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

Use of sun gear orbits to obtain the load sharing in planetary transmissions and its impact in the tooth load

The present work assesses the possibility of using the orbits described by the sun gear in order to analyse the load sharing ratio in planetary gear transmissions. Furthermore, the current work is extended to observe the impact of the floatability and different tangential pinhole position errors in the load borne in a single contact between a pair of teeth in comparison to the load per planet. Therefore, it highlights the inaccuracy of the load sharing ratio (LSR) as an indicator of the overload in one tooth of the planet. Moreover, the use of the orbits represented with respect to a rotating reference provides helpful information to determine the overloads and underloads in the planets due to the existence of a tangential error in sequentially phased transmissions. Therefore, this proposal provides a simpler solution to the measurement of the LSR in planetary transmissions with different numbers of planets than the use of strain gauges.The authors would like to acknowledge Project DPI2017-85390-P funded by the Spanish Ministry of Economy, Industry, and Competitiveness for supporting this research. Moreover, the authors acknowledge the Project PID2020-116213RB-I00 funded by the Ministry of Science and Innovation

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

Gear rattle dynamics: lubricant force formulation analysis on stationary conditions

Gear rattle is a common and inherent phenomenon to multi-stage-constant-mesh gearboxes, since this kind of transmission consist of two different types of gear pairs: active and inactive stages. The former is in charge of transmitting the energy, whilst the latter, although its teeth are engaged, is loosely connected to the output shaft. Gear rattle problematic resides in undesirable impacts and fluctuations in the inactive gears provoked by their interaction with the active stage, leading to vibrations which can produce fails in elements connected or belonging to the gearbox. In this regard, understanding the lubricant role is crucial, being this aspect the key to comprehend the dynamic behaviour of low-loaded gear transmissions and to palliate these phenomenon consequences as the ultimate goal of this research. Within this context, in this work, six formulations, which consider both entraining and squeeze fluid effects, were implemented in gear transmission models previously developed by the authors in order to calculate the hydrodynamic forces. Special attention was paid to the fluid viscosity influence on the dynamic behaviour under stationary conditions.This work has been supported by project DPI2017-85390-P funded by the Spanish Ministry of Science and Technology

Hybrid optimization approach for the design of mechanisms using a new error estimator

A hybrid optimization approach for the design of linkages is presented. The method is applied to the dimensional synthesis of mechanism and combines the merits of both stochastic and deterministic optimization. The stochastic optimization approach is based on a real-valued evolutionary algorithm (EA) and is used for extensive exploration of the design variable space when searching for the best linkage. The deterministic approach uses a local optimization technique to improve the efficiency by reducing the high CPU time that EA techniques require in this kind of applications. To that end, the deterministic approach is implemented in the evolutionary algorithm in two stages. The first stage is the fitness evaluation where the deterministic approach is used to obtain an effective new error estimator. In the second stage the deterministic approach refines the solution provided by the evolutionary part of the algorithm. The new error estimator enables the evaluation of the different individuals in each generation, avoiding the removal of well-adapted linkages that other methods would not detect. The efficiency, robustness, and accuracy of the proposed method are tested for the design of a mechanism in two examples.This paper has been developed in the framework of the Project DPI2010-18316 funded by the Spanish Ministry of Economy and Competitiveness

Banco de ensayos para el estudio del comportamiento dinámico de trenes de engranajes epicicloidales

Las transmisiones mecánicas mediante trenes de engranajes epicicloidales presentan un indudable interés desde múltiples puntos de vista debido a su excelente relación entre tamaño y potencia. No obstante el diseño óptimo de estos sistemas requiere un mejor conocimiento de su comportamiento dinámico. Persiguiendo este objetivo se ha llevado a cabo el diseño de un banco de ensayos que permite abordar la caracterización del comportamiento dinámico de este tipo de sistemas. Tras presentar brevemente las distintas posibilidades de construcción de este tipo de bancos, se describe el diseño de un banco experimental basado en la recirculación de potencia mecánica mediante el empleo de dos transmisiones planetarias idénticas con sus porta-satélites conectados mediante un eje hueco, por el interior de cual se ubica otro eje que une solidariamente los engranajes sol. De este modo es posible obtener un elevado nivel de carga mediante la aplicación de un par sobre una de las ruedas interiores mientras que el accionamiento únicamente debe proporcionar las pérdidas debidas al rozamiento. La selección del tamaño del accionamiento se ha llevado a cabo considerando la configuración específica del banco, determinando la magnitud de las pérdidas por rozamiento y la posibilidad de obtener un nivel de carga lo suficientemente elevado como para deteriorar los componentes de la transmisión, de modo que el banco pueda ser utilizado para llevar a cabo ensayos en estas condiciones. Otro aspecto que ha sido analizado es el diseño de los ejes de conexión entre los porta-satélites y engranajes sol así como el procedimiento a emplear para soportarlo en dirección radial así como sus efectos sobre las frecuencias de resonancia del conjunto. Se completa la descripción del banco con la presentación de los captadores y dispositivos para la adquisición y el acondicionamiento de las señales dinámicas

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

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”

Monitoring of misalignment in low speed geared shafts with acoustic emission sensors

The most common condition monitoring method applied to rotating machines is vibration measurement, although recently it has been proposed that acoustic emission (AE) offers additional advantages in early fault detection and low speed rotation systems. Capturing the AE signals is conditioned by the severe attenuation with distance and the presence of material discontinuities between source and sensor, therefore measurement device placement is more important than in traditional accelerometry. In this study AE signals are measured in gearboxes at misalignment conditions for the revision of signal characteristics from the generated signal due to the interaction of shafts, bearings and gears. For this purpose, several tests are performed using combinations of speed and varying load, considering the effect of lubricating oil temperature. Fixed measurements are taken over the bench supports, and on-board, where the sensors are rotating with the shafts. In parallel to acoustic emission a vibration analysis is done in order to contrast and analyze differences between both technologies at different operation states. Acquired data is processed to obtain statistical parameters from measurements in order to verify the values and tendencies due to transient phenomena related to changes in speed and load. AE provides better results than vibration employing the same time domain condition indicators. On the contrary, vibration recognizes clearly the fault through frequency analysis.This work has been supported by project DPI2017-85390-P funded by the Spanish Ministry of Science and Technology and RM16-XX012 PredictEA project funded by SODERCAN