RESEARCH PAPERS: Other Technical Papers

A Theory of Nonlinear Regenerative Chatter

[+] Author and Article Information
N. H. Hanna, S. A. Tobias

Department of Mechanical Engineering, University of Birmingham, Birmingham, United Kingdom

J. Eng. Ind 96(1), 247-255 (Feb 01, 1974) (9 pages) doi:10.1115/1.3438305 History: Received June 06, 1973; Online July 15, 2010


A mathematical theory of nonlinear chatter is developed. In this, the structure is represented by an equivalent single degree of freedom system with nonlinear stiffness characteristics and the cutting force by a third degree polynomial of the chip thickness. This model leads to a second order differential equation with nonlinear stiffness and nonlinear time delay terms from which the conditions of steady state chatter are derived. These are then discussed by applying them to an equivalent system derived from experimental data pertaining to a face milling process. The theory provides an explanation for the stages in which chatter develops and also for the “finite amplitude instability” phenomenon.

Copyright © 1974 by ASME
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