Prediction of Vertical Vibrations of a CNC <i>Router</i> Type Geometry

Abstract

Mechanical vibrations represent an important problem in machining processes performed by machine tools. They affect surface quality, tool life, and productivity. In extreme situations, chattering may appear, which can dramatically reduce the tool life. CNC router machines are particularly sensitive to vibrations, with their structure bearing resemblance to a composition of beams that are uniform in cross-section. These CNC machines are commonly used for different tasks, like engraving, cutting, and 3D printing. This work proposes a modeling methodology for vibration systems that consist of coupled thin beams subjected to vertical vibration. This methodology is used to model vertical vibrations in a CNC router machine. For this, the geometry is decomposed into beams of uniform cross-sections that are coupled at their ends. Each beam is modeled by means of the classical theory of Bernoulli–Euler for thin beams. The boundary conditions are determined by the beam couplings. In the system thus defined, fundamental frequencies are calculated using the bisection method, and then the modes are computed for the corresponding frequencies. The modal amplitudes, being time-dependent, are modeled as a state space system, considering the first m frequencies. In order to provide support to the modeling methodology, simulation experiments are performed for validation, comparing the results provided by models built with the proposed methodology against finite element models and an experimental setting with a real structure. Moreover, an analysis of the vibration model focusing on a specific component of the equipment is presented to illustrate the usefulness and flexibility of the models obtained with the proposed methodology.

Keywords

• vertical vibrations
• modal analysis
• CNC <i>router</i>