Modal analysis of back-to-back planetary gear: Experiments and correlation against lumped-parameter mode

In order to characterize the dynamic behaviour of a back-to-back planetary gear, experimental and numerical modal analysis techniques are achieved. Rotational and translational modal deflections are highlighted. Natural frequencies are compared to the results from the lumped-parameter model. The modes are presented in the numerical studies in low-frequency and high-frequency bands. Distributions of modal kinetic and strain energies are studied.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

Tooth defect detection in planetary gears by the current signature analysis: numerical modelling and experimental measurements

Monitoring transmission systems is a huge scientific focus to prevent any anomaly and malfunctioning damaging the system. Several methods were used to investigate the gears behaviour and mainly its state. And until the last century, vibrations signals were the most performing technique in this field. However, nowadays, other alternatives are considered more accurate and accessible such as controlling the motor current signals to study the behaviour of the mechanical system. Within this context, this paper aims to study the electromechanical interaction between a double stage of planetary gearboxes driven by an asynchronous machine. The model used is based on a Park transformation for modelling the asynchronous machine and a torsional model to describe the dynamic behaviour of the double-stage planetary gearbox. Through this approach, the numerical simulations illustrate the impact of the tooth gear defect on the signature of the motor current. The results obtained from the simulations will be presented in the time domain and the frequency domain using the fast Fourier transform and the Hanning window to highlight the mechanical frequencies in the phase current spectrum. This work will be distinguished by validating the numerical results using experimental measurements, which will be displayed in order to justify the sensitivity of the model developed.The authors would like to acknowledge the help provided by the project “Dynamic behaviour of gear transmissions in nonstationary conditions”, ref. DPI2017-85390-P, funded by the Spanish Ministry of Science and Technology. They would like to thank the University of Cantabria cooperation project for the doctoral training to Sfax University students

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

An electromagnetic-mechanical modeling of an induction motor and rotor shaft coupled to angular approach

Ce papier présente un modèle électromécanique pour simuler le comportement dynamique d'une machine asynchrone / arbre du rotor. Le modèle décrit dans ce travail combine un modèle de réseau de perméances d'un moteur à induction à cage d'écureuil et un modèle dynamique simple de son arbre de rotor. Un échantillonnage angulaire est utilisé pour permettre d'investiguer les variations de vitesse angulaire instantanée et de couple. Le système rotatif est décrit en se référant à la position angulaire de l'arbre. La méthodologie de couplage électromécanique est bien détaillée. En se basant sur un certain nombre de simulations, on montre l'influence des variations de couple provenant de la machine à 'induction sur le comportement dynamique du système mécanique