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Rotating Curvilinear Tools 
for EDM of 
Polygonal Shapes with Sharp Corners 
Y. Ziada, P. KoshyMcMaster University, Canada 
57thCIRP General Assembly, DresdenAugust 21, 2007
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Flushing of the interelectrode gap is of critical importance in EDM processes, in regard to machining productivity and machined surface quality 
2/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Several techniques can be used to facilitate flushing in EDM 
through-tool forced flow 
jump EDM 
jet flushing 
horizontal EDM 
3/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Another approach to flushing is to induce a relative motion between the electrodes 
ED-milling 
planetary EDM 
4/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
The present work 
involves kinematic aspects of rotating 
curvilinear 
tools 
for sinking cavities with sharp 
corners 
5/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Reuleaux Triangle 
s 
1 
2 
3 
6/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Reuleaux Triangle is a curve of constant width that can rotate inside a square 
s 
s 
7/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Kinematics of a Reuleaux Triangle 
8/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
For every revolution 
of the Reuleaux Triangle, the centroid traverses the orbit three times in the opposite direction 
The swept area is 
98.8% of that of the square 
9/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
The area of a 
Reuleaux Triangle is 70.5% of that of the square 
A circular tool for 
machining a similar corner will only be 4% of the area of the square 
10/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Replacing the complex orbit with a circular one facilitates implementation on a machine tool with a single servo-controlled axis, and entails a maximum profile deviation of only 0.003s 
25 mmc) 11/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Reuleaux Triangle tools correspond to improved removal rates and better surface quality 
b) arcing 
Stationary 25 mmc) 
RT 
25 mm 
12/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Machining of a square with a sharp corner using Reuleaux Triangle tools involves modifications to tool shape and tool path 
k= 1.93 for an included angle of 90 degrees 
≈ sks 
13/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Modification to tool path 
Y 
0.034 
number of sides 
14/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Machining of a square with a sharp corner 
Locus magnified 2X 
10 mm 
15/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Extension of the concept to machine regular polygons 
16/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Machining of a hexagon 
Locus magnified 2X 
5 mm 
17/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Machining of a non-regular polygon 
Locus magnified 2X 
5 mm 
18/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Machining of a triangle 
19/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Conclusions 
Innovative kinematic schemes motivated by the concept 
of Reuleaux Triangle for the seemingly impossible task of using rotating tools to sink polygonal shapes with sharp corners are presented 
Application of the technology enhances gap flushing while maximizing the frontal machining area 
Efforts are required to address tool wear issues resulting from the adverse geometric relative duty of Reuleaux Triangle tools 
The work represents a significant advance towards exploiting the capabilities of CNC ram EDM 
20/20
Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners 
Y. Ziada, P. Koshy 
57thCIRP General Assembly 
Dresden, Germany, August 21, 2007 
Thank you 
for your kind attention!

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Machining of sharp corners using rotating tools

  • 1. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. KoshyMcMaster University, Canada 57thCIRP General Assembly, DresdenAugust 21, 2007
  • 2. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Flushing of the interelectrode gap is of critical importance in EDM processes, in regard to machining productivity and machined surface quality 2/20
  • 3. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Several techniques can be used to facilitate flushing in EDM through-tool forced flow jump EDM jet flushing horizontal EDM 3/20
  • 4. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Another approach to flushing is to induce a relative motion between the electrodes ED-milling planetary EDM 4/20
  • 5. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 The present work involves kinematic aspects of rotating curvilinear tools for sinking cavities with sharp corners 5/20
  • 6. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Reuleaux Triangle s 1 2 3 6/20
  • 7. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Reuleaux Triangle is a curve of constant width that can rotate inside a square s s 7/20
  • 8. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Kinematics of a Reuleaux Triangle 8/20
  • 9. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 For every revolution of the Reuleaux Triangle, the centroid traverses the orbit three times in the opposite direction The swept area is 98.8% of that of the square 9/20
  • 10. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 The area of a Reuleaux Triangle is 70.5% of that of the square A circular tool for machining a similar corner will only be 4% of the area of the square 10/20
  • 11. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Replacing the complex orbit with a circular one facilitates implementation on a machine tool with a single servo-controlled axis, and entails a maximum profile deviation of only 0.003s 25 mmc) 11/20
  • 12. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Reuleaux Triangle tools correspond to improved removal rates and better surface quality b) arcing Stationary 25 mmc) RT 25 mm 12/20
  • 13. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Machining of a square with a sharp corner using Reuleaux Triangle tools involves modifications to tool shape and tool path k= 1.93 for an included angle of 90 degrees ≈ sks 13/20
  • 14. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Modification to tool path Y 0.034 number of sides 14/20
  • 15. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Machining of a square with a sharp corner Locus magnified 2X 10 mm 15/20
  • 16. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Extension of the concept to machine regular polygons 16/20
  • 17. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Machining of a hexagon Locus magnified 2X 5 mm 17/20
  • 18. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Machining of a non-regular polygon Locus magnified 2X 5 mm 18/20
  • 19. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Machining of a triangle 19/20
  • 20. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Conclusions Innovative kinematic schemes motivated by the concept of Reuleaux Triangle for the seemingly impossible task of using rotating tools to sink polygonal shapes with sharp corners are presented Application of the technology enhances gap flushing while maximizing the frontal machining area Efforts are required to address tool wear issues resulting from the adverse geometric relative duty of Reuleaux Triangle tools The work represents a significant advance towards exploiting the capabilities of CNC ram EDM 20/20
  • 21. Rotating Curvilinear Tools for EDM of Polygonal Shapes with Sharp Corners Y. Ziada, P. Koshy 57thCIRP General Assembly Dresden, Germany, August 21, 2007 Thank you for your kind attention!