Abrasion of flat rotating shapes

TL;DR

This study investigates how flat shapes erode under rotation in abrasive slurry, developing a new imaging method to quantify shape changes over time and confirming a simple radial inward movement model.

Contribution

A novel imaging and analysis technique for quantifying shape evolution during abrasion, and validation of a simple radial erosion model.

Findings

Shapes tend toward a circle as abrasion progresses.

The erosion process is well described by a model where contour points move inward proportionally to radius and its angular derivative.

Quantitative agreement between experimental data and the proposed model.

Abstract

We report on the erosion of flat linoleum "pebbles" under steady rotation in a slurry of abrasive grit. To quantify shape as a function of time, we develop a general method in which the pebble is photographed from multiple angles with respect to the grid of pixels in a digital camera. This reduces digitization noise, and allows the local curvature of the contour to be computed with a controllable degree of uncertainty. Several shape descriptors are then employed to follow the evolution of different initial shapes toward a circle, where abrasion halts. The results are in good quantitative agreement with a simple model, where we propose that points along the contour move radially inward in proportion to the product of the radius and the derivative of radius with respect to angle.