A New Method to Detect Regenerative Chatter Using Spectral Analysis, Part 1: Basic Study on Criteria for Detection of Chatter

1997 ◽  
Vol 119 (4A) ◽  
pp. 461-466 ◽  
Author(s):  
E. Kondo ◽  
H. Ota ◽  
T. Kawai
Keyword(s):  
Spectral Analysis ◽  
Numerical Simulations ◽  
Vibration Amplitude ◽  
Orthogonal Cutting ◽  
Stability Limit ◽  
Regenerative Chatter ◽  
Basic Study ◽  
Workpiece Surface ◽  
The Stability ◽  
New Criterion

The purpose of this study is to introduce a new criterion for detecting regenerative chatter by application of spectral analysis. From the regenerative chatter theory, it can be seen that the vibration amplitude perpendicular to a workpiece surface comes equal to the amplitude of surface undulation at the stability limit. So the regenerative chatter theory is applied to the criterion introduced in this study to detect regenerative chatter. Validity of this criterion was examined by using numerical simulations assumed to be orthogonal, and then experiments for verification of criterion validity were carried out using the regenerative chatter of a turning workpiece in orthogonal cutting. We concluded that this criterion is reliable enough to detect regenerative chatter.

An improved semi-analytical approach for modeling of process damping in orthogonal cutting considering cutting edge radius

2019 ◽  
Vol 234 (3) ◽  
pp. 641-653 ◽  
Author(s):  
Chang Cao ◽  
Xiao-Ming Zhang ◽  
Tao Huang ◽  
Han Ding
Keyword(s):  
Computational Efficiency ◽  
Orthogonal Cutting ◽  
Finite Amplitude ◽  
Cutting Edge ◽  
Workpiece Surface ◽  
Process Damping ◽  
Flank Face ◽  
The Stability ◽  
The Time Domain ◽  
Stability Limits

Process damping generated between the tool flank face and the wavy finish workpiece surface has a non-negligible effect on cutting dynamics and chatter stability, especially at low cutting speeds, resulting in higher stability limits. In modeling of process damping, the calculation of extruded volume is one of the most critical challenges, especially in machining with honed tools due to the complex and time-variable contact condition between the arc cutting edge and the finite amplitude wave surface. In this study, a semi-analytical method with high computational efficiency is proposed to calculate the extruded volume in cutting with honed tools. Based on this method, we construct the stability lobes under the condition of finite vibration amplitude accurately and efficiently, which overcomes the limitation of analytical methods based on the assumption of small amplitude vibrations and the low computational efficiency of numerical method. The predicted cutting stability is verified against both the experimental results and the time-domain simulation results.

scholarly journals Estimates of the bistable region in metal cutting

2008 ◽  
Vol 464 (2100) ◽  
pp. 3255-3271 ◽  
Author(s):  
Zoltan Dombovari ◽  
R. Eddie Wilson ◽  
Gabor Stepan
Keyword(s):  
Cutting Force ◽  
Metal Cutting ◽  
Classical Model ◽  
Orthogonal Cutting ◽  
Chip Thickness ◽  
Stability Limit ◽  
Force Characteristic ◽  
Inflexion Point ◽  
The Stability ◽  
Force Characteristics

The classical model of regenerative vibration is investigated with new kinds of nonlinear cutting force characteristics. The standard nonlinear characteristics are subjected to a critical review from the nonlinear dynamics viewpoint based on the experimental results available in the literature. The proposed nonlinear model includes finite derivatives at zero chip thickness and has an essential inflexion point. In the case of the one degree-of-freedom model of orthogonal cutting, the existence of unstable self-excited vibrations is proven along the stability limits, which is strongly related to the force characteristic at its inflexion point. An analytical estimate is given for a certain area below the stability limit where stable stationary cutting and a chaotic attractor coexist. It is shown how this domain of bistability depends on the theoretical chip thickness. The comparison of these results with the experimental observations and also with the subcritical Hopf bifurcation results obtained for standard nonlinear cutting force characteristics provides relevant information on the nature of the cutting force nonlinearity.

scholarly journals Fast-Scale Instability and Stabilization by Adaptive Slope Compensation of a PV-Fed Differential Boost Inverter

2021 ◽  
Vol 11 (5) ◽  
pp. 2106
Author(s):  
Abdelali El Aroudi ◽  
Mohamed Debbat ◽  
Mohammed Al-Numay ◽  
Abdelmajid Abouloiafa
Keyword(s):  
Numerical Simulations ◽  
Full Range ◽  
Weather Conditions ◽  
Current Loop ◽  
Point Tracking ◽  
Bifurcation Phenomena ◽  
Slope Compensation ◽  
Power Point ◽  
The Stability ◽  
Detailed Circuit

Numerical simulations reveal that a single-stage differential boost AC module supplied from a PV module under an Maximum Power Point Tracking (MPPT) control at the input DC port and with current synchronization at the AC grid port might exhibit bifurcation phenomena under some weather conditions leading to subharmonic oscillation at the fast-switching scale. This paper will use discrete-time approach to characterize such behavior and to identify the onset of fast-scale instability. Slope compensation is used in the inner current loop to improve the stability of the system. The compensation slope values needed to guarantee stability for the full range of operating duty cycle and leading to an optimal deadbeat response are determined. The validity of the followed procedures is finally validated by a numerical simulations performed on a detailed circuit-level switched model of the AC module.

scholarly journals Earth-size planet formation in the habitable zone of circumbinary stars

2020 ◽  
Vol 494 (1) ◽  
pp. 1045-1057 ◽  
Author(s):  
G O Barbosa ◽  
O C Winter ◽  
A Amarante ◽  
A Izidoro ◽  
R C Domingos ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Planet Formation ◽  
Terrestrial Planet ◽  
Close Binary ◽  
Habitable Zone ◽  
Density Profiles ◽  
Habitable Planets ◽  
Habitable Zones ◽  
Test Particles ◽  
The Stability

ABSTRACT This work investigates the possibility of close binary (CB) star systems having Earth-size planets within their habitable zones (HZs). First, we selected all known CB systems with confirmed planets (totaling 22 systems) to calculate the boundaries of their respective HZs. However, only eight systems had all the data necessary for the computation of HZ. Then, we numerically explored the stability within HZs for each one of the eight systems using test particles. From the results, we selected five systems that have stable regions inside HZs, namely Kepler-34,35,38,413, and 453. For these five cases of systems with stable regions in HZ, we perform a series of numerical simulations for planet formation considering discs composed of planetary embryos and planetesimals, with two distinct density profiles, in addition to the stars and host planets of each system. We found that in the case of the Kepler-34 and 453 systems, no Earth-size planet is formed within HZs. Although planets with Earth-like masses were formed in Kepler-453, they were outside HZ. In contrast, for the Kepler-35 and 38 systems, the results showed that potentially habitable planets are formed in all simulations. In the case of the Kepler-413system, in just one simulation, a terrestrial planet was formed within HZ.

Mathematical Model Establishment and Analysis on the Pipe Deformation under External Pressure with the Ovality

2013 ◽  
Vol 760-762 ◽  
pp. 2263-2266
Author(s):  
Kang Yong ◽  
Wei Chen
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Yield Strength ◽  
Residual Stresses ◽  
Numerical Simulations ◽  
Significant Influence ◽  
External Pressure ◽  
Pipe Diameter ◽  
Axial Loads ◽  
The Stability

Beside the residual stresses and axial loads, other factors of pipe like ovality, moment could also bring a significant influence on pipe deformation under external pressure. The Standard of API-5C3 has discussed the influences of deformation caused by yield strength of pipe, pipe diameter and pipe thickness, but the factor of ovality degree is not included. Experiments and numerical simulations show that with the increasing of pipe ovality degree, the anti-deformation capability under external pressure will become lower, and ovality affecting the stability of pipe shape under external pressure is significant. So it could be a path to find out the mechanics relationship between ovality and pipe deformation under external pressure by the methods of numerical simulations and theoretical analysis.

AN ADVANCED ADAPTIVE FINITE ELEMENT CODE APPLIED FOR COATING-SUBSTRATE SIMULATION

2011 ◽  
Vol 03 (01n02) ◽  
pp. 91-107 ◽  
Author(s):  
JÜRGEN LEOPOLD ◽  
KATRIN HELLER ◽  
ARNDT MEYER ◽  
REINER WOHLGEMUTH
Keyword(s):  
Finite Element ◽  
Fe Simulation ◽  
Scale Up ◽  
Computational Time ◽  
Adaptive Finite Element ◽  
Workpiece Surface ◽  
Coated Tools ◽  
Geometrical Simulation ◽  
The Stability ◽  
And Storage

The stability of coating-substrate systems influences the chip formation and the surface integrity of the new generated workpiece surface, too. Using finite element (FE) simulation, deformations, strains and stresses in coated tools, caused by external and internal loads, can be computed on a microscopic scale. Since both, the whole macroscopic tool (in mm-scale) and the microscopic coating layers (in μm-scale up to nm-scale) must be included in the same geometrical simulation model, graded high-resolution FE meshes must be used. Nevertheless, the number of nodes in the 3D computational FE grid reaches some millions, leading to large computational time and storage requirements. For this reason, an advanced adaptive finite element (AAFEM) software has been developed and used for the simulation.

Optimization of the Robust Stability Limit for Multi-Cutter Turning Processes

2015 ◽  
Author(s):  
Marta J. Reith ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Robust Stability ◽  
Optimal Parameter ◽  
Stability Limit ◽  
Boundary Function ◽  
Lower Envelope ◽  
Computation Method ◽  
Parameter Region ◽  
Dynamical Parameters ◽  
The Stability ◽  
Machining Parameter

Multi-cutter turning systems bear huge potential in increasing cutting performance. In this study we show that the stable parameter region can be extended by the optimal tuning of system parameters. The optimal parameter regions can be identified by means of stability charts. Since the stability boundaries are highly sensitive to the dynamical parameters of the machine tool, the reliable exploitation of the so-called stability pockets is limited. Still, the lower envelope of the stability lobes is an appropriate upper boundary function for optimization purposes with an objective function taken for maximal material removal rates. This lower envelope is computed by the Robust Stability Computation method presented in the paper. It is shown in this study, that according to theoretical results obtained for optimally tuned cutters, the safe stable machining parameter region can significantly be extended, which has also been validated by machining tests.

Some difficulties associated with the limit equilibrium method of slices

1983 ◽  
Vol 20 (4) ◽  
pp. 661-672 ◽  
Author(s):  
R. K. H. Ching ◽  
D. G. Fredlund
Keyword(s):  
Slope Stability ◽  
Factor Of Safety ◽  
Limit Equilibrium ◽  
Stability Limit ◽  
Limit Equilibrium Method ◽  
Soil Conditions ◽  
Side Force ◽  
Limit Equilibrium Methods ◽  
Equilibrium Method ◽  
The Stability

Several commonly encountered problems associated with the limit equilibrium methods of slices are discussed. These problems are primarily related to the assumptions used to render the inherently indeterminate analysis determinate. When these problems occur in the stability computations, unreasonable solutions are often obtained. It appears that problems occur mainly in situations where the assumption to render the analysis determinate seriously departs from realistic soil conditions. These problems should not, in general, discourage the use of the method of slices. Example problems are presented to illustrate these difficulties and suggestions are proposed to resolve these problems. Keywords: slope stability, limit equilibrium, method of slices, factor of safety, side force function.

A Dynamical Model for Studying the Stability of Thermo-Solutal Convection Under the Effect of Vertical Vibration

2005 ◽  
Author(s):  
Y. P. Razi ◽  
M. Mojtabi ◽  
K. Maliwan ◽  
M. C. Charrier-Mojtabi ◽  
A. Mojtabi
Keyword(s):  
Stability Analysis ◽  
Mechanical Vibration ◽  
Stability Limit ◽  
Lewis Number ◽  
Vertical Vibration ◽  
Wave Number ◽  
Dimensionless Wave Number ◽  
Non Linear ◽  
Linear Differential ◽  
The Stability

This paper concerns the thermal stability analysis of porous layer saturated by a binary fluid under the influence of mechanical vibration. The linear stability analysis of this thermal system leads us to study the following damped coupled Mathieu equations: BH¨+B(π2+k2)+1H˙+(π2+k2)−k2k2+π2RaT(1+Rsinω*t*)H=k2k2+π2(NRaT)(1+Rsinω*t*)Fε*BF¨+Bπ2+k2Le+ε*F˙+π2+k2Le−k2k2+π2NRaT(1+Rsinω*t*)F=k2k2+π2RaT(1+Rsinω*t*)H where RaT is thermal Rayleigh number, R is acceleration ratio (bω2/g), Le is the Lewis number, k is the dimensionless wave-number, ε* is normalized porosity and N is the buoyancy ratio (H and F are perturbations of temperature and concentration fields). In the follow up, the non-linear behavior of the problem is studied via a generalization of the Lorenz model (five coupled non-linear differential equations with periodic coefficients). In the presence or absence of gravity, the stability limit for the onset of stationary as well as Hopf bifurcations is determined.

The Machining Parameters Online Monitoring Method for Stability Prediction

2011 ◽  
Vol 141 ◽  
pp. 559-563
Author(s):  
Yong Xiang Jiang ◽  
San Peng Deng ◽  
Yu Ming Qi ◽  
Bing Du
Keyword(s):  
Dynamic Models ◽  
Grinding Wheel ◽  
Machining Accuracy ◽  
Machining Parameters ◽  
Regenerative Chatter ◽  
Monitoring Method ◽  
Good Surface ◽  
Prediction And Control ◽  
The Stability ◽  
Online Detecting

Unstable grinding due to the regenerative chatter is one of the most critical errors and a serious limitation to achieve good surface quality. The machining accuracy of CNC is greatly depending on online detecting, prediction and control ability of abnormal phenomena in machining such as chatter. Based on the mechanism of regenerative chatter, the dynamic models of cylindrical plunging are established by considering both the rotate speed of workpiece and grinding wheel. The traverse grinding can be assumed as the sum of several stepwise plunging grinding with respect to the grinding contact area. The stability caused by online detecting indexes of grinding parameters was analyzed. Grinding experiments of online chatter detecting were carried out and agreed well with the theoretical results that show good application future for online chatter detecting.

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