To avoid premature operational failure of the ESP systems, their vibration levels must be evaluated for acceptance before installation. The vibration assessment of Electrical Submersible Pump (ESP) systems and other rotating machines considers that the most important amplitude occurs in the radial orientation. Typical vibration amplitude estimation uses radial orthogonal sensors and considers the maximum vibration amplitude between the two sensor signals. However, this approach does not account for the orbit's shape, leading to an error up to 41,4% between the maximum estimated amplitude in each sensor and the maximum radial vibration amplitude, the orbit semi-major axis. This paper proposes a method to generate a frequency spectrum with invariance to the shape of the vibration orbit, namely the Orbit Semi-major Axis Spectrum. The proposed method is compared to the typical vibration amplitude estimation approach using individual sensor signals and the Full Spectrum method. The methods are applied on vibration signals from two pumps at different wear states, and results are analyzed. The estimation error of the vibration amplitude in ESP systems due to disregarding the shape of the vibration orbits is shown. The results indicate that the proposed method presented the maximum radial vibration amplitudes of each orbit frequency component (orbit semi-major axis), which is not directly possible with the Full Spectrum and is impossible with the individual frequency spectrum. The orbit semi-major axis amplitudes of the pumps were up to 28% higher than the maximum amplitude estimated from the individual orthogonal sensors.

An Electric Submersible Pump (ESP) vibration analysis was performed, considering different wear states and operational conditions. The pumps were tested with different fluid viscosities, operating points, and speeds to evaluate their vibration behavior, with the aim of providing characteristics for non-invasive differential vibration diagnosis. A specific frequency spectrum estimation method is described, focusing on the extraction of frequency component vibration amplitudes used in the petroleum industry-standard vibration analysis. A time-interval definition procedure was proposed to reduce signal amplitude losses due to variation of synchronous operating frequency. The results indicate that the frequency component peak amplitudes can be more accurately identified during synchronous frequency variation by the proposed method than by typical estimation methods. In this study, an ESP vibration differential diagnosis was achieved by analyzing relations between orders of the synchronous frequency, and by distinguishing that the synchronous component amplitude rose approximately proportionally to the square of the rotating speed; this differentiates unbalance fault from a bent shaft or a misalignment. A correlation matrix analysis is provided to demonstrate that variation in the fluid-temperature difference between the pump intake and discharge is related to the vibration amplitude variation in a pump with a vibration fault.