A new mathematical method of modeling parts in virtual CNC
lathing and its application on accurate tool path generation
Zezhong C. Chen
Received: 21 March 2017 /Accepted: 6 October 2017 / Published online: 18 October 2017
Springer-Verlag London Ltd. 2017
Abstract In industry, many taper shafts are designed with
tolerances of a few microns. To cut them in finish turning,
paths of the tool in virtual machining should be accurately
generated beforehand. For this purpose, the dimension errors
and surface roughness of the virtually cut workpiece should be
predicted. Unfortunately, the current tool path generation
methods cannot accurately calculate the errors and the rough-
ness, resulting in the taper errors larger than the part tolerance.
Our research formulates equations of the effective turning
edge to accurately calculate the dimension errors and the sur-
face roughness, and then proposes a new approach to CNC
programming for high-precision CNC turning. It lays a theo-
retical foundation of modeling parts in virtual turning and can
generate tool paths to machine taper parts with high accuracy.
Keywords CNC turning
Effective turning edge
Nomenclature in Fig. 2
Shank The main body of the tool holder in a
rectangular bar shape. For a cutting tool
with inserts, the shank supports the cutter
Base The bottom face of the tool shank when
set up in a turret.
Rake A metal-cutting tool is said to have a
rake when the top tool face, against
which the chips bear as they are being
removed, is inclined for the purpose
of either increasing or decreasing the
keenness or bluntness of the cutting
edge. If the tool face is not inclined
but parallel to the base, there would
be no rake.
The top face of the cutting portion or the
insert when the tool has a rake.
Side cutting edge
The major cutting edge of the tool that
undertakes large material removal load.
End cutting edge
The minor cutting edge that is the other
side of the cutting edge of the tool. The
end cutting edge is usually used for light
plunging and facing, and the cut-off tool
only has an end cutting edge.
Circular cutting edge
The profile of the cutter nose that is a
circular arc on the face and tangent to the
SCE and ECE.
The angle between a plane that contains
the SCE and is perpendicular to the base
and a plane that is perpendicular to the
tool feed direction.
The angle between a plane perpendicular
to the axis of the tool shank and a plane
containing the ECE and perpendicular to
Back rake The inclination of the face upward or
downward from the ECE. When the in-
clination is downward from the ECE, the
back rake is positive. If the inclination is
* Zezhong C. Chen
Department of Mechanical Engineering, Northwestern Polytechnical
University, Xi’an, People’sRepublicofChina
Department of Mechanical and Industrial Engineering, Concordia
University, Montreal, Quebec, Canada
Int J Adv Manuf Technol (2018) 95:243–256