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ADDOPT: An Additive Manufacturing Optimal Control Framework Demonstrated in Minimizing Layer-Level Thermal Variance in Electron Beam Powder Bed Fusion

Mikhail Khrenov, William Frieden Templeton, Sneha Prabha Narra

Abstract

Additive manufacturing (AM) techniques hold promise but face significant challenges in process planning and optimization. The large temporal and spatial variations in temperature that can occur in layer-wise AM lead to thermal excursions, resulting in property variations and defects. These variations cannot always be fully mitigated by simple static parameter search. To address this challenge, we propose a general approach based on modeling AM processes on the part-scale in state-space and framing AM process planning as a numerical optimal control problem. We demonstrate this approach on the problem of minimizing thermal variation in a given layer in the electron beam powder bed fusion (EB-PBF) AM process, and are able to compute globally optimal dynamic process plans. These optimized process plans are then evaluated in simulation, achieving an 87% and 86% reduction in cumulative variance compared to random spot melting and a uniform power field respectively, and are further validated in experiment. This one-shot feedforward planning approach expands the capabilities of AM technology by minimizing the need for experimentation and iteration to achieve process optimization. Further, this work opens the possibility for the application of optimal control theory to part-scale optimization and control in AM.

ADDOPT: An Additive Manufacturing Optimal Control Framework Demonstrated in Minimizing Layer-Level Thermal Variance in Electron Beam Powder Bed Fusion

Abstract

Additive manufacturing (AM) techniques hold promise but face significant challenges in process planning and optimization. The large temporal and spatial variations in temperature that can occur in layer-wise AM lead to thermal excursions, resulting in property variations and defects. These variations cannot always be fully mitigated by simple static parameter search. To address this challenge, we propose a general approach based on modeling AM processes on the part-scale in state-space and framing AM process planning as a numerical optimal control problem. We demonstrate this approach on the problem of minimizing thermal variation in a given layer in the electron beam powder bed fusion (EB-PBF) AM process, and are able to compute globally optimal dynamic process plans. These optimized process plans are then evaluated in simulation, achieving an 87% and 86% reduction in cumulative variance compared to random spot melting and a uniform power field respectively, and are further validated in experiment. This one-shot feedforward planning approach expands the capabilities of AM technology by minimizing the need for experimentation and iteration to achieve process optimization. Further, this work opens the possibility for the application of optimal control theory to part-scale optimization and control in AM.
Paper Structure (17 sections, 19 equations, 7 figures)

This paper contains 17 sections, 19 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Modeling Additive Manufacturing in State-Space
  3. Example Transport Model -- Voxelized Conduction and Convection
  4. Example Input Model -- Power Field
  5. Optimal Control Problem
  6. Implementation
  7. Demonstration in Electron Beam Powder Bed Fusion
  8. Process Model
  9. Objective
  10. Additional Constraints
  11. Convexity
  12. Power Field Approximation
  13. Results
  14. Numerical Simulation Results
  15. Experimental Results
  16. ...and 2 more sections

Figures (7)

  • Figure 1: Diagram of electron beam powder bed fusion (EB-PBF).
  • Figure 2: Voxelized conduction transport model with power field input model.
  • Figure 3: Block diagram of the ADDOPT system.
  • Figure 4: Top-down view of the target geometry for the EB-PBF experiments. White signifies areas to be melted, while black signifies areas to not melt. The varying thicknesses pose a challenge to maintaining uniform thermal distributions for current techniques.
  • Figure 5: Top: Comparison of the naive power distribution (uniform) and optimized power distribution over the course of the build. Bottom: Comparison of the resulting thermal evolutions. Note the heat build-up in the inner corners of the uniform power field's thermal profile.
  • ...and 2 more figures