Effect of axial force on the stability of milling: Local bifurcations around stable islands

Abstract

In this paper, the stability properties of milling processes are presented when the axial component of the cutting force is also taken into account as a compressive force acting on the cutting tool. The mechanism of the material removal operation is described by a one degree-of-freedom oscillator subjected to the so-called surface regeneration effect. This can be represented mathematically by a nonlinear, time-periodic, delay differential equation. The regenerative compression affects the natural frequency of the system, which is modelled through the lateral stiffness variation of the bearing support of the main spindle. This extension of the general milling model leads to the birth of stable islands within the originally unstable parameter domain. Since the exploitation of these regions may open new ways in practice for increasing the efficiency of machining, the domain of attraction is investigated qualitatively near the stability boundaries of the stable island by means of a semi-analytical method.

Chatter detection in milling processes—a review on signal processing and condition classification

“…It may lead to the Fig. 5 Percentage of the signal types processed in chatter detection literature omission of bistable zones, which are stable zones where a sizeable perturbance can still cause chatter [279,280]. The stability islands as shown in Fig.…”

“…7 are isolated zones in the SLD where the chatter condition shifts back and forth, and it is associated with the time periodicity. They are mostly dependent on the number of teeth, radial depth and the tool geometry [3,265,[280][281][282][283][284][285] and may occur even with multivariable cutters [286][287][288]. However, it is noted that when using FRF measurements for the calculation of the stability lobes, the results by Otto et al [289] showed that no stable or unstable islands were found because the probability for stability islands decrease for an increasing number of flexible eigenmodes.…”

“…7 Representation of stability islands in the SLD. a Stable island in the chatter zone, adapted from [280], and b unstable island in the rightmost stability lobe, adapted from [265] and unstable conditions. Most tests were conducted with constant DOC and different spindle speeds.…”

Continuous-time approach of sampled-data systems

“…These systems can be characterized by delay differential equations. Similar engineering problems involving time delay occur in balancing (Xu et al, 2016; Balogh et al, 2022), vehicle dynamics (Beregi et al, 2016), and machining processes (Beri and Stepan, 2021) as well, resulting in machine tool chatter. In recent years, various new methods have been developed to analyze delayed systems (Insperger et al, 2008; Liu and Kalmár-Nagy, 2010).…”