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Modeling Scenario

5-090-SolidParticleErosion-ModelingScenario

Author(s): Rich Laverty

The Boeing Company, Ridley Park PA USA

Keywords: classical mechanics solid mechanics Newton's Laws of Motion rigid body plasticity pitting ductile surface

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Abstract

Resource Image By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges material from a more ductile surface.

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Description

Examination of the solution will yield a formula for the volume of the gouge, that is, the amount of surface material eroded from a single impact.

The process of erosion is familiar to most of us from Earth science, where water or wind removes material from one location and transports it to another.

However, it is also an important industrial process. We can think of erosion more generally as solid particles, entrained by a fluid, attacking and removing material from a surface.

This process can adversely affect the performance and life of such equipment as pipes, turbines, and helicopter rotorblades. It is also the cause of the corona effect, sometimes called the Kopp-Etchells effect, experienced by helicopters where small pieces of eroded metal can oxidize and illuminate the rotorblades - a dramatic, but obviously undesirable condition for military operations.

On the other hand, erosion can have useful applications such as sand blasting, abrasive deburring, and drilling hard materials. For a process of such significance, both good and bad, an understanding of the basic physical processes involved is required to take measures to either mitigate or take advantage of its effects.

In this project we will develop a mathematical model of the cutting process by which a relatively rigid particle removes material from a ductile surface. The canonical situation would be a piece of sand striking a metal surface. The mathematical model will be in the form of a system of differential equations resulting from application of Newton's Second Law of Motion. Our model is based on the first published attempt at an analytical description of solid particle erosion.

From the solution we will be able to determine the conditions for maximum material removal, and the role played by the different physical parameters of the model. In particular, we will be interested in the angle of attack at which maximum material removal occurs.

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Authors

Author(s): Rich Laverty

The Boeing Company, Ridley Park PA USA

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