Numerical Controlled Machining
 –  Reduce time to market
 –  Early detection of errors
 –  Assist concurrent manufacturing engineering
 –   Form
 –   Fit 
 –   Function
• Prototype building can be a time-consuming process requiring a highly skilled craftsperson
 –  Time spent testing prototypes is valuable
 – Time spent constructing them is not…
• “Rapid Prototyping” (RP) methods have emerged
 –  (Solid Freeform Fabrication, Additive Manufacturing, Layered Manufacturing)
 Need for model
Stereolithography (SLA)
Stereolithography is a common rapid manufacturing and rapid prototyping technology for producing parts with high accuracy and good surface finish. A device that performs stereolithography is called an SLA or Stereolithography A pparatus.
Stereolithography is an additive fabrication  process utilizing a vat of liquid UV-curable  photopolymer "resin" and a UV laser to build  parts a layer at a time. On each layer, the laser  beam traces a part cross-section pattern on the surface of the liquid resin.
Selective Laser Sintering (SLS)
SLS can produce parts from a relatively wide range of commercially available powder materials, including polymers (nylon, also glass-filled or with other fillers, and polystyrene), metals (steel, titanium, alloy mixtures, and composites) and green sand. The physical process can be full melting, partial melting, or liquid-phase sintering. And, depending on the material, up to 100% density can be achieved with material properties comparable to those from conventional manufacturing methods. In many cases large numbers of parts can be packed within the  powder bed, allowing very high productivity.
Fused Deposition Modeling (FDM)
• Fused deposition modeling , which is often referred to by its initials FDM, is a type of rapid prototyping or rapid manufacturing (RP) technology commonly used within engineering design. The technology was developed
 by S. Scott Crump in the late 1980s and was commercialized in 1990. The FDM technology is marketed commercially by Stratasys Inc.
• Like most other RP processes (such as 3D Printing and stereolithography) FDM works on an "additive" principle by laying down material in layers. A
 plastic filament or metal wire is unwound from a coil and supplies material to an extrusion nozzle which can turn on and off the flow. The nozzle is heated to melt the material and can be moved in both horizontal and vertical directions by a numerically controlled mechanism, directly controlled by a Computer Aided Design software package. In a similar manner to stereolithography, the model is built up from layers as the material hardens immediately after extrusion from the nozzle.
• Several materials are available with different trade-offs between strength and temperature. As well as Acrylonitrile butadiene styrene (ABS)
 polymer, the FDM technology can also be used with polycarbonates,  polycaprolactone, and waxes. A "water-soluble" material can be used for making temporary supports while manufacturing is in progress. Marketed under the name WaterWorks by Stratasys this soluble support material is actually dissolved in a heated sodium hydroxide solution with the assistance of ultrasonic agitation.
(LOM)
Laminated Object Manufacturing (LOM) is a rapid prototyping system developed by Helisys Inc. (Cubic Technologies is now the successor organization of Helisys) In it, layers of adhesive- coated paper , plastic, or metal laminates are successively glued together and cut to shape with a knife or laser cutter .
8
Electron Beam Melting (EBM) • Electron Beam Melting (EBM) is a type of rapid
 prototyping for metal parts. It is often classified as a rapid manufacturing method. The technology manufactures parts by melting metal powder layer  per layer with an electron beam in a high vacuum. Unlike some metal sintering techniques, the parts are fully solid, void-free, and extremely strong. Electron Beam Melting is also referred to as Electron Beam Machining.
• High speed electrons .5-.8 times the speed of light are bombarded on the surface of the work material generating enough heat to melt the surface of the  part and cause the material to locally vaporize. EBM does require a vacuum, meaning that the workpiece is limited in size to the vacuum used. The surface finish on the part is much better than that of other manufacturing processes. EBM can be used on metals, non-metals, ceramics, and composites.
Stereolithography (SLA) photopolymer 
Laminated Object Manufacturing
3D Printing (3DP) Various materials
 
number of parts
fixture, retrieve tooling , etc.)
for feature operation j (chuck, fixture, etc..)
the machining/processing time for feature j
tool change time/part
L/UL
setup + t
 j + t
 j + t
Production time per piece
 
as:
Production cost per piece, C p
 
Ct is the perishable tooling cost
np/t is the number of pieces that can be produced per tool
Csetup is the setup resource cost for the part
(fixture, jig, steady-rest, etc)
• Rapid Prototyping?  –  Technology for producing accurate parts directly from CAD
models in a few hours with little need for human intervention.  –  Pham, et al, 1997
• Prototype?  –  A first full-scale and usually functional form of a new type or
design of a construction (as an airplane)  – Webster’s, 1998
• Model?  –  A representation in relief or 3 dimensions in plaster, papier-mache,
wood, plastic, or other material of a surface or solid  – Webster’s, 1986
 physical models
for CNC?
CE = Ced / nt + C pc / nt + C pd / n b
total parts total parts parts in a batch
16
 –  Fixture engineering and fabrication
• Set up cost (Cset)  –  Cost to set up a process
• Processing cost (C psc)  –  Cost of processing a part
• Production cost (C pdc)  –  Cost of tooling and perishables
17
Manufacturing cost
CM = Cone / nt + Cset / n b + C psc + C pdc // ntool
Total parts parts in a batch each part tool cost by parts/tool
18
reduced for CNC machining?
 
20
• CNC-RP Method : A part is machined on a 3-Axis mill with a
rotary indexer and tailstock using layer-based toolpaths from
numerous orientations about an axis of rotation.
Table Opposing
3-jaw chucks
Rotary indexer 
Round stock
End mill
1. First orientation of part section is machined
(Side View)
 
Rotate StockRotate Stock
 
 
 
 
 
7. Temporary supports are removed
 
7. Temporary supports are removed
 
 
 
from each of a set of orientations using
layer-based toolpaths
The number of rotations
required to machine a
geometric complexity
25
Methodology
• Creation of complex parts using a series of thin layers (slices) of 3-axis toolpaths generated at numerous orientations rotated about an axis of the part
• Toolpath planning based on “layering” methods used by other RP systems
• “Slice” represents visible cross-sectional area to be machined about (subtractive) rather than actual cross section to be deposited (additive)
• Slice thickness is the depth of cut for the 2½-D toolpaths
• Tool used is a flat end mill cutter with equal flute and shank diameter (or shank diameter < flute diameter)
 
current orientation
Toolpath planning using this approach is done with ease in current CAM
software (MasterCAM rough surface pocketing )
 
appended to the solid model prior to toolpath planning
• Cylinders attached to solid model along the axis of rotation
• Incrementally created during machining operation as the model is
rotated
• Model remains secured to stock material then removed (similar to
support structures in current RP methods)
 
 –  Solid model (CAD) is converted to STL format
• Facetted representation where surface is approximated by triangles
• Intersect the STL model with parallel planes to create cross sections
 
 –  Support overhanging features
Model material
Support material
Build Platform
• However:
 –  Limited accuracy in some cases
• CNC Machining is:
• CNC Machining is NOT:
• CNC machining cannot create all parts
•  No hollow parts
•  No severely undercut features
• The time consuming tasks of process and fixture planning are major factors which  prohibit CNC machining from being used as a Rapid Prototyping Process
 –  Wang et al , 1999
 –  Machined layers using robotic arm/machine tool
 –  Layers laminated in a stack 
• Merz, et al, 1994
 –  Rapid tooling
 
 –  Process planning is simplified by layer-based approach
 –  Fixtures are created in process
• The approach to CNC-RP will have to relax many of the traditional constraints
 –  Efficient machining is not a major driver (Traditional feeds/speeds not used)
 –   Not feature-based (Not necessary to machine entire feature in one setup orientation)
 –  Surface finish not as critical (Allow staircase effect)
• Goal of this research is to develop a method for CNC rapid prototyping such that:
 –  Toolpath planning, sequencing, tool sizing is automated
 –  Fixture design is created in-process, flexible, and allows access to almost all
surfaces
Methodology • Overview:
 –  Visible surfaces of the part are machined from each orientation about an axis of
rotation
 –  Long, small diameter flat end tool with equal flute and shank diameter used.
 –  Sacrificial supports (temporary features) added to the solid model and created in-
 process
 –  Begin with round stock material, clamped between two opposing chucks
• Example:
 x
 y
 z 
 y
 z 
 y
 z 
• Setup/Orientation
 –  How many rotations (setup orientations) about the axis of rotation are required?
 –  Where are they?
 –  What diameter and length tools should be used?
 –  In what order should the toolpaths be executed?
• Fixture planning
 
• Approximated as a problem of visibility (line of sight)
• A Visibility map is generated via a layer-based approach
• Tool access is restricted to directions in the slice plane (2D problem)
• Goal is to generate the data necessary to determine a minimum set of rotations required to
machine the entire surface
from one tool access direction
Determining the number of rotations
 
• Shortest Euclidean paths - Lee and Preparata, 1984
• Convex ropes - Peshkin and Sanderson, 1986
• 2D visibility cones - Stewart, 1999
Issues:
need to add collinear points to
 polygon segments
[Θa,Θb,]
[Θa,Θb,], [Θc,Θd,]
• Visibility for each polygonal chain is determined by calculating
the polar angle range that each segment of the chain can be seen.
• Since there can be multiple chains on each slice, we must consider
the visibility blocked by all other chains.
Solution approach
• We have a polygon P and its convex hull S
• For any point P i not on S, the visible range can be found by investigating points from the
adjacent CCW convex hull point to the adjacent CW convex hull point
• These points will be denoted the “left” and “right” convex hull points of P i, LCHP ( P i) and
 RCHP ( P i), respectively.
• It is only necessary to calculate the polar angles from P i to the points in the set [ LCHP ,
 RCHP ], excluding P i.
• The set is divided into, S1 and S2 where: ],[:2
],[:1
1
1
 
39
•The visible range for a point is bounded by the minimum polar angle from  P i to points in S1 and the maximum polar angle from P i to points in S2.
•This is the visible range for the point P i with respect to the boundary of its
own chain, and is denoted V(P i ).
Where:
](),([)( 12
Y  P  Min X  P  Max PiV  i S Y 
i S  X 
40
• Consider the segment defined by points in P, u and v, where:
u: P i and v: P i+1
• The intersection of visibility ranges for the points u and v and the 180º range
above the segment define a feasible range of polar angles in which the segment
could be reached.
 
RV v 
)](),1[(:2
  )]([)( 1
 
 
Problem Surfaces
(a) RV is outside of the 180º range, (b) Both RV and LV are out of the 180º range, (c)
 No visibility due to overlapping, (d) Visibility to the entire segment is not possible
since RV > LV .
I 2
42
Step two: Visibility blocked by all other chains on the slice
• V( ) j* is the visibility with respect to the chain j on which resides,
denoted  j*.
• For all obstacle chains , the polar range blocked by the chain is
denoted VB( ) j.
• The set of visible ranges for the segment is defined:
• Visibility blocked to the segment is the union of the visibility blocked by
chain j to point u and the visibility blocked by chain j to point v, intersected
with the 180º range above segment
• The set of angles blocked to the segment where:
• The set of angles blocked to points u and v where:
uv   uv
 
in the 180º range above the segment,
it can easily be seen that the set:
],[],[],[)( vuvvuuvu  LB RB LB RB LB RBVBVB
•  RBu is simply the minimum polar
angle from u to all points on the
 blocker chain
•  LBv is the maximum polar angle from
v to all points on P j , where P j is the
set of points for the blocker chain.
)]([ ux Min RB  j P  x
u )]([ vy Max LB  j P  y
v
 j j uvVBuvV uvVIS  )()()( * Recall:
•For each segment the collection of visible ranges given in polar angle about the
axis of rotation:
r bababatjk VIS  ],,,...[],,[,],,[: 21 where: r MAX = n
•From the data in [VIS ] we can formulate a set corresponding to the segments visible
from a given angle.
 
.
.
. 
.
.
. 
.
.
. 
.
.
. 
The Minimum Set Cover problem:
Given: A collection of subsets Θ s of a finite set SEG (the set of all segments)
Solution: A set cover for SEG , i.e., a subset  S’   S such that every element in SEG  belongs to at
least one member of Θ s for .'S  s
 
320º
49º140º
228º
C.H.
 A.C.
Facets
 S lice ( in )   #sgmts   time( s )   #sgmts   time( s )   #sgmts   time( s )   #sgmts   time( s )   #sgmts   time( s )
0.0025   19,566    22.750   27,285    25.812   36,199   29.390   49,975    36.623   69,212    47.122
0.0050   9,772    11.230   13,553   12.875   18,178    14.671   25,044   18.640   34,458    23.389
0.0100   4,850    5.687   6,781   6.515   9,054   7.405   12,476    9.297   17,306    11.843
0.0200   2,375    2.875   3,409   3.312   4,597    3.907   6,269   4.859   8,683   6.281
0.0400   1,182    1.453   1,655    1.718   2,159   2.032   2,974   2.453   4,123   3.141
1990 3686
STL Resolution
• Set cover problem solved as integer linear program using LINDO:
The “Jack”…
 –  Machine visible surfaces from approach direction
 –  2½-D pocketing, easily generated using current CAM software (MasterCAM, rough surface pocketing )
 –  A gouge-free approach, given flute and shank diameter are same (or shank < flute)
 –  Investigated as a rough machining approach - Balasubramanium, 1999
• Can approach finish machining using very small depths of cut
• We assume that tool length, not diameter will be active constraint
 –  To avoid collision, tool length > maximum swept diameter of part (Same as stock diameter)
 
Toolpath Planning
• Stock diameter/Tool length can be found from slice data used in VISI algorithm
 –  For each slice, find diameter of the set of points
 –  Set stock diameter to MAX
 –  Ds = MAXDIAM(CHP(slice points)) for all slices k 
 –  Set tool length to diameter of the stock Lt = Ds
• Toolpath sequencing is a significant problem
 – Need to avoid “thin web” conditions
 –  Can occur during one toolpath or from successive toolpaths
Depth of cut(max) = -Ds
Where Ds= Stock Diameter 
• For each successive toolpath
 planned in sequence, undesirable
orientations to be avoided:
• Preparatory toolpath sequence to avoid thin material conditions
• Removes bulk of stock material prior to processing remainder of toolpaths
• Choose from orientations in the solution set, or add new
Model
 
Fixture Planning
• Approach uses “sacrificial supports” to retain the prototype within the stock material
• Round stock clamped between opposing chucks
• As prototype is rotated b/w toolpaths sacrificial supports are incrementally created
• Supports cut away to remove finished part
• Current approach assumes model surfaces exist along axis of rotation
 –  Only one fixture support cylinder used on each end
 –   No change to visibility calculations
Problems:
• Start/end of cylinder 
 –   Need to have room for tool diameter to pass b/w end of part and stock 
 – Cylinder end protruding into the part must be fully “embedded”
• Use slice geometry to calculate depth of penetration where cylinder is fully attached
Part length
Pd ? Lf 
Fixture Planning • Determine first slice where fixture cylinder diameter is contained within the boundary
chain of the part ( Circle with center at axis of rotation )
Slice k=1 (0.005”) Slice k=1 (0.010”) Slice k=1 (0.015”)
Part slice boundary
Fixture cylinder diameter 
 –  Cylinders must limit deflection (torsion) caused by machining forces
• Approach
 –   Negligible bending
 –  Model as a statically indeterminate torsional shaft
Ft
Thrust force
 –  Ensures collision avoidance Dh
c = L p + 2a + 2b + 2Lf 
 
 Layer thickness: 0.005”
 Machining time: 3 hours
 
• Medical RP, one of the major territories for RP application
 – Manufacturing of dimensionally accurate physical models of the human anatomy derived from medical image data using a variety of rapid prototyping (RP) technologies
 – CNC-RP?
 – Cut any electrical conductive material regardless hardness
 –  Ignorable cutting force
 
machining process
Point contact
• Wire EDM
• Visibility problems are different
 – “Can we see it” vs. “Can we access it using a
straight line”
 
 – STEP-NC
 
 – Layer thickness 0.005”
 –  Process time ~3hours
320º
49º140º
228º
cost
 –  Usable products
 –  CNC RP
Conclusions -- continued
• The methods developed (CNC-RP and Wire EDM – RP) represent a deliberate approach at making CNC machining usable by engineers and designers, not  just machinists
• Capable of producing fully functional prototypes in the appropriate material
• Wide spread availability of CNC machines provides fast, low-cost integration to current product design processes
• Quick changeover from RP to Production setup will enable higher utilization of machines
 
71
References:
• Wang, F.C., L. Marchetti, P.K. Wright, “Rapid Prototyping Using Machining”, SME Technical
Paper, PE99-118, 1999
• Chen, Y.H., Song, Y., “The development of a layer based machining system”, Computer Aided
Design, Vol. 33, pp. 331-342, 2001
• Merz, R., Prinz, F.B., Ramaswami, K., Terk, M., Weiss, L.E., “Shape Deposition Manufacturing”,
Proceedings of the Solid Freeform Fabrication Symposium, University of Texas at Austin, pp. 1-8,
1994
• Walczyk, D.F., Hardt, D.E., “Rapid tooling for sheet metal forming using profiled edge laminations-
design principles and demonstration”, Journal of Manufacturing Science and Engineering,
Transactions of the ASME, Vol. 120, No. 2, pp. 746-754, November 1998
• Vouzelaud, F.A., Bagchi, A. & Sferro, P.F., (1992), Adaptive Laminated Machining for Prototyping
of Dies and Molds, Proceedings of the 3rd Solid Freeform Fabrication Symposium, pp. 291-300,
August 1992
• Lennings, L., “Selecting Either Layered manufacturing or CNC machining to build your prototype”,
SME Technical Paper, Rapid Prototyping Association, PE00-171, 2000
• Peshkin, M.A., Sanderson, A.C., “Reachable Grasps on a Polygon: The Convex Rope Algorithm”,
IEEE Journal of Robotics and Automation, Vol. RA-2, No. 1, March 1986
• Lee, D. T., Preparata, F. P., "Euclidean Shortest Paths in the Presence of rectilinear Barriers",
 Networks, Vol. 14, No. 3, pp. 393-410, 1984.
• Stewart, J.A., “Computing visibility from folded surfaces”, Computers and Graphics, Vol. 23, No. 5,
 pp. 693-702, 1999
• Balasubramaniam, M., “Tool Selection and Path Planning for 3-Axis Rough Cutting”, Thesis,
Department of Mechanical Engineering, The Massachusetts Institute of Technology, June 1999
• Tang, K., Woo, T.C., Gan, J., “Maximum Intersection of Spherical Polygons and Workpiece
Orientation for 4- and 5-Axis Machining”, Journal of Mechanical Design, Vol. 114, pp. 477-485,
September 1992