Related Experiment Video
Updated: Dec 19, 2025

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Essential chaotic dynamics of chatter in turning processes
1Department of Applied Mechanics, Budapest University of Technology and Economics, P. O. Box 91, H-1521 Budapest, Hungary.
Abstract:
Large-amplitude oscillations of turning operations are investigated, which can be modelled by a one degree-of-freedom damped oscillator subjected to the regenerative effect that introduces a relevant time delay in the system. In the case of large oscillations, when the cutting tool loses contact with the surface of the workpiece, the time delay is switched off, leading to a non-smooth delay differential equation. To explore the geometric structure of the global dynamics of the system, the mathematical model is approximated by means of the essential part of the spectrum in the region where the stationary cutting process may lose its stability. The trajectories embedded in the infinite-dimensional phase space are interpreted in a three-dimensional subspace and then analyzed by means of a discrete Lorenz-map. The bifurcation diagrams of the non-smooth system include chaotic windows, which are presented by numerical and semi-analytical tools and compared to the existing results in the literature.
Related Concept Videos
Dynamics of Circular Motion
Any acceleration must be produced by some force. Therefore, any force or combination of forces can cause centripetal acceleration. A few examples include the tension in the rope on a...
Dynamics Of Circular Motion: Applications
The Swing Equation
In a steady-state operation, the mechanical torque (Τm) supplied to the generator is balanced by the electrical torque (Τe)...
Rolling Without Slipping
Instantaneous Center of Zero Velocity
To analyze this, consider two points on the wheel: point A and point B. The absolute velocity of point B can be expressed as the vector sum of the absolute velocity of point A and the relative velocity of point B with respect to point A. To simplify this analysis,...
Deformation in a Circular Shaft

