Rotating machinery are known to exhibit backward whirls (BW), which means that the rotating system precesses in the direction opposite to that of its rotation. Since backward whirl is an important characteristic of the dynamic response that almost always points to significant problems and degradations within the system, it is of high interest to study, characterize and predict this phenomenon. To this end, the Campbell diagram is used to predict BW rotational speeds at steady-state operations of rotor systems to precede the critical forward whirl (FW) rotational speeds (i.e., pre-resonance BW). Still, the BW phenomenon in rotor systems that exhibit recurrent passage through critical rotational speeds during startup and coast down operations has not been fully studied and described in the literature. Notably, a recent study of startup and coast down operations found backward whirl orbits appearing immediately after the passage through the critical FW rotational speed (i.e., post-resonance BW). The difference between the well-known pre-resonance BW and this new kind of post-resonance BW phenomenon is further investigated in this paper for rotor systems with an open crack and anisotropic bearings. In addition, Full Spectrum Analysis (FSA) is employed to capture the BW zones in both numerical and experimental data. A finite element model of the cracked rotor-bearing-disk system is employed here to obtain the linear-time-variant (LTV) equations of motion for the considered system. The whirl response is obtained by the numerical integration of the LTV equations of motion. From results obtained from three different rotor configurations it is observed that the post-resonance BW has a different dynamical behavior compared with the pre-resonance BW. Furthermore, the application of the FSA has confirmed the existence of post-resonance BW zones in both numerical and experimental whirl responses. Successful application of the FSA for capturing the post-resonance BW zones of rotational speeds in the experimental response suggests that it has the potential to be a used as a powerful tool for BW-based crack detection.

已知旋转机械会表现出向后旋转（BW），这意味着旋转系统的进动方向与其旋转方向相反。由于后向旋转是动态响应的重要特征，几乎总是指向系统中的重大问题和退化，因此研究，表征和预测这种现象非常重要。为此，坎贝尔图用于预测转子系统稳态运行时的BW旋转速度，使其早于临界前旋（FW）旋转速度（即，预共振BW）。但是，转子系统中的BW现象在启动和滑行操作期间表现出通过关键转速的反复通过的现象尚未得到充分研究和描述。值得注意的是 最近对启动和滑行操作的研究发现，在通过临界FW旋转速度（即共振后BW）之后立即出现了反向涡旋轨道。本文针对具有开裂裂纹和各向异性轴承的转子系统，进一步研究了著名的共振前BW与这种新型共振后BW现象之间的区别。此外，全光谱分析（FSA）用于捕获数值和实验数据中的BW区。这里采用了裂纹转子轴承盘系统的有限元模型来获得所考虑系统的运动的线性时变（LTV）运动方程。旋转响应是通过LTV运动方程的数值积分获得的。从三种不同的转子配置获得的结果中，可以观察到，与共振前BW相比，共振后BW具有不同的动力学行为。此外，FSA的应用已证实在数值和实验涡旋响应中均存在共振后带宽区。FSA在实验响应中捕获共振后BW区域的成功应用表明，它有潜力用作基于BW的裂纹检测的强大工具。