Synthesis of Planetary Gears by Means of Artificial Intelligence Approach ‒ Graph-Theoretical Modeling

Abstract

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.

Graph-Based Models of Compound Planetary Gear Boxes

“…Introduction of a control system (aggregated with a gear) allows for changing the drives in an automatic way. There are several methods of calculation of gear ratios for these gears and particular drives [1,2,3].…”

“…Several different graphs and hypergraphs [5][6][7][8] as well as versatile graph related algebraic structures [4] were utilized for different engineering tasks e.g. synthesis of gears [1,7], modeling [2], optimization [3], evaluation of planetary gear efficiency [6] and kinematical analysis [2]. It is worth to underline that graph based methods are intensively developed just recently despite that they have been discussed since 80-ties of the XX-th century.…”

Analysis of a planetary gear modelled with a contour graph considering the decision making complexity of game-tree structures

“…On the contrary, the graph based methods have been independently and intensively developed in recent years all over the world (see e.g. [10]). The superiority of the graph-based modelling of mechanical systems consists in the fact that a graph is inseparably connected with other algebraic structures like e.g.…”

“…In the case of analysis of car gearboxes, the graph-based methodology is also efficient when incorporating additional transformations of a basic graph according to a particular gear driver [5]. An introductory comparison of the graph and contour methods for analysis of gears was done by the authors in [5,10].…”

“…trees, cycles, cliques, paths), dual graph, matrices, vector spacer of cuts and cycles, structural numbers and matroids as well as algorithms connected with these structures. By interpreting the mechanical knowledge In terms of graphs, we solve mechanical problems via graph models [11]. Versatile linear graph models were considered by Tsai [12] but Hsu's graph models of gears [13] are utilized in the following considerations.…”