In this paper, a new method for the stability analysis of interrupted turning processes is introduced. The approach is based on the construction of a characteristic function whose complex roots determine the stability of the system. By using the argument principle, the number of roots causing instability can be counted, and thus, an exact stability chart can be drawn. In the special case of period doubling bifurcation, the corresponding multiplier is substituted into the characteristic function, leading to an implicit formula for the stability boundaries. Further investigations show that all the period doubling boundaries are closed curves, except the first lobe at the highest cutting speeds. Together with the stability boundaries of Neimark-Sacker (or secondary Hopf) bifurcations, the unstable parameter domains are formed from the union of lobes and lenses.
Skip Nav Destination
Article navigation
July 2006
Research Papers
Lobes and Lenses in the Stability Chart of Interrupted Turning
Gábor Stépán
Gábor Stépán
Professor Head of Department of Applied Mechanics
Search for other works by this author on:
Róbert Szalai
Graduate Student
Gábor Stépán
Professor Head of Department of Applied Mechanics
J. Comput. Nonlinear Dynam. Jul 2006, 1(3): 205-211 (7 pages)
Published Online: November 15, 2003
Article history
Online:
November 15, 2003
Online:
November 21, 2003
Received:
August 20, 2005
Revised:
February 15, 2006
Citation
Szalai, R., and Stépán, G. (November 15, 2003). "Lobes and Lenses in the Stability Chart of Interrupted Turning." ASME. J. Comput. Nonlinear Dynam. July 2006; 1(3): 205–211. https://doi.org/10.1115/1.2198216
Download citation file:
Get Email Alerts
Numerical Simulation Method for the Rain-Wind Induced Vibration of the Three-Dimensional Flexible Stay Cable
J. Comput. Nonlinear Dynam
An Investigation of Dynamic Behavior of Electric Vehicle Gear Trains
J. Comput. Nonlinear Dynam (March 2025)
Nonlinear Dynamic Analysis Framework for Slender Structures Using the Modal Rotation Method
J. Comput. Nonlinear Dynam (March 2025)
Related Articles
Chatter Stability of General Turning Operations With Process Damping
J. Manuf. Sci. Eng (August,2009)
Increased Stability of Low-Speed Turning Through a Distributed Force and Continuous Delay Model
J. Comput. Nonlinear Dynam (October,2009)
Analysis of the Chatter Instability in a Nonlinear Model for Drilling
J. Comput. Nonlinear Dynam (October,2006)
Nonlinear Dynamics and Bifurcations of an Axially Moving Beam
J. Vib. Acoust (January,2000)
Related Proceedings Papers
Related Chapters
GA Based Multi Objective Optimization of the Predicted Models of Cutting Temperature, Chip Reduction Co-Efficient and Surface Roughness in Turning AISI 4320 Steel by Uncoated Carbide Insert under HPC Condition
Proceedings of the 2010 International Conference on Mechanical, Industrial, and Manufacturing Technologies (MIMT 2010)
On-Line a Predictive Model of Cutting Force in Turning with 3 Axis Acceleration Transducer Using Neural Network
International Conference on Advanced Computer Theory and Engineering (ICACTE 2009)
Dynamic Behavior in a Singular Delayed Bioeconomic Model
International Conference on Instrumentation, Measurement, Circuits and Systems (ICIMCS 2011)