Hybrid Modeling of Electrohydrodynamic Jet Printing

Additive manufacturing (AM) has grown quickly in popularity as a fast, flexible fabrication technique. However, the physical complexity of most AM processes makes it difficult to produce dynamical models that capture the system evolution from the beginning to the end of the process. This difficulty in model creation inhibits the application of many sophisticated control techniques that may improve process performance and reliability. This work uses a hybrid dynamical system structure and the combination of physics- and data-driven partial process models to address the modeling challenge for a specific AM technology--a microscale resolution technique called electrohydrodynamic jet printing--in which electric field is used to eject droplets from the meniscus at the end of a fluid-filled nozzle. Specifically, modeling of the fluid meniscus as a paraboloidal cap instead of a spherical cap extends the range of meniscus deformation that can be captured by the physics-driven model. In addition, the physics-driven model fidelity is improved by using equilibrium information and two-parameter correction coefficients identified from data to relax assumptions on the electric field and nozzle geometry models. Then, the maximum stable meniscus deformation is leveraged to define the limit of the physics-driven model's applicability, and for the remaining segment of the process, data-driven time-delayed linear time invariant models are identified. Finally, the complete hybrid model is validated against empirical time series data.