Coupled-Mode Flutter of a Cleaning Blade System in a Laser Printer

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This paper discusses a mechanism of a self-excited vibration of a cleaning blade in a laser printer. We present a coupled-mode flutter model using a finite element model. A stability analysis based on the proposed model is carried out. From this result, it is clarified that two modes couple each other with increasing coefficient of friction. At that time, the natural frequency of the coupled-mode is corresponding to the frequency of the self-excited vibration. This root locus reveals a typical argand diagram for coupled-mode flutter of an undamped system via so-called Hamiltonian-Hopf bifurcation. Furthermore, we discuss about the steady-state amplitude of the self-excited vibration. First, we present a nonlinear amplitude equation by extracting the unstable modes with introduction of the adjoint vector to the eigenvector of the system. Second, from consideration about the nonlinear term which is able to restrain an increasing of amplitude, we decide the nonlinear term referring to the Rayleigh's equation. Then, the unstable mode solution obtained by the method of multiple scales is reconstructed in 2-DOF system by referring to Herrmann and Roussellet's method in pipes conveying fluid. Finally, we present the theoretical equation of the steady-state amplitude. We reveal a validity of our study by a comparison between an experiment and a numerical simulation of some modified blades.
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