Simplified method to estimate the intensity of instability which causes 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 the deformation of system components, and then a periodic deformation pattern is formed on the peripheral surfaces. Such phenomena are mainly caused by the unstable vibration generated in a linear time delay system, and the stability can be analyzed by obtaining the characteristic roots of the system. However, the analytical method has the weak point that a large number of characteristic roots should be obtained for the certain discussion on the stability of the system, since the time delay system has the countable infinite number of characteristic roots. Moreover, the results are not available for a prevention measure of the phenomena, though a large amount of numerical calculation is required. The following subjects were mainly studied to overcome the above difficulties.1. By applying the concept of modal analysis and a viewpoint … More of energy balance, energy factor was newly introduced for a system with many degrees of freedom. The energy factor represents the intensity of instability for each mode. Moreover, a simplified method to analyze the stability and an optimal design procedure to prevent the pattern formation phenomena were developed by using the energy factor. These methods can give an effective index to prevention measures without obtaining the characteristic roots.2. The simplified method and the optimal design procedure were applied to two practical examples of pattern formation phenomena as the representative of a system with large degrees of freedom. One is a polygonal deformation phenomena of a paper making machine with many rubber rollers, and the other is that of a rubber roller system in which the longitudinal bending deformation of shafts is considered. As the result, it is confirmed that the present methods can be used more effectively than the previous method without the decrease in computational accuracy for the system with large degrees of freedom. Less