Abstract

A mathematical model of a flexible rotor with n degrees of freedom rolling around a flexible stator with slippage between them is proposed, as well as an approach to the exclusion of contact forces for dynamic analysis of the system. The angular velocity and amplitude of the reverse rotor precession are determined by matrix methods. It is shown that the break-in speed is not always equal to the product of the rotation speed by the ratio of the radius of the rotor to the radial clearance at the point of contact. In the case of slippage, it depends on one or another natural frequency of the rotor, which is supported by the stator, as well as on the coefficients of structural and contact friction. It was also shown that in fact, friction only sets the break-in speed, and the amplitude of the reverse precession (deflection of the rotor outside the contact point) is determined by the size of the gap at the contact point.

中文翻译：

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沿定子有许多自由度的转子打滑滚动时的振荡频率

摘要

具有n的柔性转子的数学模型提出了围绕柔性定子滚动并在它们之间滑动的自由度，以及一种排除接触力以进行系统动态分析的方法。反向转子进动的角速度和幅度通过矩阵方法确定。可以看出，磨合速度并不总是等于转速乘以转子半径与接触点径向间隙之比的乘积。在打滑的情况下，它取决于转子的一个或另一个固有频率，该固有频率由定子支撑，以及结构和接触摩擦系数。还表明，事实上，摩擦力只能决定磨合速度，