Michael Rom

Mathematical modeling of ceramic bond bridges in grinding wheels

Ceramic-bonded grinding wheels with cubic boron nitride (CBN) as grain material belong to the most efficient grinding tools available. They feature a high hardness combined with a high thermal stability and the applicability to grinding ferrous materials. However, the appropriate volumetric composition of grain and bonding material is an expensive and time-consuming process based on experience. Our objective is the mathematical modeling of grinding wheel structures for the prediction of compositions which fulfill given grinding requirements such that using trial and error methods can be avoided. For this purpose, we focus on a three-dimensional element of a grinding wheel which we call volumetric structure element. In this paper, we briefly describe our overall modeling approach and present in detail how we model the ceramic bond. For the latter, we combine analytical and discrete calculations, embedded into an iterative algorithm which ensures to meet bond volume fractions prescribed by grinding wheel specifications.

Reparametrization and Volume Mesh Generation for Computational Fluid Dynamics Using Modified Catmull-Clark Methods

A new technique is presented for using the Catmull-Clark subdivision method, modified for modeling sharp creases, to generate volume meshes used in computational fluid dynamics. Given a target surface of arbitrary genus, e.g., defined by a collection of trimmed B-spline patches, which represents an object in a flow, a simple polyhedron is constructed roughly approximating this target surface. After one Catmull-Clark subdivision, the polyhedron exclusively consists of quadrilaterals and its Catmull-Clark limit surface can be pre-computed. Points of the limit surface are projected onto the target surface and the control points of the polyhedron are adjusted by approximating the projected points. An iterative process of alternating subdivisions, projections and approximations leads to a watertight mesh consisting of untrimmed surface patches matching the given target surface. By attaching an offset mesh and a far-field mesh, a block-structured volume mesh is obtained, being well-suited for adaptive flow solvers.