We demonstrate that, despite differences in their nature, many energy beam controlled-depth machining processes (for example, waterjet, pulsed laser, focused ion beam) can be modeled using the same mathematical framework—a partial differential evolution equation that requires only simple calibrations to capture the physics of each process. The inverse problem can be solved efficiently through the numerical solution of the adjoint problem and leads to beam paths that generate prescribed three-dimensional features with minimal error. The viability of this modeling approach has been demonstrated by generating accurate free-form surfaces using three processes that operate at very different length scales and with different physical principles for material removal: waterjet, pulsed laser, and focused ion beam machining. Our approach can be used to accurately machine materials that are hard to process by other means for scalable applications in a wide variety of industries.
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