Limits to inertial vibration power harvesting: power-spectral-density   approach and its applications
  Maximum output powers of vibration-driven inertial power harvesters reported in literature exhibit sizable variations, even when normalized by the device weight or their maximum linear size. To help establish a common benchmark, we present a power-spectral-density based approach for estimating the maximum power that can be obtained using a resonant inertial power harvester from a random (aperiodic) vibration source with a given power spectral density. In the simplest case of unlimited harvester size, the maximum obtainable power is simply proportional to the maximum value of the power spectral density of vibration acceleration. We describe in detail the underlying theory and the practical method for evaluating these limits. We also present a simple analytical formula to estimate the minimum harvester size required for obtaining the maximum possible power. Specific power limits are derived as function of harvester size for three practical examples of vibration sources: (a) pneumatic power tool, (b) the body of an idling Mazda RX7 sports car, and (c) human walking motion. Characteristic power spectra and optimum design parameters (quality factor and resonant frequency) are presented for both translational and rotational harvesters. Translational harvesters generally outperform rotational ones for realistic harvester sizes, with the power tool vibrations yielding a practical power limit of ~300 mW per gram of inertial mass, followed by walking at ~1mW/g, while the vibrations of a car body yield ~0.1 mW/g or less. 
Akshay Ananthakrishnan, Inna Kozinsky and Igor Bargatin
cond-mat.other