Abstract
Flexible electronic printing technology is a scientific technology that uses an “ink” material with conductive, dielectric, or semiconductor properties printed on a flexible web substrate to achieve precise preparation of flexible electronic devices, which are widely used in information, energy, medical, and military fields. In the preparation of the printing process of flexible printed electron webs under complex working conditions, the moving web will experience substantial unstable nonlinear dynamic behavior, such as divergence, flutter, bifurcation, and chaos. Accordingly, because of the coupling effects of the complex working conditions of the magnetic field, air and nonlinear electrostatic field forces, it is indispensable to explore the nonlinear dynamic equation of the flexible printed electron web in motion. The theory of multiphysics dynamics establishes a nonlinear vibration equation for the flexible printed electron web under multiphysics conditions. The discrete nonlinear vibration equation of state space equation was obtained by the Bubnov–Galerkin method. Utilizing the Runge–Kutta technique of the fourth-order, Poincaré maps, phase-plane diagrams, power spectra, bifurcation graphs, and time history diagrams of the moving flexible printed electron web were obtained. The influences of the velocity, electrostatic field, magnetic induction intensity, and follower force on the flexible printed electron web were analyzed. In addition, the Ansoft Maxwell finite element simulation software was used to simulate the magnetic field distribution of the moving web during roll-to-roll transmission. This paper determines the stable working range of the moving flexible printed electron web, which provides a theoretical basis for the preparation of flexible printed electronic webs.
Highlights
Research on high-precision flexible printed electron webs has been focused on and applied to wearable flexible electronic devices, smart sensors, Radio Frequency Identification (RFID) tags, micro-/nanomanufactured electron webs, aerospace applications, and other fields.1,2 in the production process, the moving flexible printed electron web is inevitably affected by the coupling of friction, air, magnetic fields in the environment, and nonlinear electrostatic field forces generated during the drying and curing of the conductive ink.3 These factors cause complex nonlinear dynamic behaviors of the flexible printed electron web in motion
The discrete differential equation is derived by the Bubnov–Galerkin method, the nonlinear vibration differential equation is solved by the fourth-order Runge–Kutta technique, and the effects of the velocity of the moving flexible printed electron web, the electrostatic field, the magnetic induction intensity, and the follower force are analyzed
When Q = 2, three discrete points are distributed in the Poincaré map (b), the phase-plane diagram (c) corresponds to a regular curve, and the power spectrum (d) remains in a discrete state, which illustrates that the moving flexible printed electron web is in a threefold periodic condition
Summary
Research on high-precision flexible printed electron webs has been focused on and applied to wearable flexible electronic devices, smart sensors, Radio Frequency Identification (RFID) tags, micro-/nanomanufactured electron webs, aerospace applications, and other fields. in the production process, the moving flexible printed electron web is inevitably affected by the coupling of friction, air, magnetic fields in the environment, and nonlinear electrostatic field forces generated during the drying and curing of the conductive ink. These factors cause complex nonlinear dynamic behaviors of the flexible printed electron web in motion. The discrete differential equation is derived by the Bubnov–Galerkin method, the nonlinear vibration differential equation is solved by the fourth-order Runge–Kutta technique, and the effects of the velocity of the moving flexible printed electron web, the electrostatic field, the magnetic induction intensity, and the follower force are analyzed. Studying the relationship curve of the magnetic induction intensity between different transmission angles and the position of the wire is helpful to control the influence of the magnetic field force on the nonlinear vibration of the flexible printed electron web in motion, thereby improving the stability of the system. Substituting the dimensionless Eq (30) into Eq (29), the nondimensional form of the equation for the magnetic-gas–solid coupling nonlinear vibration of the moving flexible printed electron web under the action of the nonlinear electrostatic field is
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
