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1. A Generalized and Efficient Control-Oriented Modeling Approach for Vibration-Prone Delta 3D Printers Using Receptance Coupling

   https://doi.org/10.1109/TASE.2022.3197057  

   Edoimioya, Nosakhare; Okwudire, Chinedum E. (August 2022, IEEE Transactions on Automation Science and Engineering)

   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. 

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2. A nonlinear analysis of a Duffing oscillator with a nonlinear electromagnetic vibration absorber–inerter for concurrent vibration mitigation and energy harvesting

   https://doi.org/10.1007/s11071-023-09163-6  

   Kakou, Paul; Gupta, Sunit_Kumar; Barry, Oumar (February 2024, Nonlinear Dynamics)

   Abstract Several investigators have taken advantage of electromagnetic shunt-tuned mass dampers to achieve concurrent vibration mitigation and energy harvesting. For nonlinear structures such as the Duffing oscillator, it has been shown that the novel nonlinear electromagnetic resonant shunt-tuned mass damper inerter (NERS-TMDI) can mitigate vibration and extract energy for a wider range of frequencies and forcing amplitudes when compared to competing technologies. However, nonlinear systems such as the NERS-TMDI are known to exhibit complex stability behavior, which can strongly influence their performance in simultaneous vibration control and energy harvesting. To address this problem, this paper conducts a global stability analysis of the novel NERS-TMDI using three approaches: the multi-parametric recursive continuationWe emphasize that these assume method, Floquet theory, and Lyapunov exponents. A comprehensive parametric analysis is also performed to evaluate the impact of key design parameters on the global stability of the system. The outcome indicates the existence of complex nonlinear behavior, such as detached resonance curves, and the transition of periodic stable solutions to chaotic solutions. Additionally, a parametric study demonstrates that the nonlinear stiffness has a minimal impact on the linear stability of the system but can significantly impact the nonlinear stability performance, while the transducer coefficient has an impact on the linear and nonlinear stability NERS-TMDI. Finally, the global sensitivity analysis is performed relative to system parameters to quantify the impact of uncertainty in system parameters on the dynamics. Overall, our findings show that simultaneous vibration control and energy harvesting come with a considerable instability trade-off that limits the range of operation of the NERS-TMDI. 

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3. Parametric Analysis of Negative Capacitance Circuit for Enhanced Vibration Suppression Through Piezoelectric Shunt

   https://doi.org/10.1115/DETC2022-90616  

   Wang, Ting; Tang, Jiong (August 2022, Proceedings of the ASME 2022 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   Abstract Piezoelectric transducers are widely employed in vibration control and energy harvesting. The effective electro-mechanical coupling of a piezoelectric system is related to the inherent capacitance of the piezoelectric transducer. It is known that passive vibration suppression through piezoelectric LC shunt can be enhanced with the integration of negative capacitance which however requires a power supply. This research focuses on the parametric investigation of a self-sustainable negative capacitance where the piezoelectric transducer is concurrently used in both vibration suppression and energy harvesting through LC shunt. The basic idea is to utilize the energy harvesting functionality of the piezoelectric transducer to aid the usage of negative capacitance in terms of power supply. Specifically, the power consumption and circuitry performance with respect to negative capacitance circuit design is analyzed thoroughly. Indeed, the net power generation is the difference between available power in the shunt circuit and the power consumption of the negative capacitance circuit. There exists complex tradeoffs between net power generation and the vibration suppression performance when we use different resistance values in the negative capacitance circuit. It is demonstrated through correlated analytical simulation and experimental study that the proper selection of the resistance values in the negative capacitance circuit can result in vibration suppression enhancement as well as improved net power generation, leading to a self-sustainable negative capacitance scheme. 

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4. Designing continuous equilibrium structures that counteract gravity in any orientation

   https://doi.org/10.1038/s41598-023-34760-1  

   Redoutey, Maria; Filipov, Evgueni T. (May 2023, Scientific Reports)

   Abstract This paper presents a framework that can transform reconfigurable structures into systems with continuous equilibrium. The method involves adding optimized springs that counteract gravity to achieve a system with a nearly flat potential energy curve. The resulting structures can move or reconfigure effortlessly through their kinematic paths and remain stable in all configurations. Remarkably, our framework can design systems that maintain continuous equilibrium during reorientation, so that a system maintains a nearly flat potential energy curve even when it is rotated with respect to a global reference frame. This ability to reorient while maintaining continuous equilibrium greatly enhances the versatility of deployable and reconfigurable structures by ensuring they remain efficient and stable for use in different scenarios. We apply our framework to several planar four-bar linkages and explore how spring placement, spring types, and system kinematics affect the optimized potential energy curves. Next, we show the generality of our method with more complex linkage systems that carry external masses and with a three-dimensional origami-inspired deployable structure. Finally, we adopt a traditional structural engineering approach to give insight on practical issues related to the stiffness, reduced actuation forces, and locking of continuous equilibrium systems. Physical prototypes support the computational results and demonstrate the effectiveness of our method. The framework introduced in this work enables the stable, and efficient actuation of reconfigurable structures under gravity, regardless of their global orientation. These principles have the potential to revolutionize the design of robotic limbs, retractable roofs, furniture, consumer products, vehicle systems, and more. 

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5. Vibration Energy Harvester With Piecewise Linear Nonlinear Oscillator and Controllable Gap Size

   https://doi.org/10.1115/DETC2022-89948  

   Veney, Jacob; D’Souza, Kiran (August 2022, Volume 10: 34th Conference on Mechanical Vibration and Sound (VIB))

   Abstract Recently, vibration energy harvesting has been seen as a viable energy source to provide for our energy dependent society. Researchers have studied systems ranging from civil structures like bridges to biomechanical systems including human motion as potential sources of vibration energy. In this work, a bench-top system of a piecewise-linear (PWL) nonlinear vibration harvester is studied. A similar idealized model of the harvester was previously looked at numerically, and in this work the method is adjusted to handle physical systems to construct a realistic harvester design. With the physically realizable harvester design, the resonant frequency of the system is able to be tuned by changing the gap size between the oscillator and mechanical stopper, ensuring optimal performance over a broad frequency range. Current nonlinear harvester designs show decreased performance at certain excitation conditions, but this design overcomes these issues while also still maintaining the performance of a linear harvester at resonance. In this investigation, the system is tested at various excitation conditions and gap sizes. The computational response of the resonance behavior of the PWL system is validated against the experiments. Additionally, the electromechanical response is also validated with the experiments by comparing the output power generated from the experiments with the computational prediction. 

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