Analytical Modeling of a Segmented Bimorph Lithium Ion Battery Actuator

Abstract

Silicon composite anode-based lithium ion battery actuators have strong potential for large actuation strain, complex shape change, and large compliance tunability. This allows for actuators with potential to do work with no energy expenditure beyond parasitic losses to internal resistance. This paper studies a segmented bimorph actuator comprised of a silicon-based composite anode double-side coated on copper foil. The bimorph design allows for a nearly 360° range of motion in transverse bending and can double the capacity of the battery in comparison to a single side coated unimorph design. An Euler-Bernoulli model is developed to predict free deflection for a range of geometric configurations and states of charge of the bimorph. By modeling the charging of both active sides of the bimorph simultaneously, it is possible to achieve zero bending while still accommodating for the volumetric expansion of the silicon. The bimorph is able to achieve actuation in one given direction by charging each anode coating separately or maintaining a charge difference between the two coatings. The former method allows for the accommodated volumetric expansion of silicon while maintaining zero bending as in a conventional battery setup. The latter method allows for larger battery capacity and range of motion for a novel electrochemically-based actuation mechanism.

Analytical modeling of a multilayer, multimorph lithium-ion battery actuator

“…Models of unimorph (Gonzalez et al, 2021) and bimorph (Gonzalez et al, 2020) LIBs have been published previously by the authors and are reviewed briefly here. A schematic for an N Layer , N Seg multimorph is shown in Figure 1.…”

“…The authors have previously reported the derivation of the actuator metrics here for a unimorph and the free deflection of a bimorph (Gonzalez et al, 2020, 2021). The free deflection and blocked deflection are found by taking the free curvature κ j and finding the local deflections, then using a transformation of coordinates to find the global deflections.…”

“…For a range of β Eff values (5%–45%) with a given increment (0.5%), the deflection resulting from a best fit β Eff for various SOC is shown in Figure 7. In previous work for a two layer unimorph (Gonzalez et al, 2021) or three layer bimorph (Gonzalez et al, 2020) and for the case studies of this work, β Eff is assumed to be a linear strain constant of β = 17 % , however, the validity of this assumption is tested here. The best β Eff is defined to be the value of β Eff with the smallest root mean squared error (RMSE) between the experimental deflection tip deflection and model deflection at each SOC.…”

“…This model is further developed by the authors for predicting the free deflection (Gonzalez et al, 2018), as well as blocked force and blocked deflection of segmented unimorphs (Gonzalez et al, 2019(Gonzalez et al, , 2021. The model is then extended into a bimorph configuration to predict free deflection of a segmented bimorph (Gonzalez et al, 2020).…”