Dimensionless parameter-based numerical model for double conical dielectric elastomer actuators

Abstract

As the development of soft actuators progresses, new methods for more agile actuator control are required. While there are hardware technologies that can provide such agility (e.g. field-programmable-gate-array electronics), mathematical models tend to slow the controlling processes. For the case of double conical dielectric elastomer actuators (DCDEAs), complex material and physical models are often utilized; however, such models require extended computational time which limits real-time control and prediction, especially in small, portable applications. The foregoing problem is augmented, if agile applications require reprogramming on the fly. In this work, a parameter-based dimensionless model applicable to DCDEAs was developed. The proposed model: (a) relates a dimensionless displacement with a characteristic dimensionless voltage via a power-law equation; (b) is robust enough to accurately describe 5-Degree-of-Freedom motion; (c) is scalable (at least within the range of geometries and parameters used in this study); (d) due to its mathematical simplicity, it could be used for more agile controls. For the development of the model, multiple DCDEAs were manufactured by varying design parameters such as pre-stretch, thickness, dielectric constant, shear modulus, electrode area, and inner and outer radii. By applying the Levenberg-Marquardt best-fit algorithm to experimental data sets containing voltage and (translational and rotational) displacements, a general relationship was found between parameter-based dimensionless quantities and a general dimensionless displacement. The relationship was further simplified via a single dimensionless number related to the actuator design. The model was found to be accurately predictive for VHB4910 and VHB4905. The resulting model is simple and has potential to be used for a wide range of dielectric-elastomer materials.