Improving the Computational Efficiency of Stability Prediction in Milling Employing the Two-Dimensional Bisection Method

2016 ◽  
Author(s):  
Yakun Xie ◽  
Xiaojian Zhang ◽  
Sijie Yan ◽  
Han Ding
Keyword(s):  
Computational Efficiency ◽  
Computation Time ◽  
Stability Diagram ◽  
Two Dimensions ◽  
Bisection Method ◽  
Two Dimensional ◽  
Stability Prediction ◽  
Stability Calculation ◽  
The Stability ◽  
Analytical Time

This paper presents an effective method to improve the computational efficiency of stability prediction in milling based on the two-dimensional bisection method. Contrasted with the traditional semi-analytical time-domain methods, the proposed method for stability prediction only checks the eigenvalues of less nodes on the parameter plane with the two-dimensional bisection method, so that, the computational efficiency of stability can be improved. The novel method for milling stability calculation is comprised of the bisection method in two dimensions and the numerical integration method [NIM], its validity is testified by the comparison of the stability diagram and computation time in contrast to the NIM. The computation demonstrates that the calculated stability diagram by using the presented method agrees well with the result of NIM, while the computation time of the stability diagram can reduce to 1/4 to 3/4 compared with the original methods.

The Stability of a Radial Wall Jet

1977 ◽  
Vol 28 (4) ◽  
pp. 247-258 ◽  
Author(s):  
Yutaka Tsuji ◽  
Yoshinobu Morikawa ◽  
Masaaki Sakou
Keyword(s):  
Linear Stability ◽  
Water Flow ◽  
Wall Jet ◽  
Two Dimensional ◽  
Radial Wall ◽  
Linear Region ◽  
Stability Calculation ◽  
Amplification Rate ◽  
Vortex Patterns ◽  
The Stability

SummaryMeasured stability characteristics in a radial wall jet were compared with calculated results for a two-dimensional wall jet. It was found that the stability of the radial wall jet is similar in many respects to that of the two-dimensional wall jet. An exception is that the local amplification rate of the disturbance velocity is much higher than in the two-dimensional case. It was also found that quarter-harmonics appear in the non-linear region, as well as half-harmonics, and that their amplitude distributions show profiles similar to that of the fundamental component. Further, vortex patterns were visualised in water flow, and results corresponding to measurements in air flow and to the linear stability calculation were obtained.

The Stability of a Two-dimensional Wall Jet

1977 ◽  
Vol 28 (4) ◽  
pp. 235-246 ◽  
Author(s):  
Yutaka Tsuji ◽  
Yoshinobu Morikawa ◽  
Toshihiro Nagatani ◽  
Masaaki Sakou
Keyword(s):  
Reynolds Number ◽  
Neutral Curve ◽  
Stable Region ◽  
Wall Jet ◽  
Two Dimensional ◽  
Linear Region ◽  
Stability Calculation ◽  
Stable Curve ◽  
The Stability ◽  
Small Disturbances

SummaryThe stability of a two-dimensional wall jet was studied theoretically and experimentally. As a result of the linear stability calculation, it was found that one eigenmode is separated into two modes when the Reynolds number is large, and inside a neutral stable curve in the α, R-plane there exists another neutral curve enclosing a stable region. Experimental results of small disturbances were compared with calculated results; agreement between them was satisfactory. It was found, further, that subharmonics of a predominant disturbance velocity component appear in the non-linear region.

Experimental study of the stability and dynamics of a two-dimensional ideal vortex under external strain

2018 ◽  
Vol 848 ◽  
pp. 256-287 ◽  
Author(s):  
N. C. Hurst ◽  
J. R. Danielson ◽  
D. H. E. Dubin ◽  
C. M. Surko
Keyword(s):  
Ideal Fluid ◽  
Experimental Studies ◽  
Quantitative Agreement ◽  
Two Dimensions ◽  
Global Dynamics ◽  
Two Dimensional ◽  
Plasma Dynamics ◽  
Electron Plasmas ◽  
Precise Control ◽  
The Stability

The dynamics of two-dimensional (2-D) ideal fluid vortices is studied experimentally in the presence of an irrotational strain flow. Laboratory experiments are conducted using strongly magnetized pure electron plasmas, a technique which is made possible by the isomorphism between the drift–Poisson equations describing plasma dynamics transverse to the field and the 2-D Euler equations describing an ideal fluid. The electron plasma system provides an excellent opportunity to study the dynamics of a 2-D Euler fluid due to weak dissipation and weak 3-D effects, simple diagnosis and precise control. The plasma confinement apparatus used here was designed specifically to study vortex dynamics under the influence of external flow by applying boundary conditions in two dimensions. Additionally, vortex-in-cell simulations are carried out to complement the experimental results and to extend the parameter range of the studies. It is shown that the global dynamics of a quasi-flat vorticity profile is in good quantitative agreement with the theory of a piecewise-constant elliptical patch of vorticity, including the equilibria, dynamical orbits and stability properties. Deviations from the elliptical patch theory are observed for non-flat vorticity profiles; they include inviscid damping of the orbits and modified stability limits. The dependence of these phenomena on the flatness of the initial profile is discussed. The relationship of these results to other theoretical, numerical and experimental studies is also discussed.

scholarly journals Resonant instability in two-dimensional vortex arrays

2010 ◽  
Vol 467 (2128) ◽  
pp. 1164-1185 ◽  
Author(s):  
Paolo Luzzatto-Fegiz ◽  
Charles H. K. Williamson
Keyword(s):  
Linear Stability ◽  
Stability Boundary ◽  
Oscillatory Instability ◽  
Two Dimensional ◽  
Complex Flows ◽  
Stability Calculation ◽  
Resonant Instability ◽  
The Stability ◽  
Stability Results ◽  
Good Agreement

We examine conditions for the development of an oscillatory instability in two-dimensional vortex arrays. By building on the theory of Krein signatures for Hamiltonian systems, and considering constraints owing to impulse conservation, we show that a resonant instability (developing through coalescence of two eigenvalues) cannot occur for one or two vortices. We illustrate this deduction by examining available linear stability results for one or two vortices. Our work indicates that a resonant instability may, however, occur for three or more vortices. For these more complex flows, we propose a simple model, based on an elliptical vortex representation, to detect the onset of an oscillatory instability. We provide an example in support of our theory by examining three co-rotating vortices, for which we also perform a linear stability analysis. The stability boundary in our model is in good agreement with the full stability calculation. In addition, we show that eigenmodes associated with an overall rotation or an overall displacement of the vortices always have eigenvalues equal to zero and ±i Ω , respectively, where Ω is the angular velocity of the array. These results, for overall rotation and displacement modes, can also be used to immediately check the accuracy of a detailed stability calculation.

Waveboard Artifacts Generate Ghost Resonances Consistent with Equations for Predicting Ion Motion in Commercial Quadrupole Ion Traps

2005 ◽  
Vol 11 (1) ◽  
pp. 15-21 ◽  
Author(s):  
Kwenga F. Sichilongo ◽  
Bert C. Lynn
Keyword(s):  
Ion Trap ◽  
Ion Traps ◽  
Quadrupole Ion Trap ◽  
Stability Diagram ◽  
Two Dimensional ◽  
Quadrupole Field ◽  
Non Linear ◽  
Contour Plots ◽  
The Stability ◽  
Contour Surface

Real-time experiments involving fragmentation of the precursor molecular ion of n-butylbenzene ( m/z 134) to produce product ions C7H+7 ( m/z 91) and C7H+8 ( m/z 92), were used to observe the motion of ions in a commercial quadrupole ion trap. Initially, ghost resonance peaks were observed for excitation of the precursor ion at qz values of 0.4 and 0.5 on the qz axis of the stability diagram. Further experiments involving the generation of two-dimensional contour plots confirmed that these ghost peaks, which were in agreement with mathematical equations describing the motion of ions in a quadrupole field, arose due to waveboard artifacts. Two-dimensional contour surface plots showed non-linear secular frequency canyons from a qz value of 0.5 to higher values corresponding with higher drive radio frequency (rf) voltages on the stability diagram. This observation confirmed that ions are subjected to non-linear effects in this mass scan range. The octapole and hexapole field lines were observed at qz values of 0.65 and 0.78, respectively.

The assembly of ionic currents in a thalamic neuron I. The three-dimensional model

1989 ◽  
Vol 237 (1288) ◽  
pp. 267-288 ◽  
Keyword(s):  
Three Dimensional ◽  
State Diagram ◽  
Ionic Currents ◽  
Stability Diagram ◽  
Repetitive Firing ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Two Dimensional Model ◽  
The Stability

We have previously discussed qualitative models for bursting and thalamic neurons that were obtained by modifying a simple two-dimensional model for repetitive firing. In this paper we report the results of making a similar sequence of modifications to a more elaborate six-dimensional model of repetitive firing which is based on the Hodgkin–Huxley equations. To do this we first reduce the six-dimensional model to a two-dimensional model that resembles our original two-dimensional qualitative model. This is achieved by defining a new variable, which we call q . We then add a subthreshold inward current and a subthreshold outward current having a variable, z , that changes slowly. This gives a three-dimensional ( v, q, z ) model of the Hodgkin–Huxley type, which we refer to as the z -model. Depending on the choice of parameter values this model resembles our previous models of bursting and thalamic neurons. At each stage in the development of these models we return to the corresponding seven-dimensional model to confirm that we can obtain similar solutions by using the complete system of equations. The analysis of the three-dimensional model involves a state diagram and a stability diagram. The state diagram shows the projection of the phase path from v, q, z space into the v, z plane, together with the projections of the curves ż = 0 and v̇ = q̇ = 0. The stability of the points on the curve v̇ = q̇ = 0, which we call the v, q nullcurve, is determined by the stability diagram. Taken together the state and stability diagrams show how to assemble the ionic currents to produce a given firing pattern.

A Geometric Based Method for Distance-to-Contact Calculations in Two Dimensions

2000 ◽  
Author(s):  
C. Wu ◽  
R. W. Mayne
Keyword(s):  
Quadratic Programming ◽  
Motion Planning ◽  
Computational Efficiency ◽  
Minimum Distance ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Programming Technique ◽  
Geometric Concepts ◽  
Low Sensitivity ◽  
Polygon Method

Abstract This paper considers distance-to-contact (DTC) calculation strategies to improve computational efficiency in two dimensional motion planning. A basic DTC calculation approach is described which combines geometric concepts and iterative calculations in identifying the minimum distance between two separated objects of interest. The developed approach, termed the “Q-polygon” method, efficiently obtains the analytical minimum distance between two convex objects. The paper describes the development of the Q-polygon strategy and considers its performance in representative DTC calculations. The performance of the Q-polygon approach compares very favorably to a typical quadratic programming technique for basic DTC calculations and shows an impressive low sensitivity to increasing complexity of the considered objects.

scholarly journals Unifying description of competing orders in two-dimensional quantum magnets

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Xue-Yang Song ◽  
Chong Wang ◽  
Ashvin Vishwanath ◽  
Yin-Chen He
Keyword(s):  
Quantum Electrodynamics ◽  
Spatial Dimension ◽  
Magnetic Monopoles ◽  
Two Dimensions ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Quantum Magnets ◽  
Two Dimensional Materials ◽  
Ordered Phases ◽  
The Stability

Abstract Quantum magnets provide the simplest example of strongly interacting quantum matter, yet they continue to resist a comprehensive understanding above one spatial dimension. We explore a promising framework in two dimensions, the Dirac spin liquid (DSL) — quantum electrodynamics (QED3) with 4 Dirac fermions coupled to photons. Importantly, its excitations include magnetic monopoles that drive confinement. We address previously open key questions — the symmetry actions on monopoles on square, honeycomb, triangular and kagome lattices. The stability of the DSL is enhanced on triangular and kagome lattices compared to bipartite (square and honeycomb) lattices. We obtain the universal signatures of the DSL on triangular and kagome lattices, including those of monopole excitations, as a guide to numerics and experiments on existing materials. Even when unstable, the DSL helps unify and organize the plethora of ordered phases in correlated two-dimensional materials.

MANY-ELECTRON SCREENING EFFECT ON THE STABILITY CRITERIA OF AN ALL-COUPLING OPTICAL BIPOLARON IN TWO DIMENSIONS

1993 ◽  
Vol 07 (16) ◽  
pp. 1071-1081 ◽  
Author(s):  
ASHOK CHATTERJEE ◽  
SHREEKANTHA SIL
Keyword(s):  
Effective Mass ◽  
Carrier Concentration ◽  
Variational Calculation ◽  
Two Dimensions ◽  
Electron Screening ◽  
Two Dimensional ◽  
Stability Criteria ◽  
Screening Effect ◽  
The Stability ◽  
The Many

We perform an all-coupling variational calculation to study the many-electron screening effect on the stability criteria of a two-dimensional singlet optical bipolaron. We also show how the effective mass and the size of the bipolaron would depend on the carrier concentration.

Three-dimensional disturbances in flow between parallel planes

1960 ◽  
Vol 254 (1279) ◽  
pp. 562-569 ◽  
Keyword(s):  
Reynolds Number ◽  
Dimensional Stability ◽  
Flow Direction ◽  
Simple Procedure ◽  
Three Dimensional ◽  
Stability Diagram ◽  
Wave Number ◽  
Two Dimensional ◽  
General Answer ◽  
The Stability

The close connexion between the stability of three-dimensional and two-dimensional disturbances in flow between parallel walls has been examined and this has led to the formation of a three-dimensional stability diagram where ‘stability surfaces’ replace stability curves. The problem which has been investigated is whether the most highly amplifying disturbance at any given Reynolds number above the minimum critical Reynolds number is a two-dimensional or a three-dimensional disturbance. It has been shown that the most unstable disturbance is a two-dimensional one for a certain definite range of Reynolds number above the critical. For Reynolds numbers greater than this no definite general answer has been found; each basic undisturbed flow must be treated separately and a simple procedure has been given which, in principle, determines the type of disturbance which is most unstable. Difficulty arises in following this procedure because it requires knowledge of the two-dimensional stability curves in a certain region where this knowledge is very scanty at the moment. Althoughth is difficulty arises, in Poiseuille flow the calculations available indicate very strongly that the most unstable disturbance at any given Reynolds number above the critical is two-dimensional. Further, it is believed that this result holds for all other basic flows. A second result is that if the wave number (a) in the flow direction is specified, as well as the Reynolds number, then for a in a certain range, the most unstable disturbance is three-dimensional.

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