Simplified method to estimate the intensity of instability which causes the pattern formation phenomena in contact rotating systems

在机械工程领域中使用的许多接触式旋转系统中，在运行过程中经常会发生较大的振动，并伴随着系统部件变形的自发增长，从而在其周边表面形成周期性的变形模式。这种现象主要是由线性时滞系统产生的不稳定振动引起的，通过获得系统的特征根可以分析系统的稳定性。但是，由于时滞系统具有可计数的无穷个特征根，因此解析法的缺点是要对系统的稳定性进行一定的讨论，需要得到大量的特征根。此外，虽然需要进行大量的数值计算，但这些结果还不能用于预防这种现象的措施。为了克服上述困难，我们主要研究了以下几个课题。应用模态分析的概念和能量平衡的观点，对多自由度系统引入了能量因子。能量因子表示每个模态的不稳定性强度。利用能量因子，提出了一种简化的稳定性分析方法和防止图案形成现象的优化设计步骤。这些方法可以在不获取特征根的情况下给出有效的预防措施指标。以大自由度系统为代表，将简化方法和优化设计过程应用于两个图案形成现象的实例。一种是有多个胶辊的造纸机的多边形变形现象，另一种是考虑轴的纵向弯曲变形的胶辊系统。结果表明，对于具有大自由度的系统，本文方法在不降低计算精度的前提下，可以比以前的方法更有效地使用。少

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