Affiliations: CTVR, Stokes Institute, University of Limerick,
Limerick, Ireland | Bell Labs Ireland, Alcatel-Lucent, Blanchardstown
Industrial Park, Dublin 15, Ireland
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.
