Predictive Modeling of a Two-stage Gearbox towards Fault Detection

This research presents a systematic approach to health monitoring using dynamic gearbox models (DGM) and the harmonic wavelet transforms (HWT) for vibration response analysis. A comprehensive DGM is developed, the model parameters are identified through correlated numerical and experimental investigations, and HWT analysis is performed to illustrate the fault detection and diagnosis procedure and capability of this approach. The model fidelity is validated first by spectrum analysis, using constant speed experimental data, and secondly by HWT analysis, using non-stationary experimental data. The comparison confirms that both the frequency content and the predicted, relative response magnitudes match with physical measurements. Model prediction and experimental data are compared for healthy gear operation and seeded gear faults including a pinion with a missing tooth, tooth root crack, tooth spall and varying tooth chip severities, demonstrating that fault type and severity are distinguishable. The research shows fault modeling in combination with HWT data analysis is able to identify fault types, evaluate fault relative severity, and greatly reduce pattern recognition library development. This approach can facilitate successful fault detection, diagnosis and prognosis for gearbox systems, providing a physically meaningful connection of fault indicators to the actual fault patterns thus paving the way to real-time condition monitoring

Effects of variable loading conditions on the dynamic behaviour of planetary gear with power recirculation

Variable loads to which gearboxes are subjected are considered as one of the main sources of non-stationarity in these transmissions. In order to characterise their dynamic behaviour in such conditions, a torsional lumped parameter model of a planetary gear with power recirculation was developed. The model included time varying loading conditions and took into account the non-linearity of contact between teeth. The meshing stiffness functions were modelled using Finite Element Method and Hertzian contact theory in these conditions. Series of numerical simulations was conducted in stationary conditions, with different loading conditions. Equation of motion was solved using Newmark algorithm. Numerical results agreed with experimental results obtained from a planetary gear test bench. This test bench is composed of two similar planetary gears called test planetary gear set and reaction planetary gear set which are mounted back-to-back so that the power recirculates through the transmission. The external load was applied through an arm attached to the free reaction ring. Data Acquisition System acquired signals from accelerometers mounted on the rings and tachometer which measured instantaneous angular velocity of the carrier's shaft. The signal processing was achieved using LMS Test.Lab software. Modulation sidebands were obtained from the ring acceleration measurements as well as a non-linear behaviour in case of variable loading resulted by a transfer of the spectral density from the fundamental mesh stiffness to its second harmonic.This work was financially supported by the Tunisian-Spanish Joint Project No. A1/037038/11. The authors would like also to acknowledge the project funded by the Spanish Ministry of Science and Technology and called ‘‘Development of methodologies for the simulation and improvement of the dynamic behavior of planetary transmissions DPI2013-44860”

Automatic calculation of thresholds for load dependent condition indicators by modelling of probability distribution functions – maintenance of gearboxes used in mining conveying system

Limit values for gearbox vibration-based condition indicators are key to determine in order to be able to estimate moment when object is in a need of maintenance. Further decision making process usually might utilize simple if-then-else rule using established threshold values. If diagnostic data takes the values from the Gaussian distribution, finding the decision boundaries is not difficult. Simplistically, that comes down to standard pattern recognition technique for “good condition” and “bad condition” based on probability density functions (PDFs) of diagnostic data. This situation is becoming more and more complicated when distribution is not Gaussian. Such cases require to develop much more advanced analytically solution. In this paper, we present the case of belt conveyor’s gearbox for which PDFs of diagnostic features overlap each other because of strong influence of time varying operating conditions on spectral features. New approach to automatic threshold recognition has been proposed based on modeling diagnostic features with Weibull distribution and using agglomerative clustering to distinguish classes of technical condition, which leads to determination of thresholds separating them

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”

Gearbox Health Condition Monitoring: A brief exposition

Gearbox is a mechanical power transmission device, most commonly used to get the mechanical benefits in terms of speed and torque. The gearbox is made up of different types of gears assembled in a cascading order to perform the intended task. Failure of any rotating component inside the gearbox will terminate the working condition of the mechanical system associated with it. This causes interrupted services to the industries, which lead to expensive compensation. Especially, in an aircraft engine, it is used as an accessory drive, which provides power for hydraulic,pneumatic and electrical systems. This motivated to monitor the gearbox health condition. This paper presents a brief review of GHCM (gearbox health condition monitoring), gearbox faults, overview of time-domain features, frequency-domain features, time-frequency domain; feature extraction techniques, and fault classification techniques.The outcome of this study is to provide brief information regarding gearbox health condition monitoring

Helical gear wear monitoring: Modelling and experimental validation

Gear tooth surface wear is a common failure mode. It occurs over relatively long periods of service nonetheless, it degrades operating efficiency and leads to other major failures such as excessive tooth removal and catastrophic breakage. To develop accurate wear detection and diagnosis approaches at the early phase of the wear, this paper examines the gear dynamic responses from both experimental and numerical studies with increasing extents of wear on tooth contact surfaces. An experimental test facility comprising of a back-to-back two-stage helical gearbox arrangement was used in a run-to-failure test, in which variable sinusoidal and step increment loads along with variable speeds were applied and gear wear was allowed to progress naturally. A comprehensive dynamic model was also developed to study the influence of surface wear on gear dynamic response, with the inclusion of time-varying stiffness and tooth friction based on elasto-hydrodynamic lubrication (EHL) principles. The model consists of an 18 degree of freedom (DOF) vibration system, which includes the effects of the supporting bearings, driving motor and loading system. It also couples the transverse and torsional motions resulting from time-varying friction forces, time varying mesh stiffness and the excitation of different wear severities. Vibration signatures due to tooth wear severity and frictional excitations were acquired for the parameter determination and the validation of the model with the experimental results. The experimental test and numerical model results show clearly correlated behaviour, over different gear sizes and geometries. The spectral peaks at the meshing frequency components along with their sidebands were used to examine the response patterns due to wear. The paper concludes that the mesh vibration amplitudes of the second and third harmonics as well as the sideband components increase considerably with the extent of wear and hence these can be used as effective features for fault detection and diagnosis

Condition Monitoring of Helical Gear Transmissions Based on Vibration Modelling and Signal Processing

Condition monitoring (CM) of gear transmission has attracted extensive research in recent years. In particular, the detection and diagnosis of its faults in their early stages to minimise cost by maximising time available for planned maintenance and giving greater opportunity for avoiding a system breakdown. However, the diagnostic results obtained from monitored signals are often unsatisfactory because mainstream technologies using vibration response do not sufficiently account for the effect of friction and lubrication. To develop a more advanced and accurate diagnosis, this research has focused on investigating the nonlinearities of vibration generation and transmission with the viscoelastic properties of lubrication, to provide an in-depth understanding of vibration generating mechanisms and hence develop more effective signal processing methods for early detection and accurate diagnosis of gear incipient faults. A comprehensive dynamic model has been developed to study the dynamic responses of a multistage helical gear transmission system. It includes not only time-varying stiffness but also tooth friction forces based on an elastohydrodynamic lubrication (EHL) model. In addition, the progression of a light wear process is modelled by reducing stiffness function profile, in which the 2nd and 3rd harmonics of the meshing frequency (and their sidebands) show significant alteration that support fault diagnostic at early stages. Numerical and experimental results show that the friction and progressive wear induced vibration excitations will change slightly the amplitudes of the spectral peaks at both the mesh frequency and its sideband components at different orders, which provides theoretical supports for extracting reliable diagnostic signatures. As such changes in vibrations are extremely small and submerged in noise, it is clear that effective techniques for enhancing the signal-to-noise ratio, such as time synchronous averaging (TSA) and modulation signal bispectrum (MSB) are required to reveal such changes. MSB is preferred as it allows small amplitude sidebands to be accurately characterised in a nonlinear way without information loss and does not impose any addition demands regarding angular displacement measurement as does TSA. With the successful diagnosis of slight wear in helical gears, the research progressed to validate the capability of MSB based methods to diagnose four common gear faults relating to gear tribological conditions; lubrication shortfall, changes in lubrication viscosity, water in oil, and increased bearing clearances. The results show that MSB signatures allows accurate differentiation between these small changes, confirming the model and signal processing proposed in this thesi