On the non-uniqueness of the machining process

Abstract

The elimination of a class of possible slip-line field solutions for orthogonal machining indicates that the process is not uniquely defined. The range of possible solutions for any value of tool rake angle and interfacial shear stress is shown to be associated with large variations in the curvature of the machined chip. Machining conditions are split into two types, for one of which the machined chip will always curl, while the other has the Lee & Shaffer slip-line field as a lower limit of the solution range. The extent of the solution range for any value of friction is found to decrease with increasing rake angle. The analysis is shown to be consistent with certain experimental work available.

In situ analysis of flow dynamics and deformation fields in cutting and sliding of metals

“…These oscillations are difficult to envision in a steady flow framework. While some SLFs for continuous chip formation, which have attempted to include a pile-up region [18] or an isolated flow zone [10] in connecting the workpiece and chip surfaces, could, potentially, be used to justify flow oscillations occurring close to the free surface, these fields are inadmissible for a rigid perfectly plastic material. In addition, the shear plane oscillations observed in the present experiments are not confined to the prow surface, but occur through the chip thickness.…”

“…These analyses have been useful for predicting cutting forces, and strains in the (continuous) chip. Perhaps less well recognized is the role that SLF has played in highlighting important conceptual and phenomenological aspects of the chip formation process: non-uniqueness of deformation due to a lack of flow constraint, chip curl, prow formation and incipient failure in the prow region [9,10,12,18]. These observations have served to guide the development of finite-element simulations of machining.…”

“…Unique features of this flow are imposition of large plastic strains, strains much higher than is common in conventional materials tests, and its unconfined nature, which affords degrees of freedom not typically available in bulk deformation processing [8]. It has long been recognized that this lack of flow confinement can result in unsteady flow, plastic instabilities and non-uniqueness in flow mode [9,10]. Unsteady flow and plastic instabilities play a key role in producing the diverse variety of chip-particle morphologies and surface patterns observed in cutting, e.g.…”

“…Chip formation at small negative and positive α has been studied because of its relevance to machining with geometrically well-defined tools. Theoretical analyses of this chip formation have been based largely on SLF and upper bound methods, with the assumption of a steady laminar flow and rigid perfectly plastic material [1,9,10,18]. A few SLFs for cutting of strain-hardening materials have been proposed using experimental flow fields, but again for steady flow [19].…”

Slip-line metal cutting model with negative rake angle

“…Albrecht (1960) based his model on the existence of a stagnation point on the radius where the work material's tangential velocity vanished. Dewhurst (1978) proposed the slip-line model for metal cutting with a curled chip when using a flat-faced cutting tool. In this model the force acts between the chip and obstruction.…”