Dynamic modeling of milling and effect of tool path on machining stability

Regenerative stability theory predicts a set of optimal, stable spindle speeds at integer fractions of the natural frequency of the most flexible mode of the system. Being able to predict these phenomena therefore makes it easier to choose cutting conditions to increase productivity. The three-dimensional study of milling with a spherical tool has been done, and a part of complex shape, it is the continuation of our work previously published. Recently, several theoretical models have been developed for various applications, but there have been very few studies on the particular case of three-axis, complex shape milling. In this paper, it is planned to study the stability of milling operations with a hemispherical tool, using differential equations with delay terms. In this paper, based on the 3D study using a different model, new parameters are introduced in order to compare it with the 2D study of the paper previously published. For a 6061-T6 aluminum alloy part, the model is based on the method of discretization by delay terms of the dynamic equation. Our work has been devoted to have the machining stability lobes in 3D format, along the entire trajectory (discretized in several interpolation segments) of the tool for a flat, inclined (ascending or descending) and complex shaped surface.