NDLI: Analytical envelope surface representation of a conical cutter undergoing rational motion

Content Provider	Springer Nature Link
Author	Bi, QingZhen Zhu, LiMin Wang, YuHan Ding, Han
Copyright Year	2009
Abstract	Flank milling with a taper cutter is widely used in industry. The analytical representation of the envelope surface generated by a conical cutter undergoing rational motion is derived by bringing together the theories of line geometry and kinematics. Based on the projective duality between a point and a plane in line geometry, a cone surface is represented as two pieces of rational quadratic Bézier developable surfaces in terms of the plane coordinates instead of the traditional point coordinates. It provides a way to describe and calculate the envelope surface exactly by analyzing the trajectory of a plane undergoing a two-parameter rational motion. The rotation around the axis of the cone is adopted to ensure that the characteristic curve is located on the same piece of rational quadratic Bézier developable surface of the cone. The degenerate cases that the characteristic curve does not exist are also discussed. Examples are provided, in which the envelope surfaces of a conical cutter undergoing rational Bézier and B-spline motions are computed. The results can be applied to tool-path planning and error analysis for five-axis flank milling machining.
Starting Page	719
Ending Page	730
Page Count	12
File Format	PDF
ISSN	02683768
Journal	The International Journal of Advanced Manufacturing Technology
Volume Number	47
Issue Number	5-8
e-ISSN	14333015
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-08-06
Publisher Place	London
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Envelope surface Conical cutter Line geometry Rational motion Flank milling Computer-Aided Engineering (CAD, CAE) and Design Mechanical Engineering Production/Logistics Industrial and Production Engineering
Content Type	Text
Resource Type	Article
Subject	Industrial and Manufacturing Engineering Control and Systems Engineering Mechanical Engineering Computer Science Applications Software

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