Time-optimal CNC tool paths : a mathematical model of machining

Free-form surface machining is a fundamental but time-consuming process in modern manufacturing. The central question we ask in this thesis is how to reduce the time that it takes for a 5-axis CNC (Computer Numerical Control) milling machine to sweep an entire free-form surface in its finishing stage. We formulate a non-classical variational time-optimization problem defined on a 2-dimensional manifold subject to both equality and inequality constraints. The machining time is the cost functional in this optimization problem. We seek for a preferable vector field on a surface to obtain skeletal information on the toolpaths. This framework is more amenable to the techniques of continuum mechanics and differential geometry rather than to path generation and conventional CAD/CAM (Computer Aided Design and Manufacturing) theory. After the formulation, this thesis derives the necessary conditions for optimality. We decompose the problem into a series of optimization problems defined on 1-dimensional streamlines of the vector field and, as a result, simplify the problem significantly. The anisotropy in kinematic performance has a practical importance in high-speed machining. The greedy scheme, which this thesis implements for a parallel hexapod machine tool, uses the anisotropy for finding a preferable vector field.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2001

Author dc:creator

• Kim, Taejung, 1969-

Advisor dc:contributor.advisor

• Sanjay E. Sarma.

• Mechanical Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/8861

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/8861