Reduced-order modeling of flexible mechanisms with configuration-dependent dynamics: a modal approach

Modern formalisms in multibody dynamics allow a detailed and reliable representation of complex mechanical systems. However, high levels of accuracy and generality can only be reached at the price of more sophisticated models, which require increased computational resources. Reduction techniques have thus been developed in order to build simplified models able to capture the essential dynamics of a flexible mechanism. In this talk, a methodology is proposed to transform an initial high-order Finite Element model into a low-order and explicit model.
The reduction method is an extension of the component-mode technique established in linear structural dynamics, which accounts for the nonlinear kinematics of the mechanism. It relies on the original concept of “Global Modal Parameterization”: the motion of the assembled mechanism is described in terms of rigid and flexible modes, which depend on the mechanical configuration.
We will show that the reduction procedure leads to a consistent model, with configuration-dependent parameters. The nonlinear variations of those parameters are approximated using a piecewise polynomial interpolation. This strategy is based on an adaptive configuration space inspection algorithm, which minimizes the computational resources to satisfy a specification on the approximation error.
Several examples will be considered in the presentation: a four-bar mechanism, a parallel kinematic machine-tool, and a lightweight manipulator.