Multiscale Methods for the Flow During Grinding

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Crowson, Zakhary (2023) Multiscale Methods for the Flow During Grinding. PhD thesis, University of Nottingham.

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Abstract

When the machining process known as grinding is used, a grinding fluid is applied to regulate the temperature of the workpiece and reduce the risk of expensive thermal damage. The factors which influence the transport of this fluid are not well understood. However, they are important to understand otherwise unnecessary cost can be incurred from inefficient application of the grinding fluid.

This thesis identified three length scales of the flow during surface and creep-feed grinding, and used asymptotic methods on a multiphase model to derive a multiscale system of equations governing the flow. Under the lubrication approximation, we have shown that it is possible to calculate the flux through the grinding zone without having to solve for the flow far from the grinding zone. No extra empirical boundary conditions need to be imposed. This was done using the method of matched asymptotic expansions.

Focusing on Trizact abrasive profiles, we used two-scale homogenisation on the grinding zone flow to derive a model at realistic Reynolds numbers. We found that the angle of orientation of the abrasives influenced the velocity of the flow across the grinding zone. In particular, we observed that the angle affected the speed at which the grinding fluid was transported through the grinding zone, as well as which side of the grinding wheel that grinding fluid leaked out of.

We also identified potential regimes where the flow became turbulent in the grinding zone, finding that the onset of turbulence occurred at lower Reynolds number when there was a larger concentration of grinding fluid surrounding the abrasives. This finding supports an existing argument against the use of flooding the grinding zone prior to start-up and during the grinding process.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Billingham, John
Houston, Paul
Axinte, Dragos
Keywords: tribology, grinding operations, flow equations, Navier-Stokes equations
Subjects: Q Science > QA Mathematics > QA299 Analysis
T Technology > TJ Mechanical engineering and machinery
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 71898
Depositing User: Crowson, Zakhary
Date Deposited: 04 Oct 2023 09:23
Last Modified: 04 Oct 2023 09:23
URI: https://eprints.nottingham.ac.uk/id/eprint/71898

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