Investigation of semi-discretization method in end-milling systems for chatter vibration analysis

Abstract

In order to study the stability of end-milling systems, predict chatter phenomena and analyze vibrations or chatter patterns, we propose a novel development of the semi-discretization method based on the application of Laplace transform or Simulink. We first define the end-milling experiment, that will be used as a reference when validating the results, and the dynamic model, that will lead to the governing delay-differential equations. We then apply the semi-discretization method to the system, discretizing the time of study, and proceed to predict the time series data of vibration. In order to obtain this data, we propose two different paths. First of all, the analytical approach, where we apply Laplace transform, partial fraction decomposition and identification to each time interval, using a Matlab algorithm to build the full period. Second of all, the simulation method, where we use the tool Simulink and the concept of block diagrams for each interval, complemented with another program in Matlab if the whole period wants to be studied. Finally, we validate the results obtained from these two approaches with the ones given by the experiment, verifying that they are able to predict chatter vibrations by obtaining the time series data vibration of the system.