Machining parameters needed for stable, high-performance high-speed machining could be found using mathematical models that need accurate measurements of modal parameters of the machining system. In-process modal parameters, however, can slightly differ from those measured offline and this can limit the applicability of simple measurement methods such as impact hammer tests. To study and extract the in-process modal parameters, mathematical models are used to define two key dimensionless parameters and establish their relationships with each other and the modal parameters. Based on these relationships, the modal parameters are extracted using two analytical methods, the two-point method (TPM), and the regression method (RM). As shown with experimental studies, the RM extracts the modal parameters successfully and while being much faster than the existing iteration-based methods, it provides stability lobe predictions that match well the experimental results. Furthermore, it is noted that the natural frequency parameter is estimated with much better relative precision compared to the damping ratio and the modal stiffness parameters. © 2019 Elsevier Ltd

Vibration frequencies in machining may be employed for calculation of natural frequencies of the dominant modes in chatter and selection of chatter-free spindle speeds with large material removal rates. In this approach, it is important to investigate the relationship between the vibration frequencies, the natural frequencies, spindle speeds and depth of cuts for both stable and unstable cutting conditions. In this paper, the dominant poles of the closed loop time delay differential equation of a milling operation are calculated by successive sectioning of the complex plane and using Cauchy's argument principle. Vibration frequency and damping ratio of the closed loop machining system for each cutting condition is calculated based on the position of the dominant pole on the complex plane which provides 3D plots of the vibration frequency and closed loop damping ratio over any range of depth of cuts and spindle speeds. Finally, the findings of the analytical approach are compared to a machining experiment and a time domain simulation and differences and similarities in their predictions are discussed.