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This paper aims at investigating the effects of tooth profile modification (TPM) on the dynamic response of planetary gear train (PGT). A numerical model is carried out to calculate two major excitation sources of PGT, time-varying mesh stiffness (TVMS), and transmission errors (TEs). On this basis, a linear time-varying dynamic model of a PGT considering TVMS, TEs, and TPM is developed. Dynamic deviation factor is further introduced to describe the dynamic response of the PGT. In this paper, TPM is only applied to the external meshes firstly. Effects of TPM parameters, such as amount of TPM, normalized modification angle, and modification curve, on the excitation sources and dynamic response of the PGT are discussed in detail. Subsequently, investigation on the effects of TPM only applied to internal meshes is conducted. Finally, with the aim to obtain the optimal TPM for the minimization of dynamic load of PGT in both external and internal gear meshes, the genetic algorithm (GA) is employed. This research may shed light upon design optimization of PGT with respect to improvement of vibration performance by means of optimized TPM. [ABSTRACT FROM AUTHOR]

The transient variation of electrical parameters makes system loads fluctuate and reduces bearing capacity when the grid voltage dips. This work proposes an electromechanical coupling dynamic model of the wind turbine drivetrain to build a dynamic interconnection between the electric and drivetrain subsystems. The drivetrain subsystem that includes an improved model of the planetary gear stage is developed and validated. This improved model considers the carrier and planet bearing clearances, the connection relationship among the carrier, main shaft, and planets as well as the flexibilities of the main shaft and parallel stage shafts. The influences of the carrier bearing clearances, non-torque load and planet position angle on planet bearing loads are investigated under the low-voltage ride through (LVRT) event. The results indicate that as the LVRT occurs, the planet bearing loads reduce below the minimum requisite with a high, fluctuating system speed; considering the bearing clearances, the impacts occur in the planet bearing in the minimum load zone followed by significant stress variation; the non-torque load suppresses the planet bearing impacts in a limited range of carrier bearing clearance; the planet position angle has a significant effect on the planet bearing impacts because of the asymmetry of load and structure of the planetary gear stage. [ABSTRACT FROM AUTHOR]

A new gear tooth modification model of planetary gear system was established by considering the characteristics of tooth longitudinal crowning modification and tooth profile modification. Using this model, the influences of modification parameters on the time-varying mesh stiffness, transmission error, contact spots and dynamic response of the planetary gear system were analyzed through numerical analysis. The results show that tooth profile modification can effectively restrain the mesh stiffness sudden variation in the single and double tooth alternation of both the internal and external mesh pairs, and significantly decrease the transmission error fluctuation. However, longitudinal crowning modification has no marked influence on mesh stiffness sudden variation or transmission error fluctuation. The tooth profile modification can significantly reduce the sudden variation of tooth surface load during gear mesh course. Longitudinal crowning modification can make the tooth surface load evenly distributed in tooth width direction. When the external meshing pairs are modified at the tooth profile individually, the magnitude values of main response resonance peaks of internal meshing pairs have a great reduction, but those values of external meshing pairs change slightly. In the case of tooth profile modification of the internal meshing pairs, the phenomenon is reversed. By contrast with tooth profile modification, longitudinal crowning modification has little influence on the resonance peaks of internal and external meshing pairs. [ABSTRACT FROM AUTHOR]

To investigate the dynamical load sharing behaviors of multi-floating components in the heavy load planetary gear system, a multi-floating planetary gear system that includes a floating central component and a quasi-floating planet flexible supporting pin is employed. Then a 21 degree of freedom lumped parameters dynamical model of this system is presented to study the dynamical load sharing behaviors. Some influencing factors, such as supporting stiffness, positions error of sun or carrier, and external input load are analyzed on the dynamical load sharing of the planetary gear system with multi-floating components. The results demonstrate that the load sharing condition of the system is best when both the sun gear and planet gears are multi-floating at the same time. When the planet gear position errors remain constant, reducing the flexible pin stiffness of planet gear or increasing external input load can effectively improve the load sharing. These conclusions are verified by the relevant experiments. [ABSTRACT FROM AUTHOR]

The dynamic behavior of a single-stage planetary gear set with helical gears of multishaft automotive automatic transmissions has been studied, in which one component of the planetary gear set is imposed by additional external vertical and axial loading from countershaft gear pair in addition to the moment. Under these combined loading conditions, the contributions of the deflections of the ring gear and the carrier cannot be neglected. A three-dimensional nonlinear time-variant dynamic model considering not only the transverse, torsional, axial, and rotational motions of the gears but also the elasticity of the mounted shafts has been developed by combining the lumped parameter method with finite element method. The natural modes and the forced vibration responses due to static transmission errors have been obtained. The proposed dynamic model is employed to describe the effects of the combined external loading condition and positioning on the dynamic behavior of a four-planet system. [ABSTRACT FROM AUTHOR]

Motor current signature analysis (MCSA) is a useful technique for planetary gear fault detection. Motor current signals have easier accessibility and are free from time-varying transfer path effects. If the fault symptoms in current signals are well understood, it will be more beneficial to develop effective current signal processing methods. Some researchers have developed mathematical models to study the characteristics of current signals. However, no one has considered the coupling of rotor eccentricity and gear failures, resulting in an inaccurate analysis of the current signals. This study considers the sun gear failure of a planetary gearbox and the eccentricity of the motor rotor. An improved induction motor model is proposed based on the magnetomotive force (MMF) to simulate the stator current. By analyzing the current, the modulation relationships of gearbox meshing frequency, fault frequency, power supply frequency, and gear rotating frequency are obtained. The proposed model is validated to some extent using experimental data. [ABSTRACT FROM AUTHOR]

Flexible pins eliminate the need for straddle mounting, and therefore enable the maximum possible number of planets to be used for any particular epicyclic ratio of power transmission systems. Having more planet gears will significantly increase the input torque density. In this type of design, the pin stiffness and position tolerances are important parameters as they affect the dynamic performances significantly. The present study addresses this issue by modeling, the design of double cantilevered flexible pin, and analyzing the contributions of pin stiffness and misalignment applying the lumped parameter approach. The proposed model formulates the coupled lateral-torsional dynamic response of a planetary spur gear, including the effects of mesh stiffness and phasing as a function of pin error. The resultant equations of motion are applied to examine the effects of pin stiffness and position errors on the natural modes and structural dynamic response. The effects of pin stiffness on deviation of the tooth contact forces of the sun-planet and ring-planet gear pairs are analyzed to understand the relationship between mesh characteristic and input speed variations. The calculated supporting forces of the planet gear are examined to understand the load sharing characteristic due to pin errors, pin stiffness and input load of the power transmission system. [ABSTRACT FROM AUTHOR]

A Ravigneaux planetary gear set (RPGS) system with an unloaded floating ring gear is studied in this paper. Aiming at investigating the three-dimensional vibration response of the long planet and the dynamic load on the floating ring gear, a flexible-rigid coupling dynamic (FRCD) model is proposed by coupling the condensed substructure of finite element (FE) flexible bodies with rigid dynamic model. Relative positions of different force elements are taken into consideration, as well as time-varying mesh stiffness and gear backlash. Based on this model, the effect of sun gear positions on the dynamic response of the long planet is performed and the mechanism for the vibration of the floating ring gear is revealed. The results show that the bearing force of the long planet varies nearly linearity with sun gear positions, and dynamic loads on the floating ring gear are induced by gear mesh excitations and carrier vibrations, while the former affects impact amplitudes and the latter influences impact frequencies. A further investigation is conducted on the effects of gear backlash and support stiffness, and it is indicated that increasing the support stiffness of the floating ring gear can reduce its dynamic load significantly. [ABSTRACT FROM AUTHOR]

• A comprehensive dynamic model of PGS is established for planet bearing dynamics. • Planet bearing dynamics are studied under RRC, especially for roller-cage impact. • A trap of the roller into the cage pocket under RRC is observed and clarified. • Influences of clearances and revolution speed on bearing dynamics are analyzed. The planet bearing has become the component most likely to fail in the planetary gear set (PGS), especially for the revolution-rotation coupled (RRC) condition. However, the dynamics of the planet bearing in the PGS are still not revealed yet. To address it, this paper proposes a comprehensive dynamic model of the PGS, in which the gear mesh and roller contact excitations, as well as the centrifugal and Coriolis effect, are considered. On this basis, the dynamics of the planet bearing are investigated, particularly for the roller-cage contact. The results show that significant impacts between the roller and the cage would occur under RRC conditions and increase with the revolution speed. The most critical factor determining the roller-cage impact force is the revolution centrifugal force of the roller. The radial and cage pocket clearances show less effect but can still influence the roller-cage impact force. [ABSTRACT FROM AUTHOR]

• A novel dynamic modeling method for multistage gear transmission system considering platform motion is proposed. • Additional parametric excitations due to platform motion are deduced. • Effects of platform motion on dynamic transmission error (DTE) are investigated. • Dynamic responses with multiple combinations of platform motions are compared. For floating offshore wind turbines, platform motion is large under the impact of waves and currents leading to increasing system vibration and should be analyzed in the design phase to improve the survivability of wind turbine. However, most of the wind turbine drivetrain models lack the attention to the dynamic response caused by platform motions. In this work, a novel dynamic modeling method considering platform motion is proposed, which is suitable for any combinations of the planetary and parallel gear stages. A dynamic model of the drivetrain with platform motions is developed, which includes the concentrated mass components (CMCs) with the fixed-shaft and orbital revolution motions, the flexible gear meshes and bearings as well as the flexible shafts. The vibration modes of the drivetrain are investigated. Three kinds of platform motions are determined and applied to the drivetrain. The effects of these platform motions on the dynamic behaviors of the drivetrain are studied in-depth. The simulation results indicate that the platform motions not only introduce additional excitation frequencies to the drivetrain and increase system vibration but also increase the risk of the resonance. The proposed method can be utilized to guide the modeling and design of an offshore wind turbine drivetrain. [ABSTRACT FROM AUTHOR]

• An analytical model is developed to predict planet gear bearing load distribution. • Effects of planet gear parameters on bearing loads and service life are analyzed. • An optimal planet rim thickness achieving the maximum bearing life is obtained. • Effects of gear helix angle and bearing clearance on optimal thickness are studied. With the development of planetary gear trains (PGTs), more planet gears are designed as thin-walled structures to reduce the weight and accommodate the larger bearings so that the transmission system can achieve higher power density, improved reliability, and better compactness. However, this would make the planet gear fragile, where it could easily deform and thus influence the load distribution on the bearing. To address this problem, this study investigates the effect of the planet gear rim deformation on the bearing load distribution and its service life. By incorporating the Timoshenko three-dimensional (3D) curved beam theory and the transfer matrix method, a novel analytical model was developed that computes the planet gear rim deformation and the bearing loads. The validation of the model was conducted using a finite element (FE) simulation. Based on the proposed model, the internal states, including forces and deformations, of the planet gear rim along the circumference were examined, and the effects of the planet gear parameters and the bearing clearance on the bearing load distribution and service life were analyzed. The results show that the deformation of the planet gear rim has a significant effect on the contact load, pressure distribution, and service life of the bearing. On this basis, an optimal rim thickness that gives the maximum bearing life was obtained for different planet helix angles and bearing clearances, which can provide design guidance for the planet gear bearing with higher reliability. [Display omitted] [ABSTRACT FROM AUTHOR]

• A matrix-based method is proposed to search configurations of planetary gear sets. • Inherent and switchable connection matrix are defined for configuration structure. • A detection method of mechanical structural interference is developed. • Detection and optimization are conducted for desired transmission and step ratios. • Valid configurations are obtained with little work and experience from engineers. Better dynamic and economic performance of vehicles can be produced by increasing gears of the planetary gear trains (PGT), but a more complex structure would be required. Therefore, this paper proposes a matrix-based method for searching PGT configurations. Based on the basic connection matrix, the inherent connection matrix and switchable connection matrix are firstly established to describe the configuration structure. Then, the embedding process of shaft connection is simulated with three matrices for valid configurations, which have no mechanical structural interference. Finally, to achieve the desired transmission ratios and step ratios, detections are firstly conducted for the simple shift logic, and the optimization process of the stationary gear ratios is presented. Through this method, valid configurations can be obtained according to several design requirements without additional work from engineers. Besides, this method can also serve as a guide for both theoretical designs and practical applications of PGTs. [Display omitted] [ABSTRACT FROM AUTHOR]

With the pressing demand of reducing fuel consumption and improving driving performance, automatic transmissions (ATs) tend to have a wider ratio spread and more speeds. However, it is difficult to achieve a compact design by using only planetary gear sets (PGSs) or only parallel-axis gear pairs (PGPs). In this paper, we propose a novel multi-speed AT characterized by a combination of PGSs and PGPs on two parallel axes. All feasible clutching sequences are synthesized through a systematic procedure. Results reveal that we can obtain a nine, eleven or thirteen-speed clutching sequence by tuning the stationary ratios of PGPs. A computational model based on genetic algorithm (GA) is established to optimize the gear ratios. Within the constraints of stationary ratios and single transition shift, an optimal solution is found with a wide ratio spread. Furthermore, a matrix method is developed to analyze transmission kinematics and kinetics, which is especially suitable for computer-aided analysis of complex four degrees-of-freedom (DOFs) transmissions. Key parameters such as power flow, efficiency and clutching sequence of the proposed AT are evaluated and compared. This research may shed light upon synthesis, design and analysis of complex ATs with a wider ratio spread and more speeds. [ABSTRACT FROM AUTHOR]

• A dynamic FEM model is proposed for the whole Ravigneaux planetary gear set. • A transient high-frequency acceleration and deceleration impact is found in the floating non-loaded ring gear. • Large stress distribution is found in the middle zone between two either internal tooth roots or external spline tooth roots. • The vibration characteristics of the floating ring gear will be the excitation source for its matching clutch friction plates. When analyzing the dynamic characteristics of Ravigneaux planetary gear sets, the vibration of loaded parts is often paid more attention than non-loaded part since that it is theoretically believed to transfer no power. However, a failure problem is found that the non-loaded part does vibrate seriously and so causes the crack in the middle zone between two spline tooth roots when driving the clutch friction plates to rotate synchronously. The finite element method is applied to model the whole Ravigneaux planetary gear set with two ring gears. The simulated result proves that the floating non-loaded ring gear burdens transient high-frequency acceleration and deceleration impact from planet gears. The sectional stress distribution is analyzed for the floating ring gear under the impact. The middle zone between two internal tooth roots has large stress, and the same characteristics exists for the external spline teeth. This vibration of the floating non-loaded ring gear is the final excitation source for the clutch friction plates driven by the floating ring gear. This work is of high value for controlling the vibration level of the floating ring gear and solving the fracture fatigue problem of its matching friction plates in Ravigneaux planetary gear sets. [ABSTRACT FROM AUTHOR]