Bimorph beam model

In the following, an equivalent beam and equivalent bimorph beam model for simple IPMC actuation is first presented. Thereafter more complex actuation configurations and corresponding modeling considerations are provided. 

One way to present a gray box model of IPMC is to use an equivalent beam and an equivalent bimorph beam model and combine them with important physical properties of IPMCs Young s modulus and electromechanical coupling coefficient, determined from the rule of mixture bi-... 

To improve the modeling accuracy, the equivalent bimorph beam model of IPMC, as shown in Fig. 2.38, was developed. It assumes that IPMC has two virtual layers that have the same thickness, and under an imposed electric field, the upper and the lower layers expand or contract, opposing each other. Generally, blocking force and displacement calculations of a bimorph cantilevered beam assume outer layers and an elastic layer between [Wang et al. (1999)]. Here, however, no elastic layer is assumed. Then the relationship between input voltage, V, and induced tip displacement, s, can be written as [Wang et al. (1999)] ... 

The developed bimorph beam model of IPMC was validated using the finite element method (FEM) and the used software was MSC/NASTRAN. As the software does not directly support the electromechanical coupling, the thermal analogy technique as described in [Lim et al. (2005) Taleghani and Campbell (1999)] was used. The simulated versus measured force-displacement relationship of an IPMC actuator is shown in Fig. 2.39. The relative errors for A = 0 between the calculated values and the measured data for 2V and 3V are 2.8% and 3.7%, respectively. The equivalent Young s moduli estimated from the equivalent beam model and the equivalent bimorph beam model are 1.01 GPa and 1.133-1.158 GPa, respectively, which are very close. However, the values from the equivalent beam model... 

Equivalent Bimorph Beam Model for IPMC Actuators... 

To predict the behaviour of IPMC diaphragms, the equivalent bimorph beam model, whieh was recently introduced by Lee et al. [28], is adopted in this study. Here, the key ideas of the model are summarized. 

In the equivalent bimorph beam model (Figure 9.9), it is assumed that an IPMC has two virtual layers of the same thickness. Under an imposed electric field across the IPMC, the... 

Substituting the experimentally measured tip displacement into Equation (9.2), dsj can be obtained for a given input voltage. In the equivalent bimorph beam model, the Young s modulus E) contributing to the bending stiffness of an IPMC is determined from the blocking force Equation (9.3) of a bimorph beam ... 

For all numerical analyses, a commercial finite element analysis program, MSC/ NASTRAN [29], was used in conjunction with the equivalent bimorph beam model. A thermal analogy technique proposed by Taleghani and Campbell [30] was used to implement the electromechanical coupling effect into the finite element model. In the thermal analogy technique, the electromechanical coupling coefficient (dj/) is converted into the thermal expansion coefficient a/ as follows ... 

Parametric studies on two kinds of electrodes for circle-shaped diaphragms with a radius of 10 mm were conducted with the material properties and thicknesses shown in Table 9.2 [3]. The material properties E and dsj of the IPMC in Li" form were determined thorough the equivalent bimorph beam model [28]. The elastic modulus of Nafion in Li form and Poisson s ratios were obtained from literature [32, 33]. Figure 9.10 shows the shape of the two electrodes in a one-quarter finite element model of diaphragms. Figure 9.10a is the circle-shaped electrode and 9.10b is the ring-shaped electrode. 

In this chapter, we have described an IPMC-driven infusion micropump for recent biomedical applications. Even though the applieations of IPMCs for biomedical fields require more trials and development methods, IPMCs are still attractive materials due to their electromechanical and mechanoelectric properties. A systematic design method of an IPMC-driven micropump was introduced. In order to properly estimate the deformed shapes of IPMC diaphragms, the equivalent bimorph beam model for IPMC actuators was conveniently used, in conjunction with the finite element method. 

Lee, S., Park, H. C., Kim, K. J. and Yoon, K. J. (2004) Equivalent beam and equivalent bimorph beam models for ionic polymer-metal composite actuators, J. Control, Automation, and Syst. Eng., 10, 1012-6. 

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