The Dynamics of Multiple Pair-Wise Collisions in a Chain for Designing Optimal Shock Amplifiers

Abstract

The major focus of this work is to examine the dynamics of velocity amplification through pair-wise collisions between multiple masses in a chain, in order to develop useful machines. For instance low-cost machines based on this principle could be used for detailed, very-high acceleration shock-testing of MEMS devices. A theoretical basis for determining the number and mass of intermediate stages in such a velocity amplifier, based on simple rigid body mechanics, is proposed. The influence of mass ratios and the coefficient of restitution on the optimisation of the system is identified and investigated. In particular, two cases are examined: in the first, the velocity of the final mass in the chain (that would have the object under test mounted on it) is maximised by defining the ratio of adjacent masses according to a power law relationship; in the second, the energy transfer efficiency of the system is maximised by choosing the mass ratios such that all masses except the final mass come to rest following impact. Comparisons are drawn between both cases and the results are used in proposing design guidelines for optimal shock amplifiers. It is shown that for most practical systems, a shock amplifier with mass ratios based on a power law relationship is optimal and can easily yield velocity amplifications of a factor 5-8 times. A prototype shock testing machine that was made using above principles is briefly introduced.