Chatter, process damping, and chip segmentation in turning: A signal processing approach

An increasing number of aerospace components are manufactured from titanium and nickel alloys that are difficult to machine due to their thermal and mechanical properties. This limits the metal removal rates that can be achieved from the production process. However, under these machining conditions the phenomenon of process damping can be exploited to help avoid self-excited vibrations known as regenerative chatter. This means that greater widths of cut can be taken so as to increase the metal removal rate, and hence offset the cutting speed restrictions that are imposed by the thermo-mechanical properties of the material. However, there is little or no consensus as to the underlying mechanisms that cause process damping. The present study investigates two process damping mechanisms that have previously been proposed in the machining literature: the tool flank/workpiece interference effect, and the short regenerative effect. A signal processing procedure is employed to identify flank/workpiece interference from experimental data. Meanwhile, the short regenerative model is solved using a new frequency domain approach that yields additional insight into its stabilising effect. However, analysis and signal processing of the experimentally obtained data reveals that neither of these models can fully explain the increases in stability that are observed in practice. Meanwhile, chip segmentation effects were observed in a number of measurements, and it is suggested that segmentation could play an important role in the process-damped chatter stability of these materials

Prediction of vibration frequencies in milling using modified Nyquist method

Study of the vibration frequencies at different cutting conditions is an alternative to the use of impact hammer test for identification of natural frequencies of the machining structure and calculation of stability lobe diagrams. Vibration frequencies not only depend on the natural frequencies of the structure, but also they are dependent on the spindle speed, damping ratio of the structure and the depth of cut. Ignoring these additional parameters would lead to errors in identification of the natural frequencies of the system and considerable deviation of the calculated stability lobe diagrams from actual cutting tests. In this study modified Nyquist method is used to investigate the effects of spindle speed, depth of cut and damping ratio of the structure on vibration frequencies. The quality of frequency prediction is compared to linear and nonlinear time domain simulations and machining experiments.</p

Frequency Domain Study of Vibrations above and under Stability Lobes in Machining Systems

AbstractUsing modified Nyquist contours, the dominant poles of the closed loop delay-differential equation for machining systems such as milling are identified. Contours with constant damping ratio of the dominant poles are constructed using this method. These contours are similar in shape to the stability lobes, but move upwards and to the right as the instability parameter increases. Additionally, it is possible to study the movement of the dominant poles to the right-hand side of the complex plane as the system becomes unstable by increasing the depth of cut at a constant spindle speed. The movement of the dominant pole is shown to be towards the right (unstable) and upward (higher vibration frequency) of the complex plane. In some cases, there would be a jump of vibration frequency due to the change of the lobe number. It is also shown that the damping ratio of the structure strongly affects both the vibration frequency and the damping ratio of the dominant poles in the closed loop system. Finally, in two milling experiments with two different spindle speeds and continuously increasing depth of cuts, vibration frequencies are measured and compared to the theoretical predictions. The measurements agree with the theoretical predictions, particularly in the unstable cutting conditions

In-process identification of modal parameters using dimensionless relationships in milling chatter

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 Lt

Vibration frequencies in stable and unstable milling

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.</p

Analytical Stability Prediction in Five Axis Ball-End Milling

In five axis ball-end milling, the cutting edge is a continuous curve and the engagement with workpiece changes as the cutting tool rotates. Therefore the sensitivity to vibration varies along the cutting edge and as the tool rotates. In this paper, the vibration-force relationship (VFR) is obtained for infinitesimal length of cutting edge as a function of tool’s rotation angle. Numerical integration results in the VFR of the whole cutting edge and the tool. VFR of the tool is coupled to the dynamic vibration model of the tool and the workpiece to predict the possibility of vibrational instability. This algorithm is then used to predict the effects of changing the lead angle in a test setup with a flexible depth of cut direction. The analytical results, along with experiments demonstrate that the large lead angles considerably improve the stability of the process.</p