# Stabilization in a State-Dependent Model of Turning Processes

@article{Hu2012StabilizationIA, title={Stabilization in a State-Dependent Model of Turning Processes}, author={Qingwen Hu and Wieslaw Krawcewicz and Janos Turi}, journal={SIAM J. Appl. Math.}, year={2012}, volume={72}, pages={1-24} }

We consider a two-degree-of-freedom model for turning processes which involves a system of differential equations with state-dependent delay. Depending on process parameters (e.g., spindle speed, depth of cut) the cutting tool can exhibit unwanted vibrations, resulting in a nonsmooth surface of the workpiece. In this paper we propose a feedback law to stabilize the turning process for a large range of system parameters. The feedback law introduces a generic nonhyperbolic stationary point into…

## 6 Citations

### Global Stability Lobes of Turning Processes with State-Dependent Delay

- MathematicsSIAM J. Appl. Math.
- 2012

The spindle speed control strategy investigated in [SIAM J. Appl. Math., 72 (2012), pp. 1--24] can provide essential improvement on the stability of turning processes with state-dependent delay, and furthermore the existence of a proper subset of the stability region which is independent of system damping is shown.

### Global Hopf bifurcation of differential equations with threshold type state-dependent delay

- Mathematics
- 2014

### Stability of Systems with State Delay Subjected to Digital Control

- Mathematics
- 2014

Stability of linear delayed systems subjected to digital control is analyzed. These systems can typically be written in the form
$$ \dot{{x}}(t)={Ax}(t)+{Bx}(t-\tau)+{Cx}(t_{j-1}) \; , \quad t \in…

### Stabilization of turning processes using spindle feedback with state-dependent delay

- Mathematics, Materials Science
- 2018

We develop a stabilization strategy of turning processes by means of delayed spindle control. We show that turning processes which contain intrinsic state-dependent delays can be stabilized by a…

### Positive solutions of iterative functional differential equations and application to mixed-type functional differential equations

- MathematicsDiscrete & Continuous Dynamical Systems - B
- 2021

<p style='text-indent:20px;'>In this paper we consider the existence, uniqueness, boundedness and continuous dependence on initial data of positive solutions for the general iterative functional…

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