For fault diagnosis and predictive maintenance of rotating machinery, the phase errors generated by the integration processing of a vibration signal are an essential investigation subject. Phase errors affect the solution of mechanical systems with multiple vibration sources and also the information transmitted through the vibration that is used for fault diagnosis. This work proposes the use of phase plane, recurrence plot (RP), and cross recurrence plot (CRP) to evaluate phase shift error effects on the solution of multiple asynchronous and simple periodic functions, and on the smoothing of a Gaussian peak with white noise. Noisy peaks were smoothed twice with the triangular method and with a different number of points. The analysis of the asynchronous periodic functions and the smoothing indicated that a small phase shift changes the phase plane and the RP pattern. These changes can affect not only the accuracy of machinery fault diagnosis but also prediction for the application of timely maintenance actions.

中文翻译：

---

递归图中相移误差对旋转机械故障诊断的影响

对于旋转机械的故障诊断和预测维护，由振动信号的积分处理产生的相位误差是必不可少的研究课题。相位误差会影响具有多个振动源的机械系统的解决方案，还会影响通过振动传输的信息（用于故障诊断）。这项工作提出使用相平面，递归图（RP）和交叉递归图（CRP）来评估相移误差对多个异步和简单周期函数的解以及对具有白噪声的高斯峰平滑的影响。用三角法和不同点数将噪声峰平滑两次。对异步周期函数和平滑的分析表明，小的相移会改变相平面和RP模式。这些变化不仅会影响机械故障诊断的准确性，还会影响对及时维护措施的预测。