Jr. Pratt et Ah. Nayfeh, Chatter control and stability analysis of a cantilever boring bar under regenerative cutting conditions, PHI T ROY A, 359(1781), 2001, pp. 759-792
Citations number
52
Categorie Soggetti
Multidisciplinary
Journal title
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
A theoretical and experimental investigation into the stability of a slende
r boring bar under regenerative cutting conditions is presented. The bar ha
s been equipped with actuators and sensors for feedback control of its stru
ctural dynamics. It is modelled at the tool point by a mass-spring-damper s
ystem free to move in two mutually perpendicular directions. Our aim is to
demonstrate the effect of simple feedback control on the parameter space of
chatter-free machining in a boring process using theory and experiment. We
reinforce the notion that the system design for control should provide act
uation in two orthogonal directions because the cutting forces couple the p
rincipal modes of the tool in a complex fashion. Active control of the tool
damping in each of the principal modal directions is implemented and shown
in theory and experiment to be quite effective at suppressing chatter.
Problems caused by jumps front stable to unstable cutting due to nonlinear
regenerative chatter effects are also considered. The case where the cuttin
g forces are described by polynomial functions of the chip thickness is exa
mined. We use a perturbation technique to calculate the nonlinear normal fo
rm of the governing equations to determine the post-linear instability (bif
urcation) behaviour. The predicted bifurcation corresponds to a subcritical
Hopf bifurcation, and hence the predicted transition from stable to unstab
le cutting is not smooth and may possess hysteresis. This result is in qual
itative agreement with experimental observations. An active control techniq
ue for changing the form of this bifurcation from subcritical to supercriti
cal is presented for a prototypical, single-degree-of-freedom model.