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: yslee@ncsu.edu http://www.ie.ncsu.edu/yslee October 7, 2003
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) NCSU - YSLee
Product Design with Sculptured Surfaces NCSU - YSLee
NURBS Surface and Applications The NURBS surface interpolating four boundary curves . NURBS surface of the core pattern NCSU - YSLee
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 NCSU - YSLee
2. CAD/CAM for Polyhedral Model Machining NCSU - YSLee
Polyhedral Models and NC Machining NCSU - YSLee
Cutter Gouging Problems in Sculptured Surface Machining NCSU - YSLee
NC Cutter Path Generation Methods 2. CC-Cartesian path 3. CL-based path (offset) 1. CC-based path (Iso-parametric) 4. APT-type path NCSU - YSLee
Offset of Polygon for Cutter Location (CL) NCSU - YSLee
Three Schemes of Polyhedral Offsetting NCSU - YSLee
Deleting Interference to Avoid Gouging NCSU - YSLee
Offset of Triangles and Edges of Polyhedral Models NCSU - YSLee
Offset of Vertex in Polyhedral Models NCSU - YSLee
Local Offset Example NCSU - YSLee
Tool Path Generation for Polyhedral Machining NCSU - YSLee
Cutter Path Generation for NC Machining CC Point: Cutter contact point CL Point: Cutter location point Ball-endmill Filleted-endmill Flat-endmill NCSU - YSLee
Slicing of Offset Elements for Tool Path Generation NCSU - YSLee
Slicing the Spherical and Cylindrical Surfaces for Polyhedral Machining NCSU - YSLee
Example of Polyhedral Model Machining NCSU - YSLee
Tool Path Generation for Machining of Example 1 NCSU - YSLee
Polyhedral Machining with Fillet-Endmills Offset and Slicing of Convex Edges with Fillet Endmills NCSU - YSLee
Effective Cutting Shapes of Fillet-Endmills NCSU - YSLee
Example 2 of Polyhedral Machining NCSU - YSLee
Example 2 of Polyhedral Machining NCSU - YSLee
Computation Time for Machining Examples NCSU - YSLee
3. 5-Axis Tool Path Generation for Sculptured Surface Machining (SSM) NCSU - YSLee
5-Axis NC Machine Tools NCSU - YSLee
5-Axis Machining v.s . 3-Axis Machining (1) 3-Axis machining: 5-Axis machining: Tool accessibility Efficient in machining NCSU - YSLee
5-Axis Machining v.s . 3-Axis Machining (2) 3-Axis machining: Cutter gouge 5-Axis machining: Improved surface finish Clean-cut NCSU - YSLee
Procedure of 5-Axis Tool Path Generation Surface Model CC Path Generation Tool Path Plan CC data Kinematical Modelling Machine CL data Calculation Check of machine work-range Kinematic Config Linear trajectory planning Interference check Optimazation Joint Values NC controller Post-Processing tape format NC data NCSU - YSLee
Definition of Tool Orientation in 5-Axis Machining • Tilt angle: α u n where, r L : cutter location point CL data r L u : cutter axis vector α r C : cutter contact point CC data r C f n : normal vector of surface f : a cutter feed vector t : n x f β • Yaw angle: β f r C t NCSU - YSLee
Effect of Tool Inclination Angle in 5-Axis Machining α = 30α = 15 α = 45 α = 0 α = 90 α = 30 α = 15 α = 0 NCSU - YSLee
Effect of Tool Yaw Angle in 5-Axis Machining β = 0 β = −30 NCSU - YSLee
Cusp Height Errors in Sculptured Surface Machining 3-axis machining: ρ−η ρ η ω/2 ω 5-axis machining: h left h r ight a θ η η p 2 p 1 p 2 p 1 ω ω (a) (b) NCSU - YSLee
Finding Effective Cutting Shape in 5-Axis Machining Inclined cutter Ψ Torus ( λ L, ω L ) Instantaneous cutting profile W( θ∗ , φ∗ ) L Y L Y L P I P I Y T θ * Instantaneous cutting profile W( θ , φ ) L Z T φ * C* Local coordinate basis: X L -Y L -Z L Tool coordinate basis: X T -Y T -Z T CC Z L X L Z L X L Effective cutting shape can be found as follows: G x L = 0 G W θ , φ L = = Ψ θ , φ , λ L , ω L L, x L =0 y L z L Ψ , L 0 G x * L W θ *, φ * L = m 7 sin θ * sin φ * + m 8 sin θ * + m 9 cos φ * + m 10 y * L = z * L Ψ , L m 11 sin φ *sin θ *+ m 12 sin φ *cos θ *+ m 13 sin θ *+ m 14 cos θ *+ m 15 cos φ *+ m 16 L NCSU - YSLee
3. Optimizing Tool Path Generation for CAD/CAM Systems NCSU - YSLee
Machining of Sculptured Surfaces Traditional machining planning NCSU - YSLee 3D path planning
Rolling-Ball Method for Extracting Clear- Cut Regions A ball-end cutter Gouging free region Clean-up region Clean-up boundary Totally-gouging facets z X partially-gouging facets y gouging-free facets NCSU - YSLee
Finding the Optimal Tool Orientation for 5- Axis Surface Machining Fitting cutting shape on local part surface Y L O k 1 κ - h E( θ ) θ a h C b θ b P v C a Z L C* Using surface curvatures for w a w b w optimal tool orientation Cutting direction ( X L ) out from the paper NCSU - YSLee
Tool Collision and Gouging Avoidance in 5- Axis Machining Y L λ L * 1 ρ ZL =0 ρ ρ ρ X L CC* Cutter moves along X L -axis Y L ω L * 1 ρ XL =0 ρ ρ ρ Z L CC* Cutter moves out from the paper NCSU - YSLee
Material Removal Rate (MRR) Analysis for 5-Axis High Speed Machining = F 0 < F 0 > F 0 = + Θ ⋅ � � � � V V D moving translatio n rot dis = ⋅ = � � F V N 0 moving sur NCSU - YSLee
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 NCSU - YSLee
Optimizing 5-Axis Tool Path Generation - What is the best cutting direction? Y L O k 1 κ - h E( θ ) θ a h C b θ b P v C a Z L C* w a w b w Cutting direction ( X L ) 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 NCSU - YSLee
4. Adaptive Feed Scheduling for High Speed Machining (HSM) of Complex Surfaces NCSU - YSLee
Change of Material Engagement for High Speed Machining (HSM) C : center of circular arc R : radius of circular arc P : cutter tip. s s C M(x,y) R M(x,y) r r R V P V f c f c P V V f f C NCSU - YSLee
Adaptive Feed Scheduling For High Speed Machining (HSM) NCSU - YSLee
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 ? NCSU - YSLee
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