# Grindball

**Kristofer Leach, Juan Gomez**

This project is a cooperation work together with the laboratory for micro cutting (LFM) and institute for electric drives (IALB) at the University of Bremen. Central idea of the projects is the development of a mircoscopic axis-less grinding tool. The central element of the grinding tool is a microscopic ball, which is driven by hydraulic forces of a surrounding liquid bed. Additionally the ferromagnetic ball position is controlled by an electromagnetic field. Because of the high liquid mass flux, needed by the hydraulic driving system, the Reynolds number of the flow inside the sphere gap is increasing over the critical Reynolds number of transient turbulent flow. Therefore the hydraulic shear forces depend on the thickness of the turbulent shear layer at the ball surface. Primary topic of this research project is the fluid/structure interaction of transient turbulent shear flows in an electromagnetic controlled positioning system. Changing the position of the grinding ball the flow character of the surrounding liquid flow changes depending on th minimum gap size between the ball and its bed.

The tool consists of an abrading sphere which is mounted inside a spherical gap using a magnetic bearing. The sphere is set in rotation pneumatically with air which is led into the gap via a duct. The optimal diameter for the duct is chosen as large as possible while it should not greatly exceed the height of the spherical gap it leads into.

Standard volumetric flow rates of up to h result in astable sub-sonic flow using air. Turbulent behaviour is observedinside the spherical gap which justifies use of an LES model.During the simulation, pressureand momentum forces acting onthe sphere are determined. Sincethe rate of rotation is given asa fixed boundary condition, tangentialforce transferred on to thesphere is equivalent to the forcethat would be available to the abrasionprocess in practise. Hence,conducting a series of simulationswith varying flow rates and rotation frequencies aids in determiningthe momentum transfer and its relation to standard volumetric flowrate , and rotation frequency . Simulations show a linear correlationbetween momentum transferand rotation frequency. Momentumtransfer displays a quadraticdependence on flow rate fora stationary sphere , andthe idle rotation frequency (rotation frequency for ) can beexpressed as a root function of theflow rate.