A graphical method for the determination of the dynamic stability of machine tools

Basic Chatter Theory

“…This section will introduce the effect of rotational speed that is significant when the phase between x(t) and x(t-s) is included. The method used is the graphical approach of Guerney [14] as this is used extensively in later chapters when considering some methods of preventing chatter.…”

Extension of Chatter Theory

“…• A graphical method [1] of determining the stability boundary was presented, and the machine response used as an example had a single mode of vibration representing a one-degree-of-freedom system.…”

“…The graphical method [1] for predicting the stability chart is readily applied to this chatter receptance. For a facing operation, as considered in the previous chapter, a stability chart as shown in Fig.…”

Characterisation and Identification of Dynamic Instability in Milling Operation

“…The chart gives a broad information about the range of the combination of axial depths of cut and spindle speeds for which the system will be stable and for which it will be unstable. The usefulness and popularity of these charts as a means to predict stable cutting operations is evident by the fact that numerous researchers have used it as a foundation for their respective studies in dynamic stability of machining operations [34][35][36]. More recently, Berrios [37] extended the application of Floquet theory and parametrically excited systems to establish a new stability criterion for a half-immersion end milling operation.…”