Pattern Formation Phenomena Generated in Steel Making Machines and Automobiles and Its Countermeasures

1. 根据废弃轧辊的形状测量，多边形数在周向上随轧辊位置的变化而变化。经证实，37-多边形与第一模式（旋转模式，47.5Hz）相关联，49-多边形与第二模式（线性模式，63Hz）相关联，出现在滚动上。通过对热矫直机运行过程中的振动测量，证实了随着多边形磨损的增加，有选择地出现了一个特定的频率分量，并且在测量时刻出现了唯一的热矫直机第二固有频率分量。这意味着与第二种模式相关联的唯一49多边形在所有上层滚动上生长。提出了刚体（上部单元）通过辊子与板接触振动的二自由度解析模型，并考虑了磨损的缓速效应，对其多边形磨损进行了分析。结果表明，实际机内现象与数值分析结果吻合较好。即使我们改变辊的转速和矫直机的固有频率，也不可能从根本上防止多边形磨损。将模态分析应用于含磨损时滞系统，得到了各模态的运动方程，并推导出了一些重要参数。对系统的特征根进行了解析近似处理，研究了参数对模式形成现象的影响，并与精确解进行了比较。采用数值模拟的方法，研究了小幅度改变运行速度的对策。结果表明，交替改变两种操作速度可以延缓图案的生长速度。研究了运行速度的最佳变化方法。

1. According to the shape measurement of abandoned rolls, the polygonal number varies by roll position in the circumferential direction. It is confirmed that 37-polygon associated with the first mode (rotation mode, 47.5Hz), and 49-polygon associated with the second mode (linear mode, 63Hz), occur on the rolls.2. According to the vibration measurement of the hot leveler in operation, it was confirmed that a specific frequency component appeared selectively as the polygonal wear grew, and the only component of second natural frequency of the hot leveler appeared at the measuring time. This means the only 49-polygon associated with the second mode grew on all upper rolls.3.A two degree-of-freedom analytical model was presented in which a rigid body (the upper unit) vibrates in contact with a plate through the rolls, and was analyzed the polygonal wear taking the retardation effect of the wear into account. As the result, a good agreement between the phenomena in the actual machine and the numerical analytical results was confirmed.4. It is impossible to essentially prevent a polygonal wear, even if we change the rotating speed of the rolls and the natural frequency of the leveler.5. The modal analysis was applied to the system with time retardation by wear in order to obtain the equations of motion for each mode and some important parameters were derived. The characteristic roots of this system were treated analytically and approximately and the influence of the parameters for pattern formation phenomena was investigated, compared with the exact solutions.6. The countermeasures by changing the operating speed in a small way were studied by applying numerical simulation. As the results, it was confirmed that the growth speed of the pattern could be delayed by changing two operating speeds alternately. The optimum changing method of the operation speeds was also studied.