Design method to prevent the pattern formation phenomena in contact rotating systems

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In many contact rotating systems used in the field of mechanical engineering, a large vibration often occurs in operation along with a spontaneous growth of deformation of system components, and then a periodic deformation pattern is formed on the peripheral surfaces. The stability of such phenomena is usually analyzed by obtaining the characteristic roots of a linear time delay system. However, the analytical method is not available for a prevention measure of many-degree-of-freedom systems, since a large amount of complicated numerical computation is required. In our previous study, the numerical difficulty was overcome by applying the concept of modal analysis and by separating a characteristic equation of many-degree-of-freedom system into those of one-degree-of-freedom systems for each mode. In addition, the simplified method of stability analysis, which did not need the computation of characteristic roots, was developed by considering the energy balance. The fol- lowing subjects … More were mainly studied to improve the simplified method.1. The simplified method was applied to two practical examples in which the longitudinal bending deformation of shaft was considered. One is a model of three-roll-system which is the most basic model of a paper making machine constructed from many rolls, and the other is a model with Controlled Dumper Roll which is very effective against the pattern formation phenomena. Moreover, by combining the simplified method and the concept of optimum design, an effective method was developed to determine rationally the system parameters which prevent the occurrence of pattern formation phenomena.2. It became clear from our studies that the effect of nonlinearity contained in the system unavoidably had to be considered to get the overall property of the pattern formation phenomena and to devise the countermeasure. As a fundamental study, the nonlinear vibration phenomena generated in a viscoelastic system and a grinding system were investigated. Less