如何玩盘式制动器
How to play a disc brake
摘要：
我们考虑一个陀螺系统的作用下的小耗散和非保守的位置力，这有其起源的旋转体的旋转模型中的摩擦接触。未扰动陀螺系统的频谱在“频率-陀螺参数”平面上形成“频谱网格”，在陀螺参数零值处具有双半简单纯虚本征值。它示出，耗散力导致分裂的半简单的本征值与创建所谓的“泡沫的不稳定性”-一个环在三维空间中的陀螺参数和实部和虚部的本征值，这对应于复杂的本征值。在完全耗散的情况下，具有正定阻尼矩阵的环的本征值具有负实部，使得气泡成为潜在的不稳定源，因为它可以“出现”到具有正实部的本征值区域，这是由于不确定阻尼和非保守位置力的作用。本文用重特征值摄动理论对失稳机理进行了解析描述。作为一个例子，详细研究了受定常载荷系统约束的旋转圆弦的稳定性。发展的理论似乎给摩擦接触的旋转结构中的自激振动的机制的第一个明确的解释，这是负责这些著名的摩擦声学现象，如尖叫盘式制动器和唱歌的酒杯。
英文摘要：
We consider a gyroscopic system under the action of small dissipative and non-conservative positional forces, which has its origin in the models of rotating bodies of revolution being in frictional contact. The spectrum of the unperturbed gyroscopic system forms a "spectral mesh" in the plane "frequency -gyroscopic parameter" with double semi-simple purely imaginary eigenvalues at zero value of the gyroscopic parameter. It is shown that dissipative forces lead to the splitting of the semi-simple eigenvalue with the creation of the so-called "bubble of instability" - a ring in the three-dimensional space of the gyroscopic parameter and real and imaginary parts of eigenvalues, which corresponds to complex eigenvalues. In case of full dissipation with a positive-definite damping matrix the eigenvalues of the ring have negative real parts making the bubble a latent source of instability because it can "emerge" to the region of eigenvalues with positive real parts due to action of both indefinite damping and non-conservative positional forces. In the paper, the instability mechanism is analytically described with the use of the perturbation theory of multiple eigenvalues. As an example stability of a rotating circular string constrained by a stationary load system is studied in detail. The theory developed seems to give a first clear explanation of the mechanism of self-excited vibrations in the rotating structures in frictional contact, that is responsible for such well-known phenomena of acoustics of friction as the squealing disc brake and the singing wine glass.
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