Planetary Gear Train Research Articles

A Synthesis Method of Open-Chain Coupled Serial Linkage Mechanism Fusing Trajectory and Posture

In order to meet the motion characteristics requirements of multi-objective fusion of execution components, a synthesis method of open-chain coupled serial linkage mechanism fusing trajectory and posture is proposed. According to periodic change characteristics of the execution component trajectory and posture of the linkage mechanism, the motion characteristics equation including trajectory and posture information is established by using Fourier series. The harmonic parameters of the link trajectory and posture are calculated according to the principle of discrete Fourier transform. The complex vector theory is applied to determine the functional relationship between the harmonic parameters of the trajectory and posture and the independent variable of the linkage mechanism, and furthermore the motion synthesis equation of the open-chain linkage mechanism fusing trajectory and posture information is established. The linkage mechanism parameters are calculated using Mathcad Prime software. The single-degree-of-freedom open-chain coupled serial linkage mechanism fusing trajectory and posture information is obtained by using a noncircular gear planetary gear train to couple the connection points of the linkage mechanism. The correctness of the method is verified through an example.

Influence of eccentricity error on the orbit of a two-stage double-helical compound planetary gear train with different mesh phasing configurations

The eccentricity error is an unavoidable error during the manufacturing and mounting process and has a significant influence on the response of gear systems, especially for planetary gear train. First, based on the most basic quasi-static model, pressure angle, contact ratio and meshing stiffness are considered to be the time-varying parameters due to the eccentricity error. Then, a new quasi-static model of a two-stage compound planetary gear train with eccentricity error is established, and the accuracy of the established model is verified by analyzing the orbit result of healthy gear. Furthermore, the influence of eccentricity error on the response in the time-domain (orbit) under various error combinations is studied and discussed. Finally, it is found that the orbit of the component with eccentricity error is very different from that without eccentricity error, and the formation law of orbit for gear with eccentricity error is revealed in this paper. The results of the quasi-static model could provide a fundamental understanding to the dynamic model for the studied compound planetary gear train.

Service Performance Optimization and Experimental Study of a New W-W Type Non-circular Planetary Gear Train

To address the vibration problem in traditional W-W-type non-circular planetary gear trains during operation, this study proposes two new combinations of W-W-type non-circular planetary gear trains. The study focuses on analysing the transmission error and improving service performance. By utilizing the conjugate theory and the coordinate transformation theory, an accurate mathematical model for non-circular gears is derived. The transmission error models for the two combination forms of the non-circular planetary gear train are established using the incremental meshing line method. The analysis also examines the influence of eccentricity on the transmission error. Kinematic analysis of the multi-body dynamics model confirms that the new W-W type non-circular planetary gear train, formed by combining non-circular gears and cylindrical gears, exhibits superior transmission performance. Furthermore, a test analysis is conducted on the roller pumping unit test platform and the indicator diagrams of the pumping unit under various working conditions are obtained. The study concludes that the optimal matching mode for the sucker rod counterweight and motor frequency of the reversing device of the pumping unit is 20 kN and 20 Hz, and the dynamic balance of the pumping unit load can be achieved by adjusting the motor frequency.

Consideration of Power Transmission Characteristics in a Micro-Gear Train.

Characteristics related to power transmission in the micro-domain, based on dry rolling contact of the gears, were investigated using a 3D-printed gear train with a pitch circle diameter of 84 µm in order to experimentally compare the power transmission efficiency in the macro- and micro-domains. For a basic gear train with two intermeshing gears, it was shown that the gear train in the micro-domain was capable of transmitting power to the same extent as in the macro-domain. However, in gear trains with complex power transmission paths, assuming a planetary gear train with multiple meshing gears, it has been shown that the power transmission characteristics of micro-domain gears differ from those in the macro-domain. The use of gear trains in the micro-region necessitates consideration of the loss of transmitted torque due to contact between tooth surfaces, which is unique to the micro-region and different from its use in the macro-region.

Compound Fault Characteristic Analysis for Fault Diagnosis of a Planetary Gear Train

The carrier eccentricity error and gear compound faults are most likely to occur simultaneously in an actual planetary gear train (PGT). Various faults and errors are coupled with each other to generate a complex dynamic response, which makes the diagnosis of PGT faults difficult in practice. In order to analyze the joint effect of the error and the compound faults in a PGT, a carrier eccentricity error model is proposed and incorporated into the TVMS model by considering the time-varying center distance, line of action (LOA), meshing angle, and contact ratio. Then, the TVMS of the cracked gear is derived based on the potential energy method. On this basis, the dynamic model of a PGT with both the carrier eccentricity error and compound gear cracks as internal excitations are established. Furthermore, the meshing characteristics and dynamic responses of the PGT are simulated to investigate the compound fault features. A series of experiments are conducted to further analyze the influence of the compound fault on the vibration response. The relevant conclusions can provide a reference for the compound fault diagnosis of a PGT in practice.

An innovative transmission mechanism applicable to variable speed wind turbines

An innovative transmission mechanism, named as independently controllable transmission (ICT), is proposed inthis study. While being applied to the variable speed windturbines, the proposed ICT mechanism can transmit a steady-speed output, which is independently manipulated by acontroller and completely not affected by the fluctuant speed ofthe rotor, to the generator to generate the electric power withconstant frequency.The ICT mechanism is fundamentallycomposed of two sets of planetary gear trains and two sets oftransmission-connecting members. Two prototypes of the ICTmechanisms are assembled to examine their kinematicalcharacteristicsandtodemonstratetheirfeasibilityinengineering applications.

Planetary Gearbox Design and Development using Additive Manufacturing

Modern manufacturing technology is dominated by additive manufacturing due to its simplicity, precision, time and material savings, and flexibility in design. The purpose of this study is to propose and print a 3D model of planetary gear trains since these gear trains are more efficient than conventional gear trains and have many advantages. A planet gear trains must have collinear input and output axes in order to achieve compact space requirements. Using even spacing between the planets in a gear train allows both static and dynamic forces to be balanced. It is also possible for multiple planets to produce high torques. Finally, it is capable of providing a wide range of speeds. The printed model performed exceptionally well when it came to performance, and it can be used for both educational and industrial purposes, exhibiting the ability to withstand a high level of stress. The current paper demonstrated the process of 3D printing and the challenges involved in printing planetary gear trains, as well as possible solutions to these challenges. Finally, tolerances were reported as 0.5 mm on the final CAD model, and 0.15 mm on the last updated results.

Application of Two-Carrier Planetary Gear Trains to Shifting Gearboxes

Application of Two-Carrier Planetary Gear Trains to Shifting Gearboxes

Analysis of the Shifting Capabilities of Planetary Gear Trains with Coplanar Planet Gearsets

Analysis of the Shifting Capabilities of Planetary Gear Trains with Coplanar Planet Gearsets

Effects of Macro-Pitting Fault on Dynamic Characteristics of Planetary Gear Train Considering Surface Roughness

The planetary gearbox plays a vital role in a wide range of mechanical power transmission systems, including high-speed trains, wind turbines, vehicles, and aircraft. At the same time, the planetary gear train inside the gearbox is regarded as the most susceptible to failure in the entire transmission system. To analyze the influence of surface roughness on the dynamic characteristics of the planetary gear train, a dynamic modeling method based on fractal theory is proposed. Firstly, the tooth surface contact model was established based on the W-M fractal function, and the time-varying mesh stiffness (TVMS) of the planetary gear train was calculated under healthy and tooth macro-pitting. Then, the lumped-parameter method is introduced to construct a planetary gear train translation-torsion dynamic model that comprehensively considers TVMS and tooth backlash. The vibration acceleration signals of the planetary gear train under different macro-pitting states and surface roughness are simulated and calculated, allowing a quantificative analysis of the influence of surface roughness on system vibration response. Finally, the correctness of the model for the planetary gear train is verified by experiments. The results show that compared with the planetary gear train modeling method based on Hertz contact theory, the root mean squared error of the vibration signal of this work under a macro-pitting fault state is reduced by 8.7%, further improving the reliability of the model.

Automatic configuration analysis method of planetary gear automatic transmission

Planetary gear trains (PGT) with the aim of achieving multiple speed ratios are widely used in automatic transmission (AT). A fast configuration analysis method is of significance for improving the efficiency of AT design, and it is essential to study the automatic configuration analysis method for AT. For this purpose, the AT configuration is represented by a matrix model, which includes the structural matrix of PGT and shifting elements (SEs) matrix. Based on the proposed matrix representation, the speed relation and torque relation matrices of AT are automatically derived to analyze the kinematics and dynamics. Five performance indexes of AT configuration, specifically transmission ratio, rotation speed of components, torque transmitted by SEs, power flow, and transmission efficiency, are automatically calculated through the analysis result. The entire analysis process can be completed in 1 s on the computer. The proposed matrix model offers a unified representation for the configuration of AT derived from different synthesis algorithms. It facilitates rapid automated configuration analysis and performance evaluation, thereby positively influencing the design of automatic transmissions. Furthermore, the matrix model can be applied to the configuration synthesis of AT.

A multidirectional pendulum kinetic energy harvester system for low-power appliances in new energy buses

Wireless sensors play a crucial role in vehicle operations. The effective energy harvesting for self-powering these sensors has emerged as a critical area of interest in recent years. This paper presents a multidirectional pendulum kinetic energy harvester system (MP-KEHS) designed to power low-power sensors in vehicles. The MP-KEHS consists of four main components: an energy capture module, a motion transfer module, an energy conversion module, and an electric energy storage module. The energy capture module, comprising a mass ball and a turntable, captures omnidirectional inertial kinetic energy during vehicle acceleration, deceleration, and turning. In the motion transfer module, a one-way gear module converts the multidirectional rotations of the energy capture module into unidirectional rotations, while the planetary gear train enables speed coupling during simultaneous vehicle acceleration and turning. The energy conversion module utilizes a generator to transform rotational kinetic energy into electric energy. The electric energy storage module stores the electric energy in a supercapacitor after passing through a voltage regulator circuit, providing power to low-power devices. Using of multi-body dynamics software and Simulink, the swing angle of the mass ball was determined under four real driving cycles. Experimental results demonstrated that the average output power of the MP-KEHS reached 116.8 mW. Charging the capacitors of 220 μF, 470 μF, and 1000 μF from 0 V to 1 V takes 8 s, 24 s, and 93 s, respectively. Finally, the MP-KEHS was applied to a bus on the Liaocheng University campus, achieving an average output power of approximately 176 mW, which satisfied the power requirements of the sensors. These findings indicate that the MP-KEHS effectively harnesses the vehicle's otherwise wasted inertial energy, enabling wireless sensor self-powering.

Iterative singular value decomposition-based in-band denoising approach with envelope order analysis for sun gear fault diagnosis of planetary system under varying speed

The vibration signal of the planetary gear train is easily disturbed by the background noise, so the measured signal is complicated. In order to accurately extract the fault features, the resonance method has been widely used. However, even if the optimal resonance frequency band is found, the in-band noise still exists, so it is necessary to study an effective in-band denoising method. In this paper, an in-band denoising method based on Iterative Singular Value Decomposition (ISVD) is proposed for the fault diagnosis of the secondary sun gear of a planetary gear train, combined with the envelope order spectrum analysis. This method uses the enhanced Wavelet Packet Transform Spectral Kurtosis (WPTSK) to determine the best frequency band for the signal, and uses the ISVD method to realize the signal denoising. It sets a threshold to avoid the destruction of the useful information caused by the excessive iteration, and uses the relationship between the singular values and frequency components to reconstruct the denoised signal. Finally, the signal is converted to the fault characteristic order domain by resampling to identify the fault type of the sun gear from the envelope order spectrum. The simulation and experimental results show that compared with the Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD), the ISVD can effectively suppress the in-band noise and more accurately extract the fault characteristic order of the secondary sun gear under varying speed.

Metamaterial design and continuously adjustable mechanical properties based on novel planetary gear trains

Mechanical metamaterials have been pursuing as valuable properties attribute to the unique internal architecture, but are generally limited to the predetermined properties after manufacturing, resulting in the inability to continuously change the properties during application. Aiming for the continuously adjustable property under environments with high reliability requirements, this research developed two types of mechanical metamaterials based on planetary gear train. The principle of continuously adjustable mechanical property and dynamic characteristics of metamaterial based on planetary gear train is researched though a theoretical model of curved beam under varying radial load. Further, mechanical metamaterials based on double-layers planetary gear (DLPG) train and Ravigneaux planetary gear (RPG) train are designed. The compressive elastic modulus, shear modulus, and amplitude-frequency response are calculated and investigated with finite element simulation. The results, with an adjustable range respectively within 9–15 times and 2–3 times in compressive elastic modulus of and shear modulus, show a good agreement between the theoretical and simulated results, and illustrate the adjustability and reliability of the mechanical metamaterials based on planetary gear train. Finally, the potential configurations and applications of metamaterial based on planetary gear train are presented.

Design and Analysis of Mechanisms of 7-, 8- and 9-Speed Automatic Transmissions for Vehicle Powertrains

As the core device of engine-driven vehicle powertrains, the automatic transmission (AT) can obtain different output torques and speeds. Designing new mechanisms is the foundation for developing innovative ATs. This paper proposes an innovative design method for 7-speed, 8-speed and 9-speed AT mechanisms based on fractionated planetary gear trains (PGTs) and investigates the performance analysis of the AT mechanisms. Firstly, the detection of symmetric vertices in the PGT graph is studied, and a method for the topologic synthesis of 11-link 2-degree-of-freedom (DOF) fractionated PGTs is proposed. Secondly, the innovative design of 7-speed, 8-speed and 9-speed AT mechanisms is explored, leading to the discovery of two novel 7-speed AT mechanisms, three novel 8-speed AT mechanisms and four novel 9-speed AT mechanisms. Finally, the performance analyses of kinematics, torque, power flow and transmission efficiency of the AT mechanisms are conducted, and AMESim (Simcenter Amesim 2020.1) software is utilized to simulate speed ratios and transmission efficiencies of the AT mechanisms. The analysis and simulation results demonstrate that the nine novel AT mechanisms obtained in this study exhibit excellent overall performances. The speed ratios of each AT mechanism are reasonable, the step ratio is between 1.1 and 1.8, and the transmission efficiency exceeds 0.95. There is no cyclic power, or the cyclic power values are within an acceptable limit.

Meshing characteristics and dynamic characteristics of planetary transmission system with new tooth-type flexible ring gear

As one of the important components of the planetary transmission system, dynamic meshing characteristics of ring gear directly affect the performance of planetary transmission system load sharing and dynamic load factor. With the help of the flexibility of ring gear, the planetary gear system with flexible ring gear (FRG) can compensate for the uneven transmission torque of each branch caused by the machining error and installation error and improve the system's load sharing and dynamic load performance. An L-shaped FRG was developed in Italy to improve the traditional ring gear and was used in the latest AW101 helicopter with good feedback. By increasing the ring flexibility, the load distribution between planetary gears is more uniform, and the load-sharing performance of the system is significantly improved. Tooth wear and fracture caused by uneven load distribution can be improved. However, the structure has problems such as unbalanced loading, strength weakening, and stress concentration. In this article, the FRG's meshing and structural characteristics are analyzed in detail by constructing the parametric finite element model. Differences, advantages, and disadvantages of FRG and traditional ring gear are compared. A new type of tooth-type FRG is proposed. It has excellent structural flexibility meshing characteristics of tooth surface and avoids generating stress concentration. It improves the planetary gear train's load-sharing performance and overcomes tooth surface unbalanced loading and large amplitude fluctuation of loaded transmission errors.

A New Tree Graph Method for Synthesizing Planetary Gear Trains of Vehicle Powertrains

The function of vehicle powertrains is to transmit power from the power source (engine or electric machine) to the output shaft. Different torques and speeds of the output shaft are achieved through the structure of planetary gear train (PGT). The performance of a powertrain depends on the choice of topological structure of the PGT to a large extent. The topological synthesis of PGTs is of great significance to the design of new powertrains. A tree graph method for the topological synthesis of PGTs is proposed in this paper. Firstly, the rules for generating (N + 1)-link tree graphs from N-link tree graphs are proposed. Then, the method for adding geared edges into the tree graph is presented, and topological graphs of 1-DOF PGTs are directly synthesized from their tree graphs. A unified algorithm applicable for both open-loop and closed-loop graphs is proposed to eliminate isomorphic tree graphs and topological graphs of PGTs. The complete atlases of tree graphs and topological graphs of 1-DOF PGTs with three to ten links are obtained for the first time.

Nonlinear dynamic modeling and global instability analyses of planetary gear trains considering multi-state engagement and tooth-contact temperature effects

Nonlinear dynamic modeling and global instability analyses of planetary gear trains considering multi-state engagement and tooth-contact temperature effects

Topological Graph Representation and Configuration Synthesis for Power-Split Hybrid Transmissions of Multi-Planetary Gear Trains

Abstract Power-split hybrid transmissions are the core components of power-split hybrid electric vehicles (HEVs), and the quest for a more energy-efficient and higher-performing power-split hybrid transmission has long been the focus of study. In contrast to previously published methodologies, this paper proposes a novel approach for directly synthesizing power-split hybrid transmissions that makes use of the results of previously synthesized planetary gear trains (PGTs) rather than necessitating a resynthesis of their PGTs. A new topological graph that can construct a bridge between the PGTs and power-split hybrid transmission has been developed, reducing the computational complexity in the synthesis process. The new topological graph is obtained by adding topological characteristics of the power-split hybrid transmission to the PGT graph. A standard structure matrix is proposed to further screen out all the isomorphic configurations. The present method can generate various types of multi-PGT hybrid transmissions while avoiding mechanical structural interference. The design process of configurations for power-split hybrid transmission with three-column PGTs (3-PGT) is used as an example to prove the rationality of the method.

Study on nonlinear dynamics characteristics of dual speed dual clutch transmission system based on bond graph

The variable speed transmission system employs compound planetary gear trains and clutches. Compared to traditional aviation transmission systems, the added control parts in the variable transmission system result in a stronger coupling between components and more complex dynamic response characteristics. Modeling using the central mass method is complex and abstract. This study proposes a bond graph-based method for modeling and analyzing the dynamic behavior of the variable transmission system. The transmission system is divided into multiple component-level real-time dynamic models, and obtain a nonlinear multi-energy domain shift dynamic models based on energy flow paths coupling. The mathematical model is numerically solved using the Runge-Kutta method. Simulation results show that there is a delay in the speed response during the shifting process. Further analysis reveals that this “give and take” phenomenon is related to the mechanical structure and passive working principle of the one-way clutch. Subsequently, the time-domain response of the output speed under the hydraulic loading characteristic curves of linear, exponential, S-shaped, and composite functions, as well as the clutch torque, were studied. The impact of different hydraulic loading durations based on the exponential curve on component speed and torque was also analyzed. The simulation results provide a theoretical basis for designing low-shift impact, high-reliability, and high-performance variable transmission systems.