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Research Papers

# Cutter-Workpiece Engagement Calculations by Parallel Slicing for Five-Axis Flank Milling of Jet Engine Impellers

[+] Author and Article Information
W. Ferry

Manufacturing Automation Laboratory, University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, B.C., V6T 1Z4, Canadaferry@interchange.ubc.ca

D. Yip-Hoi

Manufacturing Automation Laboratory, University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, B.C., V6T 1Z4, Canadayiphoi@mech.ubc.ca

J. Manuf. Sci. Eng 130(5), 051011 (Aug 19, 2008) (12 pages) doi:10.1115/1.2927449 History: Received July 25, 2007; Revised January 04, 2008; Published August 19, 2008

## Abstract

Cutter-workpiece engagement maps, or cutting flute entry/exit locations as a function of height, are a requirement for prediction of cutting forces on the tool and workpiece in machining operations such as milling. This paper presents a new method of calculating tool-part intersection maps for the five-axis flank milling of jet engine impellers with tapered ball-end mills. The parallel slicing method (PSM) is a semi-discrete solid modeling technique written in C++ using the ACIS boundary representation solid modeling environment. The tool swept envelope is generated and intersected with the workpiece to obtain the removal volume. It is also subtracted from the workpiece to obtain the finished part. The removal volume is sliced into a number of parallel planes along a given axis, and the intersection curves between each tool move and plane are determined analytically. The swept area between successive tool positions is generated using the common tangent lines between intersection curves, and then removed from the workpiece. This deletes the material cut between tool moves, ensuring correct engagement conditions. Finally, the intersection curves are compared to the planar slices of the updated part, resulting in a series of arcs. The end points of these arcs are joined with linear segments to form the engagement polygon that is used to calculate the engagement maps. Using this method, cutter-workpiece engagement maps are generated for a five-axis flank milling toolpath on a prototype integrally bladed rotor with a tapered ball-end mill. These maps are compared to those obtained from a benchmark cutter-workpiece engagement extraction method, which employs a fast, $z$-buffer technique. Overall, the PSM appears to obtain more accurate engagement zones, which should result in more accurate prediction of cutting forces. With the method’s current configuration, however, the calculation time is longer.

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## Figures

Figure 2

Swept areas may not update workpiece, if slice axis is chosen improperly

Figure 3

(a) Practical method of determining slice axis, S—the half-angle tool axis orientation between the first and last tool moves. (b) Slicing of removal volume along S.

Figure 4

Illustrations showing various tapered ball-end mill/plane intersection shapes. (a) single conic, (b) composite conic, (c) truncated conic, and (d) composite truncated conic.

Figure 5

Calculation of approximate tool swept area between two elliptical intersection curves. An analytical tangent line solution was used to generate the swept area.

Figure 6

(a) Flowchart showing algorithm for swept area calculation with complex conics. (b) Graphical examples of various steps of the algorithm.

Figure 7

(a) An example of a self-intersecting toolpath. (b) A more common example of self-intersection that can occur in five-axis impeller machining.

Figure 8

(a) Engagement arcs are converted from the global coordinate system to the tool coordinate system. (b) Engagement polygon is created by moving around the perimeter of arcs and joining end points with linear segments.

Figure 1

Diagram of the various steps of the parallel slicing method (PSM)

Figure 9

Close-up of a typical cutter-workpiece engagement map. Maps are defined by a series of blocks.

Figure 10

Calculation of removal volume and finished workpiece for the five-axis milling of an integrally bladed rotor (IBR)

Figure 11

(a) and (b) Removal volume sliced into 30 planes along the average tool axis orientation. (c)–(f) Sliced removal volume at various stages of the toolpath.

Figure 12

Illustration of a cutter-workpiece engagement map from a removal volume with (a) 30 and (b) 60 slices.

Figure 13

Comparison of engagement maps calculated from the parallel slicing method (PSM) and the Manufacturing Automation Laboratory’s Virtual Machining Interface (MAL-VMI)

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