Stability Analysis of Machining with Spindle Speed Variation

2011 ◽  
Vol 223 ◽  
pp. 600-609 ◽  
Author(s):  
Andreas Otto ◽  
Gerhard Kehl ◽  
Michael Mayer ◽  
Günter Radons
Keyword(s):  
Spindle Speed ◽  
Time Varying ◽  
Exact Methods ◽  
Speed Variation ◽  
Time Varying Delay ◽  
Stability Lobes ◽  
Milling Operations ◽  
Spindle Speed Variation ◽  
The Stability ◽  
Varying Delay

In this paper the chatter stability of turning and full-immersion milling operations with spindle speed variation is studied. We present a method to calculate the stability lobes in the limit of very low and very high frequencies of the delay modulation. These approximations help to classify the results of numerically exact methods, as for example semi-discretization or multi-frequency approaches. For slowly time-varying delay, the position of the stability lobes is understandable from a simple connection between the lobes for constant and time-varying delay. Furthermore, this method can be used to estimate the efficiency of an application of spindle speed variation and helps to find optimal parameters for it.

scholarly journals Control of Chatter by Spindle Speed Variation in High-Speed Milling

2010 ◽  
Vol 112 ◽  
pp. 179-186 ◽  
Author(s):  
Sébastien Seguy ◽  
Gilles Dessein ◽  
Lionel Arnaud ◽  
Tamás Insperger
Keyword(s):  
High Speed ◽  
Spindle Speed ◽  
High Speed Milling ◽  
Speed Variation ◽  
Milling Operations ◽  
Spindle Speed Variation ◽  
Machine Tool Chatter ◽  
Parametric Studies ◽  
Sinusoidal Shape ◽  
The Stability

High-speed milling operations are often limited by regenerative vibrations. The aim of this paper is to analyze the effect of spindle speed variation on machine tool chatter in high-speed milling. The stability analysis of triangular and sinusoidal shape variations is made numerically with the semi-discretization method. Parametric studies show also the influence of the frequency and amplitude variation parameters. This modeling is validated experimentally by variable spindle speed cutting tests with a triangular shape. Stable and unstable tests are analyzed in term of amplitude vibration and surface roughness degradation. This work reveals that stability must be considered at period variation scale. It is also shown that spindle speed variation can be efficiently used to suppress chatter in the flip lobe area.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

scholarly journals The effect of time-varying delay damping on the stability of porous elastic system

2021 ◽  
Vol 5 (1) ◽  
pp. 147-161
Author(s):  
Soh Edwin Mukiawa ◽  
Keyword(s):  
Elastic System ◽  
Time Varying ◽  
Viscoelastic System ◽  
One Dimensional ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

In the present work, we study the effect of time varying delay damping on the stability of a one-dimensional porous-viscoelastic system. We also illustrate our findings with some examples. The present work improve and generalize existing results in the literature.

scholarly journals Stability Analysis for Uncertain Neural Networks of Neutral Type with Time-Varying Delay in the Leakage Term and Distributed Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Qi Zhou ◽  
Xueying Shao ◽  
Jin Zhu ◽  
Hamid Reza Karimi
Keyword(s):  
Neutral Type ◽  
Distributed Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Leakage Term ◽  
Time Varying Delay ◽  
The Stability ◽  
Uncertain Networks ◽  
Varying Delay ◽  
Stability Results

The stability problem is investigated for a class of uncertain networks of neutral type with leakage, time-varying discrete, and distributed delays. Both the parameter uncertainty and the generalized activation functions are considered in this paper. New stability results are achieved by constructing an appropriate Lyapunov-Krasovskii functional and employing the free weighting matrices and the linear matrix inequality (LMI) method. Some numerical examples are given to show the effectiveness and less conservatism of the proposed results.

scholarly journals Control of Synchronization and Stability for Nonlinear Complex Dynamical Networks with Different Dimensional Similar Nodes and Coupling Time-Varying Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Luo Yi-ping ◽  
Luo Xin ◽  
Deng Fei ◽  
Hu Jun-qiang
Keyword(s):  
Complex Dynamical Networks ◽  
Time Varying ◽  
Lyapunov Stability Theorem ◽  
Dynamical Networks ◽  
Time Varying Delay ◽  
Decentralized Controllers ◽  
Coupling Time ◽  
The Stability ◽  
Definition Of ◽  
Varying Delay

This paper discusses the stability and synchronization for the nonlinear coupled complex networks with different dimensional nodes, and the external coupling satisfies the condition of dissipation. The definition of synchronization of the complex dynamical networks is proposed as the manifold. By Lyapunov stability theorem, the decentralized controllers with similar parameters are designed to synchronize such dynamical networks asymptotically in which the characteristics are variable delayed. Finally, a numerical example is given to illustrate the effectiveness of the designed method.

scholarly journals Stability analysis for neural networks with discrete and leakage time-varying delay systems with delay-range-dependence and delay-derivative-dependence

2021 ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Neural Networks ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Decomposition Approach ◽  
Time Varying Delay ◽  
Systems Model ◽  
The Neural Networks ◽  
The Stability ◽  
Varying Delay

The paper deals with the stability problem of neural networks with discrete and leakage interval time-varying delays. Firstly, a novel Lyapunov-Krasovskii functional was constructed based on the neural networks leakage time-varying delay systems model. The delayed decomposition approach (DDA) and integral inequality techniques (IIA) were altogether employed, which can help to estimate the derivative of Lyapunov-Krasovskii functional and effectively extend the application area of the results. Secondly, by taking the lower and upper bounds of time-delays and their derivatives, a criterion on asymptotical was presented in terms of linear matrix inequality (LMI), which can be easily checked by resorting to LMI in Matlab Toolbox. Thirdly, the resulting criteria can be applied for the case when the delay derivative is lower and upper bounded, when the lower bound is unknown, and when no restrictions are cast upon the derivative characteristics. Finally, through numerical examples, the criteria will be compared with relative ones. The smaller delay upper bound was obtained by the criteria, which demonstrates that our stability criterion can reduce the conservatism more efficiently than those earlier ones.

scholarly journals Adaptive Event-Triggered Synchronization of Uncertain Fractional Order Neural Networks with Double Deception Attacks and Time-Varying Delay

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1291
Author(s):  
Zhuan Shen ◽  
Fan Yang ◽  
Jing Chen ◽  
Jingxiang Zhang ◽  
Aihua Hu ◽  
...  
Keyword(s):  
Closed Loop ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Time Varying ◽  
Time Varying Delay ◽  
Control Scheme ◽  
The Stability ◽  
High Level ◽  
Varying Delay ◽  
Event Triggered

This paper investigates the problem of adaptive event-triggered synchronization for uncertain FNNs subject to double deception attacks and time-varying delay. During network transmission, a practical deception attack phenomenon in FNNs should be considered; that is, we investigated the situation in which the attack occurs via both communication channels, from S-C and from C-A simultaneously, rather than considering only one, as in many papers; and the double attacks are described by high-level Markov processes rather than simple random variables. To further reduce network load, an advanced AETS with an adaptive threshold coefficient was first used in FNNs to deal with deception attacks. Moreover, given the engineering background, uncertain parameters and time-varying delay were also considered, and a feedback control scheme was adopted. Based on the above, a unique closed-loop synchronization error system was constructed. Sufficient conditions that guarantee the stability of the closed-loop system are ensured by the Lyapunov-Krasovskii functional method. Finally, a numerical example is presented to verify the effectiveness of the proposed method.

scholarly journals Stability Analysis of Drilling Inclination System with Time-Varying Delay via Free-Matrix-Based Lyapunov–Krasovskii Functional

2021 ◽  
Vol 25 (6) ◽  
pp. 1031-1038
Author(s):  
Zhen Cai ◽  
Guozhen Hu ◽  
◽  
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Stability Criterion ◽  
Coefficient Matrix ◽  
Positive Definite ◽  
Time Varying ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay ◽  
Insight Into

This study provides an insight into the asymptotic stability of a drilling inclination system with a time-varying delay. An appropriate Lyapunov–Krasovskii functional (LKF) is essential for the stability analysis of the abovementioned system. In general, an LKF is constructed with each coefficient matrix being positive definite, which results in considerable conservatism. Herein, to relax the conditions of the derived criteria, a novel LKF is proposed by avoiding the positive-definite restriction of some coefficient matrices and introducing additional free matrices simultaneously. Subsequently, this relaxed LKF is applied to derive a less conservative stability criterion for the abovementioned system. Finally, the effect of reducing the conservatism of the proposed LKF is verified based on two examples.

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