带有居中盘与悬臂盘的裂纹转子系统非线性响应特性分析

On Nonlinear Response of Cracked Rotor with Midspan and Overhung Disc

研究了轴上含有横向裂纹 ,刚性支承的带有居中盘和悬臂盘的双盘裂纹转子的非线性动态响应。考虑轴旋转过程中裂纹的开闭 ,推导出双盘裂纹转子的运动方程。采用仿真计算的方法 ,分析了转速、裂纹深度的变化对响应的影响 ,并且研究了盘的摆振与横向振动的区别。结果表明 ,裂纹转子随转速变化 ,响应会出现丰富的非线性特征 ;裂纹深度的增大 ,会导致系统响应出现分叉与混沌 ;外阻尼可以有效抑制非线性响应 ;盘的摆振对于裂纹的出现 ,较之横向振动 ,包含有明显的高次谐波分量 ,易于识别。

Our research on nonlinear response of cracked rotor has continued for more than ten years and is still continuing. In this paper, firstly we, considering the breathing of crack in rotation, derive motion equations for a cracked rotor with midspan and overhung disc, which is a system with eight degrees of freedom. Secondly we give simulation results, which show that both system parameters——rotating speed and crack depth——expressed in non-dimensional form, have large influence on nonlinear response. Fig.2(a) shows the Poincaré section at non-dimensional rotating speed Ω=0.446, which indicates that the response is quasi-periodic. As rotating speed increases, the torus begins to twist and bend and Fig.2(b) shows Poincaré section at Ω=0.454. At Ω=0.459 the response enters chaos as shown in Fig.2(c). At Ω= 0.466, the response leaves chaos and returns to quasi-period as shown in Fig.2(d). The non-dimensional form of crack depth is expressed by ΔK. In the neighborhood of ΔK=0.56, the response is still quasi-periodic; at ΔK=0.60, the response enters chaos. Thirdly, simulation results give some information which may be useful in fault diagnosis. Fig.4 shows that at Ω=0.41 and ΔK=0.6, power spectra show that swing vibration′s frequency components, as shown in Fig.4(a), are different from those of transverse oscillation, as shown in Fig.4(b).