Driving force profile design in comb drive electrostatic actuators using a level set-based shape optimization method
Driving force profile design in comb drive electrostatic actuators using a level set-based shape optimization method
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DOI：
10.1007/s00158-014-1130-y
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发表时间：
2015-02
影响因子：
3.9
通讯作者：
Takayo Kotani;T. Yamada;S. Yamasaki;M. Ohkado;K. Izui;S. Nishiwaki
中科院分区：
文献类型：
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作者：
Takayo Kotani;T. Yamada;S. Yamasaki;M. Ohkado;K. Izui;S. Nishiwaki
静电致动器是由静电力驱动的致动器，目前被广泛用作传感器和开关，特别是在微电子机械系统(MEMS)中。在不同类型的静电驱动器中，梳子驱动型是最受欢迎的一种，因为它具有相对较大的位移范围。在静电执行器的设计问题中，驱动力分布具有重要的工程意义。本文提出了一种梳齿驱动静电作动器的结构优化方法，该方法基于水平集的形状优化方法，提供了边界清晰的最优构型，其解在工程意义上是有效的。精确计算优化过程中结构边界上发生的静电力对于开发以规定的驱动力工作的执行器非常重要。在传统的基于水平集的形状优化方法中，由于结构边界很少与有限元节点对齐，因此在计算这些静电力时会出现不准确的情况。为了精确地计算静电力，我们开发了一种网格自适应方案，通过该方案，在优化过程的每一次迭代中，有限元节点与结构边界对齐。在下文中，我们解释了所提出的基于水平集的形状优化方法的细节，在该方法中，建立了一个多目标优化问题，以获得给定的驱动力轮廓。用伴随变量法求出了灵敏度。文中给出了四个数值算例，验证了所提优化方法的适用性。
Electrostatic actuators, actuators actuated by electrostatic forces, are now widely used as sensors and switches, especially in Micro-Electro-Mechanical Systems (MEMS). Among different kinds of electrostatic actuators, the comb drive type is one of the most popular because it has a relatively large range of displacement. In design problems for electrostatic actuators, the driving force profile is of primary engineering importance. In this paper, we develop a structural optimization method for comb drive electrostatic actuators that achieves prescribed driving force profiles, based on a level set-based shape optimization method that provides optimal configurations with clear boundaries, solutions that are valid in an engineering sense. Accurate calculation of the electrostatic forces that occur on the structural boundaries during optimization is important for developing actuators that operate with prescribed driving forces. In the conventional level set-based shape optimization methods, inaccuracies in the calculation of these electrostatic forces occur because the structural boundaries are seldom aligned with the finite element method (FEM) nodes. To precisely calculate the electrostatic forces, we developed a mesh adaptation scheme by which the finite element nodes are brought into alignment with the structural boundaries at every iteration of the optimization procedure. In the following, we explain the details of the proposed level set-based shape optimization method, in which a multi-objective optimization problem is formulated to achieve a prescribed driving force profile. The sensitivity is derived using the adjoint variable method. Four numerical examples are provided, to examine the suitability of the proposed optimization method.