Copyright © Transportation Systems
Chania, Greece, 1997
MULTI-BODY SIMULATION SOFTWARE IN THE
ANALYSIS OF MOTORCYCLE DYNAMICS
Mahbub Gani * David Limebeer ** Robin Sharp ***
* CPSE, Imperial College, London SW7 2BY, UK
** CPSE, Imperial College, London SW7 2BY, UK
*** SME, Cranfield University, Bedford MK43 OAL, UK
Abstract: A linear, straight running model of a motorcycle is developed using multi-
body simulation software. The stability properties as a function of forward speed
obtained from this model exactly match well established results found by (Sharp
1994b) , which validates the linearised equations of motion derived by the software.
This model is used to obtain time response data and FFT analysis identified the same
dominant eigenvalues found from the linear model. The counter-steering phenomenon
is then predicted using the computer generated system. Finally an enhanced model
is used to study the stability properties of a motorcycle under constant acceleration
and deceleration.
Keywords: Simulation, Linear analysis, Vehicle dynamics, Modelling, Software tools
1. INTRODUCTION
Motorcycles are elaborate mechanical systems,
comprising a number of masses, each with sev-
eral degrees of freedom and complex coupling
geometry. The task of deriving the equations of
motion of such a system proves to be time con-
suming and prone to errors for the dynamicist.
The straight running properties of motorcycles
have been extensively studied by several authors.
The most complete account has been presented
by (Sharp 1994b), where a sophisticated model
including frame flexibilities, tyre forces, tyre mo-
ments and aerodynamic forces is used to predict
the eigenvalues of the motorcycle. In contrast,
modes of operation of greater complexity, such
as certain cornering and acceleration phenomena,
have not been studied so thoroughly because the
use of manual methods to analyse such cases be-
comes quite impractical. When studying straight
running behaviour, one can decouple the pitch-
plane motion from the lateral motion and anal-
yse them independently; even so, the linearised
equations of motion take several pages to write
down. However, if one wishes to study cornering
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behaviour, for instance, one has to take account
of the many coupling terms arising from interac-
tions between in-plane and out-of-plane motions.
Tyre forces and moment descriptions also become
more elaborate. This makes the process of deriving
the equations of motion laborious and subject to
error. This means that we do not have a means
of predicting the motion of motorcycles analyti-
cally under the many circumstances that arise as
thousands of riders take to the road . This has a
bearing on questions of the safety of motorcyclists,
particularly for the police, who frequently need
to travel at high speeds and employ advanced
maneuvering techniques. Sharp has reported sev-
eral accidents that have occurred as a result. of
loss of rider control, apparently as the relevant
motorcycle entered a lightly damped oscillatory
region in the eigenspace (Sharp 1992). In industry,
the complexity involved in modelling motorcycles,
has lead to the continuing use of rules of thumb
to design and manufacture the machines, which
prejudices the product improvement.
The recent development of multi-body simulation
software gives the analyst the opportunity to au-