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Journal articles on the topic 'Planetary gear systems'
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1
Singh, Avinash. "Influence of Planetary Needle Bearings on the Performance of Single and Double Pinion Planetary Systems." Journal of Mechanical Design 129, no. 1 (March 20, 2006): 85–94. http://dx.doi.org/10.1115/1.2359472.
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Planetary gears are widely used in automotive and aerospace applications. Due to demands for greater power density, these gearsets often operate at extremely high stress levels. This has caused system level influences once considered secondary to become critical to the success of planetary gears. One such system level effect that has been largely overlooked is the influence of support structures like planetary needle bearings. There are interactions between the gear distributed loads and the resulting bearing loads and deflections that have implications for both gear and bearing designs. Also, double pinion planetary arrangements are increasingly becoming common. There are still greater interactions between the gear and bearing components in double pinion planetary arrangements. In this paper, we will examine the influence of the bearing deflections (tilt) on the gear load distribution and contact pattern. We will also show the influence of distributed gear loads on the bearing loads (moments) and deflections (tilts). Both, single and double pinion planetary arrangements will be considered. It will be shown that the tilting stiffnesses of the needle bearings have a major influence on gear contact pattern and consequently on contact and bending stresses. It will also be shown that the double pinion planetary arrangement is more likely to result in off-centered loading. Parametric studies will be performed to show the influence of a few design parameters. Theoretical derivations will be validated by numerical simulations. A system level gear analysis model will be used to illustrate the issues involved and quantify the results.
2
Yang, Tian Fu, and Shao Ze Yan. "Dynamic Simulation of Planetary Gearbox." Key Engineering Materials 584 (September 2013): 220–24. http://dx.doi.org/10.4028/www.scientific.net/kem.584.220.
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Planetary gears are the most popular transmission machinery in large reduction ratio circumstances, which is because of the advantages of compactness, co-axial and high power efficiency. Accurate dynamic model is crucial when planetary gears are used in precise positioning and controlling systems. A dynamic model considering gear backlash and bearing compliance is established in this work. A typical planetary gearbox is simulated with the model. The results prove the validity of the model and demonstrate that gear backlash and bearing compliance have significant influence on planetary gear transmission.
3
Chang, Le Hao, Geng Liu, Li Yan Wu, and Zhong Hong Bu. "Research on Vibration Influence Chart of Planetary Gear Systems." Applied Mechanics and Materials 86 (August 2011): 747–51. http://dx.doi.org/10.4028/www.scientific.net/amm.86.747.
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The common definition of vibration influence chart is proposed in this study. A 46 degree-of-freedom time-varying dynamic model with coupled translation-rotation effect is developed to simulate the vibration of an encased differential planetary gear system using lumped mass method. With the dynamic load and the acceleration on gears and bearings as references, the dynamic responses in different load cases are investigated to search the change law of concerned parameters. The parameters considered include mesh stiffness, structure stiffness, gear mass and moment of inertia. The good and poor regions for vibration are evidently presented in figures, which is convenient to conduct the parameters design of planetary gear systems.
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Ambarisha, Vijaya Kumar, and Robert G. Parker. "Suppression of Planet Mode Response in Planetary Gear Dynamics Through Mesh Phasing." Journal of Vibration and Acoustics 128, no. 2 (February 10, 2005): 133–42. http://dx.doi.org/10.1115/1.2171712.
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This work analytically derives design rules to suppress certain harmonics of planet mode response in planetary gear dynamics through mesh phasing. Planet modes are one of three categories of planetary gear vibration modes. In these modes, only the plantes deflect while the carrier, ring, and sun gears have no motion (Lin, J., and Parker, R. G., 1999, ASME J. Vib. Acoust., 121, pp. 316–321;J. Sound Vib, 233(5), pp. 921–928). The dynamic mesh forces are not explicitly modeled for this study; instead, the symmetry of planetary gear systems and gear tooth mesh periodicity are sufficient to establish rules to suppress planet modes. Thus, the conclusions are independent of the mesh modeling details. Planetary gear systems with equally spaced planets and with diametrically opposed planet pairs are examined. Suppression of degenerate mode response in purely rotational degree-of-freedom models achieved in the limit of infinite bearing stiffness is also investigated. The mesh phasing conclusions are verified by dynamic simulations of various planetary gears using a lumped-parameter analytical model and by comparisons to others’ research.
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Budzik, Grzegorz, Tadeusz Markowski, Michał Batsch, Jadwiga Pisula, Jacek Pacana, and Bogdan Kozik. "Stress Assessment of Gear Teeth in Epicyclic Gear Train for Radial Sedimentation Tank." Acta Mechanica et Automatica 14, no. 3 (September 1, 2020): 121–27. http://dx.doi.org/10.2478/ama-2020-0018.
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Abstract The paper presents the strength evaluation of planetary gear teeth designed for a radial sedimentation tank drive. A novel type of gear drive, composed of a closed epicyclic gear train and an open gear train with internal cycloidal gear mesh is proposed. Contact stress and root stress in the planetary gear train were determined by the finite element method and according to ISO 6336. The influence of the mesh load factor at planet gears on stress values was also established. A comparison of the results followed. It was observed that the mesh load factor on satellites depends mainly on the way the satellites and central wheels are mounted, the positioning accuracy in the carrier and the accuracy of teeth. Subsequently, a material was selected for the particular design of planetary gear and the assumed load. The analysis of the obtained results allowed assuming that in case of gears in class 7 and the rigid mounting of satellites and central wheels, gears should be made of steel for carburizing and hardening. In case of flexible satellites or flexible couplings in the central wheels and gears in class 4, gears can be made of nitriding steel.
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Zhou, Chi, Qi Wang, Liangjin Gui, and Zijie Fan. "A numerical method for calculating the misalignments of planetary gears." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 233, no. 10 (October 5, 2018): 2624–36. http://dx.doi.org/10.1177/0954407018804114.
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Because misalignments derived from the deflections of transmission systems have significant effects on the load capacity of planetary gears, these misalignments should be accurately considered in the analysis of planetary gears. Here, we develop a new approach for misalignment calculations of cylindrical planetary gears. A nonlinear model of a planetary gear transmission system is built based on the finite element method and nonlinear bearing theory for misalignment calculations that can precisely simulate the structural characteristics and mechanical properties of a planetary gear system. The nonlinear static equation of a planetary system is solved efficiently using the Newton–Raphson method. Gear misalignments of all the planet branches are determined by the results of the system static analysis. The reliability and advantages of the proposed method are discussed via case studies. The effects of including the variation of the planet positions and the nonlinearity of the bearing stiffness on the planetary gear misalignments under different load conditions are studied. The misalignments can be reliably determined using the proposed method for calculating the load capacity of planetary gears.
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Drewniak, Józef, and Stanisław Zawiślak. "Synthesis of Planetary Gears by Means of Artificial Intelligence Approach ‒ Graph-Theoretical Modeling." Solid State Phenomena 164 (June 2010): 243–48. http://dx.doi.org/10.4028/www.scientific.net/ssp.164.243.
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Graph-based modeling of planetary gears was applied in the presented research work for their synthesis. The tailored Hsu and contour graphs were used. Graphs encode the structure (layout) of a planetary gear and upon them - the systems of equations can be generated. These systems enable determination of rotational velocities of planetary gear elements. The method is algorithmic and simple. It allows for an easy comparison of different design solutions and selection of the most appropriate one. The list of the possible modes of operation for an exemplary planetary gear is also provided in the paper.
8
Ding, Hong. "Application of Non-Circular Planetary Gear Mechanism in the Gear Pump." Advanced Materials Research 591-593 (November 2012): 2139–42. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.2139.
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Gear pump is the most commonly used hydraulic component in hydraulic drive system.Volumetric efficiency of the traditional gear pump is low, big flow ripple causes large pressure fluctuations, makes pipes and valves vibration, noisy. The imbalance pressure on gear pump’s gears, shafts and bearings and the large radial load limits its pressure increased. Planetary gear transmission compared with ordinary gear transmission, it has many unique advantages. So the writer on the basis of the combination of proposed non-circular planetary gear pumps and gear pump works discussed the structure and working principle of the pump. The non-circular planetary gear pump with many advantages such as big flow, uniform flow, low noise and so on. It can be widely used in various hydraulic transmission systems.
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Li, Jian Ying, Qing Chun Hu, and Fu Hai Duan. "Vibration Characteristics for Planetary Geared Systems with Plastic Gears." Applied Mechanics and Materials 713-715 (January 2015): 77–84. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.77.
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A torsional dynamic model and testing model for planetary geared systems are established to study the effects on its vibration characteristics as substituting plastic gears for steel ones successively. The dynamic model is solved by using variable step Runge-Kutta method and the vibration testing experiments for four kinds of combined planetary geared systems are carried out under different rotation speed and load torque. The numerical and experimental results show that the high frequency spectra are suppressed effectively as substituting plastic gears for steel ones. The gear mesh dynamic load and vibration intensity caused by the meshing fundamental frequency and side-frequency reduce markedly when the plastic ring and planet gear substitute for steel ones together. The numerical simulations have a better consistency with the experimental results, which verifies the correctness of the conclusions.
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Lee, Bumjoo, Donghan Kim, and Young-Dae Hong. "Differential planetary mechanism of reduction gear for robotic applications." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 5 (February 5, 2017): 799–803. http://dx.doi.org/10.1177/0954406217691071.
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This study proposes a novel planetary gear mechanism composed of normal spur gears. Similar to a harmonic drive system, one pair of gears generates differential angular motion to achieve a high reduction gear ratio. While a harmonic drive system utilizes slightly different number of gear teeth between the flex spline and the circular spline to induce differential motion, a planetary gear mechanism with different gear modules is adopted for this purpose in the proposed system. Since the manufacture of special components like the wave generator and flex spline in harmonic drive system is not required here, the machinability and usability are improved. In addition, the mechanism can be achieved with a flat shape, which is crucial for various applications such as robotic systems. After the basic concept and three-dimensional design are introduced, the prototype system is presented.
11
Liu, Jing, Shizhao Ding, Linfeng Wang, Hongwu Li, and Jin Xu. "Effect of the bearing clearance on vibrations of a double-row planetary gear system." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 234, no. 2 (December 6, 2019): 347–57. http://dx.doi.org/10.1177/1464419319893488.
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The bearing clearance, external torque, and input speed can greatly affect vibrations of the planetary gear system. The double-row planetary gear systems are commonly used in the gearbox of special vehicles, which are the key parts to obtain a larger gear ratio. Although many works have been presented to study those factors on vibrations of the single-row planetary gear system, a few works were focused on vibrations of the double-row planetary gear system with the bearing clearance. To overcome this problem, a multi-body dynamic model of a double-row planetary gear system with six planet bearings and one supported bearing of the sun gear is presented. This model is the main part of a gear box transmission system. The new model is developed for studying the effect of the bearing clearance on the planetary system. The meshing stiffness and damping between the gears are obtained by current methods in the listed references, as well as the contact stiffness and damping in bearings. The liner stiffness and damping model is used. The effects of the bearing clearance, external torque, and input speed on vibrations of the system are analyzed. The results show that vibrations of the ring gear and sun gear decrease with the increment of the external torque and increase with the increment of the input speed. Moreover, a reasonable bearing clearance can be helpful for reducing system vibrations for some mating external torque and input speed conditions. The results can provide some guidance to find new method to reduce vibrations and increase the service life of planetary gear systems.
12
Olanipekun, K. A. "Estimation of a Planetary Gear Mesh Stiffness: An Approach Based on Minimising Error Function." European Journal of Engineering and Technology Research 6, no. 3 (April 30, 2021): 164–69. http://dx.doi.org/10.24018/ejers.2021.6.3.2416.
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The mesh stiffness of gear teeth is one of the major sources of excitation in gear systems. Many analytical and finite element methods have been proposed in order to determine the mesh stiffness of gears especially parallel axis spur gears. Most of these methods are not trivial because they involve complicated analyses which incorporate parameters like gear tooth error, gear spalling sizes and shapes, nonlinear contact stiffness and sliding friction before mesh stiffness can be determined. In this work, a method is proposed to determine the sun-planet and ring-planet mesh stiffnesses of a planetary gear system. This approach involves fitting a relationship between the measured natural frequencies from an experimental modal test and natural frequencies predicted using an analytical model of a planetary gear. This method is relatively easier compared to the existing methods which involve complicated analyses. For this study, the average mesh stiffness estimated is 12.5 MN/m.
13
Olanipekun, K. A. "Estimation of a Planetary Gear Mesh Stiffness: An Approach Based on Minimising Error Function." European Journal of Engineering and Technology Research 6, no. 3 (April 30, 2021): 164–69. http://dx.doi.org/10.24018/ejeng.2021.6.3.2416.
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The mesh stiffness of gear teeth is one of the major sources of excitation in gear systems. Many analytical and finite element methods have been proposed in order to determine the mesh stiffness of gears especially parallel axis spur gears. Most of these methods are not trivial because they involve complicated analyses which incorporate parameters like gear tooth error, gear spalling sizes and shapes, nonlinear contact stiffness and sliding friction before mesh stiffness can be determined. In this work, a method is proposed to determine the sun-planet and ring-planet mesh stiffnesses of a planetary gear system. This approach involves fitting a relationship between the measured natural frequencies from an experimental modal test and natural frequencies predicted using an analytical model of a planetary gear. This method is relatively easier compared to the existing methods which involve complicated analyses. For this study, the average mesh stiffness estimated is 12.5 MN/m.
14
Shuai, Mo, Ma Shuai, Jin Guoguang, Gong Jiabei, Zhang Ting, and Zhu Shengping. "Design principle and modeling method of asymmetric involute internal helical gears." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 1 (February 12, 2018): 244–55. http://dx.doi.org/10.1177/0954406218756443.
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In the field of mechanical engineering, involute helical gears are widely used. Compared with the involute spur gear, helical gears have a high bearing strength, more smooth transmission, less impact and less noise. The internal gear pairs have the features of large transmission ratio, low vibration, low noise and low wear and hence are widely used in planetary gear transmission systems. In order to meet the requirements of high strength, high speed of the modern gear transmission systems, a new type of asymmetric involute internal helical gears is designed based on conventional involute gears. This paper discusses the gear shaper cutter modeling for machining this new gear, analyzes the formation principle of asymmetric tooth profile and establishes a three-dimensional modeling by SolidWorks. Through MATLAB simulation, pressure angle, tooth number, coefficient of displacement and contact ratio of conventional and asymmetric gear are compared and analyzed. Using ANSYS, two types of gears are compared on strength in order to demonstrate superiority of asymmetric tooth and further study about the asymmetric internal helical gears.
15
Zhang, Huibo, Chaoqun Qi, Jizhuang Fan, Shijie Dai, and Bindi You. "Vibration Characteristics Analysis of Planetary Gears with a Multi-Clearance Coupling in Space Mechanism." Energies 11, no. 10 (October 9, 2018): 2687. http://dx.doi.org/10.3390/en11102687.
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Multi-clearance is the main cause for the performance and reliability decline of complicated mechanical systems. The increased clearance could induce contacts and impacts in joints, and consequently affect control accuracy. A nonlinear dynamic model of planetary gears with multi-clearance coupling is proposed in the current study to investigate the mechanism of influence of clearance on the dynamic performance. In addition, the coupling relationship between radial clearance and backlash is integrated into the multi-body system dynamics. The vibration characteristics of planetary gears with the changes of rotational velocity, clearance size and inertia load are explored. The numerical simulation results show that there are complex coupling relations in planetary gear systems, due to the multi-clearance coupling. The phenomenon of system resonance may occur with the changes of rotational velocities and clearances’ sizes. Multi-clearance coupling can significantly increase the resonant response of planetary gear systems in empty-load or light-load states.
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Vintilă, Daniela, Laura Diana Grigorie, and Alina Elena Romanescu. "Dynamic Analysis of Planetary Gear Reducer." Applied Mechanics and Materials 880 (March 2018): 87–92. http://dx.doi.org/10.4028/www.scientific.net/amm.880.87.
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This paper presents dynamic analysis of a three stage planetary gear reducer for operate a tower crane. Ordinary and planetary gears have been designed respecting the coaxial, neighboring and mounting conditions. Harmonic analysis has been processed to identify frequency response for displacements, strains and deformations. The aim of the study was to determine critical frequencies to avoid mechanical resonance phenomenon. The obtained results are based on the superposition method for solving the systems of differential equations resulting from the analysis with finite elements.
17
Xuejun, Li, Jiang Lingli, Hua Dengrong, Yin Daoxuan, and Yang Dalian. "An Analysis of the Gear Meshing Characteristics of the Main Planetary Gear Trains of Helicopters Undergoing Shafting Position Changes." International Journal of Aerospace Engineering 2021 (July 30, 2021): 1–12. http://dx.doi.org/10.1155/2021/9965818.
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The complex three-shaft three-reducer structural designs of helicopter transmission systems are prone to changes in the relative positions of shafting under the conditions of main rotor and tail rotor loads. These changes will affect the transmission characteristics of the entire transmission system. In this study, the planetary gear trains of helicopters were examined. Due to the fact that these structures are considered to be the most representative structures of the main reducers of helicopters, they were selected as the study objects for the purpose of examining the meshing characteristics of planetary gear trains when the relative positions of the shafting changed due to the position changes of the main rotor shafts under variable load conditions. It was found that by embedding the comprehensive time-varying meshing stiffness values of the main rotor shafts at different positions, a dynamic model of the relative position changes of the planetary gear trains could be established. Then, combined with the multibody dynamics software, the meshing characteristics of the sun gears, and the planetary gears, the planetary gears and the inner ring gears were simulated and analyzed under different inclinations and offsets of the shafting. The results obtained in this study revealed the following: (1) the average meshing force of the gears increased with the increases in the angle inclinations, and the meshing force between the sun gears and the planetary gears increased faster than the meshing force between the planetary gears and the inner ring gears. It was observed that during the changes in the shafting tilt positions, obvious side frequency signals had appeared around the peak of the meshing frequency in the spectrum. Then, with the continuous increases in the tilt position, the peak was gradually submerged; (2) the average meshing force of the gears increased with the increases in the offset, and the increasing trend of the meshing force between the sun gears and the planetary gears was similar to that observed between the planetary gears and the inner ring gears. It was found that when the shafting offset position changed, there were obvious first and second frequency doubling in the spectrum; (3) the mass center orbit radii of the sun gears increased with the increases in the shafting position changes, and the changes in the angular tilt position were found to have greater influencing effects on the mass center orbit radii of the sun gears than the changes in the offset positions. This study’s research findings will provide a theoretical basis for future operational status monitoring of the main transmission systems of helicopters and are of major significance for improvements in the operational stability of helicopter transmission systems, which will potentially ensure safe and efficient operations.
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Hsieh, Long Chang, and Hsiu Chen Tang. "The Kinematics of Eight-Speed Planetary Gear Hubs for Bicycles." Applied Mechanics and Materials 232 (November 2012): 955–60. http://dx.doi.org/10.4028/www.scientific.net/amm.232.955.
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Recently, bicycles are used as exercising machines and traffic vehicles. Planetary gear trains can be used as the transmission systems with multi-speed for bicycles. The purpose of this work is to propose a design methodology for the design of eight-speed internal gear hubs with planetary gear trains for bicycles. First, we propose a design concept for the design of eight-speed planetary gear hub. Then, based on this design concept and train value equation of planetary gear train, the kinematic design of eight-speed planetary gear hub is accomplished. One eight-speed planetary gear hub is synthesized to illustrate the design methodology. Based on the proposed design methodology, many eight-speed internal gear hubs with planetary gear trains can be synthesized.
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Ivanov, A. S., M. V. Fomin, M. M. Ermolaev, N. N. Kuralina, and S. V. Murkin. "Kinematic analysis of planetary lantern gear systems." Russian Engineering Research 32, no. 11-12 (October 10, 2012): 707–10. http://dx.doi.org/10.3103/s1068798x1211007x.
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Mihailidis, Athanassios, Anastasios Moisiadis, and Andreas Psarros. "Impact of backlash, manufacturing deviations and friction on the load sharing factor of planetary gear systems." MATEC Web of Conferences 287 (2019): 01003. http://dx.doi.org/10.1051/matecconf/201928701003.
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Techniques and software tools, which were recently introduced by the authors, allowed for effi-cient automatic generation of 3D gear flanks and selective meshing of the gears of a simple planetary gear system with backlash and manufacturing imperfections. Friction of the meshing gear flanks was neglected. First results were promising and showed that even in geometrically perfect planetary gear systems the torque distribution is not uniform. It was further verified that pitch errors have a strong impact on the load distri-bution and that a self-aligning sun gear significantly enhances the torque distribution among the planets. In the current study, the procedure mentioned above is enhanced in several aspects. First, the tooth friction is considered. The friction coefficient is assumed constant along the path of contact; however different values for the sun-planet and planet-ring gear mesh may be given to account for the different contact conditions. Second, deviations are generated between given limits in a stochastic way. This feature significantly reduces the time needed to setup a model. Third, the entire analysis procedure is further automated by extensively employing Python scripting, enabling the solution of successive snapshots in much shorter time. Besides the torque distribution among the planets, the mesh load factor Kγ and the deformation of the teeth, the planet bearing load is also shown.
21
Gao, Peng, Liyang Xie, and Wei Hu. "Reliability and Random Lifetime Models of Planetary Gear Systems." Shock and Vibration 2018 (September 12, 2018): 1–12. http://dx.doi.org/10.1155/2018/9106404.
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Conventional reliability models of planetary gear systems are mainly static. In this paper, dynamic reliability models and random lifetime models of planetary gear systems are developed with dynamic working mechanism considered. The load parameters, the geometric parameters, and the material parameters are taken as the inputs of the reliability models and the random lifetime models. Moreover, failure dependence and dynamic random load redistributions are taken into account in the models. Monte Carlo simulations are carried out to validate the proposed models. The results show that the randomness of the load distribution is obvious in the system working process. Failure dependence has significant influences on system reliability. Moreover, the dispersion of external load has great impacts on the reliability, lifetime distribution, and redundancy of planetary gear systems.
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Sang, Meng, Kang Huang, Yangshou Xiong, Guangzhi Han, and Zhenbang Cheng. "Dynamic modeling and vibration analysis of a cracked 3K-II planetary gear set for fault detection." Mechanical Sciences 12, no. 2 (September 9, 2021): 847–61. http://dx.doi.org/10.5194/ms-12-847-2021.
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Abstract. The 3K planetary gear system is a basic planetary transmission structure with many advantages over the 2K-H planetary gear system. However, the vibration characteristics will be more complicated due to the increase of central gears meshing with each planet gear simultaneously. In this paper, a lumped-parameter model for a 3K-II planetary gear set was developed to simulate the dynamic response. The time-varying stiffness of each meshing pair for different gear tooth root crack faults is calculated via the finite element method. By considering the effect of time-varying transmission paths, the transverse synthetic vibrations are obtained. Subsequently, the feasibilities of transverse synthetic vibration signals and output torsional vibration signals as reference for fault diagnosis are analyzed by studying the time-domain and frequency-domain characteristics of these two vibration signals. The results indicate that both the transverse synthetic vibration signals and output torsional vibration signals can be used for fault identification and localization of the 3K-II planetary gear train, and yet they both have their limitations. Some results of this paper are available as references for the fault diagnosis of 3K planetary gear trains.
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Kiracofe, Daniel R., and Robert G. Parker. "Structured Vibration Modes of General Compound Planetary Gear Systems." Journal of Vibration and Acoustics 129, no. 1 (May 8, 2006): 1–16. http://dx.doi.org/10.1115/1.2345680.
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This paper extends previous analytical models of simple, single-stage planetary gears to compound, multi-stage planetary gears. This model is then used to investigate the structured vibration mode and natural frequency properties of compound planetary gears of general description, including those with equally spaced planets and diametrically opposed planet pairs. The well-defined cyclic structure of simple, single-stage planetary gears is shown to be preserved in compound, multi-stage planetary gears. The vibration modes are classified into rotational, translational, and planet modes and the unique properties of each type are examined and proved for general compound planetary gears. All vibration modes fall into one of these three categories. For most cases, both the properties of the modes and the modes themselves are shown to be insensitive to relative planet positions between stages of a multi-stage system.
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Brassitos, Elias, and Nader Jalili. "Dynamics of integrated planetary geared bearings." Journal of Vibration and Control 26, no. 7-8 (January 14, 2020): 565–80. http://dx.doi.org/10.1177/1077546319889848.
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The gear bearing drive is a new robotic transmission that was developed by NASA for compact and lightweight robotic applications. Compared to conventional simple and compounded planetary gear trains, the mechanical assembly of the gear bearing drive does not require a planetary carrier and individual planet needle bearings to maintain the gearset alignment. Instead, the design integrates the gearing and bearing functions together such that a constant pressure angle is maintained throughout the mesh cycle by the use of cylindrical rollers that are mounted parallel to the gear mesh. This paper examines the vibration characteristics of this planetary architecture and extracts its natural frequencies and mode shapes using both analytic and finite element methods. The design is compared against a conventional system with a floating carrier for comparative analysis. A simple and systematic approach to analytically and numerically solve the dynamics of complex, multi degree of freedom gear train systems using MATLAB is presented that can be easily applied to study other complex non-linear dynamic systems.
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Hsieh, Long Chang, and Hsiu Chen Tang. "The Kinematic Design of Three-Speed Automatic Transmission for Electric Motorcycle." Applied Mechanics and Materials 284-287 (January 2013): 979–82. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.979.
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Motorcycle is invented so far more than 100 years. Because of having the advantages of light weight, cheap and fast-moving, motorcycle becomes the most popular traffic vehicle. Traditionally, the power systems of motorcycles are internal combustion engines. Recently, due to the reason of energy-saving, and carbon reduction, the engine in motorcycle is substituted by electric motor. Hence, due to the reason of pollution-free, electric motorcycle become more and more popular in city traffic. Planetary gear trains can be used as the transmission systems for electric motorcycles. The purpose of this work is to do the kinematic design of three-speed planetary gear type automatic transmissions for electric motorcycles. First, according to the train value equation of planetary gear train, The reduction ratio equations of planetary gear type automatic transmissions can be derived. Then , based on these reduction ratio equations, the kinematic design of three-speed planetary gear type automatic transmission is accomplished. Based on the proposed methodology, all three-speed planetary gear type automatic transmissions can be synthesized.
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Wang, Jungang, Shinan Yang, Yande Liu, and Ruina Mo. "Analysis of Load-Sharing Behavior of the Multistage Planetary Gear Train Used in Wind Generators: Effects of Random Wind Load." Applied Sciences 9, no. 24 (December 13, 2019): 5501. http://dx.doi.org/10.3390/app9245501.
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Load-sharing behavior is very important for power-split gearing systems. Taking the multistage planetary gear train transmission of an Million Watt (MW) wind generator as the investigation object, and based on the gear transmission system of a wind generator in a complex and changing load environment, a random wind model of a wind farm is built by using the two-parameter Weibull distribution. According to the realistic working region of the wind generator, the random wind speed is changed into time-varying input speed of the wind generator gear box. Considering the internal excitation, such as mesh stiffness, mesh damping of gear pairs and the meshing error, a dynamic model for a multistage planetary gear transmission system is built by using the lumped parameter method. The load-sharing coefficients are obtained for each planet gear pair in the same meshing period of the transmission system that is under the interaction of time-varying input speed and internal excitation. It is shown that the degree of load-sharing coefficient fluctuation for each planet gear pair of the first- and second-stage planetary gear train is significantly affected by time-varying input speed. The research results can lay a theoretical foundation for optimization and reliability of planetary gear transmission systems of wind generators.
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Li, Hongwu, Jing Liu, Jinlei Ma, and Yimin Shao. "Effect of the radial support stiffness of the ring gear on the vibrations for a planetary gear system." Journal of Low Frequency Noise, Vibration and Active Control 39, no. 4 (June 11, 2019): 1024–38. http://dx.doi.org/10.1177/1461348419844642.
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Planter gear system is one of the critical components of various industrial transmission systems. In general, the ring gear is elastically fixed with the gearbox. The gearbox materials and their assembly relationships will affect the support stiffness of the ring gear and system vibrations. In this paper, a multi-body dynamic model for a planetary gear system with the elastic support of ring gear is developed to discuss the influence of the radial support stiffness of ring gear on the system vibrations. The planet bearings are also considered in the multi-body dynamic model. The rotational speed of the planet gear and carrier from the simulation and theoretical results are compared to validate the developed multi-body dynamic model. The influences of the radial support stiffness of the ring gear, carrier moment, and sun gear speed on the time- and frequency-domain vibrations of the planetary gear system are analyzed. The results denote that the waveform and amplitude of the time-domain vibration of the ring gear are greatly affected by the radial support stiffness of ring gear as well as the peak frequency amplitude and its sidebands. The peak frequency in the spectrum of ring gear is slightly affected by the radial support stiffness. It indicates that this study can give some guidance for the vibration control approaches for the planetary gear systems.
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Hsieh, Long Chang, and Tzu Hsia Chen. "The Systematic Design of Multi-Speed Internal Gear Hub for a Bicycle." Advanced Materials Research 199-200 (February 2011): 431–35. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.431.
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The bicycle is invented so far more than 200 years. Now, bicycles are used as exercising equipments and traffic vehicles. Planetary gear trains can be used as the transmission systems with multi-speed for bicycles. The purpose of this work is to propose a design methodology for the design of multi-speed internal gear hubs with planetary gear trains for bicycles. Based on the concept of train value equation and the kinematic relationship of the members between the train circuit, we propose a design methodology for the kinematic design of multi-speed gear hubs. One multi-speed internal gear hubs is designed to illustrate the design methodology. Based on the proposed methodology, all multi-speed gear hubs with planetary gear trains can be synthesized.
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Zhang, Mian, Ming J. Zuo, Dongdong Wei, Jie Liu, KeSheng Wang, and Yongshan Wang. "Motion periods of sun gear dynamic fault meshing positions in planetary gear systems." Measurement 162 (October 2020): 107897. http://dx.doi.org/10.1016/j.measurement.2020.107897.
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Davey, Kent, Travis Hutson, Larry McDonald, Chris Ras, Roy Weinstein, Drew Parks, and Ravi Persad Sawh. "Rotating Cylinder Planetary Gear Motor." IEEE Transactions on Industry Applications 52, no. 3 (May 2016): 2253–60. http://dx.doi.org/10.1109/tia.2016.2532286.
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Hsieh, Long Chang, Hsin Sheng Lee, and Teu Hsia Chen. "An Algorithm for the Kinematic Design of Gear Transmissions with High Reduction Ratio." Materials Science Forum 505-507 (January 2006): 1003–8. http://dx.doi.org/10.4028/www.scientific.net/msf.505-507.1003.
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Planetary gear trains can be used as the transmission systems with high reduction ratio for power machinery. The purpose of this paper is to propose an algorithm for the kinematic design of planetary gear trains with high reduction ratio. Based on the concept of train value equation, we propose a new representation to present the kinematic relationship of the members of the train loop. According to this representation graph, we propose an efficient algorithm for the kinematic design of planetary gear trains with high reduction ratio. Three design examples are designed to illustrate the design algorithm. Based on the proposed algorithm, all planetary gear trains with high reduction ratio can be synthesized.
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Li, Tong Jie, Ru Peng Zhu, and He Yun Bao. "Study on Dynamic Load Sharing Behavior of Two-Stage Planetary Gear Train Based on a Nonlinear Vibration Model." Applied Mechanics and Materials 86 (August 2011): 611–14. http://dx.doi.org/10.4028/www.scientific.net/amm.86.611.
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The nonlinear torsional vibration model of a two-stage planetary gear system is established taking errors of transmission, time varying meshing stiffness and multiple gear backlashes into account. The solution of the equations is determined by using ODE45. The influences of transmission errors on the load sharing behavior are assessed and some useful theoretical guidelines for the design of planetary gear systems are provided at last.
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Liu, Yinghui, Dong Zhen, Huibo Zhang, Hao Zhang, Zhanqun Shi, and Fengshou Gu. "Vibration Response of the Planetary Gears with a Float Sun Gear and Influences of the Dynamic Parameters." Shock and Vibration 2020 (August 4, 2020): 1–17. http://dx.doi.org/10.1155/2020/8886066.
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Planetary gearboxes are widely used in mechanical transmission systems due to their large transmission ratio and high transmission efficiency. In a planetary gearbox, the sun gear is usually set to float to balance the sharing of loads among planet gears. However, this floating set will result in the variation of pressure angle, overlap ratio, and meshing phase in the meshing progress and when gear faults occur, the variation will be enlarged. In the previous studies, these parameters were reduced to constant. To study the influence of the dynamic parameters on the vibration response of planetary gearboxes under different operating conditions, a new lumped-parameter model containing the time-varying pressure angle (TVPA), time-varying overlap ratio (TVOR), and time-varying meshing phase (TVMP) is established. Based on this model, the vibration response mechanism of the sun gear is analyzed. Moreover, the comparison with the previous model is made and the rule of phase modulation caused by these dynamic parameters is revealed. By comparing the dynamic responses under different loads and rotation speeds, the phase modulation is studied in detail. Finally, the sun gear fault is introduced, and the phase modulation is analyzed in different fault degrees. This study can provide theoretical reference for the condition monitoring and fault diagnosis of planetary gearbox based on vibration analysis.
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Zhang, Xinghui, Jianshe Kang, Lei Xiao, and Jianmin Zhao. "Alpha Stable Distribution Based Morphological Filter for Bearing and Gear Fault Diagnosis in Nuclear Power Plant." Science and Technology of Nuclear Installations 2015 (2015): 1–15. http://dx.doi.org/10.1155/2015/460131.
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Gear and bearing play an important role as key components of rotating machinery power transmission systems in nuclear power plants. Their state conditions are very important for safety and normal operation of entire nuclear power plant. Vibration based condition monitoring is more complicated for the gear and bearing of planetary gearbox than those of fixed-axis gearbox. Many theoretical and engineering challenges in planetary gearbox fault diagnosis have not yet been resolved which are of great importance for nuclear power plants. A detailed vibration condition monitoring review of planetary gearbox used in nuclear power plants is conducted in this paper. A new fault diagnosis method of planetary gearbox gears is proposed. Bearing fault data, bearing simulation data, and gear fault data are used to test the new method. Signals preprocessed using dilation-erosion gradient filter and fast Fourier transform for fault information extraction. The length of structuring element (SE) of dilation-erosion gradient filter is optimized by alpha stable distribution. Method experimental verification confirmed that parameter alpha is superior compared to kurtosis since it can reflect the form of entire signal and it cannot be influenced by noise similar to impulse.
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Chavan, Nilesh, Sourabh Solanke, Prajwal Sute, Tanya Samanta, and Prof P. A. Wankhade. "Design and Analysis of Planetary Gearbox For All-Terrain Vehicle." International Journal for Research in Applied Science and Engineering Technology 10, no. 12 (December 31, 2022): 100–107. http://dx.doi.org/10.22214/ijraset.2022.47815.
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Abstract: Planetary Gear Trains are extensively used for power transmission and are the most critical component. This report focuses on the designing and analysis of a planetary gearbox for an SAE BAJA All-Terrain Vehicle (ATV). The conventional two-stage speed reduction gearbox is bulkier and has a high volume to power ratio. A planetary gearbox gives the best balance between weight and power to be transmitted. For the design procedure standard method is utilized. Based on conventional equations gear calculations are performed and subsequently, CAD modeling for various parts is done. The analysis for each component is performed and checked for its stresses. The transmission shafts and bearings are designed using the standard force equations. In addition, the design and analysis of gearbox casing is performed and the complete assembly is checked for interferences. This report also presents the advantages and limitations of planetary gear train over other transmission systems. The comparison of planetary gear system with compound spur gear system is done on the basis of volume and weight, ease in manufacturing, assembly and disassembly and aesthetical viewpoint.
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Hu, Shengyang, Zongde Fang, Yabin Guan, Xiangying Hou, and Chao Liu. "Study on Structural Vibration Characteristics of L-Shaped Flexible Ring Gear and Establishment of System Coupling Vibration Model." Machines 10, no. 5 (May 6, 2022): 339. http://dx.doi.org/10.3390/machines10050339.
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L-shaped flexible ring gear is a new solution to the non-uniform load distribution of planetary transmission systems. At present, the research on L-shaped flexible ring gear is still focused on its meshing characteristics and dynamic load sharing performance, and its structural vibration characteristics and dynamic coupling vibration characteristics with the system are not involved. Considering that the structural flexibility of the L-shaped flexible ring gear is significantly higher than that of the traditional ring gear, the structural vibration will obviously affect the load sharing and dynamic load factor performance of the transmission system, as well as the safety and reliability of the mechanism. Due to its strong structural flexibility and structural particularity, the existing dynamic analysis model is difficult to meet the requirements of analysis and design. In this paper, the coupling vibration model of L-shaped flexible ring gear planetary transmission systems is established, and the structural vibration characteristics of L-shaped flexible ring gear and its influence on the dynamic performance of the systems are deeply analyzed. The model foundation and theoretical guidance are provided for the design of L-shaped flexible ring gear and the analysis of the dynamic characteristics of flexible ring gear systems.
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Yang, Yi, Niaoqing Hu, Zhe Cheng, Jiao Hu, and Lun Zhang. "Improved Mesh Stiffness Method and Vibration Analysis of a Planetary Gear System with a Spatial Tooth Crack." Machines 10, no. 12 (December 6, 2022): 1168. http://dx.doi.org/10.3390/machines10121168.
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Dynamic modeling and analysis are generally regarded as effective tools to investigate the vibration characteristics and fault mechanisms of planetary gear systems with a tooth crack fault. In actual gearboxes, the tooth crack is always a three-dimensional spatial surface, but it was usually simplified as a two-dimensional domain in most previous studies. In this paper, the tooth crack is modeled as a spatial shape that propagates along the crack depth, length and height directions simultaneously. Based on the potential energy principle, an improved analytical method is proposed to calculate the time-varying mesh stiffness (TVMS) of a planetary gear system with a spatial tooth crack. Furthermore, a coupled translational–torsional dynamic model is established for a planetary gear system including time-varying parameters and nonlinear factors. Numerical simulations are conducted to reveal the influences of the spatial crack propagation on the TVMS and vibration responses. In addition, an experimental study is carried out on a gear transmission test rig to verify the proposed analytical method and dynamic model. The mesh stiffness calculation method of the spatial cracked tooth and corresponding analysis results in this study might provide references to detect tooth crack faults in planetary gear systems.
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Chen, Xianhua, Xingkai Yang, Ming J. Zuo, and Zhigang Tian. "Planetary Gearbox Dynamic Modeling Considering Bearing Clearance and Sun Gear Tooth Crack." Sensors 21, no. 8 (April 9, 2021): 2638. http://dx.doi.org/10.3390/s21082638.
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Planetary gearbox systems are critical mechanical components in heavy machinery such as wind turbines. They may suffer from various failure modes, due to the harsh working environment. Dynamic modeling is a useful method to support early fault detection for enhancing reliability and reducing maintenance costs. However, reported studies have not considered the sun gear tooth crack and bearing clearance simultaneously to analyze their combined effect on vibration characteristics of planetary gearboxes. In this paper, a dynamic model is developed for planetary gearboxes considering the clearance of planet gear, sun gear, and carrier bearings, as well as sun gear tooth crack levels. Bearing forces are calculated considering bearing clearance, and the dynamic model equations are updated accordingly. The results reveal that the combination of bearing clearances can affect the vibration response with sun gear tooth crack by increasing the kurtosis. It is found that the effect of planet gear bearing clearance is very small, while the sun gear and carrier bearing clearance has clear impact on the vibration responses. These findings suggest that the incorporation of bearing clearance is important for planetary gearbox dynamic modeling.
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Tsai, L. W., and E. R. Maki. "Planetary-Gear-Type Second-Harmonic Balancers." Journal of Mechanisms, Transmissions, and Automation in Design 111, no. 4 (December 1, 1989): 530–36. http://dx.doi.org/10.1115/1.3259034.
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This paper describes several mechanical balancers, based on the planetary gear trains known as the hypotrochoid and epitrochoid trains, for reducing or eliminating second-order out-of-balance in mechanical systems. It is shown that by proper arrangement of the planetary gear trains, a balancer can be obtained for the elimination of second-order shaking forces or second-order shaking moments or a combination of both shaking forces and moments. The advantage of this type of balancer is that the carrier of the gear train needs only to run at the primary speed of the mechanical system to be balanced. Therefore, the balancer can be designed to be concentric with the primary rotating shaft of the machine using the primary shaft as the carrier. For example, for the balance of the second-order shaking force of an inline four-cylinder four-stroke internal combustion piston engine, the balancer can be placed on the third main bearing or one on each of the second and fourth main bearings.
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Zhang, Xi, Xiaolin Tang, and Wei Yang. "Analysis of transmission error and load distribution of a hoist two-stage planetary gear system." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 233, no. 1 (April 23, 2018): 3–16. http://dx.doi.org/10.1177/1464419318770886.
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The research described in this study is aimed at exploring the transmission characteristics of a two-stage planetary-gear transmission system. Firstly, a novel rigid-flexible coupled dynamic model was established with the consideration of gear clearance, time-varying meshing stiffness, and the deformation of the bearing and shaft. Secondly, based on the novel dynamic model, different profile modification parameters are carried out to optimize the transmission error, load distributions, and harmonic quantity of the transmission system. The analysis results show that dynamic characteristics can be improved by optimizing the multi-stage planetary gear profile. The study provides a valuable reference for the design of multi-stage planetary-gear transmission systems of hoist industry.
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Chotiprayanakul, Pholchai, Nattakul Khamsri, and Neeracha Kumjaroen. "A design of HDPE flexible spline of harmonics gear." MATEC Web of Conferences 192 (2018): 01030. http://dx.doi.org/10.1051/matecconf/201819201030.
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In a design of a small robot, selecting a servo-motor is the most important method in designing process. Common miniature servo motors for small robots normally use conventional gear train set or planetary gear set. Gear train and planetary gear give very low gear ratio whereas its weight is too heavy. On the other hand, Harmonic gear system, which is developed from strain wave drive gearing, gives better the highest gear ratio per weight than those two gear systems. In this paper, a plastic flexible spline gear is presented in order to replace a thin metal spline. The plastic flexible spline gear is designed under gear physical requirement and servo-motor properties. The spline thicknesses are varied in a range of 1 to 4 millimetre and simulations on strength, fatigue, and torque requirement are made to verify the designs.
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Velex, P., and L. Flamand. "Dynamic Response of Planetary Trains to Mesh Parametric Excitations." Journal of Mechanical Design 118, no. 1 (March 1, 1996): 7–14. http://dx.doi.org/10.1115/1.2826860.
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An extended three-dimensional model is used for calculating dynamic tooth loads on a planetary gear set. Time dependent mesh stiffnesses are determined and an original Ritz method aimed at solving large parametrically excited differential systems is proposed. Results from the Ritz method compare favorably with those given by direct integrations for highly reduced computation times. The difference between local critical speeds (for one individual mesh) and global critical speeds (for sun or ring gear-planet meshes) on a sequential spur gear train is pointed out. Finally, it is shown that, for linear behaviors, mesh stiffnesses are largely controlling dynamic tooth loads while the influence of a floating sun or ring gear is less important.
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van der Linden, Franciscus LJ. "Modeling of geared positioning systems: An object-oriented gear contact model with validation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 7-8 (June 29, 2015): 1084–100. http://dx.doi.org/10.1177/0954406215592056.
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In aerospace positioning actuators, gear efficiencies of 85% as well as breakout forces as high as 50% of the stall load of the actuator are observed at very low temperature conditions. Due to the low efficiency and high loading, stiction in these actuators is common which can lead to limit cycles or problems with controlling the actuators. To be able to correctly predict and assess these effects using simulations, a complete actuator, including motor, inverter, load, and controller is needed. This article presents an object-based, numerically efficient gear contact in a planar environment with user-defined friction and stiffness laws. The emphasis of the modeling is not a fully detailed contact model, but the description of a gear contact model which can be used for system simulations like complete aircraft electromechanical actuators including control surfaces. The presented model is suitable for complex gearing configurations (e.g. compound planetary gears). This is enabled by breaking down the transmission into the basic gear contacts. By adding masses and constraints from an existing component library, a complete transmission can be modeled. The generated model can be used for standalone simulations or can be used in multi-domain simulations like actuator modeling, in order to analyze the complete actuator model including parts such as drives, controllers and mechanical systems. The presented models have been validated using a gear test rig for a single stage spur gear.
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Yao, Wu-Sung, and Chun-Yi Lin. "Design of Active Continuous Variable Transmission Control System with Planetary Gear." Electronics 11, no. 7 (March 23, 2022): 986. http://dx.doi.org/10.3390/electronics11070986.
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Planetary gearboxes have been employed in various applications due to their advantages of maintaining a high speed-reduction ratio, such as in wind power applications which have now become a prevailing green energy resource. A traditional power transmission machine of the wind turbine has a fixed gear-ratio mechanical gearbox for speed-increasing transmission. The purpose of this study is to propose an active continuous variable transmission (ACVT) control system with a planetary gear to apply to the wind turbine. The planetary gear holds three terminals, i.e., the ring gear, the planet carrier, and sun gear, and the motions of three terminals can be controlled purposely by the servomotors to achieve ACVT. The three different transmission types of the proposed ACVT can be operated. The dynamic characteristic of the planetary gear is expressed in block diagram form, and a pseudo derivative feedback feed-forward controller of the velocity control loop is designed for the required performance. The results can be used to verify the effect of the proposed ACVT with the planetary gear.
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Zhang, Donglin, Rupeng Zhu, Miaomiao Li, Wuzhong Tan, and Pingjun Li. "Meshing Stiffness Parametric Vibration of Coaxial Contrarotating Encased Differential Gear Train." Mathematical Problems in Engineering 2021 (February 26, 2021): 1–13. http://dx.doi.org/10.1155/2021/8950945.
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Planetary gears are widely used in mechanical transmission systems, but the vibration and noise affect their reliability and life. In this paper, the torsional dynamic model of an encased differential planetary gear with coaxial contrarotating outputs considering the time-varying meshing stiffness, damping, and phase difference of all gear pairs is established. By solving the equations of the derived system, three types of natural frequencies with different multiplicities of the system are obtained. The multiscale method is used to study the parametric vibration stability caused by the time-varying meshing stiffness, and the results are verified by numerical simulation. The dynamic characteristics of elastic meshing force are analyzed from time domain and frequency domain. The variation of the dynamic load factor of each gear pair with input speed and the relationship between its peak position and the natural frequency of the derived system are discussed. The results show that there is an unequal coupling phenomenon of meshing frequency between the meshing forces of different planetary sets. In the absence of external excitation, the meshing stiffness parameters not only excite the main resonance response of the system but also cause superharmonic resonance, subharmonic resonance, and combined resonance.
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Wang, Dan-Feng, Yu Guo, Xing Wu, Jing Na, and Grzegorz Litak. "Planetary-Gearbox Fault Classification by Convolutional Neural Network and Recurrence Plot." Applied Sciences 10, no. 3 (January 31, 2020): 932. http://dx.doi.org/10.3390/app10030932.
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Recurrence-plot (RP) analysis is a graphical tool to visualize and analyze the recurrence of nonlinear dynamic systems. By combining the advantages of the RP and a convolutional neural network (CNN), a fault-classification scheme for planetary gear sets is proposed in this paper. In the proposed approach, a vibration is first picked up from the planetary-gear test rig and converted into an angular-domain quasistationary signal through computed order tracking to eliminate the frequency blur caused by speed fluctuations. Then, the signal in the angular domain is divided into several segments, and each segment is processed by the RP to constitute the training sample. Moreover, a two-dimensional CNN model was developed to adaptively extract faulty features. Experiments on a planetary-gear test rig with four conditions under three operating speeds were carried out. The results of measured vibration demonstrated the validity of CNN and recurrence plot analysis for the fault classification of planetary-gear sets.
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Wang, Xin. "Nonlinear Dynamic Characteristics of Fixed-Axis Gear Wear in Multistage Gear Transmission Systems." Shock and Vibration 2019 (June 20, 2019): 1–11. http://dx.doi.org/10.1155/2019/5641617.
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With the increasing service life of a gear transmission system, the gear teeth become constantly worn and the gear clearance increases. The increase in the clearance will produce a series of nonlinear changes that change the stability of the system and can even cause the loss of stability. In this paper, dimensionless dynamic equations of a multistage gear transmission system that contains a two-stage fixed-axis gear and a one-stage planetary gear were derived. The wear fault was simulated by changes in the gear clearance. System bifurcation diagrams with an increase in the clearance were studied. The motion state and transition process of the multistage gear transmission system with a wear fault were studied using the Poincaré section. The change in the spectrum characteristics with an increase in the clearance was analyzed. The frequency spectrum characteristics of the wear fault were discovered. The vibration mechanism and a fault wear diagnosis method in a multistage gear transmission system were obtained.
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Xu, Xiang, Jiawei Chen, Zhongyan Lin, Yiran Qiao, Xinbo Chen, Yong Zhang, Yanan Xu, and Yan Li. "Optimization Design for the Planetary Gear Train of an Electric Vehicle under Uncertainties." Actuators 11, no. 2 (February 5, 2022): 49. http://dx.doi.org/10.3390/act11020049.
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The planetary gear train is often used as the main device for decelerating and increasing the torque of the drive motor of electric vehicles. Considering the lightweight requirement and existing uncertainty in structural design, a multi-objective uncertainty optimization design (MUOD) framework is developed for the planetary gear train of the electric vehicle in this study. The volume and transmission efficiency of the planetary gear train are taken into consideration as optimization objectives. The manufacturing size, material, and load input of the planetary gear train are considered as uncertainties. An approximate direct decoupling model, based on subinterval Taylor expansion, is applied to evaluate the propagation of uncertainties. To improve the convergence ability of the multi-objective evolutionary algorithm, the improved non-dominated sorting genetic algorithm II (NSGA-II) is designed by using chaotic and adaptive strategies. The improved NSGA-II has better convergence efficiency than classical NSGA-II and multi-objective particle swarm optimization (MOPSO). In addition, the multi-criteria decision making (MCDM) method is applied to choose the most satisfactory solution in Pareto sets from the multi-objective evolutionary algorithm. Compared with the multi-objective deterministic optimization design (MDOD), the proposed MUOD framework has better reliability than MDOD under different uncertainty cases. This MUOD method enables further guidance pertaining to the uncertainty optimization design of transportation equipment, containing gear reduction mechanisms, in order to reduce the failure risk.
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Saada, A., and P. Velex. "An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains." Journal of Mechanical Design 117, no. 2A (June 1, 1995): 241–47. http://dx.doi.org/10.1115/1.2826129.
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An extended model for determining critical frequencies for tooth loading on spur and helical gear planetary trains is proposed. Torsional, flexural and axial generalized displacements of all the components are considered and a finite element procedure is used for generality. In order to avoid modulations between meshing pulsations and the carrier angular velocity, equations are written relative to rotating frames fixed to planet centers. Depending on their architectures, complex drives are broken down in basic 12 degree of freedom elements, namely: external gear element (sun gear-planet element); internal gear element (ring gear-planet element); pin-carrier element; classical elements for shafts, bearings, couplings, etc. Details are given for elementary stiffness matrices. Due to contact conditions between mating teeth, these matrices are full and torsional, bending and traction effects are coupled. State equations point to parametrically excited differential systems with gyroscopic contributions. A first application of the model is conducted on a 3 planet epicyclic drive whose gyroscopic terms are neglected. Potentially dangerous frequencies for sun gear-planet and planet-ring gear contacts are determined and contributions of some components of the planetary train are discussed.
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Li, Ming, Yuan Luo, and Liyang Xie. "Fatigue Reliability Design Method for Large Aviation Planetary System Considering the Flexibility of the Ring Gear." Applied Sciences 12, no. 20 (October 14, 2022): 10361. http://dx.doi.org/10.3390/app122010361.
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As the foundation and core of various heavy aircraft transmission systems, the reliability level of large-scale aviation planetary mechanism restricts the economic affordability and service safety for the aircraft to a great extent. This paper takes the heavy helicopter planetary mechanism as the research object, and aims to improve the fatigue reliability level of the system. The fatigue load history of the gear teeth under the coupling of global elastic behavior of the system is calculated using a hierarchical finite element method, and the fatigue strength distribution of gear teeth is fitted based on the gear low circumference fatigue test with the minimum order statistics transformation method to provide cost-effective load and strength input variables for the system reliability prediction model. Based on this, a mapping path from the key structural elements of large-scale aviation planetary mechanism to the system reliability indexes is established, and then a new method of reliability-driven multi-objective optimization design for planetary mechanism structural dimensions is proposed. Finally, the influence law of ring gear rim thickness on the fatigue reliability of the planetary gear train is analyzed and the NSGA-Ⅱ genetic algorithm is used to determine the optimal stiffness matching result of the rim size of the designated type of large aviation planetary system. The stiffness potential of the core structural elements is maximized as a way to balance the contradiction between reliability and lightweight requirements of a large aviation planetary system.