On the influence of the lamella's elasticity on self-excited vibrations in gearboxes

Eek noise in a gearbox of a vehicle drivetrain is a phenomenon, which can arise while shifting between gears and which is not accepted by customers. Beneath audible squeaking, it can cause damage of mechanical components. There is a wide range of possible reasons for the occurrence of this effect, which strongly depends on properties of the considered gearbox (physical parameters, geometry, operation, …). From the mathematical point of view, the occurrence can be predicted using linear stability analysis of the stationary behaviour of a physically motivated gearbox model. The components of a gearbox are clutch discs being in contact, gears and elastically supported shafts. In this contribution, a rigid multibody model of the device [4] is extended by the elastic modelling of the motor's side disc (rotating Kirchhoff plate). The aim of the overall system is to analyze the shifting process. The analysis reveals that beneath instability mechanisms which are known from systems with rigid bodies, new instabilities occur incorporating of out-of-plane vibrations of the plate. In a reasonable parameter region, the first two unsymmetrical modes of the lamella have the main contribution to the instability. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic modeling and analysis of wind turbine drivetrain considering the effects of non-torque loads

With the increase of the rotor diameter and the deterioration of operating conditions, modern wind turbines suffer from more and more significant time-varying non-torque loads, which increases the burden of turbine structures especially the gearbox. Based on an aeroelastic loose coupling approach and assembly of the finite element method, an integrated drivetrain coupling analysis model including blade module, aerodynamic module, and gearbox module is established in this study. This proposed model is validated by comparing the calculation results with previous literature. Taking National Renewable Energy Laboratory 5-MW wind turbine as the research object, the gearbox vibration responses, gear meshing forces and bearing forces under non-torque loads caused by blade gravity, wind shear (WS), tower shadow (TS) and yawed inflow are studied in detail. Results show that the y-direction displacements of the gearbox, sun gear 1, sun gear 2 and gear are larger than those in x-direction because F_y or M_x generated by blade gravity, WS and TS dominates the non-torque loads. The non-torque loads lead to a non-uniform planet load sharing especially for the planetary gear stage 1. Because of the fluctuations of non-torque loads, not only the rotation frequencies of the corresponding carrier but also the multiple frequencies of the carrier 1 are observed in the frequency spectrums. The non-torque loads are mainly borne by carrier 1 bearings. Except for the blade gravity, the bearing forces caused by other unsteady inflows have obvious fluctuations.     

Eigenvalue sensitivity and parametric optimization of the large rotating systems

The contribution presents the modal synthesis method of the mathematical modelling of the large rotating systems. The condensed mathematical model is used for deriving analytical formula for eigenvalue sensitivity calculation. According to the sensitivity analysis suitable design parameters are chosen and the optimization process for the purpose of steady state response minimization in a certain operating speed area is performed. The theory is applied to a simple test‐gearbox. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Noise-induced basin hopping in a gearbox model

We investigate some dynamical effects of adding a certain amount of noise in a theoretical model for rattling in single-stage gearbox systems with a backlash, consisting of two wheels with a sinusoidal driving. The parameter intervals we are dealing with show an extremely involved attraction basin structure in phase space. One of the observable effects of noise is basin hopping, or the switching between basins of different attractors. We characterize this effect and its relation to the presence of chaotic transients.     

Noise-induced basin hopping in a gearbox model

We investigate some dynamical effects of adding a certain amount of noise in a theoretical model for rattling in single-stage gearbox systems with a backlash, consisting of two wheels with a sinusoidal driving. The parameter intervals we are dealing with show an extremely involved attraction basin structure in phase space. One of the observable effects of noise is basin hopping, or the switching between basins of different attractors. We characterize this effect and its relation to the presence of chaotic transients.     

Influence of internal parametric and kinematic excitation on nonlinear gearbox vibration

This paper deals with mathematical modelling of nonlinear vibration of large rotating shaft systems with gears and rollingelement bearings. Gearing and bearing couplings bring into the system nonlinear phenomena like impact motions due to the possibility of the mesh interruption. The motion of the system is influenced by the internal kinematic excitation in gearing and by the parametric excitation caused by periodic change of number of teeth in gear meshing. The influence of simultaneous internal kinematic and parametric excitation is investigated in dependence on revolutions of the driving shaft of a test-gearbox. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gearbox failure diagnosis based on vector autoregressive modelling of vibration data and dynamic principal component analysis

Email: mgt.liu{at}utoronto.ca Email: makis{at}mie.utoronto.ca Received on 4 August 2006. Accepted on 14 December 2006. An effective gearbox failure diagnosis helps prevent catastrophicgearbox failure and can contribute to significant economic benefits.This paper proposes a gear failure diagnosis method based onvector autoregressive modelling of high-frequency vibrationdata, dimensionality reduction applying dynamic principal componentanalysis (PCA) and condition monitoring using a multivariatecontrol chart. After extracting useful information from thevibration data obtained from distinct directions via dynamicPCA, a failure diagnosis scheme is implemented and tested usingreal gearbox vibration data. It is shown that the failure diagnosisscheme can indicate the gear teeth failure pattern when thegear is damaged, which has not been demonstrated in the previousstudies. For a comparison, PCA is applied to the same data set.The results show that the advantages of dynamic PCA over PCAfor failure diagnosis using vibration data consist not onlyin indicating more accurately the occurrence of incipient faultand the actual gear condition, but also in a much lower falsealarm rate.     

Detection of incipient gear failures using statistical techniques

Gears are important components in most power transmission mechanisms.Failures of gears can cause heavy losses in industry. Conditionmonitoring and fault diagnosis of gears is therefore importantto improve safety and reliability of gearbox operations andreduce losses caused by gear failures. This research proposesa new diagnostic approach based on the statistical analysisof data. It investigates the use of Principal Components Analysis(PCA) to detect growing local faults in a two-stage industrialhelical gearbox. In this research, the vibration signal is usedto monitor fault conditions and a broken tooth is simulatedas a local fault. Since the early detection of faults is a challenge,small fault conditions were tested first as well as severe faultconditions. In order to examine the ability of the PCA to detectfault conditions, first the PCA-based model was created fornormal operating conditions. Any unexpected event such as afault condition causes a significant deviation from the PCAmodel, which is obtained from the normal condition data of thegearbox. The Square Prediction Error (SPE) was calculated todetect the fault conditions. When the vibration signal fromthe gearbox is representative of normal operation, the valueof the SPE shows very little fluctuation and remains under acertain threshold value. However, in the presence of the faultthe SPE fluctuates considerably beyond the threshold value.It is shown that the PCA-based statistical approach cannot onlybe used to detect severe fault conditions, but that it alsoreveals small growing fault conditions at very early stage.The technique also provides information about the state of thefault such as the location of the fault as well as its severity. Received 5 March 2001. Revised 12 December 2001. Accepted 17 January 2002.     

Dynamics of a running gear with IRWs on curved tracks for a robust control development

As a major task of the DLR-internal project “Next Generation Train”, robust state feedback control with gain scheduling was sucessfully applied to guide the experimental running gear with independently rotating wheels (IRWs) at a 1:5 scaled roller rig, see [1]. However, the adaptation of the control structure to the 1:1 multibody model requires to additionally consider the properties of curved tracks. For that reason, an analytical model of a running gear with IRWs is deduced using Euler-Lagrange-equations and taking superelevation and track curvature into account. Furthermore, the complexity of the system is reduced to allow for a robust feedback control synthesis and feed-forward control including model inversion. Finally, the model is discussed and a first approach for a feed-forward control in transition curves is shown. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new nonlinear blind source separation method with chaos indicators for decoupling diagnosis of hybrid failures: A marine propulsion gearbox case with a large speed variation

The normal operation of propulsion gearboxes ensures the ship safety. Chaos indicators could efficiently indicate the state change of the gearboxes. However, accurate detection of gearbox hybrid faults using Chaos indicators is a challenging task and the detection under speed variation conditions is attracting considerable attentions. Literature review suggests that the gearbox vibration is a kind of nonlinear mixture of variant vibration sources and the blind source separation (BSS) is reported to be a promising technique for fault vibration analysis, but very limited work has addressed the nonlinear BSS approach for hybrid faults decoupling diagnosis. Aiming to enhance the fault detection performance of Chaos indicators, this work presents a new nonlinear BSS algorithm for gearbox hybrid faults detection under a speed variation condition. This new method appropriately introduces the kernel spectral regression (KSR) framework into the morphological component analysis (MCA). The original vibration data are projected into the reproducing kernel Hilbert space (RKHS) where the instinct nonlinear structure in the original data can be linearized by KSR. Thus the MCA is able to deal with nonlinear BSS in the KSR space. Reliable hybrid faults decoupling is then achieved by this new nonlinear MCA (NMCA). Subsequently, by calculating the Chaos indicators of the decoupled fault components and comparing them with benchmarks, the hybrid faults can be precisely identified. Two specially designed case studies were implemented to evaluate the proposed NMCA-Chaos method on hybrid gear faults decoupling diagnosis. The performance of the NMCA-Chaos was compared with state of art techniques. The analysis results show high performance of the proposed method on hybrid faults detection in a marine propulsion gearbox with large speed variations.     

Approach for Adaptive Sound Power Minimization of Elemental Sources in Theory and Experiments

Low frequency noise is a major issue in future aircraft with counter rotating open rotor engines. Passive noise treatments are bulky and heavy at these low frequencies. That is why active approaches are considered. The well known concept of destructive interference is used by state of the art active noise cancellation methods. The active systems are located closely to the noise source to cancel it. The microphones used for pressure minimization are in the near sound field of the noise source where active and reactive sound intensity are present. The pressure based concept is minimizing just the potential part of the acoustic energy. A new approach is proposed in this paper. It minimizes directly the net flow of acoustic energy that is transmitted into an interior. Simulation results showed that a proper estimation of acoustic power output is achieved by measuring sound intensity at a single point directly on the central axis of each secondary source. The innovative energy based active control approach (TASPM) has also successfully been validated in a laboratory environment. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Basic studies on the dynamics of rotating circular structures

In this paper the dynamic effects due to rotation of spinning circular structures will be discussed by analytical, experimental and numerical investigations. Basic phenomena of spinning are studied on the analytical solution of a spinning ring. The observed effects will be underlined by rather simple experimental investigations on a rotating wine glass. Based on this fundamental knowledge special attention has to be payed to the finite element modeling and implementation of the eigenvalue analysis of gyroscopic systems, which requires the numerical solution in complex numbers. Besides the influence of rotational speed, the disturbances due to rolling contact will be discussed on rotating tubes as well as detailed finite element models of rolling tires. The application of these techniques with emphasis to the prediction of tire noise will be outlined. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A planning model for urban housing developments

Summary A planning model for urban housing projects is developed within the framework of systems analysis. The first part gives a cost model of housing projects. Costs are shown to depend on the costs of building sites, construction costs, costs for streets and for parking facilities. The planning model takes factual and legal constraints into consideration. A housing benefit function for the evaluation of urban housing projects is developed by making use of factor analysis. Cost model and benefit model of housing projects are combined in a cost-benefit-analysis for urban planning. The model is shown to be operational by pointing out results derived in an empirical study of a large housing project in Berlin.

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Zusammenfassung Ein Modell für die Planung öffentlicher Investitionen im Wohnungsbau wird entwickelt. Ausgangspunkt ist eine Systemanalyse der Kosten städtischer Wohngebiete. Die Kosten hängen von den Gebäudekosten, den Grundstückskosten, den Straßenkosten und den Kosten für das gewählte Parksystem ab. Das Planungsmodell berücksichtigt faktische und rechtliche Nebenbedingungen, die der Städteplaner bei seinen Entwürfen zu beachten hat. Ein methodischer Ansatz für die Bewertung städtischer Wohngebiete wird aufgezeigt. Wohnwerte und Kosten werden abschließend in einer Kosten-Nutzen-Analyse städtischer Wohngebiete zusammengefaßt. Die Operationalität des Modells wird an einem praktischen Beispiel nachgewiesen.

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This paper is based on research carried out withO. M. Ungers, A. Tönjes, K. Viebering, M. Wegener, andK. P. Kistner. See for detailsH. Albach andO. M. Ungers:Optimale Wohngebietsplanung, Band I, Wiesbaden 1969.     

Noise and coupling induced synchronization in a network of chaotic neurons

The synchronization in four forced FitzHugh–Nagumo (FHN) systems is studied, both experimentally and by numerical simulations of a model. We show that synchronization may be achieved either by coupling of systems through bidirectional diffusive interactions, by introducing a common noise to all systems or by combining both ingredients, noise and coupling together. Here we consider white and colored noises, showing that the colored noise is more efficient in synchronizing the systems respect to white noise. Moreover, a small addition of common noise allows the synchronization to occur at smaller values of the coupling strength. When the diffusive coupling in the absence of noise is considered, the system undergoes the transition to subthreshold oscillations, giving a spike suppression regime. We show that noise destroys the appearance of this dynamical regime induced by coupling.     

Coupled torsion–bending dynamic analysis of gear-rotor-bearing system with eccentricity fluctuation

This study performs a coupled torsion–bending vibration responses of a gear-rotor-bearing system, which has taken time varying mesh stiffness, nonlinear bearing force and gear eccentricity into account. A 16 DOF nonlinear dynamic model of gear-rotor-rolling bearing transmission system with bending–torsion coupling is established to obtain the dynamic response to the changes of different parameters. Based on the Runge–Kutta numerical method, the dynamics of the system is investigated, which describes torsional and bending vibration properties of the system more comprehensively. The vibration responses of the gear-rotor-bearing system are discussed, and the effects of gear eccentricity and rotational speed on the system are investigated in detail. The results show that gear eccentricity and rotational speed have influences on the meshing state of gear teeth, the vibration amplitudes, the frequency multiplication and random frequency components. When the system is in a lower rotational speed, the eccentricity has greater effects on the vibration response. The proposed model and numerical results provide a useful source of reference for engineers in designing and vibration controlling such systems.     

On modelling and analysis of gear drives with nonlinear couplings

The paper deals with modelling of vibration of shaft systems with gears and rolling-element bearings using the modal synthesis method with DOF number reduction. The influence of the nonlinear bearing and gearing contact forces with the possibility of the contact interruption is respected. The gear drive nonlinear vibrations caused by internal excitation generated in gear meshing, accompanied by impact and chaotic motions are studied. The theory is applied to a simple test-gearbox. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite Element Analysis of Eigendynamics of Rolling Tires

The eigenvalue analysis of rolling tires is one part of the simulation of tire rolling noise radiation for the reduction of traffic noise. In this paper the general strategies of numerical eigenvalue analysis for nonsymmetric matrices are shown. The special effects observed on rotating bodies are discussed in details. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of effect of random perturbation on dynamic response of gear transmission system

In order to investigate the effects of random perturbation of a low-frequency excitation caused by torque fluctuations, gear damping ratio, gear backlash, meshing frequency and meshing stiffness, the random dynamic model of a single pair of three-degree-of-freedom spur gear transmission system is established. With gear meshing frequency changing, the dynamic characteristics of the gear transmission system were analyzed by bifurcation diagram, phase diagram, time course diagram and Poincaré map of the system. The effects of random perturbation caused by a low-frequency excitation caused by torque fluctuations, gear damping ratio, gear backlash, meshing frequency and meshing stiffness were comparative analyzed. Numerical simulation shows that the gear transmission system with nonlinear clearance exists rich period-doubling bifurcation phenomenon. With the increasing of the gear meshing frequency, gear transmission system will be from the chaotic motion to periodic motion by inverse period-doubling bifurcation. The effect of the meshing frequency random perturbation on the gear transmission system movement is largest. On the contrary, the effect of the meshing stiffness random perturbation on the system is minimum.     

Periodic and chaotic dynamics of motor-driven gear-pair systems with backlash

Dynamics of gear-pair systems driven by motors and presenting speed-dependent moment resistance is investigated. First, a suitable mechanical model is developed, taking into account the gear mesh backlash and static transmission error as well as the essential non-linearities due to the bearing clearance and contact characteristics. In comparison with earlier related studies, the new element of the present work is that the model developed determines the system response by simply specifying the external loads, rather than by assuming an a priori value for the constant mean angular velocity of the gear shafts. In fact, models employed in earlier research studies are shown to be obtained as special cases of the present model. The study is completed by numerical results. First, classical response diagrams are presented, illustrating the effect of the most important parameters on the system response. Finally, direct integration of the equations of motion is also performed, demonstrating the existence of quasi-periodic and chaotic long time response for selected combinations of the system parameters.