By designing an actuator composed of thin layers with different coefficients of thermal expansion (CTE) together with an electrically conductive layer, the CTE mismatch can be utilized to produce soft electrothermal actuators (ETAs). These actuators have been typically implemented using only two layers, commonly relying on Timoshenko's analytic model that correlates the temperature to the actuator's curvature. In this study, we extend the analytic model to include the thermoelectric relation present in ETAs, that is, the conductive layer's properties with respect to the operation temperature. By applying the thermoelectric relation, a minimal voltage optimization can be applied to the analytic model. Using dimensionless analysis, we optimize the ETAs performance for both bi- and tri-layer ETAs with and without the thermal modeling. The bi-layer optimization not only predicts the maximal value for the bi-layer performance but also provides the optimal thickness of each layer for any couple of materials. We validate the tri-layer analytic model experimentally by measuring the curvature for different third layer thicknesses. Finally, we optimize the tri-layer design based on the analytic model, which can achieve an improvement in curvature per voltage of >3000% over the optimal bi-layer ETA.

中文翻译：

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最小电压操作的三层电热执行器设计

通过设计由具有不同热膨胀系数（CTE）的薄层和导电层组成的执行器，CTE不匹配可用于生产软电热执行器（ETA）。这些执行器通常仅使用两层来实现，通常依赖于Timoshenko的解析模型，该模型将温度与执行器的曲率关联起来。在这项研究中，我们扩展了分析模型，以包括ETA中存在的热电关系，即导电层相对于工作温度的特性。通过应用热电关系，可以将最小电压优化应用于分析模型。使用无量纲分析，无论有无热模型，我们都针对双层和三层ETA优化了ETA性能。双层优化不仅可以预测双层性能的最大值，而且可以为任何一对材料提供每层的最佳厚度。我们通过测量不同第三层厚度的曲率，通过实验验证了三层分析模型。最后，我们基于分析模型对三层设计进行了优化，与最佳双层ETA相比，每电压的曲率可以提高> 3000％。