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Delta 3D printers can significantly increase throughput in additive manufacturing by enabling faster and more precise motion compared to conventional serial-axis 3D printers. Further improvements in motion speed and part quality can be realized through model-based feedforward vibration control, as demonstrated on serial-axis 3D printers. However, delta machines have not benefited from model-based controllers because of the difficulty in accurately modeling their position-dependent, coupled nonlinear dynamics. In this paper, we propose an efficient framework to obtain accurate linear parameter-varying models of delta 3D printers at any position within their workspace from a few frequency response measurements. We decompose the dynamics into two sub-models–(1) an experimentally-identified sub-model containing decoupled vibration dynamics; and (2) an analytically-derived sub-model containing coupled dynamics–which are combined into one using receptance coupling. We generalize the framework by extending the analytical model of (2) to account for differing mass profiles and dynamic models of the printer’s end-effector. Experiments demonstrate reasonably accurate predictions of the position-dependent dynamics of a commercial delta printer, augmented with a direct drive extruder, at various positions in its workspace. Note to Practitioners—This work aims to equip high-speed 3D printers, like delta machines, with model-based controllers to complement their speed with high-accuracy. Due to the coupled kinematic chains of the delta, complex control methodologies, some of which require real-time state measurements, are often used to achieve satisfactory control performance. Our modeling approach provides an efficient methodology for obtaining accurate linear models without the need for real-time measurements, thus enabling practitioners to design linear model-based feedforward controllers to achieve the high throughput and accuracy desired in additive manufacturing (AM). The models we develop in this paper are intended for use with feedforward vibration compensation methods, which can be beneficial for both industrial-scale AM machines that have high-powered servo motors and feedback controllers, as well as consumer-grade AM machines which use stepper motors in feedforward control.

Material extrusion (MatEx) is the one of the most widely utilized additive manufacturing (AM) methods. The key to high printing quality in MatEx lies in the synchronization between the fast motion system and the slow extrusion system. However, the synchronization is challenged by the slow response of the extrusion system. In MatEx, there are two main types of extrusion systems: Bowden and direct-drive (DD), based on different extruder-hot end arrangements. DD systems have the extruder installed directly above the hot end, providing a relatively fast extrusion response but adding more inertia to the print head. In contrast, Bowden systems position the extruder on the printer’s frame, feeding the filament to the hot end through a long Bowden tube. As a result, this setup leads to a sluggish extrusion response due to the elasticity of the long segment of filament but has a lower print head’s inertia, offering a higher positioning accuracy compared to the DD system. To leverage the advantages of both extrusion systems, this paper proposes a hybrid extrusion system design that combines a Bowden extruder with a low-mass DD extruder for filament feeding. To optimize the design and control of the extruder, a low-order model that characterizes the hybrid extruder dynamics is proposed. The model is used to design a feedforward (FF) controller that minimizes the force exerted by the DD extruder motor in the hybrid extruder while achieving the desired extrusion accuracy. The effectiveness of the proposed extruder and the FF controller is validated experimentally by demonstrating transient responses as fast as those of the standard DD extruder with up to 65% less force required from the DD extruder motor. Data collected from motor torque–mass specifications of three motor series from three different manufacturers indicate that the torque/force reduction could yield up to a 69% mass reduction in the motor used for the DD extruder, adding only 32.5% extra weight of the hot end to the print head. Hence it holds the potential to achieve the same extrusion accuracy as standard DD extruders while significantly reducing print head inertia, hence the resulting vibration of the printer, as demonstrated using a case study.

Parts produced by laser powder bed fusion (LPBF) additive manufacturing are prone to residual stresses, deformations, and other defects linked to nonuniform temperature distribution during the process. Several works have highlighted the important role scan sequence plays in achieving uniform temperature distribution in LPBF. However, scan sequence continues to be determined offline based on trial-and-error or heuristics, which are neither optimal nor generalizable. Towards addressing these weaknesses, we present, for the first time, an approach for intelligent online scan sequence optimization to achieve uniform temperature distribution in LPBF using a control theoretic approach. The thermal dynamics of the LPBF process is modeled using the finite difference method and the next best feature (for example, stripe or island) that minimizes a thermal uniformity metric is found using a control theoretic approach. In simulations, the proposed approach yields up to 8.4 times improvement in thermal uniformity compared to existing heuristic approaches.

Material extrusion (MatEx) is the predominant of the available additive manufacturing (AM) methods. High-quality MatEx AM process demands accurate synchronization between motion control and extrusion control. However, the synchronization is challenging due to nonlinearities of the flow inside the nozzle. One of the most common synchronization defects is the inaccuracies at extrusion starts and stops. To address this, material retraction and advancement processes must be applied and controlled accurately. However, feedback extrusion control is limited by the difficulties in sensing the real-time extrusion rate, and existing feedforward (FF) extrusion control methods only rely on models that are developed and identified under continuous extrusion thus do not account for the retraction and advancement processes. Besides, another method that commercial printers commonly employ to address the extrusion problem is to find the optimal printing parameter set through sequential printing tests. However, this method does not generalize well for different materials and extruders, and it could be time and material-consuming. To address these problems in adopting FF control, this paper presents a control-oriented phenomenological model (P-model) that characterizes the extrusion dynamics during the retraction and advancement processes mathematically and a model-based FF control method to compensate the dynamics by altering both the motion and extrusion command. To validate the proposed model, a novel experimental setup (Setup 1) is proposed by retrofitting a MatEx standard printer with a servo motor on its material feeding gear to reveal the extrusion force during the process. The proposed model is validated on Setup 1 by demonstrating an accurate mathematical characterization of the extrusion dynamics and in the meantime revealing the consistency between the extrusion (external) and force (internal) behavior. Additionally, the practicality and effectiveness of the P-model and the P-model-based control method are demonstrated on an unmodified commercial printer (Setup 2). By using Setup 1, the proposed control method demonstrated up to 36.61% and 90.55% reduction in deposition error during advancement and retraction, respectively when compared to a standard FF extrusion control approach. Moreover, up to 39.34% and 35.26% reductions in deposition error during advancement and retractions are observed with the proposed controller when compared to using the standard extrusion profile with a well-tuned retraction and advancement parameters set from a commercial slicer software on Setup 2. Lastly, the potential of the proposed method for enhancing printing accuracy in real-world printing is demonstrated through a practical printing application.

To enable faster production and/or the manufacture of large parts, multi-laser powder bed fusion (PBF) systems are increasingly being adopted in practice. There is also research indicating that multiple lasers could be used to improve processing conditions in PBF. However, parts produced by single-laser and multi-laser PBF are susceptible to residual stress, deformation, and other defects that are strongly associated with non-uniform temperature distribution. The authors, in their prior work, have proposed an intelligent scan sequence optimization approach, called SmartScan, that uses a physics-based thermal model to achieve uniform temperature distribution and reduced residual stress and deformation. However, SmartScan is currently only applicable to single-laser PBF systems, where it is used for optimizing the sequence of scanning features (i.e., repeating units) of a scan pattern (e.g., a stripe or island). This paper generalizes SmartScan to multi-laser systems and shows that the complexity of the resulting solution grows combinatorially as a function of the number of lasers and scanned features, making it computationally inefficient. To address this issue, it proposes a sequential approximation to the combinatorial solution of SmartScan for multi-laser PBF systems resulting in a solution whose complexity grows linearly with the number of features. Through numerical studies, the sequential approximation is shown to substantially improve computational efficiency, compared to the combinatorial approach, without significant loss of optimality. Adopting the sequential solution, simulations and experiments involving laser marking of stainless steel 316 L plates are used to demonstrate the effectiveness of SmartScan in achieving more uniform temperature distribution compared to heuristic scan sequences in multi-laser PBF. As a result, SmartScan yields up to 40% reduction in measured plate deformation compared to the heuristic approaches.

Parts produced by laser or electron-beam powder bed fusion (PBF) additive manufacturing are prone to residual stresses, deformations, and other defects linked to non-uniform temperature distribution during the manufacturing process. Several researchers have highlighted the important role scan sequence plays in achieving uniform temperature distribution in PBF. However, scan sequence continues to be determined offline based on trial-and-error or heuristics, which are neither optimal nor generalizable. To address these weaknesses, we have articulated a vision for an intelligent scan sequence optimization approach to achieve uniform temperature distribution, hence reduced residual stresses and deformations, in PBF using physics-based and data-driven thermal models. This paper proposes SmartScan, our first attempt towards achieving our vision using a simplified physics-based thermal model. The conduction and convection dynamics of a single layer of the PBF process are modeled using the finite difference method and radial basis functions. Using the model, the next best feature (e.g., stripe or island) that minimizes a thermal uniformity metric is found using control theory. Simulations and experiments involving laser marking of a stainless steel plate are used to demonstrate the effectiveness of SmartScan in comparison to existing heuristic scan sequences for stripe and island scan patterns. In experiments, SmartScan yields up to 41% improvement in average thermal uniformity and 47% reduction in deformations (i.e., warpage) compared to existing heuristic approaches. It is also shown to be robust, and computationally efficient enough for online implementation in the future.

The H-frame (also known as H-Bot) architecture is a simple and elegant two-axis parallel positioning system used to construct the XY stage of 3D printers. It holds potential for high speed and high dynamic performance due to the use of frame-mounted motors that reduce the moving mass of the printer while allowing for the use of (heavy) higher torque motors. However, the H-frame’s dynamic accuracy is limited during high-acceleration and high-speed motion due to racking – i.e., parasitic torsional motions of the printer’s gantry due to a force couple. Mechanical solutions to the racking problem are either costly or detract from the simplicity of the H-frame. In this paper, we introduce a feedforward software compensation algorithm, based on the filtered B-splines (FBS) method, that rectifies errors due to racking. The FBS approach expresses the motion command to the machine as a linear combination of B-splines. The B-splines are filtered through an identified model of the machine dynamics and the control points of the B-spline based motion command are optimized such that the tracking error is minimized. To compensate racking using the FBS algorithm, an accurate frequency response function of the racking motion is obtained and coupled to the H-frame’s and y-axis dynamics with a kinematic model. The result is a coupled linear parameter varying model of the H-frame that is utilized in the FBS framework to compensate racking. An approximation of the proposed racking compensation algorithm, that decouples the x- and y-axis compensation, is developed to significantly improve its computational efficiency with almost no loss of compensation accuracy. Experiments on an H-frame 3D printer demonstrate a 43% improvement in the shape accuracy of a printed part using the proposed algorithm compared to the standard FBS approach without racking compensation. The proposed racking compensation algorithm can be used in-conjunction with mechanical solutions, or as a stand-alone solution, to improve the performance of H-frame architectures.

Additive manufacturing (AM) is gaining attention as an alternative to traditional manufacturing processes. Of the available AM methods, material extrusion (ME) AM is predominant. High-quality ME AM demands accurate synchronization between positioning (motion) control and extrusion control, as poor synchronization leads to printing defects like over- and under-extrusion. Typically, extrusion control in ME AM is achieved via feedforward (FF) control techniques due to difficulties in sensing extrusion rate in real-time for feedback control. However, existing FF extrusion control techniques rely on simple linear models to control the highly nonlinear extrusion process, leading to quality issues like over- and under-extrusion. This paper presents two FF control strategies for mitigating over- and under-extrusion defects in ME AM. The first strategy uses a standard linear model of extrusion system but applies it to FF motion control rather than FF extrusion control. This has the net effect of synchronizing motion and extrusion control while avoiding some nonlinearities associated with the extrusion process. In the second approach, an empirical nonlinear model of the extrusion process is developed and adopted for the design of a nonlinear FF extrusion controller. Both approaches were validated experimentally on a fused filament fabrication (FFF) 3D printer, and respectively demonstrated up to 40.45% and 35.98% improvement in deposition accuracy (i.e., reduced over- and under-extrusion) compared to a standard FF extrusion control approach typically used in the literature. In addition, the proposed nonlinear FF controller was shown to be more versatile and lead to faster ME AM compared to the proposed linear FF motion control approach. A practical application of the proposed techniques for improving the quality of a variable-width pattern printed using a new concept of continuously varied extrusion was demonstrated.

Analytical and low-order numerical models are very useful for studying friction behavior of rolling element machine components like ball bearings and ball screws. This is because they provide generalizable insights into friction behavior at much lower computational costs compared with high-order numerical models like finite element analysis (FEA). While analytical and low-order numerical models in the literature are mainly focused on ball-to-groove contact friction, experimental studies have shown that ball-to-ball contact friction is also very important. This is especially true for linear ball bearings/guideways and ball screws which, unlike rotary ball bearings, do not typically make use of caged balls to prevent ball-to-ball contact. Therefore, in this paper, low-order numerical models for ball-to-ball contact friction in linear ball bearings and ball screws are developed. Furthermore, an analytical model for ball-to-ball contact friction in four-point contact linear ball bearing is derived by making simplifications to its low-order numerical model. Compared with ball-to-ball friction predictions from FEA models developed in ansys, the proposed numerical models are shown in case studies to be accurate within 7%, while computing at least three orders of magnitude faster. Moreover, case studies are used to demonstrate how the developed models can be used in practice, e.g., for the mitigation of ball-to-ball contact friction in linear ball bearings and the prediction of friction variation during the operation of a ball screw.