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

1.根据对报废轧辊的形状测量，多边形数随轧辊在圆周方向上的位置而变化。确认在辊上出现与第一模式（旋转模式，47.5Hz）相关联的37-多边形和与第二模式（线性模式，63 Hz）相关联的49-多边形。通过对运行中的热矫直机的振动测量，证实了随着多边形磨损的增长，有选择地出现了一个特定的频率分量，并且在测量时刻只出现了热矫直机的第二阶固有频率分量。这意味着只有49个多边形对应于第二种模态。3.建立了一个两自由度的分析模型，其中一个刚体（上部单元）通过轧辊与一个板接触振动，并分析了多边形磨损，考虑了磨损的延迟效应。结果表明，数值分析结果与实际机床中的现象吻合较好.即使我们改变辊的旋转速度和矫直机的固有频率，也不可能从根本上防止多边形磨损。5.对具有磨损时滞的系统进行了模态分析，得到了系统各阶模态的运动方程，并导出了系统的一些重要参数。对该系统的特征根进行了解析和近似处理，研究了参数对斑图形成现象的影响，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。作为结果，证实了图案的生长速度可以通过交替地改变两个操作速度来延迟。并对运行速度的最佳变化方法进行了研究。

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.