球面のボールエンドミル加工における加工面創成機構の理論解析

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This paper clarifies the generating mechanism of machined surface by ball-nosed end milling through geometric analysis. The problem definition is to determine a height of cusp at a voluntary position in milling a spherical surface with a plane cutting edge of straight flute. It is assumed that tool axis is on the plane perpendicular to the feed direction. The necessary and sufficient conditions for identifying the tool rotating angle and its cutting edge at the specified position are originally formulated and their solving procedures based on Newton-Raphson method are mentioned. The number of solutions in these conditions is analyzed and explained geometrically. It is found that a certain area is cut maximum three times by the same edge, regardless of its edge shape. The machined surface by the two and three flutes of end mills are simulated and illustrated graphically with use of a geometric modeling system. A machined surface is illustrated as a combination of colored area corresponding to applied cutting edges, and it is helpful to understand the generating mechanism of machined surface. The computing time to detect the shape of cusp is about one third of that by a previous method reported. Conclusions are briefly mentioned.
公益社団法人精密工学会の論文
1999-10-05