An estimate of spherical impactor energy transfer for mechanical frequency up-conversion energy harvester

Vibration energy harvesters, which use the impact mechanical frequency up-conversion technique, utilize an impactor, which gains kinetic energy from low frequency ambient environmental vibrations, to excite high frequency systems that efficiently convert mechanical energy to electrical energy. To take full advantage of the impact mechanical frequency up-conversion technique, it is prudent to understand the energy transfer from the low frequency excitations, to the impactor, and finally to the high frequency systems. In this work, the energy transfer from a spherical impactor to a multi degree of freedom spring / mass system, due to Hertzian impact, is investigated to gain insight on how best to design impact mechanical frequency up-conversion energy harvesters. Through this academic work, it is shown that the properties of the contact (or impact) area, i.e., radius of curvature and material properties, only play a minor role in energy transfer and that the equivalent mass of the target system (i.e., the spring / mass system) dictates the total amount of energy transferred during the impact. The novel approach of utilizing the well-known Hertzian impact methodology to gain an understanding of impact mechanical frequency up-conversion energy harvesters has made it clear that the impactor and the high frequency energy generating systems must be designed together as one system to ensure maximum energy transfer, leading to efficient ambient vibration energy harvesters.