Contribution to the study of the dynamic behavior of planetary gears in nonstationary regimes in presence of defects

ABSTRACT: The present PhD study is focused on analyzing the dynamic behavior of planetary gear transmissions in non-stationary conditions in presence of defects. The strategy of this thesis is based on building a numerical model which is referred to a test bench composed of a test planetary gear set mounted back to back with reaction gear set which allow the power recirculation. First of all, modal analysis techniques were studied to characterize the dynamic behavior of the system. a comparative study between three modal analysis techniques was carried out in order to determine the modal properties in different running condition. Stabilization diagram and Modal assurance criterion were used to estimate the obtained modes. Experimental and numerical modes of each technique were compared and discussed. In addition, the effect of load and meshing stiffness variation on the modal parameters were highlighted. The study of the dynamic behavior of the model corresponding to the test bench was performed initially in stationary conditions where the speed and the torque are constant. Modulation sidebands are highlighted through numerical simulations issued from a three-dimensional model and experimental measurements. Influence of the gravity of carrier on the dynamic response were also investigated taking into account the interaction between meshing gears, the weight of the planet carrier systems. Then, the dynamic behavior under non-stationary excitations such as the variable load, variable speed and run up regimes was investigated. Time frequency analysis was developed to characterize frequency of vibration signals issued from non-stationary operating conditions. Numerical results obtained by the Short Time Fourier Transform are validated through vibration measurements on test bench during operation under these conditions. However, a non linear model of the model taking into account the Hertzian stiffness was developed and studied in non stationary regime presented by the variable load and run up regime. Finally, the dynamic response of the system in presence of two kinds of defect was analyzed and discussed in stationary and non stationary regimes. Order tracking method was used to identify the defects in run up and variable loading condition for the simulated and experimental determined signals

Dynamic behavior of the nonlinear planetary gear model in nonstationary conditions

The nonlinear effects in gearboxes are a key concern to describe accurately their dynamic behavior. This task is difficult for complex gear systems such as planetary gearboxes. The main aim of this work is provide responses to overcome this difficulty especially in non-stationary operating regimes by investigating a back-to-back planetary gearbox in steady conditions and in run up regime. The nonlinear Hertzian contact of teeth pair is modeled in stationary and non-stationary run-up regime. Then it is incorporated to a torsional model of the planetary gearbox through the different mesh stiffness functions. In addition, motor torque and external load variation are taken into account. The nonlinear equations of motion of the back-to-back planetary gearbox are computed through the Newmark-β algorithm combined with the method of Newton-Raphson. An experimental validation of the proposed numerical model is done through a test bench for both stationary and run-up regimes. The vibration characteristics are extracted and correlated to speed and torque. Time frequency analysis is implemented to characterize the transient regime during run-up.This research work was supported by the Spanish Ministry responsible of Science and Technology through the project DPI2017-85390-P. The authors gratefully thank the University of Cantabria cooperation project which supports the doctoral trainings of students of Sfax University. The authors also acknowledge the Tunisian Project No. “19PEJC10-06”

Operational modal analysis using order-based analysis in a two-stage planetary gear with mechanical power recirculation

Modal analysis techniques are considered as the most used of techniques allowing the characterization of the dynamic behaviour in systems such as planetary gear transmission. During operational conditions, the modal behaviour can be altered. The main purpose of this paper is to estimate the Modal Properties (MP) of two-stage planetary gear during non-stationary regimes using a further version of Operational Modal Analysis (OMA). The natural frequencies and modal damping are determined by Order Tracking (OT) and processed using diagram stability tool. Moreover, the modelling and the treatment of the non-stationary regimes were established. The proposed technique proves that order-based OMA can extract resonances which are related to the interaction between structural modes and the rotational speed harmonics. The experimental measurements are compared to the obtained results via a numerical model. It proves that the natural frequencies and modal damping are significantly dependent on the load.The authors would like to acknowledge the support of the Project DPI2017-85390-P funded by the Spanish Ministry of Economy, Industry, and Competitiveness to this research

Effect of load and meshing stiffness variation on modal properties of planetary gear

Modal analysis of mechanical transmissions allows identification of critical frequencies and corresponding vibration modes. Major research works are done under constant loading conditions. However, load fluctuation can lead to variability in stiffness characteristics. Also, in the case of gear transmission, the fluctuation of mesh stiffness is rarely considered in the modal analysis. In this paper, a modal analysis of planetary gear transmission is investigated for different loading conditions and under mesh stiffness fluctuation. Hammer impact tests are carried out and the vibrations on fix ring are measured with different levels of load. During each test, natural frequencies are identified through frequency response function. The obtained results are correlated against the corresponding tridimensional lumped parameter of the test rig. Distributions of modal strain and kinetic energy for different loading conditions are studied as well as the effect of mesh stiffness variation on the natural frequencies.This paper was financially supported by the Tunisian-Spanish Joint Project No. A1/037038/11. The authors would like also to acknowledge project ‘‘Development of methodologies for the simulation and improvement of the dynamic behavior of planetary transmissions DPI2013-44860” funded by the Spanish Ministry of Science and Technology. Acknowledgment to the University of Cantabria cooperation project for doctoral training of University of Sfax’s students

Operational modal analysis using order-based analysis in a two-stage planetary gear with mechanical power recirculation

Modal analysis techniques are considered as the most used of techniques allowing the characterization of the dynamic behaviour in systems such as planetary gear transmission. During operational conditions, the modal behaviour can be altered. The main purpose of this paper is to estimate the Modal Properties (MP) of two-stage planetary gear during non-stationary regimes using a further version of Operational Modal Analysis (OMA). The natural frequencies and modal damping are determined by Order Tracking (OT) and processed using diagram stability tool. Moreover, the modelling and the treatment of the non-stationary regimes were established. The proposed technique proves that order-based OMA can extract resonances which are related to the interaction between structural modes and the rotational speed harmonics. The experimental measurements are compared to the obtained results via a numerical model. It proves that the natural frequencies and modal damping are significantly dependent on the load.The authors would like to acknowledge the support of the Project DPI2017-85390-P funded by the Spanish Ministry of Economy, Industry, and Competitiveness to this research

Frühzeitige Erkennung von Schäden in Planetenradgetrieben unter verschiedenen Betriebsbedingungen

Planetary gear transmissions are sensitive to various running environmental factors. These external conditions keep these systems often subjected to faults and/or malfunction especially in gears components. So, it is a crucial task to spot in advance all kind of degradation that could lead to a harmful event or accident to the system. In the same context, this study aims to investigate the case of combined faults detection and analyse their impact on the vibration dynamic response in a two stages planetary gear transmission in diverse operating conditions. For this, a Lumped Mass Model (LMM), referred to a real test rig where experimental tests, is established. In this model, the Time Varying Mesh Stiffness (TVMS) were modelled in different frameworks and configurations such as the healthy, the single and the combined damage conditions. After acquiring acceleration signals from the model, time, frequency and order analysis data processing were executed to generate health related data for the planetary gear. Consequently, it is concluded that the system vibration response is sensitive to the internal excitation particularly the case of combined defects. The obtained results show the ability of the developed model to identify the frequency characteristics of defect and the transmission in each configuration. The experimental and simulated results are compared and correlated.Das Planetengetriebe/Das Umlaufrädergetriebe ist empfindlich gegen verschiedene Umweltfaktoren. Die (Umweltfaktoren) lassen sich in das ganze System und vor allem in den Komponenten des Getriebes eine Störung auslösen. Aus diesem Grund, von Anfang an, ist es sehr wichtig, jede Art von Abbau die eine schädliche Wirkung hat oder zu dem Ausfall des Systems führen könnte, zu erkennen. Gleichzeitig, diese Studie zielt darauf ab, den Fall der kombinierten Fehlererkennung zu untersuchen und deren Auswirkungen auf die schwingungsdynamische Reaktion in einem zweistufigen Planetengetriebe unter verschiedenen Betriebsbedingungen zu analysieren. Dazu, wird ein Modell der konzentrierten Masse (Lumped Mass Model [LMM]), bezogen auf einen realen Prüfstand, in dem, experimentelle Teste durchgeführt werden, erstellt. In diesem Modell wurde die Zeitlich variierende Maschensteifigkeit (Time Varying Mesh Stiffness [TVMS]) in verschiedenen Rahmenbedingungen und Konfigurationen nämlich der Gesundheit, dem Einzel- und dem kombinierten Schadenszustand modelliert. Nach dem Erfassen von Beschleunigungssignalen aus dem Modell, wurden Zeit-, Frequenz- und Ordnungsanalyse-Datenverarbeitungen durchgeführt, um Daten, bezüglich zu der Gesundheit, für das Planetengetriebe zu generieren. Folglich, wird es festgestellt, dass die Schwingungsantwort des Systems ist empfindlich gegen die innere Erregung, ganz besonders, im Fall von kombinierten Defekten. Die vorliegenden Ergebnisse zeigen die Fähigkeit des entwickelten Modells, die Frequenzeigenschaften von Defekten und die Übertragung in jeder Konfiguration zu identifizieren. Die experimentellen und simulierten Ergebnisse werden verglichen und korreliert.The authors would like to acknowledge Project DPI2017-85390‑P funded by the Spanish Ministry of Economy, Industry, and Competitiveness for supporting this research.” Acknowledgment to the University of Cantabria cooperation project for doctoral training of University of Sfax’s students