Abstract
The occurrence of chatter in milling processes was investigated in this study. The prediction of the stability lobes of metal cutting processes requires a model of the cutting force and a model of the dynamic machine tool behavior. Parameter uncertainties in the models may lead to significant differences between the predicted and measured stability behavior. One approach towards robust stability consists of running a large number of simulations with a random sample of uncertain parameters and determining the confidence levels for the chatter vibrations, which is a time-consuming task. In this paper, an efficient implementation of the multi frequency solution and the construction of an approximate solution is presented. The approximate solution requires the explicit calculation of the multi frequency solution only at a few parameter points, and the approximation error can be kept small. This study found that the calculation of the robust stability lobe diagram, which is based on the approximate solution, is significantly more efficient than an explicit calculation at all random parameter points. The numerically determined robust stability diagrams were in good agreement with the experimentally determined stability lobes.
Highlights
Chatter vibration is one of the strongest limitations in maximizing the material removal rate of the metal cutting processes in industrial applications
This study found that the calculation of the robust stability lobe diagram, which is based on the approximate solution, is significantly more efficient than an explicit calculation at all random parameter points
Because we are interested in the parameter uncertainties of the dynamic machine tool behavior, the frequency response function (FRF) were measured under different test conditions, and at least 10 measurements were carried out in each case
Summary
Chatter vibration is one of the strongest limitations in maximizing the material removal rate of the metal cutting processes in industrial applications. Hajdu et al [9] investigated the robust stability behavior of turning processes by considering the uncertainties directly in the frequency response function (FRF) of the machine tool structure, instead of considering the model parameter uncertainties. These studies revealed that a very significant numerical effort is required in robust stability analysis, and that the calculation time increases as the number of the uncertain parameters increases. The main advantage of the frequency domain methods is that a large number of structural eigenmodes can be considered without a significant increase in the calculation time, because the FRFs are used as a model of structural dynamics.
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