The document proposes using rotating curvilinear tools shaped like Reuleaux triangles to efficiently machine polygonal shapes with sharp corners using electric discharge machining (EDM). A Reuleaux triangle can rotate inside a square while maintaining contact with the edges, machining 98.8% of the square's area. This approach improves flushing in the interelectrode gap compared to stationary circular tools, enabling higher removal rates and better surface quality. The kinematics of rotating Reuleaux triangle tools are analyzed and the concept is extended to machine regular and irregular polygons.

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!