Kinematical and Efficiency Analysis of Planetary Gear Trains by Means of Various Graph-Based Approaches

Drewniak, J.; Kopeć, J.; Zawiślak, S.

doi:10.1007/978-3-319-19740-1_12

Cited by 11 publications

(4 citation statements)

References 13 publications

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“…In order to determine the directions of the flow of power streams and to estimate the power losses in the meshing, it is necessary to determine the magnitudes and directions of the angular velocity vectors of the gears and carriers of each gear subsystem in advance (blocks, units, or branches) [195]. In practice, the Willis formula [12][13][14][15][16][17]163,178] is often used for this purpose, although graph methods (linear, contour, signal flow, bond graphs, matroids, and hypergraphs) are gaining more and more recognition, thanks to their advantages [143,162,[164][165][166][167][168][169][171][172][173][174][175][176][177][179][180][181][182][183][184][185][186]189,192,194]. The nomograph method and, especially, the lever analogy are also promising as universal methods for kinematics, statics, and power flow analysis of the most complex PSHEV planetary transmission [88,[118][119][120][121]126,[128][129]…”

Section: Analysis Of the Kinematics Of Series-parallel Gearsmentioning

confidence: 99%

“…At this stage of calculations, it is possible to determine the magnitudes and directions of the torque without considering power losses, using graphical and analytical methods, including the free body diagram [172,173] and lever or nomograph methods [119][120][121]126,[128][129][130][144][145][146]149,155]. The most popular techniques due to the possibility of automating calculations are the methods of classical directed or undirected graphs, signal graph, and contour graphs [12,142,[144][145][146]162,169,177]. In Appendix C of this paper, the free body diagram method was used.…”

Section: Static Analysis Without Considering Meshing Frictionmentioning

confidence: 99%

See 1 more Smart Citation

Power Flow in Coupled Three-Row Series-Parallel Planetary Gear System, Part I: Without Power Losses

Drewniak,

Kądziołka,

Rysiński

et al. 2023

Energies

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So far it is believed that, for every series-parallel planetary gear system (PGS), as a coupled gear, a very harmful phenomenon of power circulation must occur in at least one of its closed circuits. In this paper (Part I) and in the next two (Part II and Part III), it will be shown that it is possible to construct a three-row series-parallel PGS in which this phenomenon can be avoided. For this purpose, in Part I, a detailed analysis of the kinematics and statics of a planetary gear with power circulation inside a closed loop was carried out. The determination of the angular velocities of gears and carriers is carried out using Willis formulas and the graphical-analytical method (for verification), while the torques are determined using free body diagrams. The magnitudes of angular velocities and torques were used to determine the directions of power flows with improved energy balance equations in the reference frame related to the stationary gear body and, additionally, only to verify the energy balance equation in the mobile reference frame related to the carrier hi (i=2,5,8). The improvement of the methods was based on the use of the original concept of distinguishing active torque from reactive torque, as well as active power from reactive power, which made it very easy to determine the directions of the power flow. The determined paths of the power flow, including the power circulation in the analysed PGS, are presented graphically.

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Section: Analysis Of the Kinematics Of Series-parallel Gearsmentioning

confidence: 99%

Section: Static Analysis Without Considering Meshing Frictionmentioning

confidence: 99%

Power Flow in Coupled Three-Row Series-Parallel Planetary Gear System, Part I: Without Power Losses

Drewniak,

Kądziołka,

Rysiński

et al. 2023

Energies

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“…Нагрузочная способность зубчатой планетарной передачи, определяемая в соответствии с приведенными выше зависимостями, ее габариты при заданном моменте на выходном валу, а также потери мощности на трение являются основными технико-экономическими показателями механизма [14,15].…”

Section: исследование технико-экономических показателей зубчато-роликовой планетарной передачиunclassified

Influence of Parameters of a Planetary Gear with Internal Meshing on Its Technical and Economic Indicators

Suntsov

Vychuzhanina

Perminova

2021

Vestnik IzhGTU imeni M.T. Kalashnikova

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Конструкции зубчатой планетарной передачи, содержащей эксцентриковое водило, один-два сателлита и неподвижное центральное колесо с внутренними зубьями, отличающиеся роликовым исполнением механизма снятия движения с сателлитов, обладают высокой нагрузочной способностью и высоким коэффициентом полезного действия при большом передаточном отношении в одной ступени (конструкции защищены патентами на изобретения). Для оптимизации параметров указанных планетарных механизмов и улучшения их технико-экономических показателей получена зависимость, определяющая соотношение между допускаемыми нагрузками в зацеплении колес, соответствующими контактной и изгибной прочности зубьев, от их числа и передаточного отношения. Установлено, что при больших передаточных отношениях (более 17) нагрузочная способность передач этого типа лимитируется изгибной прочностью зубьев колес. На основании этого определялся допускаемый момент на выходном валу передачи и отношение его к объему неподвижного центрального колеса, от которого зависят масса и объем передачи в целом. Показано, что наибольшей нагрузочной способностью при заданном передаточном отношении и объеме неподвижного центрального колеса (следовательно, и объеме передачи в целом) обладает планетарная передача с разницей чисел зубьев сателлита и центрального колеса, равной единице. Коэффициент полезного действия (КПД) планетарной передачи с роликовым исполнением механизма снятия движения с сателлитов определялся экспериментальным путем на специально созданной установке, содержащей электромагнитное нагружающее устройство и тензометрические датчики крутящего момента (при рациональных параметрах передачи, ее передаточном отношении, не превышающем 60, и наиболее распространенной степени точности изготовления (7-8) КПД равен 85…90 %). КПД аналогичной передачи с традиционным цевочным механизмом снятия движения с сателлитов примерно на 5 % ниже КПД зубчато-роликовой передачи. С ростом передаточного отношения КПД зубчато-роликовой планетарной передачи изменяется так же, как и КПД традиционной передачи (падает).

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“…3 FINITE VOLUME APPROACH Several authors have already modelled the lubricant fluxes and power losses of planetary gears with finite volume approaches [37][38][39][40][41][42][43][44]. In this research, the Global Remeshing Approach (GRA) [45], previously developed by the author, was applied to a cycloidal gear set.…”

Section: Power Loss Of Gearsmentioning

confidence: 99%

Development of a computational fluid dynamics simulation tool for lubrication studies on cycloidal gear sets

Concli¹,

Maccioni²,

Gorla³

2020

Int. J. CMEM

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In the last decades, the growing mechatronic sector has promoted the development of more and more compact and efficient gearboxes. The margins of improvement are still big even if, sometimes, finding the optimal solutions is a trial and error procedure. For this reason, the development of dedicated tools for the optimization of the geometry and configuration of gearboxes can significantly increase the development effectiveness and help in reducing design costs. Moreover, having a more efficient solution could also reduce thermal problems during operation and increase the system reliability. The so-called 'thermal limit', i.e. the maximum transmittable power without an overheating of the systems, is particularly critical for high power density and compact solutions. Those relies mainly on planetary, harmonic and cycloidal architectures. While many empirical or analytical prediction models can be found in literature for the prediction of the power losses associated with the gear meshing and the bearing, few reliable models are nowadays available for the losses associated with the interaction with the lubricant, i.e. hydraulic losses. Experimental and computational fluid dynamics studies on parallel axis as well as planetary gear sets have been presented in the past. The goal of this research is the extension of the applicability range of those numerical approached to cycloidal kinematics for which no studies at all are available with respect to the hydraulic losses. The main challenge in numerically simulate the lubricant splashing in a cycloidal reduced is related to the topological modification of the computational domain during operation. For this purpose, a specific mesh handling technique, based on a 2.5D mesh, capable to handle the variations of the geometry of the domain was developed in the OpenFOAM® environment. The capability to analytically control the mesh generation at each time step ensures a very high numerical stability and a very high computational efficiency of the solution. Eventually, the approach was systematically applied to a real geometry and the results compared with those obtained for other gear architectures with comparable performances in terms of dimensions and reduction ratios.

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Kinematical and Efficiency Analysis of Planetary Gear Trains by Means of Various Graph-Based Approaches

Cited by 11 publications

References 13 publications

Power Flow in Coupled Three-Row Series-Parallel Planetary Gear System, Part I: Without Power Losses

Power Flow in Coupled Three-Row Series-Parallel Planetary Gear System, Part I: Without Power Losses

Influence of Parameters of a Planetary Gear with Internal Meshing on Its Technical and Economic Indicators

Development of a computational fluid dynamics simulation tool for lubrication studies on cycloidal gear sets

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