HYBRID LAYERED MANUFACTURING

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					                   HYBRID LAYERED MANUFACTURING
                    Direct Rapid Metal Tool Making Process

K P Karunakaran, Sreenathbabu Akula and Vishal Pushpa
Mechanical Engineering Department, Indian Institute of Technology, Bombay, India


         Abstract: Fabrication of direct metallic tools presented here combines synergic MIG-MAG welding
         and CNC machining processes in order to exploit the benefits of both while avoiding their limitations.
         A PC/PLC based low cost XYZ manipulator is fabricated with stepper motor diver in open loop
         control. The tool head will hold the welding torch and milling cutter. At any time either milling or
         welding will take place, for that the welding gun can be moved up and down with a pneumatic
         operation. The welding parameters such as current, voltage, arc length etc are controlled externally.
         The framework also consists of a software program which uses the zeroth order edge approximation
         uniform slicing strategy to calculate each slice thickness to be deposited with the required metal as
         successive layers from lower to topmost layer with the welding process. Further it generates the
         required CNC code for machining from top to bottom layer direction of the deposited metallic layers to
         attain the required contour profile shape with user specified accuracy. By attaining this cutting edge
         technology the manufactures find metallic RP in the adventure of the growing years.

         Keywords: Rapid Prototyping, STL File, CNC Machining, MIG-MAG Welding, Molds and dies.


1. INTRODUCTION                                             successful RP process for making paper based
                                                            prototypes, have been used for making metallic
The demand for shorter development time, time-to-           laminated tools and parts [6]. The metallic
market and reduced product life cycle resulted for          laminates in this method are bolted together rather
the emergence of a new paradigm called Rapid                than gluing or brazing, thus it lacks the complete
Prototyping (RP) or Layered Manufacturing (LM)              adhesion between layers. This method is not
process [1, 2]. The success of automotive,                  suitable for processes such as injection molding
electronics,    telecommunications,      biomedical,        where liquid metal is involved. Furthermore, this
packaging appliances, leisure and sports industries         LOM process suffers from high material wastage
in responding to rapidly varying customers demand           and inherent inability to have adaptive layer
for higher quality standards with lower costs               thickness [7].
depend on the ability to develop the product with                Various droplet production processes thermal
the application of state-of-art technology.                 spraying, micro-casting and welding have been
     Layered Manufacturing introduced in late 80’s          developed for making metallic objects and tools to
as a design visualization tool, has revolutionized          improve the deposition quality and to attain the
the way products are designed and manufactured              desired contour profile shape. Comparatively three-
today. Although the prototypes could be made out            dimensional welding has the ability to produce
of only soft material, very soon, innovative                strong, fully homogeneous dense metal parts in
methods of making the short-run and production              layers [8]. Adaptation of a weld cladding technique
tools were developed, called as Direct Rapid                has enabled the production of parts wider than
Tooling Processes [3].                                      normally possible from single weld beads. But
     Selective Laser Sintering (SLS) is the                 attaining the required surface finish and required
commercially successful metallic RP process so              contour profile is difficult with the weld deposition
for. Direct Metal Sintering relies on laser induced         [9]. So to attain better dimensional accuracy and
melting of powder particles together. Since                 surface quality for building metallic dies and molds
significant thermal gradient exist using this route,        it was proposed to develop a unique methodology
the powder bed temperatures are controlled to a             with a hybrid approach of an additive and
value just below the powder melt temperature to             subtractive processes comprising MIG-MAG
produce parts with minimum internal stresses.               welding and CNC machining respectively.
Porosity is a problem that is normally reduced by
post sintering or infiltration [4, 5].
     The principles of Laminated Object
Manufacturing (LOM) another commercially
2. HYBRID LAYERED MANUFACTURING                           the deposited metallic layers from top to bottom
                                                          layer direction to attain the required contour profile
The proposed Hybrid Layered Manufacturing                 shape with user specified accuracy.
(HLM) process has a numerical controlled system
that integrates the synergic MIG-MAG welding              2.1 Slicing Strategies
process [10], which provides the controlled heat
and mass transfer with precise depth of bead              Fabrication of the prototype model through RP
penetration, and CNC milling process, which               process requires the thickness of each layer to be
enhances both the surface quality and dimensional         found before deposition of the material. To
accuracy with great manufacturing agility.                calculate the Slice Thickness, i.e the distance
Synchronization of welding process and work-              between the top profile contour and bottom profile
piece/substrate motion with milling operation offer       contour of a specific layer [12, 13].
a new accelerator way of building desired metal
parts and tools [11].                                     Based on the layer thickness, the slicing strategies
                                                          can be broadly grouped into two.
The aim and scope of the proposed process is               Uniform Slicing where the layer thickness is
 To develop a RP machine for making injection                same for all layers of the object
    molds and dies.                                        Adaptive Slicing where the thickness of each
 To develop the know-how to retrofit any                     layer is dependant on the local geometric
    exiting CNC machining center with the above               properties and the user specified cusp height.
    RP capability.
 To develop the software required for this HLM           Slicing schemes can be classified based on the edge
    process that does                                     approximation, that is how each bottom and top
    - Slicing process                                     contour is connected with respect to the build
    - Path generation to control welding torch and        direction [14].
    milling cutters                                        Zeroth Order Edge Approximation: The edges
    - Generation of codes to control process                   of the layers are along the build direction. The
    parameters such as spark initiation,                       boundary of the final part will be a stepped
    - Control the speed and feed of the milling                approximation of the CAD model.
    cutter                                                 First Order Edge Approximation: The slice
    - Post-processing to make the code suitable for            thickness has been formed by a curve of first
    the controller of any CNC m/c                              order i.e. a straight line. This is also referred to
                                                               as ruled slicing.
The HLM process consists of a software program             Higher Order edge approximation.
which uses the zeroth order edge approximation
uniform slicing strategy of the RP paradigm to            The stereolithography (STL) file of the body is
calculate each slice thickness that to be deposited       sliced at regular intervals with the consideration of
with the required filler metal as successive layers       Flat Surfaces, Peak Points and Branching
from lower to topmost layer with the welding              constraints to form the Coarse Slices and then
process. Further in accordance to the first order         further to have Fine Slices as shown in Figure 1
edge approximation slicing strategy of RP it              and Figure 2.
generates the required CNC code for machining of




          Tool to be built         Coarse Slicing          Uniform Slicing           Adaptive Slicing
                                           Fig.1 Slicing Strategy




           Coarse Slicing          Coarse Slice 1          Coarse Slice 2             Coarse Slice 3
                                        Fig.2 Coarse Slicing Process
                     Layer to be deposited             Weld Path           Deposited Layer
                                                    Fig.3 Weld Path

     In a Coarse Slicing, the number of loops in the           motion and the inner part is filled with raster
top z_level and that in the bottom z_level will be             approach. These area-fill paths are then fed to the
the same i.e, for each loop in the bottom z_level              drive controller that integrates the welding machine
there will be a corresponding loop at the top level.           to initiate the welding arc and the XY table of the
In this slicing process it is essential to establish the       HLM machine for deposition of the model in a
mapping between the top and bottom contours of a               layer-by-layer fashion as shown in Figure 3.
coarse slice.                                                       The weld path is optimized to transfer heat
     In Fine Slicing, each individual coarse slice is          uniformly over the layer as the heat build-up due to
further sub-divided in accordance to the user                  the welding process may result in part
defined/required uniform slice or adaptive slice               malformation and collapse of the structure. With
thickness.                                                     the consideration of the limitations of the welding
     Though the above slicing procedure for the                process the path for the welding gun has to be
STL file takes more computational time, the results            generated to deposit the filler metal for attaining
will be more accurate with the simplification of the           the required slice profile shape and thickness.
geometry of the complex CAD model. The first                   Control of parameters and trajectory is added to the
step i.e, Coarse Slicing is helpful in establishing            start and the end portions of the weld in order to
contour mapping and in eliminating branching                   make their thickness and width similar to that of
constraint. The second step, Fine Slicing is an                the central portion of the weld. The number of
iterative process to calculate slice thickness based           discrete joints of weld passes will decrease
on the local curvature of the body. The data                   precision of the work piece. To improve the
attained through the Fine Slices is utilized for the           deposition speed and precision it is essential to
path generation of the MIG-MAG welding gun,                    minimize the number of weld passes and joints
and face milling operation.                                    between them.

2.2 Weld Path                                                  2.3 Face Milling

For the proposed HLM process shrinkage and                     The width and height of the weld bead depends on
machining allowances are to be added to                        the applied voltage, diameter of the filler wire and
compensate the shrinkage of the deposited filler               weld speed. The deposited weld bead will be
metal during the solidification and to eliminate the           generally in convex shape. Due to the heat sink, the
weld defects of undercut and blowhole defects. For             penetration is lower at the initial position. Thus the
that reason contours of the slice are provided with            weld bead thickness is higher than the normal
offset. The outer contours will have a positive                portion of the weld. These uneven portions of the
offset while the inner ones with negative offset               layer will influence succeeding layer metal
value. So during the zeroth order edge slicing                 deposition. And at the end portions of the weld
strategy the top and bottom z_level contours of a              pass, because of the viscous nature of the molten
layer are merged to obtain the union of the outer              metal, an inclined shape is created. After a few
contour and intersection of inner contours. To the             layer depositions, a significant deviation from the
Fine Slice contours thus obtained after offsetting             originally expected shape will be accumulated.
and merging is passed for mesh generation in order             Face Milling of the slice as shown in Figure 4
to achieve the zigzag tool path segments for the               ensures the correct vertical height accuracy of the
weld deposition [15]. To minimize the surface error            built layer.
the outline of the contour is filled with vector




                          Face Milling              End Milling              Scan Milling
                                            Fig 4 CNC Milling Operation
     On the newly deposited layer a thin oxide layer      halting the welding process and activating the face
will be formed due to the oxidation phenomenon.           milling process and vice versa. For this operation a
Subsequently if the next layer is deposited on the        pneumatic system is used to swivel between
top surface of previous layer, a significant bond is      welding gun and the milling cutter. So that at any
not achieved. Initially small in size, the defect is      time either welding or milling operation will only
amplified with succeeding multi-layer deposition          take place. The necessary functions for the
until the deposition is not feasible. To minimize         operation of synergic MIG-MAG welding machine
and correct this deviation, a face milling operation      with shielding gas were monitored through the
is performed on the top surface of the deposited          numerical controller. While the majority of the
metallic layer.                                           welding process parameters such as current,
                                                          voltage, arc gap, shielding gas composition etc are
2.4 End Milling                                           controlled externally.

With the welding process, attaining the accurate          3.2 Rough Machining the near-net shape of the
contour profile shape of the coarse slice is difficult.   tool to final dimensions
For that end milling operation is performed to
attain the shape and accuracy. The tool path of the       Face milling operation is performed on the top
end mill is generated in accordance to first order        surface of each deposited metal layer to get the
edge approximation. Slicing with first order edge         required thickness of the layer. The instability of
approximation will be made use of ruled surfaces          arc     welding       process     may       cause    a
[16]. As the coarse slice passes the information of       malfunction/defect in the middle of the weld bead.
loops between the top and bottom layers a ruled           To minimize the deviation and correct the vertical
surface has to be find within the upper limit             height accuracy of the built layer in successive
deviation. In order to calculate the deviation, a line    multiple layer deposition, face milling operation is
is fitted to connect a point in the bottom loop and       performed on all the horizontal surfaces of the
the corresponding point in the top loop without           deposited layer. Repeating the above process of
violating the tolerance constraint ‘cusp height’. The     layer deposition and face milling operations to
corresponding point in the top loop is the one            generate near net layers deposited one over the
having the same surface normal vector and nearest         other from bottom most to top layer till a casting
to the bottom point. The tool path generated              like rough shape is obtained.
contains a list of vertices that contains the co-               As the size of the deposited layer is made to be
ordinates of the points. These paths are then fed to      little bit larger than the actual required profile
the HLM machine for the generation of the final           shape considering into account the shrinkage and
shape of the model by scan milling using a flat end       weld defects, the edges of the layers are still rough.
mill cutter as shown in Figure 4.                         The tool path of the end mill is generated for
                                                          machining the final casting like rough shape from
3. METHODOLOGY                                            top to bottom layer direction of the deposited
                                                          metallic layers to attain the required contour profile
The proposed HLM process consists of the                  shape with user specified accuracy in accordance to
following stages:                                         first order edge approximation strategy slicing
 Building a near-net shape of the tool.                  principle of RP paradigm.
 Rough Machining the near-net shape of the
     tool to final dimensions                             3.3 Heat treatment for stress relieving and
 Heat treatment for stress relieving and                 strengthening
     strengthening
 Finish Milling to get the required surface finish       The temperature gradients within the deposited
     and quality.                                         layer with the severity of cooling, influences on the
                                                          generation of internal stresses and on the resulting
3.1 Building the near-net shape of the tool               microstructure of the final deposited layer. The
                                                          stress distribution consists of nearly uniform
The substrate plate is rigidly placed with proper         tension in the newly deposited layer, with tension
fixtures on the XY table, and its motion is guided        at the top of the substrate and nearly uniform
by motor drives. The required weld paths are              compression at the bottom half of the substrate. To
generated in relation to the Fine Slice contours for      relieve these undesirable residual stresses, a
deposition of the layer thickness is used to deposit      suitable heat treatment is performed using
the bottom most layer with a simple zigzag pattern.       normalizing and annealing processes. As these
As the metal deposition in the bottom most layer is       residual stresses are unchecked, they may induce
completed the shielding gas nozzle is turned off          warping, loss of edge tolerance and delaminating
and the switching functions are invoked to change         thereby reducing the strength and influencing on
over between welding and face milling process by          the tool life.
     The material homogeneity of the prototype to
be obtained in the proposed method is between
those of cast and machined parts. Thus, this process
is not suitable for making forging dies where very
high impact forces are encountered. The die used in
injection molding, die casting and sheet metal
forming undergo considerably less fatigue loading
during the operation, so these tools can serve the
purpose even without any homogenization
operation such as Hot Isostatic Pressing (HIPping)
process. Further these die halves are free from
overhanging features, as they need to open and
close in operation. Building such dies and mold
with free from re-entrant profiles by the proposed
methodology will not require support structure,
thus making the process less complicated.
                                                          Fig 5a. XYZ Manipulator
3.4 Finish machining

Finish mill all the contour profiles of the tool to the
required surface finish.

4. IMPLEMENTATION

Machined and fastened structure of XYZ
manipulator is fabricated as shown in Figure 5 for
the proposed process with low investment cost. The
horizontal X, Y motions are attained by the
movement of substrate table on ball lead screw
arrangement and vertical Z motion is achieved by
the movement of tool head. Each axis has its
motion control by an individual stepper motor in
open loop drive with rapid and linear
                                                          Fig 5b. XYZ Manipulator
interpolations, such that all 3 axes can be moved
simultaneously. The maximum transverse in X, Y
& Z axis is 400, 300 & 300mm respectively with
an accuracy of 0.05 mm and maximum attainable
speed of 2500mm/min. The load on the XY table
can bear up to 100kg.
     The arrangement of tool head as shown in
Figure 6 is made to hold the MIG-MAG welding
torch and the face-milling cutter. The welding torch
is connected to the wire feeder, shielding gas
nozzle and power source of the weld machine. For
the face-milling cutter a motor is fitted on a fixed
frame from which it is driven through a belt and
spline shaft. The welding gun is made to move up
and down with a pneumatic controller after                   Fig 6a Tool Head
completing the metal deposition for the desired
layer thickness. This arrangement makes sure that
at any time either milling or welding will only take
place. The NC codes M08 and M09 are used to
invoke the switching functions of the pneumatic
piston to move up and down respectively. Further
the NC codes M03 and M04 are made to control
the on/off of the welding torch during the metal
deposition as per the requirement. Adequate
isolation to protect the motion control electronics
from welding spikes is implemented. Process
parameters such as welding current, voltage, arc             Fig 6b Tool Head
length, weld speed and shielding gas of welding        5.4 Weld Path
process are controlled externally and the tool         The area-filled weld paths along with the face mill
change, spindle speed, coolant, etc of the milling     paths are generated and can be viewed as in Fig 7.4
process are governed through the numerical control
of the software.

5. CASE STUDY

A step-by-step processing of a sample model is
described in this below section. All the subsequent
sequence of operations is carried out on it to
generate the weld deposition paths and the coarse
slice machining paths.                                        Fig 7.4 Weld path for a uniform slice

5.1 Input Model                                        5.5 Milling Paths

Using the Pro/E CAD package, a solid model             The .STL model is fed for the machining path
bracket without any overhang features is drawn as      generation. The paths thus generated along with the
shown in Figure 7.1 and its STL output file is         tool withdrawal and reentry points can be viewed
generated. This .STL file acts as an input for the     in Figure 7.5.
software. Then the user defines the process
parameters required for the further subsequent
sequence of operations to be carried out on it to
generate the weld deposition paths and the coarse
slice machining paths.

5.2 Coarse Slice Model

Next the .STL model is coarse sliced to generate
the coarse slice levels as shown in Figure 7.2. This                Fig 7.5 Machining paths
is followed by generation of the solid coarse slices
and their display                                      5.6 Output Files

                                                       The output files generated from the software i.e,
                                                       the weld deposition path, face mill cutter path and
                                                       the coarse slice-machining path are of standard NC
                                                       format as in Figure 7.6. These output files are fed
                                                       to the NC drive controller to generate the milling
                                                       and deposition paths.

                                                       N0001 G28 Z0
      Fig 7.1                      Fig 7.2             N0002 G28 X0 Y0
  Model dimensions           Coarse slices display     N0003 M08 // To move pneumatic piston down
                                                       N0004 G10 L2 P1 X99.0 Y97.0 Z-160.0
5.3 Uniform Slice Model                                N0005 G55
                                                       N0006 G90 G01 G21 F800
The model is uniformly sliced in accordance to the     N0007 G00 X0 Y0
user-defined settings and the uniform layers are       N0012 M03    // To initiate the welding process
generated to display as shown in Figure 7.3.           :  :
                                                       :  :
                                                       :  :
                                                       N0200 M04 // To turn off the welding process
                                                       :  :
                                                       :  :
                                                       :  :
                                                       N1000 M09 // To lift the pneumatic piston up
                                                       N1005 M30

           Fig 7.3 A uniform slice/layer                 Fig 7.6 NC file format generated by software
                                                                                          35
                                                                                          30




                                                                               HARDNESS
                                                                                          25
                                                                                          20
                                                                                          15
                                                                                          10
                                                                                           5
                                                                                           0
                                                                                               1   2   3   4   5   6   7   8   9

                                                                                                       LAYER NUMBER


Fig. 8 Test Tool Build with HLM       Fig 9 SEM Image Microstructure of Fig 10 Hardness variation with Layer
             process                              Layer                              number

6. DISCUSSION                                                strength can be improved by subjecting the
                                                             produced tool to HIPping process.
Traditionally dies and molds for injection molding,               Experimental trails are performed with MIG-
forging, and die-casting are manufactured using              MAG machine on a clean Mild Steel substrate plate
CNC machining process. Initially the metal blocks            of size 100X 100X 12 mm3 that is free of initial
of annealed condition are rough machined with                residual stresses. A DIN 8559 weld wire with
HSS and Carbide tool cutters. Further smooth                 diameter size 1.2 mm was used to deposit the metal
finish milling is operated on it at a low feed rates         in short circuit mode with proper weld parameters.
and to achieve the desired accuracy and shape an             The composition of shielding gas used is of 80%
EDM process is performed. The time needed for                Ar + 20% CO2. Total ten number layers are
these process to machine or configure the die shape          deposited on the substrate plate, with the weld
will increase significantly for harder materials, as         speed of 12 mm/sec as show in the Figure 8. A
the feed rate and spindle speeds have to be reduced.         simple zigzag weld path was generated to built the
So time and cost incurred in the manufacture of the          test trail tool. The average layer thickness of metal
tools cannot be justified for small and medium               deposition is 2.1 mm with a bead width 2.4–2.8
batch production. But during the last two decades            mm. For initial test trails no external cooling
the steep acceleration in product and market                 procedure was implemented to monitor the
variations demanded for higher quality standards             microstructure and induced residual stresses. As
with lower costs.Direct production of the metal part         shown in Figure 9 the SEM images showed a fine
is unique among current RP techniques. Although              microstructure formation with a hardness of 28
MIG-MAG welding cannot generate the required                 HRC. But the hardness varied for each layer as
accuracy, it is economical, safe, portable and easy          shown in Figure. 10.
to maintain. Adequate isolation to protect the                    Complex shapes and sizes are possible with
motion control electronics from welding spike is             least number of jigs and fixtures. The process does
implemented. The number of joints of weld passes             not pose any restriction or loss of accuracy on the
decrease the precision, so the reduced number of             prototype as its size grows. Since the part size is
weld passes and joints in the deposited layer to             limited only by the transverse available on the
enhances the speed and precision of weld                     CNC machine, larger CNC machine can be used to
deposition. With welding process, all the desired            produce larger tools. The size of the prototype thus
material properties cannot be attained. Strength of          attained is independent of its accuracy and is
the weld depends mainly on the availability of               limited only by the table transverse. The tools
suitable filler wires. The material homogeneity and          produced using this process may be inferior to their

  Characteristic                          SLS                                        Proposed HLM
Principle             Powder Metallurgy (PM).                         GMAWelding and CNC machining.
Slicing type          Uniform slicing of 0th order edge.              Adaptive slicing with 1st order edge
                                                                      approximation is possible.
Accuracy              Limited by particle and layer sizes.            Same as CNC machining
Density               Porous part.                                    Density close to 100% can be achieved.
Post-processing       Impregnation with copper in a furnace is No post processing for density
                      required which takes several hours.             improvement.
Strength              Since it is not totally steel, not very strong. Strength depends only on the availability
                                                                      of suitable filler wires
Overall cycle time    Slower than HLM process.                        Much faster than SLS process.
Available as          A complete and expensive machine.               A retrofit or complete machine.
                  Table 1 Comparison of popular SLS process and proposed HLM process
conventional counterparts in composition and tool       Proceedings of Solid Freeform Symposium, Austin,
life but these will generate the final products as      Texas, 1994, 371-378.
accurate as any other tool. The overall cycle time of   6. Dickens, P.M. Principles of design for
product development is much faster than current         Laminated Tooling. International Journal of
existing commercial RP system. Thus the proposed        Production Research, 1997, Vol. 35(5), 1349-1357.
RP machine will help bring down the cost and time       7. Bryden, B.G. Wimpenny, D.I. and Pashby,
to make these tools drastically. Therefore,             I.R. Manufacturing production tooling using metal
popularizing this process among Indian Industries       laminations. Rapid Prototyping Journal, 2001,
will help them cut down their product development       Vol.7(1), 52-59.
cycle time and the cost of the product. It even         8. Spencer, J.D., Dickens, P.M. and Wykens,
enables them to justify the manufacture of these        C.M. Rapid prototyping of metal parts by three-
tools even for small volume production. The agility     dimensional welding. Proceedings of the Institution
they thus gain will help them compete effectively       of Mechanical Engineers, 1998, Vol.212, PartB,
in the local and global market.                         IMechE, 175-182.
                                                        9. Song, Y.A, et. al. 3D Welding and milling - A
7. CONCLUSIONS                                          direct approach for fabrication of injection molds.
                                                        Proceedings of Solid Freeform Symposium, Austin,
     Today, metallic prototypes can be made only        Texas, 1999, 793-800.
using the SLS based RP. These machines typically        10. The microprocessor revolution – synergic
cost as much as RS. 150 lakhs and make use of           pulsed MIG/MAG welding. Welding & Metal
proprietary material. The structure of the              Fabrication, 1999, March, 17-18.
prototypes obtained from SLS process is porous          11. Zhang, Y., Chen, Y., Li, P., and Male, A.T.
and weak and hence these are suitable only for          Weld deposition-based rapid prototyping: a
short pre-production runs. Furthermore, in order to     preliminary study. Journal of Materials Processing
get the desired quality, impregnation with copper is    Technology, Vol 135(2-3), 2003, 347-357.
required which takes several hours. As compared to      12. Dolenc, A. and Makela, I. Slicing procedures
this process, the proposed RP machine will be very      for layered manufacturing techniques. Computer-
fast and accurate. The structure obtained will be       Aided Design, 1994, Vol 26(2), pp119-126.
very dense in the proposed process since it uses        13. Kulkarni, P. and Dutta, D. An accurate
solid wire fillers, which are cheap as well. In spite   slicing procedure for layered manufacturing.
of its high speed and accuracy, the proposed            Computer-Aided Design, 1996, Vol. 28(9), 683-
machine will be very cheap in terms of initial          697.
investment and running cost. Going by low cost,         14. Jager, P.J., Broek, J.J and Vergeest, J.S.M.
short cycle time and tool life provides solution for    A comparison between zero and first order
new      product     development     with    today’s    approximation       algorithms      for     layered
requirements where the customer’s choice demands        manufacturing. Rapid Prototyping Journal, 1997,
variety in small numbers.                               Vol. 3(4), 144-149.
     The proposed methodology can be developed          15. Rajan, V.T., Srinivas, V., and Tarabini, K.
entirely as new RP system or even retrofit to the       A. The optimal zig-zag direction for filling a two-
existing 3-axis CNC machine thus reducing the           dimensional region. Rapid Prototyping Journal,
investment cost.                                        2001, Vol. 7(5), 231- 240.
                                                        16. Hope, R.L., Roth, R.N., and Jocabs, P.A.
                                                        Adaptive slicing with sloping layer surfaces. Rapid
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