Research Papers

Analysis of the Frictional Vibration of a Cleaning Blade in Laser Printers Based on a Two-Degree-Of-Freedom Model

[+] Author and Article Information
Go Kono, Yoshinori Inagaki, Hiroshi Yabuno, Tsuyoshi Nohara, Minoru Kasama

Graduate Student gogogoh20@gmail.comGraduate Student y_inag_2001@yahoo.co.jpProfessor, Member of ASME yabuno@mech.keio.ac.jpDepartment of Mechanical Engineering,  Keio University, 3-14-1, Hiyoshi Kouhoku-ku, Yokohama, Kanagawa 223-8522 Japan Researcher Department of Engine & Control Equipment, Mitsubishi Heavy Industries, Ltd., 1200, Higashi Tanaka, Komaki, Aichi 485-8561 Japantsuyoshi.nohara@mhi.co.jp Key Technologies Laboratory, Fuji Xerox Co., Ltd., Sakai 430, Nakai-cho, Ashigarakami-gun, Kanagawa 259-0157 Japanminoru.kasama@fujixerox.co.jp

J. Comput. Nonlinear Dynam 7(1), 011006 (Aug 15, 2011) (9 pages) doi:10.1115/1.4004469 History: Received September 10, 2010; Accepted June 02, 2011; Published August 15, 2011; Online August 15, 2011

This research aims to analyze the dynamics of the self-excited vibration of a cleaning blade in a laser printer. First, it is experimentally indicated that that the self-excited vibration is not caused by the negative damping effect based on friction. Next, the excitation mechanism and dynamics of the vibration are theoretically clarified using an essential 2DOF link model, with emphasis placed on the contact between the blade and the photoreceptor. By solving the equations governing the motion of the analytical model, five patterns of static equilibrium states are obtained, and the effect of friction on the static states is discussed. It is shown that one of five patterns corresponds to the shape of the practical cleaning blade, and it is clarified through linear stability analysis that this state becomes dynamically unstable, due to both effects of friction and mode coupling. Furthermore, the amplitude of the vibration in the unstable region is determined through nonlinear analysis. The obtained results show that this unstable vibration is a bifurcation classified as a supercritical Hamiltonian-Hopf bifurcation, and confirms the occurrence of mode-coupled self-excited vibration on a cleaning blade when a constant frictional coefficient is assumed.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Schematic diagram of toner cartridge in a laser printer

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Figure 2

Observation results with respect to changing rotational speed

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Figure 3

Observation result of the vibration at 50 rpm

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Figure 4

Two-degree-of freedom analytical model of the cleaning blade

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Figure 5

Bifurcations of each variable and configurations of the static equilibrium states when μ = 0. The colors in the bifurcation diagrams correspond to the configuration of the states shown.

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Figure 6

Bifurcations of each variable and configurations of the static equilibrium states when μ = 0.3. The bifurcations of each variable pertubate, and the configurations of the states are no longer symmetrical.

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Figure 7

Stability of the static states when μ = 0. The dotted lines represent unstable deflections, and the solid lines represent stable deflections.

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Figure 8

Variance of the stability of state (b) with respect to friction. A Hamiltonian-Hopf bifurcation is generated on the stable branch with the inclusion of friction.

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Figure 9

Argand Diagrams of state (b) when μ = 0.3, showing the region of instability

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Figure 10

Magnitude of each term of aden . The second order coefficients E3 E4 , E4 E5 , and E5 E6 are the governing terms in the amplitude.

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Figure 11

Amplitude of the vibration on the 2DOF blade model. The nonzero amplitude is stable, while the zero solution is unstable, making this a supercritical bifurcation.

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Figure 12

Elements of 2DOF analytical model

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Figure 13

Experimental apparatus

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Figure 14

Experimental setup

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Figure 15

Motion of the contact point with respect to time



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