Structure synthesis of planetary gear trains using graph partitioning

Hussen, Hamed A.; Esmail, Essam L.; AL-Mayali, Maasi F

doi:10.1063/5.0066868

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…In third step, geared graphs are detected from parent graphs and spanning trees. The rooted graph of an N-link, F-DOF PGT comprises (𝑁 + 1) vertices and (2 𝑁 − 𝐹 − 1) edges; hence, the number of independent loops can be obtained from 𝐿 = 𝑒 − 𝑣 + 1 [25][26][27][28]. The link assortment arrays of a spanning tree and a parent graph are expressed as [𝑉 1 , 𝑉 2 , 𝑉 3 , … , 𝑉 𝑚 ] and [𝑉 2 , 𝑉 3 , … , 𝑉 𝑚 ] , respectively.…”

Section: Synthesis and Analysis Of Planetary Gear Trainmentioning

confidence: 99%

“…Shanmukhasundaram and colleagues [19] examined the recursive, non-recursive, and acyclic graph-based approaches in depth. Graph theory enabled the modeling of PGT kinematic structure as well as the advancement of structure synthesis methodologies [20][21][22][23][24][25][26][27][28]. In this paper, geared graphs for a given number of links and DOF are enumerated using a method that makes use of the correspondence between spanning-tree graphs and parent graphs.…”

Section: Introductionmentioning

confidence: 99%

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Genetically compatible graphs for planetary gear train synthesis

Nafeh¹,

Esmail²

2022

QJES

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Planetary gear trains (PGTs) are used in a wide range of mechanical applications. Graphs are used to represent PGTs. PGTs are classified into single-planet and multi-planet gear trains depending on the number of vertices in the second level of the graph. In this paper, a novel method for synthesizing PGTs up to the second level is developed. The first step in the synthesis process is the enumeration of spanning trees. A combinatorial analysis is then used to obtain the link assortment arrays and categorize them into families. Based on the parent graphs and spanning trees, the geared graphs are generated for each family. For simplicity, the steps of the newly developed genetically compatible graphing method are applied to 5-link, 1-DOF planetary gear trains. The synthesis steps are programmed in MATLAB.

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Section: Synthesis and Analysis Of Planetary Gear Trainmentioning

confidence: 99%