The Conceptual Systems Of Multi-symmetry Structures And Symmetry Quantifications In Mechanics And Their Applications

Symmetry structures are widely existed in mechanical parts, components and systems. Based on the study of a variety of mechanical products, the concepts of multi-symmetry structures, symmetry degree, and symmetry-breaking degree in mechanics are proposed. In order to use structure symmetry in the process of product design and manufacturing, in this paper, plenty of multi-symmetry structure design knowledge (MSDK) is extracted, a model that can estimate parts’assembly efficiencies using their symmetry degrees is established and pinion assembly strategies for improving the load sharing of symmetry-breaking planetary gear sets are proposed. The detailed approaches, contents, and achievements are listed as follows:1. From the perspective of multi-symmetry subjects and references, the classification of multi-symmetry mechanical structures is studied. The relation between symmetry subject and symmetry reference is examined, and the concept of multi-symmetry mechanical structure is established, which involves several multi-symmetry stacking relations such as composition, combination, serial and parallel connections, et al. A systematic symbolic representation of multi-symmetry in mechanical structures is also proposed.2. To acquire the design application knowledge of multi-symmetry used in mechanical structures, a model that is capable of representing any multi-symmetry mechanical structure has been studied and a data mining platform which includes structure symmetry database, basic knowledge database, data mining algorithm database has been built. Some composition and combination symmetry design application knowledge used in those mechanical structures is mined and extracted. To illustrate the process of how to implement these knowledge during a product design, a new multi-chamber vane pump with stable output flow is innovated.3. The concept of symmetry degree applicable to mechanical structures is proposed, and factors that may affect it are analyzed. Using structure symmetry decomposition map, a math model of symmetry degree applicable to structure with single symmetry subject is established. In tlhe DFA field, the calculation of symmetry degree of mechanical parts is studied. First, according to the operating differences in the process of grasping and orienting a part, the symmetry subjects of a part are classified into orienting-type symmetry subjects and contour-type symmetry subjects. Then, on the basis of the existing concept of total symmetry angle (TSA) proposed by Boothroyd, a new concept of total correcting angle (TCA) is proposed. Finally, a part "symmetry degree-assembly efficiency" prediction model is established, which is applicable to parts with both single and multiple symmetry subject. Case studies and model comparisons indicate that the proposed model acquires more accurate results.4. The concept of symmetry-breaking degree applicable to mechanical structures is proposed, and factors that may affect it are analyzed. Uneven loading sharing among pinions usually occurs in symmetry-breaking planetary gear sets, and pinion assembly strategies aiming at improving this are studied. First, the best pinion phase angle model is established. Then, the influences of both assembly sequence and phase angles of pinions on the loading sharing of floating planetary gear sets with 4-6 pinions are studied. Finally, general pinion assembly strategies, combining pinion sequence rules and orientation rules, are proposed. Results indicate that the proposed strategies not only improve the loading sharing conditions dramatically but also acquire robustness.