Static lumped parameter model for nested PZT cellular actuators with exponential strain amplification mechanisms

A static lumped parameter model is proposed for the design and analysis of nested piezoelectric cellular actuators with exponential strain amplification mechanisms. Piezoelectric ceramic material, such as Lead Zirconate Titanate (PZT), has large stress and bandwidth, but its extremely small strain, i.e. only 0.1%, has been a major bottleneck for broad applications. We have proposed a "nested rhombus" multi-layer mechanism for PZT actuators, which increases strain exponentially through its hierarchical cellular structure, for over 20% effective strain. To drive a large load, however, care must be taken in the design of the strain amplification structure. Through kinematic and static analysis this paper addresses how the output force and displacement are attenuated by the joint stiffness and beam compliance involved in the strain amplification mechanism. An insightful lumped parameter model is developed to quantify the performance degradation and facilitate design trade-offs. A prototype nested PZT cellular actuator that weighs only 15 g has produced 21% effective strain (2.49 mm displacement from 12 mm actuator length) and 1.7 N blocking force.