Generalized model for dynamics and stability of milling of titanium alloys by integrating process damping, multiple modes and multiple delays

Machining dynamics modelling and chatter stability prediction are important for milling of titanium alloys to improve machining productivity and surface quality. Since titanium alloys are typically machined at low spindle speeds, process damping plays an important role in dynamics and stability of milling of titanium alloys. What is more, multiple modes and multiple delays, resulting from the complexity of milling systems and processes, significantly affect chatter stability of milling. However, there is a lack of comprehensive dynamical models capable of studying how these three factors influence chatter stability. To address this gap, this paper proposes a generalized dynamic model for milling of titanium alloys considering process damping, multiple modes and multiple delays. A time-domain chatter prediction method related to the generalized dynamic model is proposed by extending the Gaussian quadrature-based method. Experiments are conducted on multi-mode cutting systems using both uniform and variable pitch cutters to validate the proposed dynamic model and chatter prediction method. The impacts of multiple modes and multiple delays on chatter stability are investigated considering the presence of process damping. Experimental validation and simulation show that in order to accurately predict chatter stability of milling of titanium alloys at low spindle speed, all dynamic modes should be taken into account whether the modes are well separated or not. Even if the low-frequency modes are much more rigid than the high-frequency modes, low-frequency modes may be dominant in milling of titanium alloys and should be considered in the prediction procedure of chatter stability. In addition, it is observed in both simulations and experiments that variable pitch angles can improve the chatter stability limit in the process damping zone.