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This paper deals with a nonstationary vibration of a rotor due to its collision with a guard during passage through a critical speed. An unbalanced rigid rotor supported by springs and dampers is accelerated at a constant angular acceleration and collides with an annular guard supported by springs and dampers. This dynamic process is calculated by the Runge-Kutta method, and effects of system-parameters on the process are discussed. The collision phenomenon is analyzed through two different theories. In the collision theory, the law of conservation of momentum and the coefficient of restitution are used in order to obtain rotor and guard velocities after collision. The impulse of the force induced by collision is assumed to be equal to the momentum change before and after collision. In the contact force theory, the contact force is assumed to be proportional to the overlapped displacement of the two bodies. Few differences are observed between the calculated responses based on the two theories. In some cases, the rotor executes a diverging backward whirl due to the friction force that occurs during collision with the guard and can not pass through the critical speed. The criteria maps for nonoccurrence of the backward whirl are shown.

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In machines that handle flexible media with flat belts, it is necessary to prevent belt skew for the machines to operate at higher precision and maximum efficiency. However, the skewing mechanism has not yet been clarified. Therefore, in order to establish a method that could be used to analyse the skew of a flat belt, a simulation system is developed using a commercial finite element code (MARC). Also, the skew mechanism in two-and three-roller systems is also studied through simulations and clarified to show that the skew rate equals the spiral angle of the belt wrapping around the roller. Moreover, it is found that a steering roller that is set in an optimal position is needed to reduce belt skew efficiently. The analytical method and the findings from this study are useful in designing any flat-belt mechanism. NOTATION B width of belt (mm) C effective friction factor in the modified Coulomb friction model d S belt skew with rotating angle dy (mm) dy small rotational angle of the driving roller (deg) D diameter of the driving roller and driven roller (mm) D Ã effective diameter of the driving roller and driven roller (considering thickness of the belt) (mm) D s diameter of the steering roller (mm) E Young's elastic modulus of the belt (MPa) F n normal reaction force between two contact bodies (N) F t friction force in the tangential direction between two contact bodies (N) L travelling distance of the belt in the handling direction (mm) L Ã factual travelling distance of the belt (mm) L b length of the belt (mm) L c span distance of two roller axes (mm) L r length of the rollers (mm) S skew displacement of the belt (mm) S b slip between the driving roller and the belt in the handling direction ¼ D * y=2 À L (mm) S br relative slip between the driving roller and the belt in the handling direction ¼ S b =L (%) S r belt skew rate ¼ S=Lð%Þ t thickness of the belt (mm) T 0 initial tension of the belt (N) V b travelling velocity of the belt in the handling direction (mm/s) V r relative velocity of two contact bodies (mm/s) V z skew velocity of the belt (mm/s) X i , Y i position of the steering roller, i ¼ 1-7 (mm) a relative misalignment angle of the driven roller for out-of-plane (deg) b relative misalignment angle of the driven roller for in-plane (deg) g expanded angle of the belt spiral line on rollers (deg) d rotational angle of the driving roller per step in simulation (deg/step) D 1 , D 2 spiral lead of the belt on the driving roller and the driven roller respectively (mm) The MS was Downloaded from e misalignment direction angle of the steering roller (deg) y rotational angle of the driving roller (deg) m coefficient of friction between two contacting bodies n Poisson's ratio of the belt material B misalignment angle of the steering roller (deg) f effective contact angle of the belt on the roller surface (deg) o rotational speed of the driving roller (r/min)

The present study treats a paper wrinkle appearing in a fixing roller unit of printers or copiers with electro-photographic process. An experiment shows that a wrinkle always occurs, when an A4-sized paper is tilted by 3 degrees against a horizontal fixing roller unit without a heating devise and is fed to a roller nip. The wrinkle appears in the middle of the paper width. Computer simulations were carried out to illustrate this wrinkle occurring process. The simulation model consists of a rigid cylindrical driving roller, a driven rubber roller, a paper, and a guide plate. The paper is assumed to be an isotropic elastic-plastic body. The results reveal the following wrinkle occurring process. When the tilted paper is fed to the rollers, the center part of the paper leading edge firstly enters the roller nip and is pulled by friction forces in the nip. Then paper wavy bending deformations appear in front of the nip. A steep slope of the deformation is crushed and yielded in the nip. After this, a neighbor area of the yielded point gathers together and a folded wrinkle is formed. Further, this type of wrinkle is liable to occur when the paper tilt angle, Young's modulus, or coefficient of friction is large, or when the paper yield stress is small.