Layer-to-Layer Stability of Linear Layerwise Spatially Varying Systems: Applications in Fused Deposition Modeling

Abstract

Closed-loop control applications for additive manufacturing (AM) technologies introduce unique challenges in control-oriented modeling and controller development. There have been developments in current literature to model the temporal and spatial dynamics of AM processes. The temporal dynamics of AM processes are often modeled using tools from fluid dynamics and mechanics to represent the material deposition and the motion of the deposition system. Spatial dynamics are often modeled by representing the spreading dynamics of the deposited material in the layerwise spatial domain. An important challenge with the spatial dynamics of AM processes is to understand the performance of the layer-to-layer (L2L) spatial dynamics under spatial disturbances in the system. To this end, this article presents a linear layerwise spatially varying (LLSV) systems modeling framework to represent the L2L spatial height evolution of a generic AM process. The proposed unifying modeling framework can easily represent various AM processes. An L2L stability measure is provided as a performance measure for the spatial dynamic state of an AM process. L2L stability is a novel analysis tool to understand and analyze the spatial characteristics of AM processes. Fundamental L2L stability definitions for a nominal system model and a system model with known Gaussian spatial noise are presented. Theoretical robustness bounds for L2L stability are experimentally compared to a fused deposition modeling (FDM) process. The results show that the theoretical robustness bounds given in this work provide an important foundation for developing novel closed-loop L2L spatial control applications.

Stress Flow Guided Non-Planar Print Trajectory Optimization for Additive Manufacturing of Anisotropic Polymers

“…Similarly, print trajectory planning for non-planar robotic deposition is studied in [20], ignoring, however, stress flow alignment and further manufacturability constraints for the printing; the same holds for [13]. Full end-to-end implementation for non-planar FFF optimization requires knowledge of the extrusion dynamics [21,22], machine kinematics [15,23], and efficient trajectory optimization formulations [24,23] that consider process constraints [15], material, printed geometry [25,26,27], and stress flow field [14]. Consequently, improving the non-planar printing process performance is not trivial and requires developing advanced methods to optimize print path trajectories for arbitrary geometries under a given stress flow field and material extrusion constraints.…”

“…While this possibility has been demonstrated in customized applications, currently there exists no rigorous framework that exploits the anisotropic material properties to improve mechanical strength of FFF through non-planar printing. The quality of LCP printed parts largely depends on a) the quality of slicing in the desired layer thickness across all layers and how each layer supports a subsequent one (see [27] for 2.5D printing), and b) the quality of trajectory generation in each layer and the homogeneous spacing of the deposited lines (see [32] for 2.5D printing). Previous approaches [14] have successfully tackled the optimization problem for isotropic materials such as polylactic acid (PLA), neglecting the practical constraints of high-quality FFF printing.…”

Stress Flow Guided Non-Planar Print Trajectory Optimization for Additive Manufacturing of Anisotropic Polymers

“…A critical challenge in FFF is ensuring the reliability and repeatability of the process under changing process conditions. On most current applications, the challenge is partially caused by a lack of in-situ sensors, control-oriented models, and closed-loop control strategies [3]. A possible approach to improve performance is through modeling printed bead outputs as a function of input parameters [4], [5].…”

“…2 Control and Automation Group, Inspire AG, 8005 Zürich, Switzerland. 3 NematX AG, 8093 Zürich, Switzerland. Corresponding author: E. C. Balta, efe.balta@inspire.ch.…”

Closed-loop control of dielectric permittivity for 3D-printed radio-frequency devices

“…There has been significant work to apply closed-loop feedback control to AM processes. The design of an effective control policy relies upon a good predictive model of the system, which has motivated several recent results on control-oriented modeling of layer deposition/solidification [5]- [7]. The potential of various control methods have also been examined to control mechanical properties within 3Dprinted parts.…”