Research Papers

Virtual Five-Axis Flank Milling of Jet Engine Impellers—Part II: Feed Rate Optimization of Five-Axis Flank Milling

[+] Author and Article Information
W. B. Ferry

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

Y. Altintas

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

J. Manuf. Sci. Eng 130(1), 011013 (Feb 15, 2008) (13 pages) doi:10.1115/1.2815340 History: Received November 29, 2006; Revised September 07, 2007; Published February 15, 2008

This paper presents process optimization for the five-axis flank milling of jet engine impellers based on the mechanics model explained in Part I. The process is optimized by varying the feed automatically as the tool-workpiece engagements, i.e., the process, vary along the tool path. The feed is adjusted by limiting feed-dependent peak outputs to a set of user-defined constraints. The constraints are the tool shank bending stress, tool deflection, maximum chip load (to avoid edge chipping), and the torque limit of the machine. The linear and angular feeds of the tool are optimized by two different methods—a multiconstraint based virtual adaptive control of the process and a nonlinear root-finding algorithm. The five-axis milling process is simulated in a virtual environment, and the resulting process outputs are stored at each position along the tool path. The process is recursively fitted to a first-order process with a time-varying gain and a fixed time constant, and a simple proportional-integral controller is adaptively tuned to operate the machine at threshold levels by manipulating the feed rate. As an alternative to the virtual adaptive process control, the feed rate is optimized by a nonlinear root-finding algorithm. The virtual cutting process is modeled as a black box function of feed and the optimum feed is solved for iteratively, respecting tool stress, tool deflection, torque, and chip load constraints. Both methods are shown to produce almost identical optimized feed rate profiles for the roughing tool path discussed in Paper I. The new feed rate profiles are shown to considerably reduce the cycle time of the impeller while avoiding process faults that may damage the part or the machine.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

(Left) Finite element model of the tool with point-load cutting forces at the middle of each cutting force element. (Right) Free body diagrams of x, y, and z forces on each beam element.

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Figure 2

Force and boundary conditions for a finite beam element

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Figure 3

(a) Block diagram of the virtual cutting process. (b) z-domain block diagram of a closed-loop SISO adaptive-feed control system for a general CNO.

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Figure 4

Block diagram of the closed-loop multiconstraint adaptive-feed control system. The maximum P value from the virtual cutting process is used to select the P(z) and z−1P(z) values required to correctly limit the feed of the system.

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Figure 5

In a tool path segment i, the tool travels a distance, Δdi, and rotates a total angle, Δθi, in the same time period, Δt. Angular feeds must be scaled with tool tip feeds to preserve this tool path geometry.

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Figure 6

Virtual cutting process modeled as a nonlinear function of tool tip feed. Peak outputs are normalized so that they become zero when equal to their respective constraints.

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Figure 7

Lines represent different CNOs as a function of feed. The optimum feed is feed at which one CNO is zero and all others are below zero.

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Figure 8

Upper plots show tool stress and tool tip feed for the entire tool path. Middle and lower plots show closeups of tool stress limiting the output. When engagements change, both tool stress and feeds are increased/decreased until the peak tool stress is equal to its constraint.

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Figure 9

Multiconstraint adaptive-feed control optimization results for the IBR roughing tool path. With the given constraints, the cycle time has been reduced by about 45%. Note how different constraints are active during different parts of the tool path.

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Figure 10

Comparison of multiconstraint adaptive-feed control and nonlinear root-finding optimization algorithms. Feed profiles from both methods are almost identical. In both methods, a 45% reduction in cycle time was achieved with the given constraints.

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Figure 11

Illustration showing the finite element model of the cutting tool and the assembly of the global stiffness matrix and global nodal force vector



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