Nonlinear and linearized gray box models of direct-write printing dynamics

Abstract

Purpose The purpose of this study is to develop nonlinear and linearized models of DW printing dynamics that capture the complexity of DW while remaining integrable into control schemes. Control of material metering in extrusion-based additive manufacturing modalities, such as positive displacement direct-write (DW), is critical for manufacturing accuracy. However, in DW, transient flows are poorly controlled due to capacitive pressure dynamics – pressure is stored and slowly released over time from the build material and other compliant system elements, adversely impacting flow rate start-ups and stops. Thus far, modeling of these dynamics has ranged from simplistic, potentially omitting key contributors to the observed phenomena, to highly complex, making usage in control schemes difficult. Design/methodology/approach The authors present nonlinear and linearized models that seek to both capture the capacitive and nonlinear resistive fluid elements of DW systems and to pose them as ordinary differential equations for integration into control schemes. The authors validate the theoretical study with experimental flow rate and material measurements across a range of extrusion nozzle sizes and materials. The authors explore the contribution of the system and build material bulk modulus to these dynamics. Findings The authors show that all tested models accurately describe the measured dynamics, facilitating ease of integration into future control systems. Additionally, the authors show that system bulk modulus may be substantially reduced through appropriate system design. However, the remaining build material bulk modulus is sufficient to require feedback control for accurate material delivery. Originality/value This study presents new nonlinear and linear models for DW printing dynamics. The authors show that linear models are sufficient to describe the dynamics, with small errors between nonlinear and linear models. The authors demonstrate control is necessary for accurate material delivery in DW.