Computational Geometric Techniques for Sculptured Surface Manufacturing and CAD/CAM Yuan-Shin Lee, Ph.D., P.E. North Carolina State University Raleigh, NC 27695-7906 U. S. A. E-mail:
[email protected] October 7, 2003
http://www.ie.ncsu.edu/yslee
Outlines
Introduction of Sculptured Surface Machining (SSM) CAD/CAM for Polyhedral Model Machining 5-Axis Tool Path Generation in CAD/CAM Machining Potential Field (MPF) for Complex Surface Manufacturing High Speed Machining (HSM) of Sculptured Surfaces Constant Material Removal Rate for HSM Adaptive Feedrate Scheduling for HSM Conclusions NCSU - YSLee
1. Introduction of Sculptured Surface Machining (SSM)
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Product Design with Sculptured Surfaces
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NURBS Surface and Applications
The NURBS surface interpolating four boundary curves.
NURBS surface of the core pattern
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Product Geometric Modeling and Manufacturing - Conceptual model: - Physical model: clay model - Descriptive model : engineering drawing - Mathematical model: - Computational model: Wireframe model Surface model Solid mode Non-manifold model NCSU - YSLee
Introduction to Sculptured Surface Machining (SMM)
Copy milling
NC milling
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2. CAD/CAM for Polyhedral Model Machining
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Polyhedral Models and NC Machining
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Cutter Gouging Problems in Sculptured Surface Machining
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NC Cutter Path Generation Methods
1. CC-based path
2. CC-Cartesian path
(Iso-parametric)
4. APT-type path NCSU - YSLee
3. CL-based path (offset)
Offset of Polygon for Cutter Location (CL)
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Three Schemes of Polyhedral Offsetting
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Deleting Interference to Avoid Gouging
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Offset of Triangles and Edges of Polyhedral Models
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Offset of Vertex in Polyhedral Models
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Local Offset Example
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Tool Path Generation for Polyhedral Machining
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Cutter Path Generation for NC Machining CC Point: Cutter contact point CL Point: Cutter location point
Ball-endmill
Filleted-endmill NCSU - YSLee
Flat-endmill
Slicing of Offset Elements for Tool Path Generation
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Slicing the Spherical and Cylindrical Surfaces for Polyhedral Machining
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Example of Polyhedral Model Machining
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Tool Path Generation for Machining of Example 1
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Polyhedral Machining with Fillet-Endmills Offset and Slicing of Convex Edges with Fillet Endmills
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Effective Cutting Shapes of Fillet-Endmills
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Example 2 of Polyhedral Machining
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Example 2 of Polyhedral Machining
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Computation Time for Machining Examples
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3. 5-Axis Tool Path Generation for Sculptured Surface Machining (SSM)
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5-Axis NC Machine Tools
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5-Axis Machining v.s. 3-Axis Machining (1) 3-Axis machining:
5-Axis machining:
Efficient in machining
Tool accessibility
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5-Axis Machining v.s. 3-Axis Machining (2) 3-Axis machining:
Cutter gouge
5-Axis machining:
Improved surface finish
Clean-cut
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Procedure of 5-Axis Tool Path Generation Surface Model
Tool Path Plan
CC Path Generation
CC data
Machine Kinematic Config
Kinematical Modelling CL data Calculation
Check of machine work-range Linear trajectory planning Interference check Optimazation
Joint Values
NC controller tape format
Post-Processing
NC data NCSU - YSLee
Definition of Tool Orientation in 5-Axis Machining • Tilt angle: α
n u rL rC
f
where, rL: cutter location point CL data u : cutter axis vector rC: cutter contact point CC data n : normal vector of surface f : a cutter feed vector t:nxf
α
• Yaw angle: β β
f rC t
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Effect of Tool Inclination Angle in 5-Axis Machining α = 45 α = 90 α = 30 α = 15 α=0
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α = 30 α = 15 α=0
Effect of Tool Yaw Angle in 5-Axis Machining β=0
β = −30
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Cusp Height Errors in Sculptured Surface Machining 3-axis machining:
ρ−η
ρ
η
ω/2 ω
5-axis machining:
h le ft
h r ight
a
η
p1
θ
η
p1
p2
ω
ω
(a)
(b) NCSU - YSLee
p2
Finding Effective Cutting Shape in 5-Axis Machining Instantaneous cutting profile W(θ∗ , φ∗)L
Inclined cutter ΨTorus (λL, ωL) YL
PI
PI
YL
YT
θ* ZT
Instantaneous cutting profile W(θ,φ)L φ* C* CC
Local coordinate basis: XL-Y L-ZL Tool coordinate basis: XT -YT -ZT
ZL
XL
ZL
XL
Effective cutting shape can be found as follows: W θ, φ L =
W θ *, φ* L =
xL = 0 yL zL x*L y*L z*L
G G
= Ψ θ , φ, λ L, ωL L,x L=0 Ψ, L
0
G
= Ψ,L
m7 sinθ * sin φ* + m8 sinθ * + m9 cosφ* + m10 m11 sin φ*sinθ *+m12 sin φ*cosθ *+m13 sinθ *+m14 cosθ *+m15 cosφ*+m16
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L
3. Optimizing Tool Path Generation for CAD/CAM Systems
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Machining of Sculptured Surfaces
Traditional machining planning
3D path planning NCSU - YSLee
Rolling-Ball Method for Extracting ClearCut Regions A ball-end cutter Gouging free region
Clean-up region
Clean-up boundary
Totally-gouging facets
z y
X
partially-gouging facets
gouging-free facets
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Finding the Optimal Tool Orientation for 5Axis Surface Machining Fitting cutting shape on local part surface YL Ok
1 -h
κ
E(θ )
θa
h
θb
Pv
Cb
Ca ZL
C* wa
Using surface curvatures for optimal tool orientation
wb w
Cutting direction (XL) out from the paper
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Tool Collision and Gouging Avoidance in 5Axis Machining YL λL* 1
ρZL=0
XL CC* Cutter moves along X L-axis
YL
ωL *
1
ρ XL=0
ZL CC*
Cutter moves out from the paper
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Material Removal Rate (MRR) Analysis for 5-Axis High Speed Machining F 0
* * * * Vmoving = Vtranslation + Θ rot ⋅ Ddis * * F = Vmoving ⋅ N sur = 0
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Optimizing 5-Axis Tool Path Generation in CAD/CAM Q: Is it possible to find the best path distribution for SSM?
(Total tool path length = 425.02 units, tool path number = 41, given tolerance = 0.005 units)
Sculptured surface design
Traditional tool path planning
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Optimizing 5-Axis Tool Path Generation - What is the best cutting direction? YL Ok
1 -h
κ
E(θ )
θa
h
θb
Pv
Cb
Ca ZL
C* wa
wb w
Cutting direction (XL) out from the paper
Machining strip width (dependent of λ, ω)
Optimal cutting direction NCSU - YSLee
Machining Potential Field (MPF) for Sculptured Surface Machining Q: Is it possible to find the best path distribution for SSM?
Sculptured surface design
Machining potential patches
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4. Adaptive Feed Scheduling for High Speed Machining (HSM) of Complex Surfaces
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Change of Material Engagement for High Speed Machining (HSM) C : center of circular arc R: radius of circular arc P: cutter tip.
s C
s
M(x,y)
R
M(x,y) r
r V
V P
fc
V
P
fc
V
f
R
f
C
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Adaptive Feed Scheduling For High Speed Machining (HSM)
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Adaptive Feed Scheduling for High Speed Machining (HSM)
Material engagement analysis
Adaptive feedrate scheduling
Machine acceleration analysis NCSU - YSLee
Conclusions
Modeling of complex surfaces for product development CAD/CAM for polyhedral model machining 5-Axis machining of sculptured surfaces High Speed Machining (HSM) can greatly benefit manufacturing process by shortening the machining time and reducing the manufacturing cost. HSM CAD/CAM shares an increasing market in recent years and the trend will continue. NCSU - YSLee
Thank you !!
Any Question ?
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