The effectiveness of a piezoelectric bimorph to perform mechanical work against various spring-type loads

The equations governing the energy and work relations for a piezoelectric bimorph working against a spring-type load are derived. A work cycle is assumed in which a piezoelectric bimorph pushes against a spring, compressing it, after which the spring is latched in position, ready to transfer its energy in a process where it can be used. The energy stored in the spring is calculated and related to the electrical energy taken in by the bimorph to enable it to compress the spring. An effectiveness μ is defined as the ratio of the energy transferred by the bimorph and the energy put in by the generator. Three types of springs are considered: a helical spring, attached at the tip to generate a moment M at the tip that depends on the rotation α of the tip; a coil spring, attached at the tip to provide a force F, proportional to the deflection; and a gas spring acting uniformly over the entire length of the bimorph, with a pressure p that is proportional to the displaced volume V. The effectivenesses μM, μF, μP are calculated. The maximum effectiveness is found as the spring constant KM, KF, Kp is varied.