The dynamics of the turning process of a thin-walled cylinder in manufacturing is modeled using flexible multibody system theory. The obtained model is time varying due to workpiece rotation and tool feed and retarded, due to repeated cutting of the same surface. Instabilities can occur due to these consecutive cuts that must be avoided in practical application because of the detrimental effects on workpiece, tool and possibly the machine. Neglecting the small feed, the stability of the resulting periodic system with time-delay can be analyzed using the semi-discretization method. The use of an adaptronic tool holder comprising actuators and sensors to improve the dynamic stability is then investigated. Different control concepts, two collocated and two model-based, are implemented in simulation and tuned to increase the domain of stable cutting. Cutting of a moderately thin workpiece exhibits instabilities mainly due to tool vibration. In this case, the stability boundary can be significantly improved. When the instability is due to workpiece vibration, the collocated concepts fail completely. Model based concepts can still obtain some improvements, but are sensitive to modeling errors in the coupling of workpiece and tool.
The synthesis problem for optimal control systems in the class of discrete controls is under consideration. The problem is investigated by reducing to a linear programming (LP) problem with consequent use of a dynamic version of the adaptive method of LP. Both perfect and imperfect information on behavior of control system cases are studied. Algorithms for the optimal controller, optimal estimators are described. Results are illustrated by examples.
The paper presents a study of a possible application of structure embedded piezoelectric actuators to enhance the performance of a rotating composite beam exhibiting the coupled flexural-flexural vibrations. The discussed transversal and lateral bending modal coupling results from the directional properties of the beam's laminate and ply stacking distribution. The mathematical model of the beam is based on an assumption of cross-sectional non-deformability and it incorporates a number of non-classical effects. The final 1-D governing equations of an active composite beam include both orthotropic properties of the laminate and transversely isotropic properties of piezoelectric layers. The system's control capabilities resulting from embedded Macro Fiber Composite piezoelectric actuators are represented by the boundary bending moment. To enhance the dynamic properties of the composite specimen under consideration a combination of linear proportional control strategies has been used. Comparison studies have been performed, including the impact on modal coupling magnitude and cross-over frequency shift.