Stability and Stabilization of Systems with Time Delay (original) (raw)

State-dependent delay in regenerative turning processes

Nonlinear Dynamics, 2006

Stability of a two degrees of freedom model of the turning process is considered. An accurate modeling of the surface regeneration shows that the regenerative delay, determined by the combination of the workpiece rotation and the tool vibrations, is in fact statedependent. For that reason, the mathematical model considered in this paper is a delay-differential equation with state-dependent time delay. In order to study linearized stability of stationary cutting processes, an associated linear system, corresponding to the statedependent delay equation, is derived. Stability analysis of this linear system is performed analytically.

Fold Bifurcation in the State-Dependent Delay Model of Milling: Analytical and Numerical Solutions

Volume 4: 8th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A and B, 2011

The standard models of the milling process describe the surface regeneration effect by a delay-differential equation with constant time delay. In this study, an improved two degree of freedom model is presented for milling process where the regenerative effect is described by an improved state dependent time delay model. The model contains exact nonlinear screen functions describing the entrance and exit positions of the cutting edges of the milling tool. This model is valid in case of large amplitude forced vibrations close to the near-resonant spindle speeds. The periodic motions of this nonlinear system are calculated by a shooting method. The stability calculation is based on the linearization of the state-dependent delay differential equation around these periodic solutions by means of the semi-discretization method. The results are validated by an advanced numerical time domain simulation where the chip thickness is calculated by means of Boolean algebra.

ORIGINAL ARTICLE Time modeling in high-speed machining of mold pocket

Numerical control milling (NCM) at high speed is the most used machining process in the manufacture of molds because it offers high productivity and workpiece surface quality. The aim of this work is to establish a methodology to evaluate the rough machining time, during high speed milling. In pocket machining, a 2.5D milling has been considered. The proposed approach considers the roughing cutting time as the ratio of the pocket volume by the removed material rate. The pocket is divided into volumes distributed according to the real radial depth. Since the radial depth varies during machining, the removed material rate is not constant. In this paper, an experimental study is carried out to validate models of machining time calculation. The obtained results show that the proposed method offers fast and easy calculation of the machining time of pocket roughing.

Time modeling in high-speed machining of mold pocket

The International Journal of Advanced Manufacturing Technology, 2011

Key Variables in the Control of Lead Time in Spinning Mills

Fibres and Textiles in Eastern Europe, 2016

An investigation of various factors which affect the lead time in spinning mills which produce 14.76 tex (40 Ne) carded yarns linear density is reported. For this study, data were collected from 27 mills producing 14.76 tex carded yarns of linear density. The important parameters which affect the lead time were obtained by principal component analysis of the data. Correlation matrix and multiple regression analysis were carried out taking into account the lead time as the dependent variable and HOK (the number of Operative Hours required to produce 100 kg of yarn), FQI (Fibre Quality Index), YQI (Yarn Quality Index) and spindle production as independent variables. The reliability of the data was checked by Cronbach's alpha, which indicated 0.839. Other tests such as the Kruskal-Wallis test, Durbin Watson test, KMO (Kaiser-Meyer Olkin) and Bartlett's test were also done to find out their association. The results show that of all the parameters considered the, lead time exerts maximum influence on spindle production, HOK and the yarn quality index in carded counts.

Effect of Modal Parameters on Both Delay-Independent and Global Stability of Turning Process

Journal of Mechanical Engineering and Automation, 2012

The model fo r regenerative vibration of linear orthogonal turning process is a second order time -invariant delay differential equation. Stability analysis resulted in lobes that combine to give transition curve that separates the paramete r space of spindle speed and depth of cut into stable and unstable subspaces. It is found that there is a subspace of the stable subspace in which the turning process is delay-independent stable. The size of this subspace is found to be a function of modal parameters and increases with damping ratio of the tool. Non -linear analysis of turning by some investigators suggests that subcritical bifurcations always occur thus the need to design a portion of the subspace of delay -independent stability for global stability. The subspace of global stability is also theoretically and quantitatively demonstrated to increase faster than the driving increase in damp ing ratio.

Cycle time prediction in high-speed milling operations for sculptured surface finishing

2006

This work studies the cycle time prediction of high-speed milling for sculptured surfaces with high feed rates. Experiments and predictions were focused on representative surfaces of dies and molds, whose geometric complexity and complexity distribution were modified parametrically. CNC programs for machining these surfaces were executed in a HURON KX-10 machining center with a SIEMENS 840D controller, with different levels of programmed feed rate. Discrepancies between programmed and actual feed rates were evaluated. A mechanistic approach for cycle time evaluation in high-speed milling of sculptured surfaces is proposed. The mechanistic model construction is based on: (a) the frequency distribution (histogram) of linear interpolation path lengths in the CNC program and (b) a characterization of the machine tool for brisk (large changes in tool path direction) and smooth movements (small changes in tool path direction). Two case studies were used to demonstrate the effectiveness of the proposed approach (a set of representative sculptured surfaces with spherical caps and a forging die surface). Comparing the actual cycle time versus ideal cycle time under programmed feed rates up to 16 m/min, discrepancies of 300-800% were found. The proposed model is capable of predicting cycle time with a maximum error of 5-22%.

Analyzing and estimating delays in wood chipping operations

Biomass & Bioenergy, 2009

Forestry a b s t r a c t Productivity studies are still frequently used to describe, understand and improve forest operations. Delays are recognized as being one of the major factors that limit chipper productivity in most operations and are therefore an integral part of most time studies.

Machining time in rough milling

Materials Technology, 2008

Numerical controlled (NC) milling is widely used in the manufacturing industry because of its high productivity and workpiece surface quality. Work to establish a methodology to evaluate the rough machining time, during high speed milling, is reported. In face machining, 2?5-dimensional milling approach has been considered. The objective is to predict optimal values of cutting speed to minimise both time and cost of die production. Optimum and economical values of cutting speed give respectively minimum production time and minimum production cost. An experimental study has been carried out to validate models for production time and cost in high speed milling. The cutting parameters analysed are cutting speed and feed per tooth.

Stability and Stabilization of Systems with Time Delay (original) (raw)

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