UBC Theses and Dissertations
Solid modeller based milling process simulation Spence, Allan Douglas
Continuing advances in manufacturing automation stress reducing the need for direct operator attention. In totally unstructured environments, this will be achieved only with extensive improvements in sensor design and machine intelligence. Milling operations, however, are largely predictable. Within tolerances, information on the geometry and material properties of the cutter and part is available, and the applicable constraints are known. Indeed, current practice is to use CAD/CAM programs to plan the cutter paths in advance of actual part production. This thesis proposes extension of the path planning function to a solid modeller based milling process simulation system. The system predicts the cutting forces, torques and deflections in advance, and automatically schedules the maximum safe feed rate before machining takes place. On the factory floor, technological data from the solid modeller is used to assist in recognizing unexpected events, and when necessary to warn of upcoming cutting condition changes. The required milling process simulations are shown to depend on cutter immersion geometry calculated by the solid modeller. Constructive solid geometry (CSC) is shown to be particularly useful in reducing the complexity of the immersion calculations with general part shapes. Rather than simultaneously examining every detail of the part definition, the intersection of the milling cutter is separately analyzed with each block and cylinder primitive. Individual results are then combined by applying the same Boolean operators and tree used in the overall part definition. Substantial increases in simulation speed are achieved through application of CSG redundant primitive elimination methods. Representation issues, cutter path segmentation and local boundary evaluation techniques are explored to avoid repeated calculations with irrelevant primitives. Computational geometry strategies for identifying only the locally significant paths in a cutter path chain are proposed, and compared to existing strategies. It is shown that under given assumptions this problem has a linear intrinsic complexity. Often after applying these methods the cutter-part intersection geometry reduces to a single immersion interval. In such cases an especially rapid simulation technique is used. Beyond a laboratory demonstration of the principle, industrial usefulness of the methods requires that the milling process simulations be carried out in a systematic and efficient manner. Existing methods work incrementally by summing differential elements along the cutter axis, slightly rotating the cutter, and stepping forward along the path. In contrast, this thesis develops analytical solutions that, for 2 1/2 dimensional parts, eliminate the need for axial summations. To improve upon repeated sampling at many cutter rotation angles, numerical methods and calculus techniques are used to rapidly determine extreme forces, torques, and deflections. Finally, when the part boundary is simple, piecewise functions are used to accelerate simulation along the cutter path. The algorithms are implemented, and the simulation accuracy verified by experimental measurement of instantaneous, average and maximum resultant forces, average torque, and surface error. For process planning, a continuously varying feed rate is automatically scheduled to respect imposed average torque, maximum resultant force and surface error constraints. Additional simulation and cutter-part intersection geometry data is calculated to assist with online monitoring and control tasks. Without surrendering the responsiveness of an online solution, upcoming sudden part geometry changes are communicated to a customized adaptive controller, allowing it to safely pass through regions where dangerous force transients would normally occur.
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