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The heel is the face with the largest diameter respectively the largest distance to the
central axis. The toe represents the face with the smallest diameter. In order to get a
solid 3D body the cross section is revolved around the central axis by 360°. Finally
this extruded body is getting triangulated as described by [3].
The tool envelope is modeled by an extrusion of the tool profile depending on the
process kinematics, see figure 4. Like the workpiece, the tool is meshed by triangula-
tion as well.
Modeling of Tool Profile
Extrusion of Tool (Enveloping Body)
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1
13
2
12
3
11
4
10
5
6
9
8
7
Triangulation of Surface
Fig. 4.
Modeling and triangulation of tool
The data for workpiece, tool and process kinematics can be imported in the soft-
ware from an ASCII file in the neutral data format. This data format is a common one
in gear industry and developed by [5].
2.3
Simulation Method
When the modeling is finished a geometrical penetration calculation is conducted
within the manufacturing simulation. During this calculation the 3D bodies of work-
piece and tool envelope penetrate each other in compliance with the kinematics. The
penetration is realized by ray-tracing as described by [6]. The calculated penetration
volume can be interpreted as the undeformed chip geometry resulting from the cutting
process, see figure 5. With this undeformed geometry different characteristic values,
like the chip thickness h
cu
, can be calculated. It has to be mentioned that the penetra-
tion calculation is a geometrical calculation, i.e. that no plastic deformations and
thermal effects are considered.
In order to accelerate the penetration calculation bounding-boxes and Binary Space
Partitioning (BSP) trees are used as depicted from [6]. An additional approach to
accelerate the simulation is the calculation of the penetration by General-purpose
Computing on Graphics Processing Units (GPGPU) as published by [7] where
OpenCL, CUDA, PGI Accelerator are used in combination with graphics processing
units (GPU) in order to increase the performance.
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