Modeling, Analysis and Estimation of Vehicle Systems
Ground vehicles are subject to random vibrations in the vertical direction due to stochastic guideway irregularities. The vertical motions of vehicles affect the ride comfort of passengers and goods as well as the ride safety. The ride comfort can be eval
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W. Scbieblen Univenity of Stuttprt, Stuttaart, FRG
ABSTRACT Ground tion
vehicles due
vehicles ride
are subject to random vibrations in the vertical direc-
to stochastic guideway irregularities. The vertical motions of affect
the ride comfort of passengers and goods as well as the
safety. The ride comfort can be evaluated from the accelerations of
the human body while the criterion on ride safety follows from the dynamic
wheel
requires itself
loading. a
and
differential methods,
A thorough dynamical analysis of vehicle vibrations
mathematical modeling of the guideway roughness, the vehicle the
sensation
of the human being. The resulting stochastic
equations may be analysed by spectral density or covariance
respectively.
However, it is often cumbersome and difficult to
obtain reliable information on the parameters of the total dynamical system. Therefore, parameter estimation methods have to be applied in vehicle dynamics for improved results.
W. Schiehlen et al. (eds.), Analysis and Estimation of Stochastic Mechanical Systems © Springer-Verlag Wien 1988
W. Schiehlen
244
1. INTRODUCTION The stochastic analysis of vehicle vibrations and their consequences to the ride characteristics requires an overall investigation of guideway roughness, vehicle dynamics and human response to vibration exposure. Moreover, have
the
to
parameters
of the guideway and vehicle equations of motion
be estimated from measurements resulting in the inverse problem
with respect to the analysis. Many
aspects of these problems have been treated in numerous publi-
cations, thods
see
are
Robson [1), Dinca [2) and Hedrick [3). Two fundamental me-
available
for
the
investigation of vehicle vibrations: the
spectral density analysis in the frequency domain and the covariance analysis sed
in the time domain. In these lectures both methods will be discusand
compared
from a general point of view.
A first comparison for
the most simple vehicle model has been presented in [4]. background
for
complex
vehicles
traveling
The theoretical
with constant speed can be
found in [5). First results of the parameter estimation using time domain methods
are
due
to
Kozin
and
Kozin
[6],
Wedig
[7]
and Ref. [8].
Applications to vehicle systems have been presented by Kallenbach [9] and ScMfer [ 10) .
2. MODELING OF VEHICLE SYSTEMS
and
The
primary
models
of vehicle systems refer to guideway roughness
the
vehicle components represented by the elements of multibody sy-
stems. 2.1 Excitation by Guideway Roughness The
guideway roughness results with respect to the four wheels of a
two-axle
vehicle in four random processes summarized in a 4xl-vector ex-
Vehicle Systems
245
citation process erl(s)) where
s
T
(1)
is the space coordinate of the longitudinal motion of the vehicle, Fig.l. Since the 2xl-vector process (s) of the rear axle is r only delayed by the axle distance !:J.s the 2xl-vector process ef(s) of ' the front axle is discussed in more detail.
e
en Ct>
erl (t)
Fig. 1 Numerous charact
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