Multi-stage Gearboxes Research Articles

A Multi Domain Modeling Approach for the CFD Simulation of Multi-Stage Gearboxes

The application of Computer-Aided Engineering (CAE) tools in mechanical design has consistently increased over the last decades. The benefits introduced by virtual models in terms of time and cost reductions are the main drivers for their exploitation in industry as well as for research purposes in academia. In this regard, Computational Fluid Dynamics (CFD) can be exploited to study lubrication and efficiency of gears. However, the mesh handling complexities deriving from the boundary motion is still a concern for its application to multi-stage gearboxes. In this work, an innovative multi domain partitioning method for the simulation of a two-stage industrial speed reducer is presented. The implemented solution foresees the combination of two remeshing strategies, namely GRA (Global Remeshing Approach) and GRAMC (GRA with Mesh Clustering), and resulted in a computationally effective performance. The results were compared with experimental data obtained with measurements on the real system, providing a good agreement in the power losses prediction. Considering the complexity of obtaining such results experimentally, the proposed numerical algorithm can offer substantial benefits for an estimation of the transmissions’ efficiency in various operating conditions. The numerical model was built in the open-source environment OpenFOAM®.

A mathematical model of vibration signal for multistage wind turbine gearboxes with transmission path effect analysis

The sensor-perceived vibration signals of multistage wind turbine gearboxes have more complex frequency features than that of single-stage gearboxes since there are more meshing vibration sources and more complicated transmission paths inside them, which lead to difficulties in condition monitoring and fault diagnosis. Aiming to understand the vibration frequency features of multistage wind turbine gearboxes, a mathematical vibration model of healthy wind turbine gearboxes is developed and the spectral structure of the model is deduced by adopting Fourier series analysis. In the vibration model, the time-varying transmission paths from all the meshing vibration sources to the fixed sensor are considered, and the equivalent transmission path functions of the time-varying transmission paths are proposed for the first time. The theoretical derivations are validated by both simulations and engineering tests using two cases of 2.0MW industrial wind turbine gearboxes. The findings in this work are not only applicable to the gearboxes studied in this paper, but also to other similar multistage gearboxes, which can provide a priori spectral structure for the multistage gearbox to assist its condition monitoring and fault diagnosis.

Cyclostationary-based Multiband Envelope Spectra Extraction for bearing diagnostics: The Combined Improved Envelope Spectrum

Bearing diagnostics is a field of intensive research, focusing nowadays mainly in complicated machinery (e.g. planetary gearboxes, multi-stage gearboxes, etc.) operating under varying conditions (e.g. varying speed and load), as they still provide challenges in terms of accuracy and time of detection/diagnosis. One of the most common methods for bearings diagnostics is Envelope Analysis, where a filter is usually applied around an excited frequency band and the signal is enveloped, obtaining the Squared Envelope Spectrum. However, as the bearing damage may excite several frequency bands simultaneously, band-pass filtering around only one frequency band may not be sufficient for the detection of the bearing fault under the presence of noise. Recently, the IESFOgram (Improved Envelope Spectrum via Feature Optimisation-gram) has been proposed, based on either the Cyclic Spectral Correlation or the Cyclic Spectral Coherence, in order to select the optimal frequency band and extract the corresponding Improved Envelope Spectrum. In this paper the method is extended towards the extraction of the Combined Improved Envelope Spectrum (CIES), performing a multi-band integration of the bivariable map around multiple resonant frequencies that are carriers of the bearing damage signature. The proposed method is applied, tested and evaluated on experimental data and the results are compared with state-of-the-art band-selection tools.

THEORETICAL RESEARCH OF THE VIBROACOUSTIC DYNAMICS OF THE CUTTING TOOLS FOR MILLING RECESSING AND CHAIN MORTISE WOODWORKING MACHINES

Milling recessing machines are designed to select mortises with end mills of the rectangular-shaped sockets. To the characteristic features of these machines, distinguishing them from the machines of the milling group is the additional oscillatory movement of the milling cutter on the chain ridged machines. The sockets are selected with the rectangular shape of the milling chain. These machines are operated at constant spindle speeds. Therefore, in these machines there are no multistage gear boxes with a large number of the spindles. These features lead to the fact that the vibrations of the cases of the speed boxes of woodworking machines (unlike metal-cutting machines) are much less and, accordingly, the intensity of their sound radiation is also less. The frequency of the rotation of the cutting tool is significantly higher. Therefore, it can be assumed that the main source of the noise that exceeds sanitary standards is the workpiece cutting tool system. The purpose of theoretical studies with obtained results show the analytical dependencies of the active sound pressure levels created by the cutting tool of the milling recessing and chain mortise machines providing for geometrical, physic-mechanical parameters of the tool and technological cutting conditions. The used acoustic source models are monocle for the tool of the milling recessing machines and a linear source for the milling chain and the noise levels obtained on their basis showed that for engineering calculation it is necessary to determine the oscillation velocities of the sources on their own oscillation modes. The speeds of the oscillations are determined from the differential oscillation equations; the solutions are obtained taking into account the cleat boundary conditions. The calculation of the noise spectra makes it possible at the design stage of both similar equipment and technological processes of the wood processing to determine the magnitudes over the maximum allowable values and in fact at the same stage to design noise protection systems.

Vibration-based angular speed estimation for multi-stage wind turbine gearboxes

Most processing tools based on frequency analysis of vibration signals are only applicable for stationary speed regimes. Speed variation causes the spectral content to smear, which encumbers most conventional fault detection techniques. To solve the problem of non-stationary speed conditions, the instantaneous angular speed (IAS) is estimated. Wind turbine gearboxes however are typically multi-stage gearboxes, consisting of multiple shafts, rotating at different speeds. Fitting a sensor (e.g. a tachometer) to every single stage is not always feasible. As such there is a need to estimate the IAS of every single shaft based on the vibration signals measured by the accelerometers. This paper investigates the performance of the multi-order probabilistic approach for IAS estimation on experimental case studies of wind turbines. This method takes into account the meshing orders of the gears present in the system and has the advantage that a priori it is not necessary to associate harmonics with a certain periodic mechanical event, which increases the robustness of the method. It is found that the MOPA has the potential to easily outperform standard band-pass filtering techniques for speed estimation. More knowledge of the gearbox kinematics is beneficial for the MOPA performance, but even with very little knowledge about the meshing orders, the MOPA still performs sufficiently well to compete with the standard speed estimation techniques. This observation is proven on two different data sets, both originating from vibration measurements on the gearbox housing of a wind turbine.

A new strategy of instantaneous angular speed extraction and its application to multistage gearbox fault diagnosis

Owing to its unique benefits, Instantaneous Angular Speed (IAS) has become the focus of a great deal of research for monitoring mechanical parts of rotating machines in the past few years. However, the efficacy of IAS-based signal processing techniques essentially depends on the estimation method of IAS and the complexity of the mechanical system. When it is applied to complex systems like turbines, gearboxes, conventional IAS itself still has some flaws and insufficiencies such as longer data stream, quantization noise and structural noise. In order to address these issues, this paper proposes an alternative IAS estimation approach named Instantaneous Angular Phase Demodulation (IAPD) IAS together with an improved procedure involving signal reconstruction, empirical mode decomposition (EMD) and envelope analysis. Thereafter, two kinds of multistage gearboxes under different working conditions are developed to experimentally demonstrate the accuracy and effectiveness of the new IAS measurement. Analysis results suggest that the quantization noise can be significantly reduced or even avoided in the IAPD-IAS signal compared with the conventional IAS signal. Moreover, by means of the new procedure, the computational efficiency can be greatly improved and fault characteristics are dramatically enhanced in the envelope spectrum where deterministic frequency component and its harmonics corresponding to fault characteristics are displayed clearly.

Diagnosis of Localized Faults in Multistage Gearboxes: A Vibrational Approach by Means of Automatic EMD-Based Algorithm

The gear fault diagnosis on multistage gearboxes by vibration analysis is a challenging task due to the complexity of the vibration signal. The localization of the gear fault occurring in a wheel located in the intermediate shaft can be particularly complex due to the superposition of the vibration signature of the synchronous wheels. Indeed, the gear fault detection is commonly restricted to the identification of the stage containing the faulty gear rather than the faulty gear itself. In this context, the paper advances a methodology which combines the Empirical Mode Decomposition and the Time Synchronous Average in order to separate the vibration signals of the synchronous gears mounted on the same shaft. The physical meaningful modes are selected by means of a criterion based on Pearson’s coefficients and the fault detection is performed by dedicated condition indicators. The proposed method is validated taking into account simulated vibrations signals and real ones.

Analysis of Dynamic Excitation Behavior of a Two-stage Spur Gearbox

In times of engine downsizing and lightweight design, the dynamic and acoustic behavior of multi-stage gearboxes is becoming increasingly important. One parameter is the manufacturing quality of the gears which can be expressed by DIN standard and is influenced among other things by the production process.The presented objective is the analyzation of the dynamic behavior with focusing dynamic interactions of two-stage gearboxes. To achieve this goal, gears with different micro geometries and the interactions between the meshes are investigated mathematically. Therefore, a dynamic multi body simulation model is presented in which gear meshes will be described as force coupling elements.

Novel spectral kurtosis technology for adaptive vibration condition monitoring of multi-stage gearboxes

Novel spectral kurtosis technology for adaptive vibration condition monitoring of multi-stage gearboxes

Gearbox Condition Estimation Using Cyclo-Stationary Properties of Vibration Signal

The paper explores the cyclo-stationary properties of vibration signals for estimation of gearbox condition. The advantage of such approach may be clearly seen especially for so called multi-faults problem, i.e. for more than one faults that occurred in the system. In complex mechanical systems like multistage gearboxes, such situation may be often seen. Although this approach becomes more and more popular, it has been noticed that there is difficult to find examples highlighting its potential, especially for real industrial situations. In order to fill partially the gap, the paper deals with the multi fault detection in complex mechanical systems like multi-stage gearboxes: fixed axis and planetary. It has been discussed that during the operation in such machines many faults may appear simultaneously and the classical method like envelope analysis is difficult to use. The paper presents the use of cyclo-stationary properties of signals to identify and characterize sources of modulation. From Spectral Correlation Density Map or more precisely Spectral Coherence Map have been observed the number of sources with different properties of modulation. It is shown that the number of harmonics is important for a kind of fault extraction and interpretation. This approach has been applied to two, three and five stage gearboxes used in mining industry. Vibration signals received in industrial environment during normal operation of objects are considered. It has been also proposed the simple diagnostic feature to estimate the changes of condition with application to a planetary stage in a 5-stage gearbox.

Vibration Monitoring for Local Tooth Damage in Multistage Gearboxes

An adaptive approach was applied for local tooth damage diagnostics in gearboxes. The expediency of adaptation was proved experimentally for the new diagnostic feature, the sum of normalized sideband amplitudes. The positive correlation between mesh amplitudes and their sideband amplitudes was found experimentally for the first time. Novel adaptive vibration condition monitoring technology for local tooth damage in gearboxes was developed and experimentally validated. The experimental results showed an increase in effectiveness of the diagnostics when the adaptive technology was used.

An exactly soluble model of a system containing arbitrary isotropic bilinear and biquadratic exchange interactions

In times of engine downsizing and lightweight design, the dynamic and acoustic behavior of multi-stage gearboxes is becoming increasingly important. One parameter is the manufacturing quality of the gears which can be expressed by DIN standard and is influenced among other things by the production process.The presented objective is the analyzation of the dynamic behavior with focusing dynamic interactions of two-stage gearboxes. To achieve this goal, gears with different micro geometries and the interactions between the meshes are investigated mathematically. Therefore, a dynamic multi body simulation model is presented in which gear meshes will be described as force coupling elements.