Effective mass of powder beds subjected to low magnitude vibration and its application to binary systems: Part 1—experimental methodology

Abstract

Spring and damper models of the mechanical properties of powder beds rely on treating the distributed mass of the powder bed as a point mass, or effective mass, which differs from the real bed mass. This paper presents an experimental methodology to determine the effective mass of powder beds at low applied vibration (<0.1 g) where the bed remains a coherent entity, using a vibrating bed of powder surmounted by a top-cap mass. Two types of transfer functions, apparent mass T fa , defined as a ratio of base force to base acceleration, and acceleration transmissibility T aa , defined as a ratio of top-cap acceleration to base acceleration, were used for the determination. Theoretical analysis demonstrates that it is possible to estimate experimentally the effective mass from only the slope d T fa /d T aa below half of the resonant frequency, without any arbitrary fitting parameters. Powders were enclosed in a vertical, open, cylindrical vessel, surmounted by a top-cap mass plus accelerometer, and subject to vibration at the base, through an impedance head consisting of an accelerometer and force transducer. Experiments were performed on a range of sample powders, including glass spheres, sands, polyethylene and rubber powders. The experimental transfer function data conformed to the theoretical trends, and the slope corresponding to the effective mass was dependent upon sample powders, top-cap and the bed masses. Furthermore, a comparison of the experimental effective mass data and theoretical values based upon Rayleigh's energy method was made. Results showed a reasonable agreement between the experimental data and the Rayleigh's approximation.