Dynamic coupled vibration analysis of a large wind turbine gearbox transmission system

A lumped-parameter coupled nonlinear dynamic model for one large multi-stage wind turbine gearbox transmission system is established comprehensively including wind varying load, mesh stiffness, dynamic transmission error, gravity, and bearing nonlinear characteristics to obtain the gearbox dynamic response. The vibration differential equations of the drive-train are deduced through the Lagrange’s equation. On the basis of that, the dynamics of wind turbine gearbox is investigated by a Runge-Kutta numerical method that includes simultaneous internal and external excitations. The results show that the dynamic response of the partial component is mainly superposed by high-frequency component caused by the internal excitation and low-frequency component caused by the external excitation. In medium-speed stage and high-speed stage, the vibration amplitude has obvious fluctuation, and the multiple frequency and random frequency components become increasingly obvious with increasing rotational speed and eccentricity at gear and bearing positions. Axial vibrations of the system also have some fluctuation. The bearing has self-variable stiffness frequency, which should be avoided in engineering design stage. The study results provide a theoretical foundation for dynamical characteristics evaluation and dynamic optimization of a large wind turbine gearbox transmission system

Nonlinear vibration modeling and bifurcation characteristic study of a planetary gear train processing device

In this paper, a nonlinear torsional vibration model with meshing errors, time varying meshing stiffness, damping coefficients and gear backlashes was established and dimensionless equations of the system are derived in the planetary gear train processing device. The paper analyzed the nonlinear dynamic behavior of the device which was used to machine the Circular-Arc-Tooth-Trace cylindrical gear. By using the method of numerical integration, the bifurcation diagrams are obtained and the results indicate that the processing device has abundant bifurcation characteristics with the change of the dimensionless speed, and the damping ratios, gear backlashes and meshing errors of meshing pairs could influence the vibration greatly. The bifurcation diagrams reveal that increasing the damping ratios can change the bifurcation and the chaos can be avoid when the damping ratios are bigger enough, reducing the gear backlashes can reduce the dimensionless displacement amplitudes, increasing the meshing errors can make the bifurcation diagrams shift left for a distance, and alternating load torque with large amplitude will cause complex chaos phenomenon. The study can help to avoid the fatigue failure and instabilities caused by chaos and it also contribute to improving the performance of the processing device

A review of gear housing dynamics and acoustics literature

A review of the available literature on gear housing vibration and noise reduction is presented. Analytical and experimental methodologies used for bearing dynamics, housing vibration and noise, mounts and suspensions, and the overall geared and housing system are discussed. Typical design guidelines as outlined by various investigators are given

Bifurcation Observation of Combining Spiral Gear Transmission Based on Parameter Domain Structure Analysis

This study considers the bifurcation evolutions for a combining spiral gear transmission through parameter domain structure analysis. The system nonlinear vibration equations are created with piecewise backlash and general errors. Gill’s numerical integration algorithm is implemented in calculating the vibration equation sets. Based on cell-mapping method (CMM), two-dimensional dynamic domain planes have been developed and primarily focused on the parameters of backlash, transmission error, mesh frequency and damping ratio, and so forth. Solution demonstrates that Period-doubling bifurcation happens as the mesh frequency increases; moreover nonlinear discontinuous jump breaks the periodic orbit and also turns the periodic state into chaos suddenly. In transmission error planes, three cell groups which are Period-1, Period-4, and Chaos have been observed, and the boundary cells are the sensitive areas to dynamic response. Considering the parameter planes which consist of damping ratio associated with backlash, transmission error, mesh stiffness, and external load, the solution domain structure reveals that the system step into chaos undergoes Period-doubling cascade with Period-2m (m: integer) periodic regions. Direct simulations to obtain the bifurcation diagram and largest Lyapunov exponent (LE) match satisfactorily with the parameter domain solutions

Tribological And Dynamical Study Of An Automotive Transmission System

The transmission system is critical for automotive and heavy duty equipment due to its prominent role in the powertrain system, which is often challenged with degraded torque capacity and harsh dynamic response. Simulation-guided design can provide appropriate guidelines to resolve these problems with virtual analyses. In current study, the tribological and dynamical study of an automatic transmission is performed at two levels: a wet clutch and powertrain. In this dissertation, tribological study is performed for a wet clutch based on the thermohydrodynamic (THD) analysis that takes the following factors into account. • The groove effect (depth, area, and pattern) is investigated for lubrication analysis; • The elastic-plastic asperity contact model is used to predict the contact pressure; • The heat transfer during the entire cycle of engagement from slip to lock to detachment is covered; • The engagement time and the temperature profile are predicted for torque and thermal analysis. With large engagement cycles, the friction lining of a wet clutch is worn off due to the material degradation at high load/temperature condition. By relating the wear behavior with the mechanism of thermal degradation and thermomechanical degradation, a physics-based wear model is proposed for the first time to analyze the wear process in a wet clutch. The predicted wear rate falls within nearly 95% confidence interval of the test results. Discrepancies of simulation are primarily due to limited availability of input data and model assumptions. Therefore, an uncertainty quantification analysis of the wear model is performed using the Monte Carlo simulations. In addition, a comprehensive parametric analysis of the clutch wear is considered with various factors, including groove design (waffle pattern shows the minimum wear), material properties and operational configurations (rotational speed plays the most influential role). The dynamics of transmission directly affects the performance of the powertrain. The coupling effects of the key transmission components are examined. Of particular interests are the stick-slip behavior of the wet clutch and backlash of the gear train. Through simulation of the powertrain, the main source and the pattern of vibration propagation in the driveline are examined. Major vibration is observed during inappropriate clutch engagement

CAE Methods on Vibration-based Health Monitoring of Power Transmission Systems

This thesis focuses on different methods to analyze power transmission systems with computer software to aid in detection of faulty or damaged systems. It is split into three sections. The first section involves utilizing finite element software to analyze gear stiffness and stresses. A quasi-static and dynamic analysis are done on two sets of fixed axis spur gears and a planetary gear system using ABAQUS to analyze the stress, strain and gear mesh stiffness variation. In the second section, the vibrational patterns produced by a simple bevel gear system are investigated by an experiment and by dynamic modeling in ADAMS. Using a Fast Fourier Transform (FFT) on the dynamic contact forces, a comprehensive frequency-domain analysis will reveal unique vibration spectra at distinct frequencies around the gear mesh frequencies, their super- and sub- harmonics, and their side-band modulations. ADAMS simulation results are then compared with the experimental results. Constraints, bearing resistant torques, and other key parameters are applied as closely as possible to real operating conditions. The third section looks closely at the dynamic contact forces of a practical two-stage planetary gear. Using the same FFT approach in the second section, a frequency-domain analysis will reveal distinct frequencies around both the first-stage and the second-stage gear mesh frequencies, and their harmonics. In addition, joint time-frequency analysis (JTFA) will be applied to damaged and undamaged planetary gear systems with transient start-up conditions to observe how the frequency contents of the contact force evolve over time

Bifurcations and chaos in a gear assembly with clearances for solar array drive assembly

Solar array drive assembly is an important part of the spacecraft. It is used to rotate the solar panels. The gear assembly in solar array drive assembly plays a key role in transferring power safely. Nonlinear behavior of gear assembly, like the chaotic motion, can highly affect the stability and operating life of solar array drive assembly. Clearances in gear assembly which were neglected for simplification in past years have increased the risk of failure and become a problem in accurate control. To investigate the clearances effect on nonlinear behavior, this paper establishes a new dynamic model of the gear assembly with bilateral clearances. The main difference comparing to general spur gears is its unique hysteresis stiffness may also influence the clearance effects. Transformation of the hysteresis loop is observed from theoretical equations using different parameters. Bifurcations and chaotic analysis of the system are carried out by numerical simulations in this study. The results show that the variation of clearances may induce the chaotic behavior into gear transmission even when the primary response is stable. When the system step into the chaotic region, it has a high risk of unstable vibration and fuzzy output. The influence of excitation frequency on the chaotic motion of the system is also provided. Chaos thresholds are calculated to avoid nonlinear behavior of the system in design and control. This study makes it possible to predict the unstable clearance interval in this system and avoid the system stepping into chaotic motion. Analyzing and predicting the chaotic behaviors can contribute to the further studies on design and control of the solar array drive assembly

Transmission characteristics of planetary gear wear in multistage gear transmission system

Gear tooth surface wear is a common failure mode. It takes a long time and can cause other major faults. The wear fault signal is weak and hard to identify. This paper reveals the transmission characteristics of the planetary gear wear and the relationship between multistage gear meshing through the transmission characteristic analysis. Taking the multistage gear transmission system fault simulation test rig as the research object, a three-dimensional solid rigid-flexible coupling model of the system was established. The contact force signals from each pair of gears in the state of planetary gear wear were obtained by dynamic simulation. The test signals of the fixed-axis gearbox and planetary gearbox were obtained under normal and planetary gear wear states. Comparing the transmission characteristics of the system under normal and planetary gear wear states, the vibration mechanism of the wear fault and the correlative characteristic between gearboxes were revealed

Effects of bearing configuration in wind turbine gearbox reliability

AbstractThis paper investigates the impact on the reliability of different configurations of planet bearings. The studied bearings are located in the low-speed planetary stage of a wind turbine gearbox. The bearing stiffness matrix for each kind, cylindrical and tapered roller bearing (CRB and TRB), is included in the electro-mechanical drive-train simulation tool presented here. The system defined in Matlab/Simulink is co-simulated along with a wind turbine defined in an aeroelastic software. Moreover, the normal production design load case (DLC 1.1) is used to compute the bearing response to different turbulence seeds. From this, the fatigue and reliability of the bearings is calculated using the damage equivalent load and the first-order reliability method (FORM), where the L10h life is used as a limit state. The results indicate a relation between the reliability index and the bearing dynamic rating. However, when the actual parameters from the manufacturer are used, the TRB shows higher reliability even though its damage equivalent load is higher across the wind speed range