壓電元件最佳化設計

Abstract

壓電材料因具有轉換機電能之壓電效應，被廣泛應用於各種元件設備如超音波元件、倒車雷達、散熱風扇元件之中。在壓電元件眾多設計目標之中，探討元件整體機電轉換能力之機電耦合因子 (electromechanical coupling coefficient , Kd) 無疑為設計上重要之考量。本研究透過整合壓電理論分析與結構最佳化設計之方法，推導適用於模擬壓電元件屬於梁構造之壓電複合梁元素 (piezoelectric beam element) ，並利用推導之元素模擬梁型壓電元件之靜態位移，此結果與套裝有限元素軟體ABAQUS模擬結果相互吻合；同時並利用推導之元素針對目前廣泛使用之壓電風扇元件進行機電偶合因子之最佳化設計，其結果與利用解析式設計結果相比對亦充分吻合。此外，亦針對由彈性材料內嵌壓電材料之壓電致動元件，透過結構最佳化演進法 (evolutionary structural optimization，簡稱ESO) ，並提出利用模態追蹤之方法，設計出優化機電偶合因子之元件拓樸形狀。

According to the piezoelectric effects, piezoelectric materials have been widely used in all kinds of devices including ultrasonic devices, reverse sensors, and cooling fans. These applications require goals such as high electromechanical energy conversion and thus raising electromechanical coupling coefficient (Kd) becomes a major consideration. In this study, we integrate piezoelectric theory analysis and finite element method to deduce piezoelectric beam element capable of simulating piezoelectric devices. By using the deduced element, we simulated the static displacement of the piezoelectric beam. The results agreed with the results simulated from ABAQUS. Furthermore, we design the widely used piezoelectric fans by using the deduced element to optimize Kd. The results agreed with the results derived from the analytical method. For the piezoelectric actuator, using evolutionary structural optimization (ESO) and the so-called mode tracking method to design the topology of piezoelectric actuator with optimized Kd.