The self-excitation damping ratio: A chatter criterion for time-domain milling simulations

Regenerative chatter is known to be a key factor that limits the productivity of high speed machining. Consequently, a great deal of research has focused on developing predictive models of milling dynamics, to aid engineers involved in both research and manufacturing practice. Time-domain models suffer from being computationally intensive, particularly when they are used to predict the boundary of chatter stability, when a large number of simulation runs are required under different milling conditions. Furthermore, to identify the boundary of stability each simulation must run for sufficient time for the chatter effect to manifest itself in the numerical data, and this is a major contributor to the inefficiency of the chatter prediction process. In the present article, a new chatter criterion is proposed for time-domain milling simulations, that aims to overcome this draw-back by considering the transient response of the modeled behavior, rather than the steady-state response. Using a series of numerical investigations, it is shown that in many cases the new criterion can enable the numerical prediction to be computed more than five times faster than was previously possible. In addition, the analysis yields greater detail concerning the nature of the chatter vibrations, and the degree of stability that is observed

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

An experimental investigation of chatter effects on tool life

Tool wear is one of the most important considerations in machining operations as it affects surface quality and integrity, productivity and cost. The most commonly used model for tool life analysis is the one proposed by F.W. Taylor about a century ago. Although the extended form of this equation includes the effects of important cutting conditions on tool wear, tool life studies are mostly performed under stable cutting conditions where the effect of chatter vibrations are not considered. This paper presents an empirical attempt to understand tool life under vibratory cutting conditions. Tool wear data are collected in turning and milling on different work materials under stable and chatter conditions. The effects of cutting conditions as well as severity of chatter on tool life are analyzed. The results indicate significant reduction in tool life due to chatter as expected. They also show that the severity of chatter, and thus the vibration amplitude, strongly reduces the life of cutting tools. These results can be useful in evaluating the real cost of chatter by including the reduced tool life. They can also be useful in justifying the cost of chatter suppression and more rigid machining systems

Vibration absorbers for chatter suppression: A new analytical tuning methodology

Vibration absorbers have been widely used to suppress undesirable vibrations in machining operations, with a particular emphasis on avoiding chatter. However, it is well known that for vibration absorbers to function effectively their stiffness and damping must be accurately tuned based upon the natural frequency of the vibrating structure. For general vibration problems, suitable tuning strategies were developed by Den Hartog and Brock over 50 years ago. However, the special nature of the chatter stability problem means that this classical tuning methodology is no longer optimal. Consequently, vibration absorbers for chatter mitigation have generally been tuned using ad hoc methods, or numerical or graphical approaches. The present article introduces a new analytical solution to this problem, and demonstrates its performance using time domain milling simulations. A 40-50% improvement in the critical limiting depth of cut is observed, compared to the classically tuned vibration absorber. © 2006 Elsevier Ltd. All rights reserved

Percolation in living neural networks

We study living neural networks by measuring the neurons' response to a global electrical stimulation. Neural connectivity is lowered by reducing the synaptic strength, chemically blocking neurotransmitter receptors. We use a graph-theoretic approach to show that the connectivity undergoes a percolation transition. This occurs as the giant component disintegrates, characterized by a power law with critical exponent $\beta \simeq 0.65$ is independent of the balance between excitatory and inhibitory neurons and indicates that the degree distribution is gaussian rather than scale freeComment: PACS numbers: 87.18.Sn, 87.19.La, 64.60.Ak http://www.weizmann.ac.il/complex/tlusty/papers/PhysRevLett2006.pd

Molecular Model of the Contractile Ring

We present a model for the actin contractile ring of adherent animal cells. The model suggests that the actin concentration within the ring and consequently the power that the ring exerts both increase during contraction. We demonstrate the crucial role of actin polymerization and depolymerization throughout cytokinesis, and the dominance of viscous dissipation in the dynamics. The physical origin of two phases in cytokinesis dynamics ("biphasic cytokinesis") follows from a limitation on the actin density. The model is consistent with a wide range of measurements of the midzone of dividing animal cells.Comment: PACS numbers: 87.16.Ka, 87.16.Ac http://www.ncbi.nlm.nih.gov/pubmed/16197254 http://www.weizmann.ac.il/complex/tlusty/papers/PhysRevLett2005.pd

Model and parameter dependence of heavy quark energy loss in a hot and dense medium

Within the framework of the Langevin equation, we study the energy loss of heavy quark due to quasi-elastic multiple scatterings in a quark-gluon plasma created by relativistic heavy-ion collisions. We investigate how the initial configuration of the quark-gluon plasma as well as its properties affect the final state spectra and elliptic flow of D meson and non-photonic electron. We find that both the geometric anisotropy of the initial quark-gluon plasma and the flow profiles of the hydrodynamic medium play important roles in the heavy quark energy loss process and the development of elliptic flow. The relative contribution from charm and bottom quarks is found to affect the transverse momentum dependence of the quenching and flow patterns of heavy flavor decay electron; such influence depends on the interaction strength between heavy quark and the medium.Comment: 16 pages, 7 figure

Compliance error compensation in robotic-based milling

The paper deals with the problem of compliance errors compensation in robotic-based milling. Contrary to previous works that assume that the forces/torques generated by the manufacturing process are constant, the interaction between the milling tool and the workpiece is modeled in details. It takes into account the tool geometry, the number of teeth, the feed rate, the spindle rotation speed and the properties of the material to be processed. Due to high level of the disturbing forces/torques, the developed compensation technique is based on the non-linear stiffness model that allows us to modify the target trajectory taking into account nonlinearities and to avoid the chattering effect. Illustrative example is presented that deals with robotic-based milling of aluminum alloy

On Bootstrap Percolation in Living Neural Networks

Recent experimental studies of living neural networks reveal that their global activation induced by electrical stimulation can be explained using the concept of bootstrap percolation on a directed random network. The experiment consists in activating externally an initial random fraction of the neurons and observe the process of firing until its equilibrium. The final portion of neurons that are active depends in a non linear way on the initial fraction. The main result of this paper is a theorem which enables us to find the asymptotic of final proportion of the fired neurons in the case of random directed graphs with given node degrees as the model for interacting network. This gives a rigorous mathematical proof of a phenomena observed by physicists in neural networks