Automatic Hexahedral Mesh Generation for Rotating Machine

Abstract

In this paper, an automatic hexahedral mesh generator for rotating machines is proposed. In the proposed method, hexahedral mesh with well-shaped elements is generated by means of transformation of coordinates of the analysis model. The main feature of this method is its applicability for meshing models with cylindrical shape due to provided coordinate transformation forward and backward between Cartesian coordinate system and the cylindrical coordinate system. The previously proposed hexahedral mesh generation method could easily control the mesh density and generate well-shaped elements. However, applying that method to rotating machines, due to their cylindrical shape always generates bad-shaped elements. Therefore, we improved and extended this mesh generation method to become fully applicable for meshing complex cylindrically shaped domains of the rotating machines. By using the newly proposed method, a well-shaped hexahedral finite element meshes could be generated suitable for fast and accurate finite element analysis of any cylindrically shaped domains.

Performance Comparison of Various Hexahedral Element Quality Metrics via Parametric Distortion of an Ideal Element

“…The first metric defined by Maeda et al [2004], which will be denoted by f 1 from now on, is nothing but the sum of the ratio of minimum-maximum edge lengths on the six faces. Mathematically, it can be expressed as follows:…”

Hexahedral Mesh Smoothing by Means of Particle Swarm Optimization

“…Bu qali*mada kullanilan son metrik, yine Maeda ve arkada*larinin ba,ka bir qali*malarinda [6] tanimlami* oldugu kalite metrigine dayanmaktadir. [6]'da tanimlanmi* olan metrik, (7) numarali denklemdeki gibi duzenlenmi,tir: …”

“…X., y, Zi, ***, Xk, Yk, zk) in sadele,mi, hali F(xjl,YI,z1r.r, Zi, .., Xk, Yk, Zk) olacaktir), Amav Fonksiyonlarinin Tanimlanmasi Optimizasyonda kullanilacak olan ama,c fonksiyonu, bir ag kalitesi metriginden tulretilmelidir. Bu qali*mada[4],[5] ve[6]'daki metrikler temel alinmi*tir. Bu metriklerden ilki, Knupp tarafindan tanimlanmi* olan durum sayisi metrigidir[4].Knupp'un metrigi a*agidaki denklemdeki gibi Bu denklemdeki T matrisi, bir elemandaki dugum noktasi koordinatlarindan olu,turulmu, bir matris olup, ITI Frobenius normu olmak kaydiyla 4T)= ITI IT 1olarak ifade edilebilir.…”