Modelling and simulation of mechanical systems with displacement limitations

Abstract: Systems with displacement limitations have an abrupt change in the characteristics of the system for a certain displacement. This type of event often occurs in engineering applications and it is of importance to find out how this sudden contact can influence the behaviour of the system. The dynamic behaviour of an impact oscillator with initial clearance is studied both experimentally and theoretically. It is observed that the experimental system obtains very complex behaviour with subharmonic and chaotic response. The behaviour is found to be very sensitive to changes in parameter values. It is also shown that this complex behaviour can be predicted by a simple mathematical model of the system. It is shown that specific geometric features in numerically obtained chaotic attractors of impacting systems can also be found in experimentally obtained attractors. As a consequence, these features provide a diagnostic tool for impact studies. The modelling and simulation of two engineering systems with displacement limitations, a front wheel suspension and an overhead power system, are also presented. Three non-linear models of a front wheel suspension are derived and compared to each other. The models are derived according to physical parameter values of the MacPherson strut wheel suspension of a car (SAAB 9000). The most appropriate model is further studied with respect to nonlinear effects. An overhead power system with contact breaking is also modelled and the behaviour of the model is studied. The model has three degrees of freedom and includes specifications of impact conditions between the pantograph head and contact wire, lateral movement of the wire due to the zigzag span, and friction between the pantograph head and the contact wire. For the problems investigated, different geometric representations of the motion, such as time histories, phase plane portraits, Poincaré sections, bifurcation diagrams and cellmappings are used to visualise the behaviour of the studied systems. The representations used depend on the type of behaviour that is occurring. It is also shown how to make animations of the system behaviour using a standard MCAEsystem. The geometric representations of a single coordinate and animation of the complete system is an excellent combination when trying to get an understanding of the behaviour of the system under investigation. In order to make it a realistic possibility for an engineer to use the methodology presented in this work, these tools must be integrated in a user friendly computer environment where data created in one application can easily be used in another application. The design environment should be independent of software suppliers and it should be easy to add new methods and new tools whenever necessary. A prototype of an integrated design environment for mechanical systems is developed. A specification of a relational database structure for mechanical systems is defined and implemented in a practical software environment. The database is accessible to multiple engineering application programs and supports a flexible environment for the continuing development of new applications.