The mechanics of continuous chip formation in oblique cutting in the absence of chip distortion. Part 1—Theory

Abstract

An analysis of oblique cutting applicable to the case when chip distortion does not occur is proposed. This is based on the realisation that material removal occurs in the normal cutting plane. This enables us to postulate the existence of an equivalent orthogonal cutting operation for any oblique operation. Thus if in the oblique operation performed with a tool of given geometry at an obliquity angle i, a layer of material of width W 1 and thickness t 1 is removed at a speed V then the equivalent orthogonal operation is performed with the same tool removing a layer of the same width at the same speed but with the uncut chip thickness reduced to t 1 cos i. It is hypothesized that the chip thickness t 2 and the normal component of the chip speed ( V c) n in oblique cutting are equal, respectively, to the chip thickness ( t 2) e and the chip speed ( V c) e in the equivalent orthogonal cutting operation. As a consequence of this hypothesis the normal shear plane angle φ n can be expressed in terms of the angle of obliquity i, the normal rake angle α n and the shear plane angle in orthogonal cutting φ 0. The reduced shear force component in the normal plane ( fs) 1 is shown to be equal, approximately, to that occurring in the equivalent orthogonal cutting operation. By analogy, the reduced force component acting normal to the cutting edge direction in oblique cutting ( f c) n is assumed to be equal to ( f c)0 , the reduced force component acting normal to the cutting edge direction in the equivalent orthogonal cutting operation. These expressions for ( fs) 1 and ( f c) n allow the normal chip/rake face “friction” angle, β n , to be calculated for any desired value of obliquity angle provided that the orthogonal values β 0 and φ 0 are known. If, in addition, the shear stress acting along the Merchant shear plane, τ, is known (e.g. from orthogonal cutting tests) then all of the reduced force components acting in the normal cutting plane can be computed. Finally, it is shown that the reduced force component in the plane of the rake face acts along the direction of chip flow, whence the reduced force component parallel to the cutting edge direction f 2 can be calculated from a knowledge of the value of the reduced force component acting along the line of greatest slope of the rake face f 1 and the chip flow angle η c , since f 2 = f 1 tan η c .