Dynamic Lumped Parameter Modeling and Stability Analysis of Planar Hydraulically Amplified Dielectric Elastomer Actuators

Hydraulically amplified dielectric elastomer actuators (HADEAs) comprise a hyper-elastic inflatable membrane filled with an incompressible dielectric fluid and partially covered with a pair of electrodes. Applying voltage to the electrodes induces Maxwell pressure, attracting them and forcing the peripheral membrane to inflate. We present a dynamic lumped parameter model (LPM) of a HADEA and discuss the dynamic response and the actuator's stability. The total kinetic energy was determined with a Lagrange description for the fluid flow. Lubrication theory was used to estimate the viscous fluid friction losses between the electrodes. Stability analysis of the dynamic LPM shows a Lyapunov stable node moving with the applied voltage, and a saddle point representing the snap-through instability in the actuator. A dynamic finite element model (FEM) was developed for comparison. The dynamic responses of the LPM showed a good agreement with the FEM while overestimating the viscous losses in the presence of a slight angle between the electrodes.