The object of this paper is to propose a new phase-cycle analysis for gear and bearing diagnostics of rotating machinery which synthesises the theory of angle-time cyclostationary (AT-CS). The motivation for this research came from bearing diagnostics which is confronted by the inevitable smearing phenomenon due to bearing slip. The bearing signal under non-stationary conditions is neither jointly second-order cyclostationary (CS2) nor pseudo-cyclostationary (pseudo-CS) and, hence, most CS2 tools are subjected to loss of diagnostics information. The proposed phase-cycle analysis is believed to propound the study of the kinematics of gears and bearings, and it will significantly modify the prevailing historical interpretation of the bearing slip. In this paper, the phase-cycle analysis which is based on the theory of AT-CS is named the “cyclomap” because it can provide much more information about the kinematics of cyclostationary and cyclo-non-stationary signals. The cyclomap shows some interesting features in delineating the energy distribution of the kinematical properties of machines at an angular period of interest. In order to further study the properties of the cyclomap, it is systematically compared to the well-known order-frequency cyclic modulation coherence in diagnosing the CS2, pseudo-CS, and second-order cyclo-non-stationary signals of the experimental datasets.

本文的目的是提出一种用于旋转机械齿轮和轴承诊断的新相循环分析，该分析综合了角时间循环平稳（AT-CS）理论。这项研究的动机来自于轴承诊断，轴承诊断面临着由于轴承滑动而不可避免的涂抹现象。非平稳条件下的轴承信号既不是联合二阶循环平稳(CS2)，也不是伪循环平稳(pseudo-CS)，因此，大多数 CS2 工具都会丢失诊断信息。所提出的相周期分析被认为促进了齿轮和轴承运动学的研究，并将显着修改轴承滑动的流行历史解释。本文将基于AT-CS理论的相位周期分析称为“周期图”，因为它可以提供更多关于周期平稳和周期非平稳信号的运动学信息。环图显示了一些有趣的特征，可以描绘机器在感兴趣的角周期内运动学特性的能量分布。为了进一步研究环图的性质，在诊断实验数据集的CS2、伪CS和二阶环非平稳信号时，将其与众所周知的阶频循环调制相干性进行系统比较。