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Computational Geometric Techniques for Sculptured Surface Manufacturing and CAD/CAM Yuan-Shin Lee, Ph.D., P.E. North Carolina State University Raleigh...
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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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