Concept System and Application of Point Group Symmetry in Mechanical Structure Design

Symmetry has been widely and deeply researched in basic science, and many mature results have been obtained so far. However, the widespread existence of symmetry in applied science is not in direct proportion to the attention it has received. Through a large number of examples studies, almost all mechanical structures are found to have symmetry, and most of them have the characteristics of point group symmetry. Therefore, the concept of point group symmetry in crystallography was extended to the field of machinery and adjusted according to the mechanical structures. First of all, the classification of mechanical point group symmetry is proposed, and how point group symmetry is applied in machinery is illustrated with examples. Then, the requirements of symmetry are analyzed and compared. Furthermore, the data mining software RapidMiner is used to mine the association rules between requirements and symmetry. Based on the mining results, the four selection principles of point group symmetry are summarized to provide ideas for structure design. Finally, a new type of gear pump with radial force balancing is invented by comprehensively using the mining results and selection principles.

[1]  Lisa L. Everett,et al.  The double cover of the icosahedral symmetry group and quark mass textures , 2010, 1011.4928.

[2]  Alphose Zingoni,et al.  Group‐theoretic exploitations of symmetry in computational solid and structural mechanics , 2009 .

[3]  Steen A. Andersson,et al.  General canonical correlations with applications to group symmetry models , 2010, J. Multivar. Anal..

[4]  Richie Nimmo,et al.  Animal Cultures, Subjectivity and Knowledge: Symmetrical Reflections Beyond the Great Divide , 2012 .

[5]  Sean N. Brennan,et al.  Observability and Controllability of Nonlinear Networks: The Role of Symmetry , 2013, Physical review. X.

[6]  E. V. Chuprunov,et al.  The application of group theory to the description of pseudosymmetry , 2011, Biology Bulletin Reviews.

[7]  Xudong Jiang,et al.  LBP-Structure Optimization With Symmetry and Uniformity Regularizations for Scene Classification , 2017, IEEE Signal Processing Letters.

[8]  Stanislav Yu. Lukashchuk,et al.  Approximate symmetry group classification for a nonlinear fractional filtration equation of diffusion-wave type , 2018 .

[9]  S. Balaji,et al.  Internal symmetry in protein structures: prevalence, functional relevance and evolution. , 2015, Current opinion in structural biology.

[10]  Hector Sabelli,et al.  Asymmetry, Symmetry and Beauty , 2010, Symmetry.

[11]  James J. P. Stewart,et al.  Symmetry groups for unit cells in solids , 1998, J. Comput. Chem..

[12]  Michael Leyton.  Group Theory and Architecture , 2001 .

[13]  Francisco G. Montoya,et al.  Symmetry in Engineering Sciences , 2019, Symmetry.

[14]  Fang Zhen Song,et al.  The Frequency Veering Phenomena of the Beams of Cantilever Screen , 2012 .

[15]  Barry M. Trost and,et al.  On the Question of the Symmetry of Formally Symmetrical π-(Allyl)palladium Cationic Intermediates in Allylic Alkylations , 1996 .

[16]  Jun Li,et al.  Symmetry Hierarchy of Man‐Made Objects , 2011, Comput. Graph. Forum.

[17]  Ralph R. Martin,et al.  Detecting design intent in approximate CAD models using symmetry , 2010, Comput. Aided Des..

[18]  Péter L. Várkonyi,et al.  Symmetry, Optima and Bifurcations in Structural Design , 2006 .

[19]  Qingying Qiu.  Part Assembly Efficiency Prediction Model Based on Multi-symmetry Features , 2017 .

[20]  Zhifeng Yao.  Effects of Impeller Type on Pressure Fluctuations in Double-suction Centrifugal Pump , 2011 .

[21]  Vito Di Gesù,et al.  Symmetry as an Intrinsically Dynamic Feature , 2010, Symmetry.