There are many fabrication processes in modern manufacturing, but current modeling and simulation tools only simulate a few unit processes based on different geometry models. To overcome the data exchange problem between different models, this paper studies various in-process geometry models together with their working systems / prototypes for traditional manufacturing processes. Novel hybrid multiple-machining and layered manufacturing processes are presented to identify critical issues. Working towards a vision of pervasive modeling and simulation, a unified Voxel-based in-process geometry model for multiple-machining and layered manufacturing simulations is proposed and discussed.

1. 1 Copyright © 2005 by ASME
Proceedings of IMECE2005:
2005 ASME International Mechanical Engineering Congress and Exposition
November 5-11 2005, Orlando Florida
IMECE2005-82573
TOWARDS A UNIFIED IN-PROCESS GEOMETRIC MODEL FOR MULTIPLE MACHINING AND
LAYERED MANUFACTURING
Peiling Liu, C.F. Zhu, B. Song
Singapore Institute of Manufacturing Technology
Tel: (+65) 67938356
plliu@SIMTech.a-star.edu.sg
Singapore 638075
W.F. Lu
National University of Singapore
Y.Q. Lu, X.M. Ding
Institute of High Performance Computing of Singapore
ABSTRACT
There are many fabrication processes in modern
manufacturing, but current modeling and simulation tools only
simulate a few unit processes based on different geometry
models. To overcome the data exchange problem between
different models, this paper studies various in-process
geometry models together with their working systems /
prototypes for traditional manufacturing processes. Novel
hybrid multiple-machining and layered manufacturing
processes are presented to identify critical issues. Working
towards a vision of pervasive modeling and simulation, a
unified Voxel-based in-process geometry model for multiple-
machining and layered manufacturing simulations is proposed
and discussed.
Keywords: Modeling and Simulation, In-process Model,
Multiple Machining, Layered Manufacturing
INTRODUCTION
Compared with the sharp decline in computing cost,
worldwide material and machine tool prices are surging.
Saving material and manufacturing cost through pervasive
application of modeling and simulation (M&S) is not only
technically possible, but also makes business sense in today’s
increasingly competitive environment.
There are many fabrication technologies in modern
manufacturing industries. In addition to the traditional
manufacturing processes such as machining, forging, casting,
and welding, Layered Manufacturing (LM) technologies have
developed rapidly in the past decade. A wide variety of
models and simulation methods for traditional manufacturing
processes especially machining, have been developed for
different purposes based on a range of principles and
techniques [1]. For instance, the B-rep model is used for
prismatic parts, the section method was developed for pre-
forging design, the Z map has been customized for 3-axis
milling while the Dexel and the Octree have been developed
for 5-axis machining.
LM differs significantly from traditional fabrication
technologies in the sense that a part is produced by adding
rather than removing materials. Unlike traditional machining
simulation, LM simulation research is still in its infancy [2-3],
although water level section methods for LM simulation have
been published in a few papers.
Despite the fact that simulations are becoming more
widely used, there is a lack of integration with manufacturing
processes. Most work focuses on the individual process being
simulated. Significant gaps remain in M&S technology –
particularly in the provision of a general in-process model
(IPM) that can be integrated across diverse manufacturing
processes [4]. To overcome the data exchange problem
between different models, we extend the concept of the in-
process model from machining process to manufacturing
process and propose a unified in-process geometry model for
multiple machining and layered manufacturing simulations.
This paper reports our studies on various IPMs for traditional
manufacturing simulation together with the developed
working systems/prototypes, and discusses a novel unified
Voxel-based IPM for multiple machining and layered
manufacturing.
NOMENCLATURE
B-Rep: Boundary Representation
CSG: Constructive Solid Geometry
IPM: In-process model
LM: Layered manufacturing
MM: Multiple machining
M&S: Modeling and simulation

2. 2 Copyright © 2005 by ASME
IPM FOR TRADITIONAL MANUFACTURING
The in-process model represents the state of the product at
each step in the machining process. It is a 3D geometrical
construct that reflects the results of the machining operations.
This model allows the user to visually verify that the
machining operations have been defined accurately and that
their sequence is correct. It can be automatically re-generated
when there are changes in the product design, machining
parameters or sequence of the operations [1]. In this section,
the geometric representation techniques of IPMs for traditional
manufacturing simulation are presented.
Boundary Representation (B-rep)
The first choice of IPM should be naturally the geometry
model used in commercial Computer Aided Deign (CAD)
system, B-rep. The benefits of using the same geometry model
for CAD as the IPM are obvious. The CAD geometry model is
matured and available through CAD development kit, so there
is little need to develop a new geometry model kernel. Sharing
a common geometry model with CAD, the IPM facilitates
seamless integration of CAD-CAPP-CAM.
An automatic forging design and manufacture system was
developed by the authors in 1986, in which pre-form forging
IPMs were the same as the CAD system CV/MUDUSA
running on VAX-11/750 computer [5-7]. However, the
creation of pre-form forging IPMs took days of calculation
and often failed due to Boolean operation failure.
With a great deal of research effort in the last two
decades, the B-rep geometry model has been improved
significant in term of Boolean operation stability, but the B-
rep based IPMs are still limited to 2.5-axis milling (Figure 1).
Park reported a prismatic IPM generation method that
employed a polygon extrusion algorithm to sweep a ball-nose
cutter [1].
Figure 1: 2.5-axis IPMs
Section Representation
Since the integrated B-rep IPMs can not be created inside
a CAD geometry model, a new, ad-hoc cross-section-wire-
frame based approach was proposed in a forging die
CAD/CAM (Computer Aided Manufacturing) system [5]. The
aim was to use a series of paralleled cross-section drawing to
represent 3D shapes. Figure 2b depicts the section
representation of circled 3D shapes in Figure 2a.
The cross section IPM is widely used in many
commercial CAD/CAM systems. I-DEAS from SDRC uses
water level cross-section as an IPM for generative machining.
In a traditional NC programming environment, a significant
amount of time is spent trying to visualize the in-process stock
as it goes through various process stages. With I-DEAS, the
wireframe section in-process stock model can be created for
downstream applications such as toolpath generation, process
planning, fixture designing, and clamp positioning.
Figure 2: Section representation of 3D shape
A part can be sectioned along the X, Y and Z axes (Figure
3). The Z-axis section is usually called water level section. For
3-axis milling, the water level section could have many loops,
which causes complications in the set operation between
sections. X and Y sections are single half loops and the Z
value is unique for every points. Thus simplifying the set
operation considerably.
Figure 3: Section representation
A working system for using IPM in pre-forging design is
described in [5]. A drawing sheet with part sections is first
(a)
(b)

3. 3 Copyright © 2005 by ASME
created first using the BACIS command language of
CV/MEDUSA CAD system. Since there are many sections in
a drawing sheet, each section wire-frame is assigned to a
different layer according to its Y distance, and a certain
number of sections can be looped through layers. Then each
cutter section is moved to its cutter location and compare with
the part sections. The overlap between the cutter section and
the part section will be removed from the part section. A real
milling IPM is obtained from the collection of the result
sections.
The display of sections is provided by line segments and
can be confusing when there are too many lines, i.e. there is a
need to render the IPM as a realistic 3D image. In order to
calculate the surface normal required for rendering, the section
wire frame is divided along the X direction by the same step
over of Y direction. A so-called regulated section is formed to
facilitate the calculation of surface normal and interpolation of
points between the sections. A given node in one section is
linked to a node in the next section. A node’s normal can be
calculated from the four neighboring nodes. Figure 4 shows
the regulated section representation.
Figure 4: Regulated section representation
The regulated section can also be used to accelerate set
operation between cutter section and part section. Calculation
of intersections and trimming between two sections are time
consuming and the re-ordering of the line segments requires
more computing time. This can be improved with the
regulated sections, where the line segments are indexed by
both cutter section and part section. Only the line segments
with the same index are compared and trimmed, there is mo
need to trim two line segments. If all the line segments fall on
the regulated nodes, there is no need to trim two line
segments. The set operation can be simplified to the
comparison of two Z values, which is very fast and stable.
Hence, the Z map representation of IPM emerges [6].
Z Map
If all the section line segments fall on the nodes, the
object surface can be represented by the Z values of the nodes.
A map of Z values represents the object geometry. In t
computer language terms, the Z map can be expressed as a
two-dimension array Z[i, j], where i represents the index in X
direction and j represents the index in Y direction. The XY
position of the Z map can be calculated by i or j times grid
size.
Figure 5: Needle bed sample of classic Z Map model
The best analogy for a Z map is a needle bed, where
needles are uniformly distributed over the XY plane (Figure
5). The tip of every needle touches the object surface that it
represents. A milling simulation can be seen as the tool cutting
through the needle bed. These needles can be described in
mathematical terms as z-axis aligned vectors, passing through
grid points on the XY plane. A Z map representation can be
used effectively for surfaces that are visible looking
“downwards” on the XY plane. Since 3-axis milling parts are
composed of surfaces visible from the z direction, they can be
expressed effectively by the Z map representation. With a Z
map representation, the machining process can be simulated
by cutting the Z map vectors with the cutter.
Figure 6 shows an example of 3-axis milling simulation
system that was developed by the first author in 1990. The
system was using DOS Extender for Z Map and SVGA for Z
Map rendering. The GUI and NC toolpath wireframe display
was coded with High C graphics library. The GUI and mouse
control developments were very hard job and this was not
resolved until the arrival of Windows 95 and OpenGL.

4. 4 Copyright © 2005 by ASME
Figure 6: Example of Z Map IPM based milling simulation using DOS Extender and SVGA
The vectors in a Z map have direction and length and are
infinitely thin without volume. The top of each vector, where
the Z map and object meet, is just a point having no shape. Only
at this point the Z map and the object meet with each other. Z
map models cannot provide accurate object geometry outside
these points. There are many ways of interpolating the geometry
between grid points in order to render a Z map model. For
example, forming a triangle from three neighboring Z values.
It is obvious that the XY resolution of the Z map grid
determines the precision of a Z map model. A finer grid has
greater precision but requires increased memory. For a part of
1m*1m, the size of the Z map is 1000x1000 if the precision is
1mm, but it increases to 2000x2000 if the precision is 0.5mm.
Reducing the model size and achieving suitable precision
becomes a critical issue in a Z map.
One of the solutions is to balance Z precision and XY
precision. We used an integer array to replace the more common
floating array of a Z map, which reduces the Z map size by half.
At the same time, this improves the Boolean operation speed
because the comparison of integers is much faster than the
comparison of floats. The memory requirement of a Z map is
halved again by compressing the Z map file section by section,
similar to image compression.
Because of the simplicity of its data structure and fast
computation time, the Z map model is used by most commercial
CAM software [7-9]. However, a Z map can not approximate
vertical wall very well since it always has a slope as showed in
Figure 7. This is not a problem for forging die design since there
are always draft angles in forging parts, but it is a serious
problem for milling parts since profiling nearly always creates
vertical walls.
Figure 7: Classic Z Map model with vertical walls
Extended Z Map
Since the precision of the Z map is determined mainly by
XY resolution along the vertical walls, increasing the resolution
along these walls while reducing memory is a key issue.
Fortuitously, one important feature of 3-axis milling can be
leveraged. Viewing from the top, the vertical walls only cover a

5. 5 Copyright © 2005 by ASME
small percentage of the Z direction projection, so it should be
possible to use finer resolution along the vertical walls while
maintaining a rough resolution in the planar area. This was the
initial idea for an extended Z map.
In our research, at least one grid on a z-map is segregated
into sub-cells. Only grids corresponding to intricate features on
the surface of an object are assigned sub-cells to improve the
representation of object features. Figure 8a illustrates the plan
view of the z-map grid with sub-cells 52the front sectional view,
while Figure 8b shows the sectional view.
(a)
(b)
Figure 8: Extend Z Map with sub-cells along vertical walls
The size of the grid can be reduced through using sub-cells.
But the precision of the XY dimension is still limited by the size
of sub-cells. For a sub-cell of 0.1mm, the best precision is
0.1mm in XY plane. There is a need to represent XY
dimensions precisely. Instead of using vectors in the sub-cells,
we use sticks in the sub-cells that have volumes and surface
geometry. A B-rep surface model can be represented precisely
using a map of B-rep sticks (Figure 9).
Figure 9: Stick method
Milling simulation with stick method involves Boolean
operation between cutter and stick. Figure 10 shows different
stick shapes after cutting. The experiments with B-rep stick
model are very slow and a huge B-rep model is created. To
simplify stick and Boolean operation, a polygon is used instead
of real surface in a stick cell. The data structure of a polygon is
much simpler than that of a B-rep which needs a group of
complicated pointers to maintain a double wing data structure.
Figure 10: Different shapes of stick elements
The real world objects are not always uniform in the XY
plane and can be any shape. Nodes are used to enhance sub-cell
precision in object face representations. For example, one edge
of the sub-cell may have two overlapping nodes to represent a
vertical face. The nodes of a sub-cell may not be uniformly
distributed over XY plane. Figure 11 depicts an exploded plan
view of a portion of the z-map grid with nodes 54. Figure 12
illustrates how stick method represents a circular hole and
vertical walls.
Figure 11: Extended sub-cells to approximate vertical wall
Figure 12: Extend Z map to represents a circular hole
44
52 5252

6. 6 Copyright © 2005 by ASME
Figure 13: Extended Z map IPM based NC simulation examples

7. 7 Copyright © 2005 by ASME
Figure 13 shows shop floor examples of extended Z Map
IPM based NC simulation and verification that was developed in
Singapore Institute of Manufacturing Technology and
implemented in precision engineering industry for a decade. The
detailed description of the extended Z map IPM can be found in
two patents [10, 11].
Z map has many alias or hybrid cousins such as ray casting,
Z buffer etc. When a group of virtually light rays pass through
an object from Z direction, there will be intersections between
the light ray and the object. These top and bottom Z values are
stored in the depth buffers of the graphics card and used for
hidden surface removal algorithm. This process was called ray
casting or tracing technology and is used for many graphics
application such as volume rendering.
UNIFIED MODEL FOR MM AND LM SIMULATION
Layered Manufacturing (LM) refers to the process of
fabricating three-dimensional objects from CAD-generated solid
models, layer by layer. A computer generated model of a part
usually contains surface information. Slicing programs
mathematically slices the model into sequential horizontal layers
and generates the specific toolpath for each layer. This toolpath
file is then downloaded into the LM hardware for fabricating the
part layer by layer.
LM has revolutionized the process of prototyping complex
geometric designs, but the geometric design of LM parts is still
using traditional B-rep models, interfacing through a STL
(Stereo Lithography) format. Several problems are difficult to
solve using conventional geometry based approaches. These
problems include estimation of mass properties, interference
detection, tolerancing and implementation of CSG (Constructive
Solid Geometry) operations.
Most of the published LM simulation methods are modeled
on water level sections which is the boundary of material
deposition at this height. A wire frame model with a collection
of these sections gives a rough visual description of the final
shape of the LM part. It can be used to predicate the surface
roughness in a certain orientation. A covered section wire frame
with thickness would provide a much better visual image but
demands more memory. Further improvement utilizes OpenGL
to display a toolpath build file section by section. The
simulation opens a graphical window, specifies different colors
for different materials, and starts the deposition process along
the toolpath on the layer. When a material is finished, the
simulation runs for other materials on the same layer. When a
layer is finished, a new layer will be deposited on top of the
finished layer, until all the layers of the part are stacked
sequentially. Surface and internal defects can be verified from
the envelope view or sectional view.
Chandru (1995) proposed a Voxel-based modeling for LM
parts design [12], but there is little information about voxel-
based modeling of LM processes, although it has been a popular
approach for multiple machining process simulation [13].
The term Voxel represents a volume element in space
decomposition geometrical model schema, just like the term
pixel denotes a picture element in raster graphics (Figure 14).
Voxelization is the process of converting a 3D object into a
Voxel model. Volume graphics, voxelization and volume
rendering have attracted considerable research in recent years.
However, all of this work is directed at the display of volume
data, mainly for medical applications.
Figure 14: Voxel method
Further analyzing the Voxel model, it is believed that the
Voxel-based volume modeling is a very promising approach to
the unified IPM for multiple machining and layered
manufacturing simulation. As a natural clone of the LM
technology, the Voxel model of an object and the object
fabricated using an LM closely resemble each other since both
are made of layers of small cells. It eliminates the STL format
and eases accomplishments of tasks such as estimation of errors
in the physical parameters of the fabricated objects, tolerance
and interference detection. Furthermore, Voxel based models
permit the designer to analyze the LM object and modify it at
the voxel level leading to the design of custom composites of
arbitrary topology. In this paper a simplified Voxel-based IPM
is proposed to unite the new LM and traditional machining
simulation. Figure 15 depicts an example of the Voxel model.
Figure 15 Example of Voxel model
The memory requirements of traditional Voxel models are
enormous. There is a need to store the voxel array in
compressed form and use algorithms that will operate directly
on the compressed data, especially when the material is
homogenous, where internal voxels could be represented by
boundary voxel extension. It is possible to convert the voxel
array into some other more compact representation and
reconvert them into voxels when required. The original
geometric representation must be kept and voxelization
algorithms are used when necessary. This is especially valuable

8. 8 Copyright © 2005 by ASME
since design data are mainly generated from conventional CAD
system.
A voxel-based system should be able to update the display
at interactive rates. Current graphics rendering systems cannot
provide a level of rendering performance on Voxel models that
is comparable to their polygon-rendering performance. Parallel
algorithms and hardware support for volume rendering are the
focus of current research efforts. We only render boundary
voxel by a patented color list, which effectively avoid expensive
ray-casting of huge internal voxels. The rendering of a Voxel
model is easily achieved by rendering a points cloud. However,
internal voxel display is not possible with this method and needs
more study.
Figure 16 illustrates the framework of the unified Voxel-
based IPM for LM and MM. The Voxel based LM simulation
can be achieved by the voxelization of the road shapes, which
are similar to a pipe along the LM toolpath. Boolean addition
between the road shape voxel and the base voxel is fast and
stable, independent of the model shape, which is a critical issue
with B-rep. One layer of road shapes would make a B-rep based
solid modeler very slow, since B-rep Boolean operation is
dependent on model shape.
Figure 16: Framework of Unified IPM for MM and LM
During the novel combined LM and MM, such as shape
deposition manufacturing, an LM part needs to be inserted with
an electronic device and milled to a certain shape. The unified
LM-machining simulation displays the machining process in
which the initial LM generated workpiece is incrementally
converted into the finished part. The Voxel representation is
used to model efficiently the state of the IPM, which is
generated by successively subtracting tool swept volumes from
the workpiece. The Voxel representation also simplifies the
computation of regularized Boolean set operations and of
material removal volumes. By using the material removal rate
measured by the number of removed voxels, the feedrate can be
adjusted adaptively to increase machining productivity. The
preliminary results of the IPM are shown in Figure 17. Figure
17b demonstrates the Voxel model of a test part created from its
solid model as depicted in Figure 17a, which is the first step
towards to the unified in-process geometry model for multiple-
machining and layered manufacturing simulation. Further
research is on-going and more results will be published in the
near future.
CONCLUSIONS
Manufacturing advanced products with heterogeneous
materials such as embedded electronics requires applying the
combined MM and LM technologies. Modeling and simulation
of hybrid MM and LM processes is essential for the integration
of various activities related to product design, manufacturing
process planning, toolpath generation, and machine inspection.
However, no unified in-process geometry model for MM and
LM has been found. Based on the study of various modeling
and simulation methods including B-rep, section method, Z
map, and extended Z map, a Voxel-based in-process geometry
model for the novel hybrid multiple machining and layered
manufacturing processes is proposed and discussed in this
paper. The preliminary experiment demonstrates encouraging
results. With nearly twenty years of research and development
on IPMs for machining, it is believed that the Voxel-based
volume modeling is a very promising approach to the unified
IPM towards the vision of pervasive modeling and simulation in
manufacturing industry
Figure 17: Experiment result of Voxel model
(a)
(b)

9. 9 Copyright © 2005 by ASME
ACKNOWLEDGMENTS
The authors would like to thank Dr Matthew Pritchard and
Dr Fang Fengzhou for their internal review of the paper with
valuable comments and polishing of the writing.
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