Modified Zener Theory to Accurately Predict Impact Force Histories for Soft Impactors Employing Spiral Sensing

While predicting the impact force histories from the Zener impact model with different material properties of impactors, several discrepancies were observed and reported in this article. To overcome these discrepancies, a modified Zener model is proposed to accurately calculate impact force histories. In the original Zener theory, nonlinear Hertzian contact law was used, and it was assumed that impact forces are transmitted through natural intensity factors depending on coupled physical properties of the plate and the impactor. However, when the force histories were predicted, a diverging trend appeared for softer materials with elastic moduli below 20 GPa. It is hypothesized that the primary reasons for this divergence are due to the contact time delay and the viscoelastic dissipation of energy, which are not considered in current Zener models. Several modifications of the model have been proposed since its inception, but it has been found that they are not independently sufficient to accurately predict impact force histories. In this article, a modified Zener theory is proposed introducing two new parameters in the governing differential equation derived from the sensor phase lag index and the dominant frequency band through a set of experiments employing a spiral sensing mechanism followed by an optimization process. The spiral lag index shows an unexpected peculiar trend with soft impactors (< 20 GPa), which are distinctly different from hard impactors and are judicially incorporated in the model. Furthermore, the force histories are accurately reconstructed with the proposed modifications.