Toroidal versus ball nose and flat bottom end mills

  • S. Bedi
  • F. Ismail
  • M. J. Mahjoob
  • Y. Chen


This paper compares the surface roughness along and across the feed directions produced by toroidal, ball nose, and flat bottom end mills. The study is conducted numerically and by cutting tests of aluminium. The results show that the toroidal cutter inherits the merits of the other two cutters; it produces small scallops across the feed direction, and low roughness along the feed direction.


5-axis machining Ball end mills Feed mark Flat end mills Scallop height estimation Toroidal end mill 



scallop height


radius of curvature of surface


inclination angle



subtended angle between the point of contact on the tool profile and the surface


surface roughness


offset distance of insert from tool axes for toroidal cutter


cutter radius


radius of insert for toroidal cutter


feed per tooth


undercut height

y, β, γ

intermediate variables


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Copyright information

© Springer-Verlag London Limited 1997

Authors and Affiliations

  • S. Bedi
    • 1
  • F. Ismail
    • 1
  • M. J. Mahjoob
    • 1
  • Y. Chen
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of WaterlooWaterlooCanada

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