Contributions to the analysis of vibrations and acoustic emissions for the condition monitoring of epicyclic gearboxes
Condition monitoring of machines through vibration analysis has been successfully applied on different types of machines for several decades. However, there are still some mechanical systems where its use has not given the same good results. Epicyclic gearboxes (EG) belong to this group of systems. Due to its special characteristics, EG are used in a wide range of applications within the drive technology, mostly when high power transmission is required. Machines dealing with high power transmission are typically critical, which means that a large part of the process in which they are involved depends on their appropriate operation. Hence, there is a high interest on a solution that can effectively detect failures in EG at an early stage, before they evolve and produce major breakdowns.
Probably the most important reason for the deficient results of failure detection on EG through vibrations is the poor knowledge about the characteristics of the vibrations generated in EG. In an EG, each planet gear meshes with the sun gear and ring gear simultaneously. Hence, the number of meshing processes is equal to twice the number of planet gears, being one half of them internal and the other half external. Depending on the geometry of the gearbox, phase differences between all meshing processes can exist. These phase differences are also present in the vibrations generated in each of the meshing processes. This key point is one of the fundamentals for understanding the vibrations generated in EG. The second fundamental point relates to the influence of the measurement arrangement on the measured vibrations. For example, in the most typical case, vibrations are measured with a sensor mounted on the outer part of the ring gear of a planetary gearbox (one of the possible configurations of EG). During operation, the carrier plate rotates concentric with the sun gear. Since the planet gears are mounted on the carrier plate, they rotate around their own axis and revolve around the sun gear. Consequently, the points of contact between the meshing gears, that is the location of the sources of vibrations, also revolve around the sun gear. On the other hand, the sensor remains steady, so that the distance between the sensor and the points of generation of vibrations changes continuously. This phenomenon acts an amplitude modulation of the vibrations generated in the meshing of each planet with the sun and ring gear and repeats once per revolution of the carrier. The amplitude modulation functions acting on the vibrations generated on different planets are time-shifted according to the relative angular position between the planets. These two fundamental points determine the spectral structure of the vibrations measured on an EG. Thus, the vibrations measured on different types of non-faulty EG can present different shapes in their spectra.
The use of acoustic emissions (AE) as a tool for the condition monitoring is not new, however it is only in the last years it has expanded. Most auspicious results have been found in bearing diagnosis. Its use for gear diagnosis has focused only on conventional fixed-axis gearboxes. The AE signals generated during the meshing of two spur gears consist typically of a train of bursts over a continuous background noise. It has been postulated that the bursts are produced at the pure rolling portion of the meshing period, whereas the continuous AE is produced in the portion where a combination of rolling and sliding occur. In the case of EG, the relative phase between the different meshing processes and the influence of the measurement arrangement must be considered, as was explained for the vibrations. Furthermore, there is a third point that must be considered: due to its high frequency nature the AE signals generated in the meshing of gears are essentially random. Still, they convey valuable information in form of hidden periodicities.
Two theoretical models are developed, one for the vibrations and one for the AE generated on a planetary gearbox when measured with a sensor installed on the outer part of the ring gear. Care is taken in presenting the development and analysis of the models in a step-by-step manner, so that it can be used as a basis for the development of similar models for the other configurations of EG (i.e. solar and star) and/or other sensor positions.
The vibration model considers all vibrations as deterministic. Accordingly, the stationary approach (i.e. the analysis of the frequency spectrum) is sufficient. It is shown that, although different planetary gearboxes can produce different spectral structures of the vibrations, they can be classified in four groups depending on the phase differences existing between the meshing processes and the relative angular position between the gear planets.
Differently, the AE model considers the amplitude and the time of arrival of the AE bursts as random processes. The model is analyzed separately for its deterministic and stochastic part. It is shown that the stationary approach applied to both parts is unable to reveal the information contained on the signal and, therefore, is less apt for failure diagnosis purposes. Conversely, the cyclostationary approach is able to reveal the hidden periodicities present on the signal. Therefore, it is best suited for diagnosis purposes. Since the cyclostationary theory still remains to some extent unknown, its most important concepts, results and signal processing tools are presented and illustrated through an example.
Finally, the stationary and cyclostationary approach are used for the analysis of vibrations and AE measured on a planetary gearbox test bench. Measurements under two types of seeded defects are investigated: localized planet bearing defect and single-tooth flank defect of one planet gear. Encouraging results were observed from the AE measurements. However, it is concluded that more work is needed to validate the proposed methodology. Results from industrial measurements are also presented. Here, no fault was observed; however, the measurements provided valuable information for the development of the models. Furthermore, a relation between the amplitude of the AE and the rotational speed of the gearbox, and the load acting on the gearbox was observed. This was further studied in the planetary gearbox test bench by taking measurements under different conditions of load and rotational speed.