微撓性雙穩態機構之製造、測試與特性分析與微彈簧性質探討

Fabrication, Testing and Characterization on Micro Compliant Bistable Micromechanism and Study on Properties of Microspring

吳佐群(Cho-Chun Wu)

指導教授 ： 陳榮順 ； 林孟儒

國立清華大學/工學院/動力機械工程學系/博士(2013年)

https://doi.org/10.6843/NTHU.2013.00332

摘要

本研究推導一個由V型樑尺寸和材料參數組成之判別式D，用以決定V型微機構中是否會發生雙穩態現象。當判別式D > 0，此結構沒有雙穩態現象；當D < 0時，則此結構可以產生雙穩態現象。本研究成功地製造具有不同的樑長與傾斜角度之V型樑微結構，測試其是否具有雙穩態現象，並和理論推導出之判別式D做比較。比較理論與實驗的結果，發現是一致的，證明所推導的判別式D能有效的判斷雙穩態是否會發生。其中傾斜角，樑長l和t/w值三個參數，對雙穩態現象會有明顯的影響。由研究結果發現，較大的傾斜角只需要較短的臨界樑長度就有雙穩態現象，較長的V型樑長度則只要較小的臨界傾斜角就有雙穩態現象。亦即V型樑雙穩態結構具有較長樑長或較大的傾斜角，比較容易得到雙穩態現象。然而太大的傾斜角或太短的V型樑將較易斷裂。此外，t/w值越大越不容易有雙穩態現象，反之，較小的t/w比值較容易顯示雙穩態現象。由分析的結果發現， t/w比值越小越好。若是尺寸要在微系統的適用範圍，亦即公釐以下，t/w比值最好不要大於1。此外，相較於已發表的文獻所具有雙穩態現象之傾斜角(一般小於3.5度)，本研究所製造之雙穩態結構具有較大的傾斜角(5度)。
微彈簧通常使用於微機電的致動器，用於傳遞力量及儲存能量。其中，方型彈簧具有抵抗橫向力與抵抗橫向變形的優勢。當微彈簧用於微機電裝置時，為了具有較佳的操縱性，必須避免其非線性行為。本論文研究微彈簧方型結構之垂直樑寬度WS，微彈簧厚度T，方型結構之水平樑寬度BS，以及方型彈簧之彈簧圈數N，這四個尺寸參數尺寸對位移之非線性關係。將數值模擬的結果，使用線性迴歸的方法可以得到不同尺寸彈簧的力量與位移之達芬方程式(Duffing equations)，由此達芬方程式可以得到線性彈簧常數k與三次方彈簧常數k3。結果發現，在同樣的彈簧圈數下，彈簧常數k 會隨著彈簧厚度的增加而減少。但是在同樣的彈簧厚度下，k 是隨著彈簧圈數的增加而增加。較大的N值會導致k3有較大增幅。水平樑厚度、垂直樑厚度及彈簧厚度對k 與 k3的關係非常類似，都是隨著參數的增加，k 與 k3的絕對值會非線性減少。所以，非線性行為不容易發生於較厚的彈簧，較多圈數的彈簧以及較寬的方型彈簧。將上述不同尺寸的方型彈簧的達芬方程式之線性彈簧常數k與三次方彈簧常數k3，利用統計之迴歸方法，可以得到k與k3由 T，BS，WS與N四個尺寸參數為變數構成的迴歸方程式，利用此迴歸方程式，即可將方型彈簧的尺寸參數，代入求得k與k3，代入達芬方程式，就可以判斷此方型彈簧，在多少作用力下，就會產生本文所定義之非線性行為，用此種方式，就可以在設計方型微彈簧時，預估非線性變形行為之發生。

關鍵字

撓性機構 ； 雙穩態機構 ； 微彈簧 ； 微機電

並列摘要

A determinant D as a criterion, in terms of structural and material properties, is theoretically derived to determine if the bistability can occur for micro mechanically bistable mechanisms. When D < 0, the mechanism will display bistable behavior if an appropriate force is applied to push the bistable mechanism; while D > 0, bistable behavior cannot occur. The proposed V-beam bistable mechanisms have been successfully fabricated with different beam length and tilted angle. Experiments were conducted to validate the theoretical study for bistability. Comparing the theoretical solutions to the experimental results, it shows that both agree well with each other. It also concludes that to design an enabled bistable V-beam mechanism, the tilted angle should be larger, for the same beam length; while the beam length has to be longer for the same titled angle. The ratio of beam thickness to width, t/w, has effect on bistable phenomena of V-beam mechanism. It is more easily found bisatble phenomena when V-beam mechanism with smaller t/w value. It is found that t/w value had better less than 1 as the structure dimension being sub millimeter. The developed determinant D is used to predict if a designed bistable mechanism can equip with bistable behavior or not, providing the structural sizes and material properties. As a result, researchers can save their trial works when design a bistable mechanism. The V-beam with larger tilted angle up to 5° have been successfully fabricated to act as a bistable mechanisms, in comparison to 3.5° tilted angle in the existing literatures.
Microsprings are often used in MEMS actuators to transmit force and to restore its original position by its spring force after a movement. Due to larger stiffness and better capability of resisting lateral forces, box microspring has the advantages of resisting induced transverse forces and preventing lateral deformation, comparing to other microsprings. To have better operation, the nonlinear behavior of microspring should be avoided when it is utilized in MEMS devices. It is known that the sizes of microspring can significantly affect the performance of microspring. In this work, we report the effect of box microspring sizes on the nonlinear deformation of microspring. The width of vertical beam of rectangular frames WS, the thickness of microspring T, the width of horizontal beam of rectangular frames BS, and the spring number of box microspring N are used as the parameters to investigate the effect of the sizes on the nonlinear force. The finite element software COMSOL Multiphysics is employed as the simulation tool. From simulation results, nonlinear deformation of micro box spring is regressed as Duffing equations. Moreover, from simulation data, the linear spring constant k and cubic spring constants k3 of Duffing equation could be determined and expressed in terms of T, BS, WS, and N by utilizing the regression analytical method. It is found that nonlinear deformation is harder found for thicker, wider, and more turns springs. The simulated results of this work can be used to design the microspring in an actuator such that the nonlinear deformation may be avoided.

並列關鍵字

Compliant Mechanism ； Bistable Mechanism ； Microspring ； MEMS

參考文獻

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