Modeling of Flexible Bodies for the Study of Control in the Simulink Environment

Abstract

When studying complex mechatronic systems, it is useful to build models able to simulate both the dynamics of the phenomenon and the control system applied. Typically, the bodies involved are modeled as rigid bodies. In this work, a technique for modeling flexible bodies in Simulink environment is presented. Simulink is a powerful instrument where it is quite easy to integrate control algorithms with complex systems. The solution developed is presented and applied to a machining center. Modern machining centers ensure a level of accuracy that traditional manual machines cannot reach. Simulations of the working process considering vibrations are needed to obtain high precision machining. These simulations aim to determine the error in the position of the tool and to help designers in finding the optimal solution in terms of machining velocity and precision. This work is focused on the carriage of a machine tool moving along horizontal guides, typically named Z-axis. The axis is actuated and borne by a linear motor; therefore, movable constraints must be modeled. A finite-element (FE) model of the carriage was reduced with a Craig-Bampton reduction to provide the mass and stiffness matrices for an in-house Matlab simulation code. The rigid constraints of the carriage were implemented in the model as moving stiffnesses, and their value was set to obtain continuity of the constraints in the discrete model. In the end, a map of different vibrational configurations is proposed to visualize the possible errors that a machining process can generate.

Keywords

• model
• deformable body
• finite-element method
• moving constraints
• machining center