Abstract
An approximate numerical analysis of slip-line fields is presented which requires one tenth the computing time of the matrix operator method. The analysis retains the structure of the matrix method but the matrix operators for force and displacement calculation and for the calculation of slip-line curvatures are replaced by simple algebraic expressions. These are developed from the approximation that slip-line elements may be replaced by circular arcs. The approximations have been tested on slip-line fields for free machining and machining with applied chip tension in which the angular extents of the assumed arcs have been as large as 0.6 radians. They have been found to be adequate at a better than 5% degree of accuracy except for levels of friction stress between chip and tool greater than 80% of the chip material shear flow stress.
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