Stability Prediction for Low Radial Immersion Milling

Abstract

Traditional regenerative stability theory predicts a set of optimally stable spindle speeds at integer fractions of the natural frequency of the most flexible mode of the system. The assumptions of this theory become invalid for highly interrupted machining, where the ratio of time spent cutting to not cutting (denoted ρ) is small. This paper proposes a new stability theory for interrupted machining that predicts a doubling in the number of optimally stable speeds as the value of ρ becomes small. The results of the theory are supported by numerical simulation and experiment. It is anticipated that the theory will be relevant for choosing optimal machining parameters in high-speed peripheral milling operations where the radial depth of cut is only a small fraction of the tool diameter.

Stability of up-milling and down-milling, part 1: alternative analytical methods

“…In addition to Hopf bifurcations, period doubling bifurcations are also a typical form of instability, as it was shown analytically by Insperger and Sté-pán [21], Corpus and Endres [29], Bayly et al [22], Davies et al [20], via numerical simulation by Zhao and Balachandran [26], and confirmed experimentally by Bayly et al [22] and Davies et al [20]. The nonlinear analysis of Stépán and Szalai [30] showed that this period doubling bifurcation is also subcritical.…”

“…Usually, a finite dimensional approximate transition matrix is used to predict stability properties. Several analytical methods have been developed to determine the stability boundaries for milling [11,[17][18][19][20][21][22][23]. Numerical simulation can also be used to capture the interrupted nature of the milling process [24][25][26][27][28], but the exploration of parameter space via time domain simulation is inefficient.…”

Delay, Parametric Excitation, and the Nonlinear Dynamics of Cutting Processes

“…The contact time ρτ is considered to be so short that the position of the tool, and also the chip thickness, do not change during this time. Davies et al [2000Davies et al [ , 2002, and Bayly et al [2001] analyzed this approximation theoretically and experimentally, too. The equations of motion can be constructed for the two parts of the tool motion in the following way.…”

Three-dimensional stability prediction and chatter analysis in milling of thin-walled plate

“…Merdol and Altintas [2] put forward the multifrequency solution for low radial immersion milling. Davies et al [3] utilized the time-domain solution technique for predicting the stability of highly interrupted machining. Mann et al [4] took advantage of the temporal finite element analysis (TFEA) method in order to approximate the milling process more accurately, which made it possible for obtaining the surface location error and stability simultaneously.…”