Journal
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
Volume 53, Issue 7, Pages 1904-1912Publisher
SCIENCE PRESS
DOI: 10.1007/s11431-010-3185-3
Keywords
five-axis NC machining; rotary cutter; cutter envelope surface; normal curvature; third-order point contact
Funding
- National Natural Science Foundation of China [50835004, 50775147]
- National Basic Research Program of China (973 Program) [2005CB724103]
- Science & Technology Commission of Shanghai Municipality [07JC14028]
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In this paper, the geometric properties of a pair of line contact surfaces are investigated. Then, based on the observation that the cutter envelope surface contacts with the cutter surface and design surface along the characteristic curve and cutter contact (CC) path, respectively, a mathematical model describing the third-order approximation of the cutter envelope surface according to just one given cutter location (CL) is developed. It is shown that at the CC point both the normal curvature of the normal section of the cutter envelope surface and its derivative with respect to the arc length of the normal section can be determined by those of the cutter surface and design surface. This model characterizes the intrinsic relationship among the cutter surface, cutter envelope surface and design surface in the neighborhood of the CC point, and yields the mathematical foundation for optimally approximating the cutter envelope surface to the design surface by adjusting the cutter location.
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