. Figure 1 shows
road surface has been assumed to be flat and even in 7)
most cases, even though actual roads inevitably have the structure of our software system, which can
some undulations and unevenness. Our trial for handle the tire side force, the longitudinal force, and
analyzing the braking performance of a vehicle on the self aligning torque. The software was
uneven roads is briefly explained in Chapter 3. developed in a Matlab/Optimization toolbox
environment to support the use of a wide range of
(2) Vehicle dynamics control and state estimation 6, 7)
In recent years, various kinds of control systems tires and test facilities.
have been offered in vehicles on the market to Examples of established MF models are shown in
improve the vehicle dynamic behavior and safety. Figs. 2 and 3. These figures show that the models
The control algorithms of these systems and the state
estimation techniques, which estimate the state
variables of vehicle motion and tire characteristics FFllaa tt B Bee ltlt M M//CC TTrraaileile rr VVeehhiiclcle Me Measeasuurrememenentt . .. . . .
etc., are the key technologies used in the
development of all these control systems. Chapter 4 InIntteerfarfaccee a anndd PPrree--PPrroocceessssiinngg
discusses some of our former studies in this < < wwiitthh//wwiitthouthout CCoonnssttrraaiinened Cd Coondindittiioonnss > >
category. MMeaseasuurreded D Daattaa
OnOnee S Stteepp
(3) Analysis of driver-vehicle system MMFF Co Coeeffifficciieennttss IIddenenttiiffiicatcatiioonn
One of the most pressing and important problems CoCoeeffifficciieennttss MMFF Pu Purree S Slliipp Pa Parraammeetteerrss
facing automobile manufacturers is the reduction of IIddenenttiiffiicatcatiioonn
the number of traffic accidents while increasing PaParraammeetteerrss MMFF C Coommbbinineedd S Sllipip
< w< wiitthh//wwiitthouthout IIddeenntitiffiiccaatitioonn PaParraammeetteerrss
traffic safety. Given that almost accidents are CCoonnssttrraaiinened Cd Condiondittiiononss > >
caused by human-related factors, the study of driver-
vehicle closed-loop systems is extremely important.
Our recent study in this field is introduced in Fig. 1 Structure of tire model identification system.
R&D Review of Toyota CRDL Vol. 38 No. 4
3
identified by our system agree with the measured vehicle chassis elements on braking performance
data very well. Figure 2 shows the so-called have rarely been reported. Then, analytical and
friction circle or friction ellipse, and Fig. 3 shows experimental studies were performed, in which the
the braking force characteristics of a passenger braking performance of straight-running vehicles on
vehicle tire (PV tire) and a commercial vehicle tire uneven roads and the influence of chassis elements
8)
(CV tire) on ice road. From Fig. 3, we can see that on that performance were investigated.
there are rather large differences between the two For the analysis, a model for simulating of vehicle
kinds of tires, namely, the maximum braking force behavior was developed based on the half car model,
divided by the vertical load of the CV tire is smaller as shown in Fig. 4. The tire braking force
than that of the PV tire, and the decrease in the characteristics that depend on the vertical load and
braking force after the peak of the CV tire is much the wheel slip ratio were described by the Magic
larger than that of PV tire. These differences may be Formula explained in a former chapter. In the
caused by the difference in the inflation pressure, simulation, vehicle responses such as the
which relates to the vertical load distribution per unit deceleration of the vehicle, the stopping distance
area in the contact patch, and therefore a difference after braking and the tire vertical load can be
in the generation of water between the tire and the
icy road may be induced. In this case, the pressure
was set to 220 kPa for the PV tire and 705 kPa for 1500 Camber angle 0 deg
the CV tire. Plots : measurements
3. Braking performance on uneven roads ) 6 kN Curves : MF model
N1000
(
Although vehicle behavior during steering and/or e
c
r
braking has been studied very widely for many o 4 kN
ng F
years, most studies have assumed the road surface to i
k
a 500
be even and flat. The analysis of vehicle behavior r
B Vertical Load 2 kN
on uneven roads is thought to be very important,
however, when considering actual roads. On the
other hand, it seems that many studies of brake Slip Ratio
systems and their performance have been 00 0.2 0.4 0.6 0.8 11
undertaken, but that analyses of the influence of (a) Passenger vehicle tire : 195/65R15
5.0
6000 Vertical Load 5 kN Camber angle 0 deg
10 deg Camber angle 0 deg 4.0 Plots : measurements
Plots : measurements ) 40 kN Curves : MF model
N
) Curves : MF model k
N 4000 6 deg e (3.0
c
( r
e o
c 4 deg F
r g
n 26 kN
Fo i 2.0
e ak
d r
Si2000 Slip Angle 2 deg B
1.0
Vertical Load 14 kN
Braking Force (N) 0 deg Slip Ratio
0.00 0.2 0.4 0.6 0.8 1
0
0 2000 4000 6000 (b) Commercial vehicle tire : 11R22.5
Fig. 2 Combined slip characteristics on dry road Fig. 3 Pure braking force characteristics on ice road.
(Passenger vehicle tire : 195/65R15).
R&D Review of Toyota CRDL Vol. 38 No. 4
4
calculated, provided the vehicle initial speed, the (C) Harder suspension bush ( kxf = 330 kN/m,
time history of the brake fluid pressure and the c = 800 Nsec/m )
xf
longitudinal road profile are given as inputs. (D) Higher tire inflation pressure + Larger damping
Figure 5 shows the calculated and measured of shock absorber + harder suspension bush
values for the influence of the chassis elements' In Fig. 5, the difference in the stopping distance
characteristics on the braking performance, in which between each vehicle and the standard vehicle is
the parameters of the chassis elements were changed indicated as a ratio (%) relative to the stopping
from those of a standard vehicle (see Table 1) as distance of the standard vehicle both for calculated
shown below. and measured results. Positive values indicate a
(A) Higher tire inflation pressure ( k = 215 kN/m ) shorter stopping distance than the standard.
tf
(B) Higher tire inflation pressure + Larger damping Although some differences can be seen in the figure,
of shock absorber ( c = 1350 Nsec/m ) overall we can say that the tendency for the chassis
f
elements to influence the braking performance as
calculated agrees rather well with the experiments.
In addition, the influences of the longitudinal
8.0
6.0 Experiment
4.0 Calculation
2.0 (A)
0.0 (B) (C) (D)
ference Ratio of -2.0
Dif -4.0
Stopping Distance (%)
-6.0
Fig. 4 Vehicle model and symbol notation. Fig. 5 Comparison of stopping distance between
calculation and experiments.
Table 1 Parameter values of standard vehicle.
R&D Review of Toyota CRDL Vol. 38 No. 4
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