Quantitative analysis of impact measurements using dynamic load cells

Abstract

A mathematical model is used to estimate material properties from a short duration transient impact force measured by dropping spheres onto rectangular coupons fixed to a dynamic load cell. The contact stress between the dynamic load cell surface and the projectile are modeled using Hertzian contact mechanics. Due to the short impact time relative to the load cell dynamics, an additional Kelvin–Voigt element is included in the model to account for the finite response time of the piezoelectric crystal. Calculations with and without the Kelvin–Voigt element are compared to experimental data collected from combinations of polymeric spheres and polymeric and metallic surfaces. The results illustrate that the inclusion of the Kelvin–Voigt element qualitatively captures the post impact resonance and non-linear behavior of the load cell signal and quantitatively improves the estimation of the Young's elastic modulus and Poisson's ratio. Mathematically, the additional KV element couples one additional differential equation to the Hertzian spring-dashpot equation. The model can be numerically integrated in seconds using standard numerical techniques allowing for its use as a rapid technique for the estimation of material properties. Keywords: Young's modulus, Poisson's ratio, Dynamic load cell