A method for calculating abrasive sharpness in abrasive wear

Abrasive wear holds significant importance in industrial and agricultural production, often leading to high losses, energy consumption, and pollution in machinery. The geometric characteristics of abrasives participating in wear play a crucial role. Based on the characteristics of two-body abrasive wear, this study presents a complete computational workflow from abrasive contour acquisition to average sharpness calculation. The work employs the equivalent circle method to divide particle profiles into two parts: the area inside and outside the equivalent circle. According to abrasive wear characteristics, only the contour sharpness outside the equivalent circle is calculated, substantially reducing computational workload while improving efficiency. Furthermore, more precise sharpness values are obtained by dynamically selecting the highest point on the external arc of the equivalent circle to either its two intersection points or tangent points with the circle. Scanning arc segments to identify secondary peak positions ensures that protruding parts of particles are not omitted in sharpness calculations. For three-body abrasive wear, a criterion for distinguishing rolling versus sliding of approximately triangular particles is proposed, providing a basis for estimating material wear. Finally, the computational methods proposed herein are validated using Rabinowicz's classical model and Stachowiak's wear experiments. The results demonstrate that material wear increases with abrasive particle sharpness in both two-body and three-body abrasive wear, confirming the reliability of the proposed methods.