Generating cutter swept envelopes in five-axis milling by two-parameter families of spheres

Authors:
Eyyup Aras
Affiliations:
Department of Mechanical Engineering, University of British Columbia, 1000 University Boulevard, Vancouver, BC, Canada, V6T 1Z4
Venue:
Computer-Aided Design
Year:
2009

Citing 7
Cited 3

Numerical control programming in APT

Numerical control programming in APT
Sweeping of three-dimensional objects

Computer-Aided Design
Computing rational parametrizations of canal surfaces

Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Generating swept solids for NC verification using the SEDE method

SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Scientific Visualization

IEEE Computer Graphics and Applications
A Scan Line Algorithm for Rendering Curved Tubular Objects

PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Geometric Modeling for Swept Volume of Moving Solids

IEEE Computer Graphics and Applications

Complete swept volume generation, Part I: Swept volume of a piecewise C1-continuous cutter at five-axis milling via Gauss map

Computer-Aided Design
Complete swept volume generation - Part II: NC simulation of self-penetration via comprehensive analysis of envelope profiles

Computer-Aided Design
HelSweeper: Screw-sweeps of canal surfaces

Computer-Aided Design

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents an efficient parametric approach of determining the shape of the envelope surface by a generalized cutter that follows five-axis tool path during NC machining. In this approach the cutter is modeled as a canal surface. By considering the tool motions the cutter is decomposed into a set of characteristic and great circles which are generated by two-parameter families of spheres. The center of a sphere from these families is described by two parameters which represent the spine curve and the tool path, and the radius of the sphere is described by one parameter representing the spine curve. Considering the relationship between characteristic and great circles the grazing points on the tool surface are identified. Analytically it is proven for the NC cutter geometries that any point on the envelope surface is located at the intersection of the characteristic and great circles. Then based on the proofs a closed-form solution for computing the grazing points generated by a surface of revolution is presented. The presented methodology is reduced to a simpler parametric form when the NC cutters are described by pipe surfaces.