Nonlinear and linearized gray box models of direct-write printing dynamics
ISSN: 1355-2546
Article publication date: 21 August 2020
Issue publication date: 28 November 2020
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.
Keywords
Acknowledgements
Support for this research was provided in part by NSF CAREER Award CMMI 1708819 and NSF GRFP Award DGE-1343012. The authors wish to acknowledge Professor Yael Vodovotz and Drs Sravanti Paluri and John Frelka for their training, guidance, and support during rheology testing, and for the usage of rheometers. They acknowledge Ashley Allison Armstrong and Professor Amy J. Wagoner Johnson for providing hydroxyapatite build material for this work. They acknowledge Stephen Bedard for early work on the nonlinear modeling presented here. They acknowledge Kevin Wolf for machining custom reservoir holders.
Corrigendum: It has come to the attention of the publisher that the article Simeunović, A. and Hoelzle, D.J. (2020), “Nonlinear and linearized gray box models of direct-write printing dynamics”, published in the Rapid Prototyping Journal, Vol. ahead-of-print No. ahead-of-print https://doi.org/10.1108/RPJ-12-2018-0303 contains a number of equations that have been found to be incorrect. The equations affected are equations 2 and 12. Equation 2 was arranged inaccurately and equation 12 was incorrect . These errors do not affect the subsequent parts of the article, and they have now been corrected in the online version. The authors sincerely apologise for this.
Citation
Simeunović, A. and Hoelzle, D.J. (2020), "Nonlinear and linearized gray box models of direct-write printing dynamics", Rapid Prototyping Journal, Vol. 26 No. 10, pp. 1665-1676. https://doi.org/10.1108/RPJ-12-2018-0303
Publisher
:Emerald Publishing Limited
Copyright © 2020, Emerald Publishing Limited