4569846498

192 Multibody Systems Approach to Vehicle Dynamics
EIG0000003 Mode 1 Frequency 1.1943 (Hz)
EIG0000003 Mode 2 Frequency 11.1645 (Hz)
Fig. 4.57 MSC.ADAMS prediction of the modes of vibration of the simplified
quarter vehicle model
An MSC.ADAMS model consisting exactly of the model as sketched
above can be used to calculate undamped linear modes in a more exact
fashion, giving two modes of vibration as might be expected but slightly
differing numerical results.
The modal solution uses the ADAMS/Linear product, which in turn uses
numerical perturbation methods to estimate mass and stiffness matrices
about an operating point before solving for eigenvalues in the normal fashion.
For purely mechanical systems such as the one modelled it can be
relied upon to give good quality results. However, for systems where forces
are time dependent and are modelled in specific ways (e.g. as differential
equations for modelling turbocharger behaviour as described in Chapter 6,
or tyre relaxation length modelling) then the results are not necessarily
reliable at the time of writing and must be examined on an individual basis
before confidence is placed in them. MSC.ADAMS and other software
packages are subject to ongoing modification and development and so
functionality of this nature should be evaluated periodically; such evaluations
should be part of the software commissioning process within individual
organizations, particularly if critical decisions are to be based on
software output.
The estimates given above are a simplification of the real analytical solution
to the system. Such a solution is obtained using the equations of
motion taking x b and x t in this example to represent the vertical displacements
of the body and tyre respectively. The equations are written by
inspection thus:
mx˙˙ k( x) k ( x x)
(4.72)
t t t t b b t
mx˙˙ k( xx)
b b b t b
These can be arranged more conveniently as:
mx˙˙ x( k k ) x ( k )
t t t t b b b
mx˙˙ x( k) x(
k)
b b t b b b
(4.73)
(4.74)
(4.75)