Model Reduction for Efficient Time-Integration of Planar Non-Linear Flexible Multibody Models

A reduction method is proposed for efficient time-integration of compliant mechanism models that undergo large deflections. Of particular importance for the modelling of this class of mechanisms is the accurate description of geometric non-linearities, as stiffness characteristics can change significantly during deflection. A finite element based flexible multibody approach is used to describe the compliant mechanism in terms of independent coordinates. Geometric transfer functions are applied to express the configuration and deformed state in terms of the independent coordinates. The modelling of large deflections requires using a sufficient number of finite elements to ensure that deformations remain small in a co-rotational context. Increasing the number of elements, increases, besides the number of degrees of freedom, the largest eigenfrequency in the model. This reduces the allowable step size in explicit time-integrator methods. For the proposed reduction method, we aim to suppress the unwanted high frequency modes to increase the allowable step size. This is accomplished by first choosing, where possible, coordinates that remain small during simulation as independent coordinates. Such coordinates are well suited to be reduced using linear projection methods such as modal projection for suppressing the high frequency modes. The configuration and deformed state of the mechanism is subsequently determined with the geometric transfer functions. Consequently, a significant increase in the allowable step size is realized, while retaining the geometric non-linear effects that are contained in the geometric transfer functions. The effectiveness of the method is demonstrated by two planar examples: a compliant straight guidance that undergoes large deflections and a flexible manipulator.