結合系統動力學與黏彈性材料建模之慣性測量單元於隔振平台設計與效能驗證

Abstract

本研究針對高精度慣性測量單元(IMU)在動態環境下之抗振性能進行深入探討，核心目的為建立具物理意義之黏彈性模型，並導入於IMU隔振系統之設計與性能分析中。研究方法採用擴展型Maxwell黏彈性模型對隔振材料進行參數化建模，透過三項實驗技術，拉伸試驗、靜態剛度測試及動態機械分析(DMA)進行材料性質之量測與參數反饋，精確識別矽膠(Silicone)與丁腈橡膠(NBR)在不同應變與頻率下之黏彈行為。根據所得材料模型，建立IMU系統六自由度(6DOF)完整動力學模型，分析不同隔振器元件佈置方式與結構設計參數對結構系統耦合程度之影響，並探討在何種條件下能實現動態完全解耦與軸向響應獨立性。 為驗證模型準確性與實用性，本研究進行多階段驗證流程，包含有限元素法(FEA)模擬分析、振動台實驗與古典衝擊試驗。分析結果顯示，建立之黏彈性模型不僅能合理描述材料在寬頻率範圍內之力學行為，亦能準確預測隔振器於實際組裝後的動態反應。進一步針對IMU內部之關鍵感測元件，陀螺儀與加速度計進行VRE(Vibration Rectification Error)性能評估，探討材料性質與隔振結構對感測器穩定性與量測誤差的影響。研究結果指出，透過合適之材料選擇與結構解耦設計，能顯著抑制外部振動進入IMU核心結構，進一步降低VRE效應，提升感測精度與長期穩定性。 本研究成功整合材料實驗、理論建模、動態模擬與系統驗證四大構面，提出一套可延伸至其他精密感測平台之隔振設計與建模流程，具備高度工程應用價值。所建模型可作為未來高性能IMU開發與設計最佳化之理論依據，亦有助於進一步提升航太、精密導航與動態監測等領域對於振動抑制與感測精度的整體表現。

This study investigates the vibration mitigation performance of high-precision Inertial Measurement Units (IMU) under dynamic environments, with the core objective of establishing a physically meaningful viscoelastic model and applying it to the design and performance analysis of IMU isolation systems. An extended Maxwell viscoelastic model was adopted to parameterize isolation materials, supported by three experimental techniques: tensile testing, static stiffness measurement, and Dynamic Mechanical Analysis (DMA). These methods enabled precise characterization and parameter identification of the viscoelastic behavior of silicone and nitrile rubber (NBR) across varying strains and frequencies. Based on the obtained material models, a comprehensive six-degree-of-freedom (6DOF) dynamic model of the IMU system was developed to analyze how different isolator arrangements and structural design parameters influence system coupling and to determine conditions under which dynamic full decoupling and axial response independence can be achieved. To validate the accuracy and practical applicability of the model, a multi-stage verification process was conducted, including Finite Element Analysis (FEA), vibration table testing, and classical shock experiments. The analysis demonstrated that the established viscoelastic model not only accurately describes material mechanical behavior over a wide frequency range but also reliably predicts the dynamic response of isolators after assembly. Furthermore, critical IMU sensing components—gyroscopes and accelerometers—were evaluated for Vibration Rectification Error (VRE) performance, examining how material properties and isolation structure design impact sensor stability and measurement error. Results indicate that appropriate material selection combined with effective structural decoupling design can significantly suppress external vibrations transmitted into the IMU core, thereby reducing VRE effects and enhancing measurement precision and long-term stability. This research successfully integrates four key aspects: materials experimentation, theoretical modeling, dynamic simulation, and system-level validation. It proposes a versatile isolation design and modeling workflow applicable to other precision sensing platforms, offering high engineering value. The developed models provide a theoretical foundation for the optimization and development of next-generation high-performance IMU, supporting improved vibration suppression and sensing accuracy in aerospace, precision navigation, and dynamic monitoring applications.