Abstract :
[en] This talk concerns the numerical simulation of mechatronic systems, such as robots, machine-tools or modern vehicles. In general, a mechatronic system is composed of various technological components: a mechanism, actuators, sensors, and control units. For critical applications, it is also necessary to account for elastic deformations in the mechanism.
The generalized-alpha method has been initially developed for the dynamic simulation of flexible mechanical structures, which are represented by lightly damped second-order ODEs. Usually, those equations are obtained after a finite element spatial discretization, with the consequence that they are affected by a large number of high-frequency modes with a purely numerical origin. The generalized-alpha method has very interesting properties in this context, such as an adjustable amount of high-frequency numerical dissipation, A-stability, second-order accuracy, and a high level of computational efficiency.
A mechanism with elastic components can be described using the nonlinear finite element formalism. Due to the presence of kinematic constraints, the equations of motion are second-order DAEs, and we shall consider the generalized-alpha method for the direct simulation of the index-3 problem. In particular, some results about the convergence and the stability of the algorithm will be discussed.
Finally, a mechatronic system involves mechanical and non-mechanical components, and it is thus modelled as a mixed set of second- and first-order DAEs. We will show that those coupled equations of motion can also be solved in the time domain according to the generalized-alpha scheme. An important problem is then associated with the selection of the parameters of the method.
The presentation will be illustrated by academic and non-academic applications, for example in vehicle dynamics and in robotics.
