Matthew A. Davies, Christopher J. Evans, Timothy J. Burns
In this paper, we provide experimental, numerical and analytical evidence suggesting that the onset of segmented chip formation is the result of a Hopf bifurcation in the material flow. We modify the conventional one-dimensional model for orthogonal cutting by introducing the concept of a local plastic deformation zone that accounts for indentation of the material near the tool tip. A one-dimensional, partial differential equation (PDE) model, similar to those used to describe the formation of adiabatic shear bands is developed to describe chip formation. Numerical simulations of this model are compared with experimental results; both are suggestive of a Hopf bifurcation and the subsequent development of relaxation oscillations. Based upon these observations, a simplified ordinary differential equation model that treats the shear zone as a control volume moving with the tool is developed. These results lead to an interpretation of metal cutting as a thermomechanical feedback process, which is similar in many ways to an open chemical reactor
Proceedings of IUTAM Symposium of New Applications of Non-Linear and Chaotic Dynamics in Mechanics
, Evans, C.
and Burns, T.
The dynamics of chip formation in machining, Proceedings of IUTAM Symposium of New Applications of Non-Linear and Chaotic Dynamics in Mechanics, Ithaca, NY
(Accessed February 20, 2024)