Instability conditions due to structural nonlinearities in regenerative chatter

Chatter is an instability condition in machining processes characterized by nonlinear behavior, such as the presence of limit cycles, jump phenomenon, subcritical Hopf and period doubling bifurcations. Although the use of nonlinear techniques has provided a better understanding of chatter, neither a...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear dynamics 2009-06, Vol.56 (4), p.415-427
Main Authors: Vela-Martínez, Luciano, Jáuregui-Correa, Juan Carlos, González-Brambila, Oscar Manuel, Herrera-Ruiz, Gilberto, Lozano-Guzmán, Alejandro
Format: Article
Language:English
Subjects:
Automotive Engineering
Bifurcations
Canonical forms
Chatter
Classical Mechanics
Control
Dynamical Systems
Eigenvalues
Engineering
Hopf bifurcation
Machining
Mechanical Engineering
Multiscale analysis
Original Paper
Period doubling
Qualitative analysis
Representations
Stability analysis
Stiffness
Structural stability
Vibration
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Chatter is an instability condition in machining processes characterized by nonlinear behavior, such as the presence of limit cycles, jump phenomenon, subcritical Hopf and period doubling bifurcations. Although the use of nonlinear techniques has provided a better understanding of chatter, neither a unifying model nor an exact solution has yet been developed due to the intricacy of the problem. This work proposes a weakly nonlinear model with square and cubic terms in both structural stiffness and regenerative terms, to represent self-excited vibrations in machining. An approximate solution is derived by using the method of multiple scales. In addition, a qualitative analysis of the effect of the nonlinear parameters on the stability of the system is performed. The structural cubic term gives a better representation of the nonlinear behavior, whereas the square term represents a distant attractor in the stability chart. Instability due to subcritical Hopf bifurcations is established in terms of the eigenvalues of the model in normal form. An important contribution of this analysis is the representation of hysteresis in terms of new lobes within the conventional stability limits, useful in restoring stability. This analysis leads to a further understanding of the nonlinear behavior of regenerative chatter.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-008-9411-x