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.

The friction and imbalance of components in rotating machines are some of the most recurrent failures that significantly increase vibration levels, thus affecting the reliability of the devices, the shelf life of its elements, and the quality of the product. There are many publications related to the different techniques for the diagnosis of friction and imbalance. In this paper, an alternative and new phase-shift empirical mode decomposition integration (PSEMDI) method is proposed to transform the acceleration into its velocity and displacement in order to construct the phase plane and recurrence plot (RP) and analyze the friction. The focus of PSEMDI and RP is to analyze nonlinear failures in mechanical systems. In machinery fault diagnosis, the main reason for using RP is to solve the integration of acceleration, and this can be achieved by phase-shifting the intrinsic mode function (IMF) with the empirical mode decomposition (EMD). Although the highest IMFs contain some frequencies, most of them have very few; thus, by applying the phase shift identity, the integration can be carried out maintaining the nonlinearities. The proposed method is compared with Simpson’s integration and detrending with the EMD method (here referred to as SDEMDI). The experimental RP results show that the proposed method gives significantly more information about the velocity and displacement spectra and it is more stable and proportional than the SDEMDI method. The results of the proposed integration method are compared with vibration measurements obtained with an interferometer.