| Summary: | 博士 === 國立成功大學 === 機械工程學系碩博士班 === 91 === The continued development of high-precision NC manufacturing techniques, together with the requirement to machine an increasing variety of freeform and complex surfaces, has resulted in a demand for specialized milling and shaping cutters. While a review of the published literature reveals an abundance of material relating to the manufacture of such cutters, typically these studies assume that experienced engineers operating on a more-or-less trial-and-error basis will carry out tool fabrication. As yet, no systematic integrated modeling approach for the design of these cutters has been proposed. Accordingly, this current paper adopts a differential geometry approach to construct a geometric model of these cutters. Furthermore, a process of reverse envelope is used to design the necessary sectional profiles of the grinding wheel based upon the required helical angle and groove section of the cutter. In this way, this paper proposes a comprehensive method that can facilitate the automatic design of milling and shaping cutters with a helical cutting edge. This paper concerns itself chiefly with the machining theory and design models associated with the newly developed helical rotating milling and shaping cutters.
Taking the maximal outer radius of the grooved section of the cutter as its basis, this paper first develops a generic model for a grinding wheel that is capable of manufacturing many different forms of cutter. Then, taking the same maximal outer radius, two grinding methods are proposed, i.e. axial and normal section methods, to manufacture cutters of the same form. The paper discusses the design models for many different forms of cutter with reference to three different types of cutting edge curve. For a constant rotating cutter speed, it is demonstrated how a simple two-axis NC machining operation may be used to complete grinding of the cutter in a single manufacturing pass through the application of suitable axial and radial grinding wheel feeding speeds. Furthermore, this paper presents a compensatory grinding operation that remedies the problem of residual revolving surface following the initial grinding process. The problems associated with the design model of these types of cutters are investigated. The use of a supplementary planar curve cutting edge to resolve the problems of over-cutting and non-existence of the cutting edge at the upper part of ball-end and end-mill cutters is also considered, together with the smooth conjunction of this supplementary curve with the original helical cutting edge on the shank.
This paper also develops the use of the differential geometry modeling method mentioned previously for application to the design modeling of specialized helical rotating shaping cutters. Based upon a concept of equidistance and equivalence, this paper develops models for the helical surface and the corresponding torus planar cutting edge for a cutter that comprises a helical cutting edge on a cylindrical shank surface. Having established the helical groove on the cylindrical shank of the shaping cutter, the corresponding grinding wheel profile, and the design parameters for the shank groove and the cutter, the lead angle of helical shaping cutters and the set-up principles for such cutters is discussed. Finally, the proposed models are verified numerically through a process of computer simulation.
The numerical results confirm the validity and accuracy of the theoretical models proposed for specialized milling and shaping cutters proposed in this current paper.
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