Design and calibration of spherical particles with embedded inertial measurement unit: preserving kinematic equivalence

Abstract

This study presents the design, verification, and calibration of a spherical inertial sensor particle engineered to achieve kinematic equivalence with a solid sphere. Utilizing micro-electro-mechanical systems inertial measurement unit technology, this 40 mm particle is capable of measuring triaxial acceleration up to ±16g (g = 9.81 m/s²) and triaxial angular velocity up to ±2000°/s, with a high sampling rate of 1000 Hz sustained over one hour. The sensor particle features a dual-layered spherical structure designed to ensure equivalence in shape, density, center of mass, moment of inertia, and elastic modulus compared to a solid sphere. The performance of the sphere is calibrated and verified with a series of physical experiments. The experiment of the sphere freely sinking in still water confirmed the accuracy of the data measured by the sensor particle and its equivalence to a solid aluminum sphere. This study provides a more representative tool for measuring particle motion information in homogeneous dense granular experiments.