以雙頻雙模態激發法驅動之一維行進波式直線型壓電位移平臺

Abstract

壓電位移平臺由於其高扭矩輸出、低噪音，且電磁干擾極小等優點，因此被廣泛使用於光學定位系統以及醫療器材等需精密定位之運動平臺。然而行進波式直線型壓電位移平臺由於受到有限邊界之影響，波會受到反射波干涉以致不易穩定生成行進波而造成效率不高。過去的研究中發展數種可以穩定在有限結構中穩定生成行進波的方法，其中一種是在結構中藉由激發兩相鄰振動模態，進而疊合出行進波的方法，稱為「雙模態激發法」。然而，傳統的雙模態激發法是藉由驅動單一頻率來激發兩相鄰模態，為了控制對該二模態之貢獻在特定比例，驅動頻率會被限制在某一特定位於該二相鄰模態對應之共振頻率之中間頻率，而驅動頻率又會影響產生之行進波波速，因此無法兼顧產生行進波之品質以及調整行進波之波速。本研究提出了一種新方法，稱為「雙頻雙模態激發法」，其是以兩頻率來激發兩相鄰模態，一個頻率只激發一個模態，並以驅動頻率進行波速調整。 本研究所使用之結構為一不鏽鋼基板，上面黏貼一壓電致動器做為振動源。為了驗證本方法之可行性，本研究基於歐拉-伯努力樑理論，推導此一結構之統御方程式，用以預測結構之振動行為，並以解析及數值方法求得該方程式的解，其中包含了結構之共振頻率與模態，以及頻率響應。接著利用所求得之解，分析雙頻雙模態之驅動條件。為了確認行進波之生成、方向、波速、品質，本研究分別開發了基於形態開運算之行進波軌跡追蹤演算法，以及基於希爾伯特變換定義之損失函數，以分析結構之位移時空圖，並藉此探討驅動頻率、相位、振幅等參數對生成行進波之影響。 實驗部分則先製作該結構之原型，並以阻抗分析儀量測該原型之共振頻率以確認該原型與理論之一致性。再來以掃描式雷射都卜勒振動計量測結構於單頻驅動下之振幅，得到該結構之頻率響應函數。接著以該頻率響應函數作參考，以驅動電壓補償，使結構於雙頻雙模態驅動時得以滿足最佳化位移振幅比值，並在掃描式雷射都卜勒振動計量測下確認行進波之生成並計算其波速。結果確認了理論與實驗的高度一致性，確認了雙頻雙模態法可以有效生成可調波速之行進波。最後則實際以此平臺原型進行載物推動，結果證實在可以運用頻率來改變波速，進而控制載物推動速度。 總而言之，本研究提出了雙頻雙模態激發法驅動一維行進波式直線型壓電位移平臺，並以理論和實驗驗證了該方法。這種新的驅動方法具有對於在簡單結構上進行多維度精密操作可有巨大的應用潛力。

Due to its high torque, low noise, and negligible electromagnetic interferences, piezoelectric motors are widely used for precision motion, such as optical positioning systems and medical devices. However, for traveling-wave type linear piezoelectric motor, it is difficult to stably generate traveling waves in finite structure. The reason is that once wave meets the boundaries, the wave will reflect and interfere with the original incident wave. In past studies, several methods have been developed to stably generate traveling waves in finite structures. “Two-mode excitation method” is to generate traveling waves by exciting two adjacent vibration modes of the structure. However, the conventional two-mode excitation method excites two adjacent modes by single frequency. In order to fix the contribution of the two modes as a specific ratio, the driving frequency is limited to a specific frequency, and this frequency determines the generated traveling wave velocity, thus, it is impossible to maintain the traveling wave quality and simultaneously adjust the traveling wave velocity. This research proposes a new method, called “two-frequency two-mode excitation method,” using two frequencies to excite two adjacent modes. Each mode is excited only by one frequency such that the traveling wave speed can be adjusted by the driving frequency used. The structure in this research is one piezoelectric actuator attached on a stainless-steel shim. To verify the feasibility of this method, based on the Euler-Bernoulli beam theory, this research derived the governing equation of the structure to predict the vibration behavior, obtaining the solution of the equation by analytical and numerical methods, including resonance frequencies, mode shapes of the structure, and the frequency response. Then, with the obtained solution, the driving criteria of two-frequency two-mode are analyzed. To confirm the generation, direction, wave speed, and quality of the traveling wave, this study developed the traveling wave trajectory tracking algorithm based on the morphological opening and defined the loss function based on the Hilbert transform to analyze the spatial-temporal graph of the structure. In this way, the influence of parameters such as driving frequency, phase, and amplitude on the generation of traveling waves was discussed. In the experimental part, the resonance frequency of the fabricated prototype was measured by impedance analyzer to confirm the consistency between the prototype and the theory. Then, the amplitude and phase of the structure vibration under one-frequency driving was measured by a scanning laser Doppler vibrometer, and the frequency response function of the structure was obtained. Next, this frequency response function was used as a reference to compensate the driving voltage to meet the optimal displacement-amplitude ratio. When the structure is driven by two-frequency two-mode method, the traveling wave was observed by the scanning laser Doppler vibration measurement. The results confirm the high consistency between theory and experiment. Finally, the prototype of this platform was used to drive object and the results confirmed that the object moving velocity can be adjusted by varying the driving signal. In conclusion, this research proposed a new two-frequency two-mode excitation method to drive one-dimensional traveling-wave type linear piezoelectric moving stage. The method was verified by theory and experiment. This new excitation method has potential for multi-dimensional precise manipulation of simple structures.