Full Content is available to subscribers

Subscribe/Learn More  >

An Object-Space Based Machining Simulation in Milling: Part 1 — By Natural Quadric and Flat Surfaces

[+] Author Affiliations
Eyyup Aras

University of British Columbia, Vancouver, BC, Canada

Paper No. DETC2009-87635, pp. 709-719; 11 pages
  • ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 29th Computers and Information in Engineering Conference, Parts A and B
  • San Diego, California, USA, August 30–September 2, 2009
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4899-9 | eISBN: 978-0-7918-3856-3
  • Copyright © 2009 by ASME


This two-part paper presents an efficient parametric approach to updating workpiece surfaces represented by the Z-map vectors. The methodology is developed for up to 3 1/2 1/2-axis machining in which a tool can be arbitrarily oriented. In calculations the Automatically Programmed Tool (APT)-type milling cutters represented by the natural quadrics, planar and the toroidal surfaces are used. The machining process is simulated through calculating the intersections between the Z-map vectors and the tool envelope surface which is modeled by using a tangency function. Part 1 of this two-part paper presents the methodology for the cutters with natural quadrics and planar surfaces. For those surfaces intersection calculations are performed analytically. The geometric complexity of a torus is higher than those of the natural quadric and planar surfaces. Furthermore if the torus has an arbitrary orientation then the intersection calculations for the torus present great difficulties. In NC machining typically a torus is considered as one of the constituent parts of a cutter. In this case only some parts of the torus envelopes, called contact-envelopes, can intersect with Z-map vectors. For this purpose in Part 2 of this two-part paper an analysis is developed for separating the contact-envelopes from the non-contact envelopes. Then a system of non-linear equations in several variables, obtained from intersecting Z-map vectors with contact envelopes, is transformed into a single variable non-linear function. Later using a nonlinear root finding analysis which guarantees the root(s) in the given interval, those intersections are addressed.

Copyright © 2009 by ASME



Interactive Graphics


Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature

Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In