Phase equilibria in the system K2O-FeO-MgO-Al2O3-SiO2-H2O-CO2 and the stability limit of stilpnomelane in metamorphosed Precambrian iron-formations

1989 ◽  
Vol 102 (4) ◽  
pp. 478-491 ◽  
Author(s):  
Takashi Miyano ◽  
Cornelis Klein
Keyword(s):  
Phase Equilibria ◽  
Stability Limit ◽  
The Stability ◽  
Iron Formations

Heating experiments on gudmundite

1966 ◽  
Vol 36 (276) ◽  
pp. 1123-1125 ◽  
Author(s):  
A. Horrell Clark
Keyword(s):  
Experimental Data ◽  
Ternary System ◽  
Phase Equilibria ◽  
Stability Limit ◽  
The Stability

SummaryIn the absence of published experimental data on phase equilibria in the ternary system Fe-Sb-S and on the stability relations of gudmundite (FeSbS) and berthierite (FeSb2S4) , some preliminary investigations on the upper stability limit of natural gudmundite are briefly described. On heating in vacuo, As-free gudmundite broke down between 269° and 288°C, an approximate upper stability limit of 280±10°C conforming to the stability relations of the associated phases.

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.

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.

Stall inception mechanisms in a contra-rotating fan operating at different speed combinations

2019 ◽  
Vol 234 (8) ◽  
pp. 1041-1052 ◽  
Author(s):  
MP Manas ◽  
AM Pradeep
Keyword(s):  
Pressure Ratio ◽  
Pressure Sensors ◽  
Stability Limit ◽  
Leading Edge ◽  
Axial Direction ◽  
Tip Leakage Flow ◽  
Stall Inception ◽  
Unsteady Pressure ◽  
Stall Cells ◽  
The Stability

Contra-rotating fan is a concept that can possibly replace the present-day conventional fans due to its several aerodynamic advantages. It has the potential to improve the stability limit and can achieve a higher pressure ratio per stage. One of the advantages of a contra-rotating fan is its capability to operate both the rotors at different speeds. In the present study, experiments are carried out at different speed combinations of the rotors and the stall inception phenomenon is captured using high-response unsteady pressure sensors placed on the casing upstream of the leading edge of rotor-1. The unsteady pressure data are investigated using wavelet and Fourier analysis techniques. It is observed that the mechanism of stall inception is different for different speed combinations. The pre-stall disturbances fall in different frequency ranges for different speed combinations. For the range of speed combinations investigated, the frequency of appearance of stall cells of rotor-1 does not depend on the speed of rotor-2. A higher speed of rotation of rotor-1 leads to a higher frequency of appearance of stall cells and a lower speed of rotation of rotor-1 leads to a lower frequency of appearance of stall cells. For all the speed combinations, there is a range of frequency where no disturbance is observed and this range is termed as the ‘no-disturbance zone’. Disturbances are observed at lower frequencies and at frequencies close to the blade passing frequency. In order to understand the flow physics in detail, computational analysis is carried out for different speed combinations of the rotors. For a higher speed of rotor-2, it is observed that the suction effect of rotor-2 is significant enough to pull the tip-leakage flow towards the axial direction. Thus, the suction effect of rotor-2 plays a significant role in determining the stall of the stage.

scholarly journals Stability Analysis of Milling Process with Multiple Delays

2020 ◽  
Vol 10 (10) ◽  
pp. 3646 ◽  
Author(s):  
Yonggang Mei ◽  
Rong Mo ◽  
Huibin Sun ◽  
Bingbing He ◽  
Kun Bu
Keyword(s):  
Stability Limit ◽  
Helix Angle ◽  
Milling Process ◽  
Machining Process ◽  
Multiple Delays ◽  
Calculation Time ◽  
Discretization Algorithm ◽  
Cutting Chatter ◽  
Regeneration Effect ◽  
The Stability

Cutting chatter is extremely harmful to the machining process, and it is of great significance to eliminate chatter through analyzing the stability of the machining process. In this work, the stability of the milling process with multiple delays is investigated. Considering the regeneration effect, the dynamics of the milling process with variable pitch cutter is modeled as periodic coefficients delayed differential equations (DDEs) with multiple delays. An adaptive variable-step numerical integration method (AVSNIM) considering the effect of the helix angle is developed firstly, which can discretize the cutting period accurately, thereby improving the calculation accuracy of the stability limit of the milling process. The accuracy and efficiency of the AVSNIM are verified through a benchmark milling model. Subsequently, a novel spindle speed-dependent discretization algorithm is proposed, which is combined with the AVSNIM to further reduce the calculation time of the stability lobes diagram (SLD). The simulation experiment results demonstrate that the proposed algorithm can effectively reduce the calculation time.

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