Curvilinear Tool Paths for Pocket Machining

References and Acknowledgments

Outline

Some Historical Perspective -
Boeing has been manufacturing aerospace systems for a long time.

Systems are a lot more complex now!

Applying Math to Manufacturing Problems

Machining Process Production Flow
(The View from 30,000 Feet)

Curvilinear Tool Paths for Pocket Machining

Pockets in Delta IV Rocket Isogrid Skin Panels

Conventional Parallel-Offset Tool Path

The Math Problem

Conventional vs. Curvilinear Tool Paths

Overview of the Method

What Kind of Machining and Pockets Can be Handled in the Present Approach?

Some Parameters of Interest

Examples of how geometry input determines a tool path

Overview of Curvilinear Tool Path Generation

Solve Eigenvalue Problem

Alternatively, can solve even simpler elliptic PDE problem

Constant-value Contours of PDE Solution u

Constant-value Contours of a PDE Solution u

Step through tool path generation for a particular example.

First, numerically solve the PDE.

Next, spiral outward between contours of the fundamental eigenfunction to create tool path orbits.

Spiral outward (continued)

Get tool path, then smooth it (orbit-to-orbit, point-to-point)

Excavating One Layer of a Pocket

Feed Rate (Trajectory) Optimization

Introduce parametric spline rep. of tool path

Trajectory Optimization
Could use the following formulation.

Instead, we found it more useful to treat s, and not t, as the independent variable, & changed the problem.

Feed Rate Optimization Results

Feed Rate Optimization Results

Pockets in Delta IV Rocket Isogrid Skin Panel

Delta IV Isogrid Tool Paths Compared

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Metal Cutting Experiments at UC-Berkeley

Generally, Save Up to 30% Machining Time

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Consider contours of the principal eigenfunction for the Laplacian on a standard M-shaped pocket region.

Could use higher order PDE eigenfunctions in a process planning step to consider alternative ways to automatically decompose a pocket for machining.

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Possible Extension of Curvilinear Tool Path Method for a Pocket with Padup Region

Possible Extension of Curvilinear Tool Path Method for a Pocket with Padup Region

Extensions of Present Tool Path Method

Use it in Design For Manufacture (DFM) of Padups?

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