Chatter Stability Analysis of the Variable Speed Face-Milling Process

2000 ◽  
Vol 123 (4) ◽  
pp. 753-756 ◽  
Author(s):  
Sridhar Sastry, ◽  
Shiv G. Kapoor, ◽  
Richard E. DeVor, and ◽  
Geir E. Dullerud
Keyword(s):  
Discrete System ◽  
Milling Process ◽  
Face Milling ◽  
Solution Technique ◽  
Dimensional System ◽  
Multiple Time ◽  
Time Varying ◽  
Variable Speed ◽  
Finite Dimensional ◽  
Industrial Grade

In this study, a solution technique based on a discrete time approach is presented to the stability problem for the variable spindle speed face-milling process. The process dynamics are described by a set of differential-difference equations with time varying periodic coefficients and time delay. A finite difference scheme is used to discretize the system and model it as a linear time varying (LTV) system with multiple time delays. By considering all the states over one period of speed variation, the infinite dimensional periodic time-varying discrete system is converted to a finite dimensional time-varying discrete system. The eigenvalues of the state transition matrix of this finite dimensional system are then used to propose criteria for exponential stability. Predicted stability boundaries are compared with lobes generated by numerical time-domain simulations and experiments performed on an industrial grade variable speed face-milling testbed.

scholarly journals Controllability of nonlinear stochastic systems with multiple time-varying delays in control

2015 ◽  
Vol 25 (2) ◽  
pp. 207-215 ◽  
Author(s):  
Shanmugasundaram Karthikeyan ◽  
Krishnan Balachandran ◽  
Murugesan Sathya
Keyword(s):  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Multiple Delays ◽  
Multiple Time ◽  
Time Varying ◽  
Nonlinear Stochastic Systems ◽  
Finite Dimensional ◽  
Linear Stochastic Systems ◽  
Theoretical Results

AbstractThis paper is concerned with the problem of controllability of semi-linear stochastic systems with time varying multiple delays in control in finite dimensional spaces. Sufficient conditions are established for the relative controllability of semilinear stochastic systems by using the Banach fixed point theorem. A numerical example is given to illustrate the application of the theoretical results. Some important comments are also presented on existing results for the stochastic controllability of fractional dynamical systems.

The Effects of Variable Speed Cutting on Vibration Control in Face Milling

1990 ◽  
Vol 112 (1) ◽  
pp. 1-11 ◽  
Author(s):  
S. C. Lin ◽  
R. E. DeVor ◽  
S. G. Kapoor
Keyword(s):  
Vibration Control ◽  
Vibration Suppression ◽  
Experimental Studies ◽  
Cutting Speed ◽  
Milling Process ◽  
Face Milling ◽  
Force Model ◽  
Trajectory Design ◽  
Variable Speed ◽  
Milling Force Model

This paper discusses the use of variable speed cutting for vibration control in the face milling process. Both simulation and experimental results show that the self-excited vibrations that can occur during constant speed cutting, and hence put limitation on the possible size of cut, can be suppressed by continuously varying the spindle speed. Through both analytical and experimental studies, the shape of variable speed trajectory has been examined, in terms of both the trackability by the spindle servo system and performance in terms of vibration suppression. It was found that a sinusoidal wave because of its acceleration and jerk characteristics can be tracked more precisely than some other periodic waves. The dynamic face milling force model was used to study the effects of speed trajectory parameters, namely, the frequency and amplitude. The results, in general, show the method to be fairly robust to the specific nature of the machining situation in terms of both processing conditions and system dynamics. Speed trajectory design was, however, shown to be somewhat dependent upon the nominal cutting speed and dominant frequencies of the system.

scholarly journals Uniform boundary controllability of a discrete 1-D Schrodinger equation

2015 ◽  
Vol 7 (2) ◽  
pp. 259-270
Author(s):  
Z. Hajjej ◽  
M. Balegh
Keyword(s):  
Schrödinger Equation ◽  
High Frequency ◽  
Discrete System ◽  
Schrodinger Equation ◽  
Dimensional System ◽  
Boundary Controllability ◽  
Finite Dimensional ◽  
Boundary Observability ◽  
Spurious Modes ◽  
Uniform Controllability

In this paper we study the controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D Schrodinger equation with a boundary control. As for other problems, we can expect that the uniform controllability does not hold in general due to high frequency spurious modes. Based on a uniform boundary observability estimate for filtered solutions of the corresponding conservative discrete system, we show the uniform controllability of the projection of the solutions over the space generated by the remaining eigenmodes.

scholarly journals An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems

2016 ◽  
Vol 26 (1) ◽  
pp. 15-30 ◽  
Author(s):  
Andreas Rauh ◽  
Luise Senkel ◽  
Harald Aschemann ◽  
Vasily V. Saurin ◽  
Georgy V. Kostin
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Control Strategies ◽  
Open Loop ◽  
Distributed Parameter ◽  
Dimensional System ◽  
State Equations ◽  
Large Space ◽  
Finite Dimensional ◽  
Spatially Distributed

Abstract In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finite-dimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance, and parameter estimation techniques. Here, the modeling is based on the method of integrodifferential relations, which can be employed to determine accurate, finite-dimensional sets of state equations by using projection techniques. These lead to a finite element representation of the distributed parameter system. Where applicable, these finite element models are combined with finite volume representations to describe storage variables that are—with good accuracy—homogeneous over sufficiently large space domains. The advantage of this combination is keeping the computational complexity as low as possible. Under these prerequisites, real-time applicable control algorithms are derived and validated via simulation and experiment for a laboratory-scale heat transfer system at the Chair of Mechatronics at the University of Rostock. This benchmark system consists of a metallic rod that is equipped with a finite number of Peltier elements which are used either as distributed control inputs, allowing active cooling and heating, or as spatially distributed disturbance inputs.

Robust stability and memory state feedback control for a class of switched nonlinear systems with multiple time-varying delays

2021 ◽  
pp. 107754632098598
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Multiple Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Common Lyapunov Function ◽  
Suggested Approach ◽  
Aggregation Techniques

This study is concerned with the stability analysis and the feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Unusually, more general time delays, which depend on the subsystem number, are considered. In this regard, by constructing a novel common Lyapunov function, using the aggregation techniques and the Borne and Gentina criterion, new algebraic stability and feedback stabilization conditions under arbitrary switching are derived. The proposed results are explicit and obtained without searching a common Lyapunov function through the linear matrix inequalities approach, considered a difficult matter in this case. At last, two numerical simulation examples are shown to prove the practical utility of the suggested approach.

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