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.

scholarly journals Stability Analysis of Distributed Order Fractional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
H. Saberi Najafi ◽  
A. Refahi Sheikhani ◽  
A. Ansari
Keyword(s):  
Stability Analysis ◽  
Characteristic Function ◽  
Differential Equations ◽  
Density Function ◽  
Robust Stability ◽  
Fractional Differential Equations ◽  
Stability Condition ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.

scholarly journals Global Exponential Robust Stability of Static Interval Neural Networks with Time Delay in the Leakage Term

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Leakage Term ◽  
Interval Neural Networks ◽  
Global Exponential Robust Stability ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

The stability of a class of static interval neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, we obtain some sufficient conditions ensuring the global exponential robust stability of the networks. The results in this paper extend the corresponding conclusions without leakage delay. An example is given to illustrate the effectiveness of the obtained results.

A New, Necessary and Sufficient Vertex Solution for Robust Stability Check of Unstructured Convex Combination Matrix Families

2015 ◽  
Author(s):  
Rama K. Yedavalli
Keyword(s):  
Robust Stability ◽  
Convex Combination ◽  
Convexity Property ◽  
Ecological Principles ◽  
Sign Structure ◽  
Previous Solution ◽  
Peer Community ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Complete Dependence

This paper revisits the problem of checking the robust stability of matrix families generated by ‘Unstructured Convex Combinations’ of user supplied or externally supplied Vertex Matrices. A previous solution given by the author for this problem involved complete dependence on the quantitative (eigenvalue information) of a set of special matrices labeled the Kronecker Nonsingularity (KN) matrices. In this solution, the ‘convexity’ property is not explicit and transparent, to the extent that, unfortunately, the accuracy of the solution itself is being questioned and not embraced by the peer community. To erase this unforunate and unwarranted image of this author (in this specific problem) in the minds of the peer community, in this paper, the author treads a new path to find a solution that brings out the convexity property in an explicit and understandable way. In the new solution presented in this paper, we combine the qualitative (sign) as well as quantitative (magnitude) information of these KN matrices and present a vertex solution in which the convexity property of the solution is transparent making it more elegant and accepatble to the peer community, than the previous solution. The new solution clearly underscores the importance of using the sign structure of a matrix in assessing the stability of a matrix. This new solution is made possible by the new insight provided by the qualitative (sign) stability/instability derived from ecological principles. Examples are given which clearly demonstrate effectiveness of the new, convexity based algorithm. It is hoped that this new solution will be embraced by the peer community.

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.

Stability of Heat Pipes in Vapor-Dominated Systems

1999 ◽  
Author(s):  
Pouya Amili ◽  
Yanis C. Yortsos
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Oil Recovery ◽  
Critical Rayleigh Number ◽  
Stability Limit ◽  
Wave Number ◽  
Nuclear Waste Repository ◽  
Geothermal Systems ◽  
Dimensionless Numbers ◽  
The Stability

Abstract We study the linear stability of a two-phase heat pipe zone (vapor-liquid counterflow) in a porous medium, overlying a superheated vapor zone. The competing effects of gravity, condensation and heat transfer on the stability of a planar base state are analyzed in the linear stability limit. The rate of growth of unstable disturbances is expressed in terms of the wave number of the disturbance, and dimensionless numbers, such as the Rayleigh number, a dimensionless heat flux and other parameters. A critical Rayleigh number is identified and shown to be different than in natural convection under single phase conditions. The results find applications to geothermal systems, to enhanced oil recovery using steam injection, as well as to the conditions of the proposed Yucca Mountain nuclear waste repository. This study complements recent work of the stability of boiling by Ramesh and Torrance (1993).

An Analytical Design Method for Milling Cutters With Non-Constant Pitch to Increase Stability

2000 ◽  
Author(s):  
Erhan Budak
Keyword(s):  
Surface Finish ◽  
Design Method ◽  
Stability Limit ◽  
Analytical Stability ◽  
Chatter Vibrations ◽  
Constant Pitch ◽  
Improved Stability ◽  
Limited Frequency ◽  
The Stability ◽  
Explicit Relation

Abstract Chatter vibrations result in reduced productivity, poor surface finish and decreased cutting tool life. Milling cutters with non-constant pitch angles can be very effective in improving the stability of the process against chatter. In this paper, an analytical stability model and a design method are presented for non-constant pitch cutters. An explicit relation is obtained between the stability limit and the pitch variation which leads to a simple equation for optimal pitch angles. A certain pitch variation is effective for limited frequency and speed ranges which are also predicted by the model. The improved stability, productivity and surface finish are demonstrated by several examples.

Criteria for the Stability Limit Prediction of High Speed Centrifugal Compressors With Vaneless Diffuser: Part I — Flow Structure Analysis

2020 ◽  
Author(s):  
Carlo Cravero ◽  
Davide Marsano
Keyword(s):  
Rotational Speed ◽  
High Speed ◽  
Stability Limit ◽  
Vaneless Diffuser ◽  
Centrifugal Compressors ◽  
Vaned Diffuser ◽  
High Rotational Speed ◽  
Lower Accuracy ◽  
The Stability ◽  
Computational Resources

Abstract High-speed centrifugal compressor requirements include a wide operating range between choking and stall especially for turbocharging applications. The prediction of the stability limit at different speeds is still challenging. In literature, several studies have been published on the phenomena that trigger the compressor instability. However, a comprehensive analysis of criteria that can be used in the first steps of centrifugal compressors design to predict the stability limit is still missing. In previous work the authors have already presented a criterion, so called “Stability Parameter”, to predict the surge line of centrifugal compressors based on a simplified CFD approach that does not require excessive computational resources and that can be efficiently used in the preliminary design phases. The above methodology has demonstrated its accuracy for centrifugal compressors with vaned diffuser, but a lower accuracy has been detected for vaneless diffusers. Before proceeding to identify additional criteria focused on compressors with vaneless diffuser, an in-depth fluid dynamics analysis has been necessary. This analysis has been also carried out through fully 3D unsteady simulations to allow identifying the real phenomena linked to the trigger of the instability of centrifugal compressors. It has been found how these phenomena are strongly related to the rotational speed, in particular have been shown the key role of the volute at high rotational speed.

Sign in / Sign up

Export Citation Format

Share Document