Geometric Contributions to 3-Axis Milling of Sculptured Surfaces

Abstract

When we are trying to shape a surface X by 3-axis milling, we encounter a list of problems: First we have to decide if locally the milling tool I: is able to move along the surface such that its envelope during the motion is the given surface. This is a question involving the curvatures of X and I:. Second, we want to avoid that while milling in one part of X, I: intersects another, already finished, part of the surface. This is a problem which involves global shape properties of the surface and can be successfully attacked by considering the general offset surface of X with respect to I:. Third, in practice a cutting-tool is not able to perform a 2-dimensional motion along a surface. It has to trace out a finite number of piecewise smooth paths such that the resulting surface does not differ from X too much. This question again involves, in the limit case of very small error tolerance, only the curvatures of X and I:. If we allow larger scallop heights, the path finding also requires the study of local and global properties.

Geometric simulation of locally optimal tool paths in three-axis milling

“…The next touching point of the tool will be chosen in this direction on the boundary of the processed patch. The suggested moving direction is similar in [26] in a different computational approach using Dupin-indicatrices.…”

“…Namely, the angle between the tool axis and the surface normal changes to much on a curved surface, which leads to uneven abrasion of the tool. The computed moving direction could be combined with other tool path generation algorithms as suggested also in [26].…”

“…A method for approximating the processed part of the surface around a contact point, for generating the widest stripe along a tool path and for investigating local and global millability with a given cutting tool is presented in [9] and [26]. The condition for collisionfree manufacturing is expressed in terms of the curvature indicatrices of the part surface and the tool surface at their touching point.…”

“…Investigation of surface curvatures at the touching point of the target surface and the cutting tool concludes that the most efficient tool feed direction in three-axis milling, which can minimize the total length of necessary tool paths, is the principal direction of the maximal normal curvature [2], [3], [26]. Namely, this "steepest ascending" tool path leaves the widest track (processed stripe) on the machined surface, as also shown in [26]. The same conclusion is formulated in [1], where a torodial shaped cutter is investigated on a four and five axis machine.…”

Screw rotor manufacturing via 5-axis flank CNC machining using conical tools

“…Inspired by industrial needs, efficient and highly accurate manufacturing of free-form objects has been of interest for several decades [1][2][3][4][5][6]. Computer numerically controlled (CNC) machining is the leading subtractive manufacturing technology and even though nowadays additive manufacturing is increasing its share on the manufacturing market [7], certain types of mechanical components like turbine blades or engine components are, due to the stiffness requirements, preferred to be manufactured from a single material block.…”