黃元茂臺灣大學：機械工程學研究所孫德沛Sun, Te-PeiTe-PeiSun2007-11-282018-06-282007-11-282018-06-282006http://ntur.lib.ntu.edu.tw//handle/246246/61369本研究利用方框形結構對稱的特性，設計振動子四個頂角的運動軌跡與超音波馬達，並適當調整所輸入的電壓訊號，使超音波馬達具有x方向與y方向移動與z方向轉動的三個自由度運動。建立振動子與滑動子的等效振動模型，並以水平與垂直方向的振動系統，模擬振動偶合致動機制的情況。分析過程中，假設簡諧振盪力作用在振動子上，並將振動偶合式摩擦作動機制分成分離與碰撞接觸的兩個時期來討論。在分離時期間，振動子與滑動子的動作互不影響，並以振動子與滑動子垂直方向的幾何位置關係作為從分離至碰撞接觸時期的邊界條件。碰撞時期則視為部份彈性碰撞的過程，並從接觸區域變形的觀點來討論振動子與滑動子間的接觸力情況，再以庫倫摩擦定律所求得接觸面間的摩擦力來推導滑動子的運動速度，而碰撞至分離的邊界條件則採用接觸力為零的條件求得。此摩擦致動機制所得之方程式以四階Runge-Kutta method作為數值分析方法，分析影響振動偶合機制特性的各項因素與馬達特性，並實體製作三自由度運動之超音波馬達，藉由實驗驗證此摩擦致動機制的正確性。本研究在馬達無負載的情況下，振動子與滑動子的預負載為4.0N，垂直與水平方向壓電致動力分別為4.5N與5.0N，與其相位差為120°時，計算結果滑動子具有最快運動速度，於x或y方向皆為90.3 mm/s；實驗量測所得滑動子與振動子突起接觸點之x方向與y方向最快速度分別為69.8 mm/s與68.3 mms，此二實驗值與計算結果之誤差分別為22.7%與24.4%；實驗量測所得轉子最高轉速為2.16 rad/s，進而可得轉子與突起接觸點於x方向或y方向速度分量皆為65.7 mm/s，此速度分量與計算結果之誤差為28.3%。而在此最高運轉速度的操作條件下，計算結果在滑動子受 0.82 N之阻抗推力負載時，具有最高運轉效率為55.3%；實驗量測所得滑動子在x與y方向受到0.63N與0.61N之阻抗推力負載時，具有最高運動效率分別為43.5%與41.1%，此二實驗值與計算結果之誤差分別為21.3%與25.7%；而實驗量測轉子在受阻抗扭矩負載為0.018Nm，即轉子與突起接觸點於x方向所受阻抗推力負載為0.58N時，轉子具有最高運轉效率為37.6%。This study employs the symmetrical characteristics of a square frame to design motion trajectories of the four projections on the square frame and an ultrasonic motor. Adjusting input voltages allows a slider to move in the x direction or y direction or a rotor to rotate along the z axis. Equivalent vibratory models of the vibrator and slider are generated. The horizontal and vertical vibratory systems are used to simulate the coupling driving mechanism. With the assumed harmonic driving forces acting on the vibrator, the time domain of the driving mechanism system is divided into two periods：the separated period and the impact period. During the separated period, no interference occurs between motions of the vibrator and the slider. The boundary condition changed from the separated period to the impact period depends on the configurations of the vibrator and the slider. During the impact period, impact between the vibrator and the slider can be considered as partially elastic impact. The contact force between the vibrator and the slider is calculated by the material deformation of contact surfaces. The Coulomb law is then used to derive the velocity of the slider. If the contact force is zero, it means that the system is transient from the impact period to the separated period. This friction driving mechanism utilizes the 4-th Runge-Kutta method to simulate effects of the vibratory coupling system. A prototype of the ultrasonic motor is fabricated and tested. When the preload of the vibrator and the slider is 4.0 N, the vertical and horizontal piezoelectric driving forces are 4.5 N and 5.0 N, respectively, and the phase angle difference are 120°, the calculated fastest speed can be obtained to be 90.3 mm/s in the direction. The measured fastest speeds of the contact point between the slider and the vibrator in the x and y directions are 69.8 mm/s and 68.3 mm/s, respectively. The deviations between these two speeds obtained from testing and the calculated result are 22.7% and 24.4%, respectively. The fastest rotational speed of the rotor obtained from testing is 2.16 rad/s. Based on this rotational speed, both speed components at the contact point between the rotor and the vibrator in the x or y direction are 65.7 mm/s. The deviation between the measured and the calculated results is 28.3%. With the preload of 4.0 N, the vertical and horizontal piezoelectric driving forces of 4.5 N and 5.0 N and the phase angular difference of 120°, adjusting the thrust load of 0.82N acting on the slider can yield the highest calculated efficiency of 55.3%. The measured highest efficiencies of the slider moving in the x direction and the y direction are 43.5% and 41.4%, respectively, when applying the thrust loads of 0.63 N and 0.61 N in the x and y directions. The deviations between the two efficiencies based on the measured and calculated data are 21.3% and 25.7%, respectively. When applying the torque load of 0.018 Nm on the rotor (the equivalent thrust load of 0.58 N at the contact point of the rotor and the vibrator in the x direction), the highest measured efficiency of rotor is 37.6%.中文摘要…………………………………i 英文摘要……………………………………ii 目錄……iv 圖目錄………………………vi 表目錄……………………………………………x 符號表……………………………………xi 第一章 緒論………………………………………………………1 1.1 研究動機…………………………………………………1 1.2 文獻回顧…………………………………………………3 1.2.1 超音波馬達的發展過程……………………………3 1.2.2 超音波馬達文獻回顧與分類………………………4 1.2.2.1 波傳振動機制…………………………………5 1.2.2.2 摩擦作動機制…………………………………11 1.2.2.3 激振振動子的方式……………………………22 1.2.2.4 結構與振動型態方式…………………………23 1.2.2.5 統體波與表面波………………………………24 1.2.3 超音波馬達作動機制文獻回顧……………………25 1.3 研究目的…………………………………………………26 1.4 研究方法…………………………………………………27 1.5 本文架構…………………………………………………27 第二章 馬達設計與運動特性分析………………………………29 2.1 多自由度超音波馬達的設計……………………………29 2.1.1 馬達概念的產生……………………………………29 2.1.2 振動子的設計………………………………………30 2.1.3 馬達整體的設計……………………………………32 2.2 馬達運動模型分析………………………………………36 2.2.1 分離時期運動分析…………………………………39 2.2.2 接觸時期運動分析…………………………………47 2.2.3 馬達運動特性分析………………………………………56 第三章 運動模型之數值分析…………………………………59 3.1 數值方法與應用…………………………………………59 3.2 邊界條件之分析…………………………………………61 3.3 數值模擬與流程…………………………………………63 第四章 實驗……………………………………………………65 4.1 實驗目的…………………………………………………65 4.2 馬達架構…………………………………………………65 4.3 實驗組立架構與實驗方法………………………………67 4.4 實驗步驟…………………………………………………69 第五章 計算與實驗之結果………………………………………71 5.1 振動子與滑動子垂直方向位移計算結果………………71 5.2 運動特性計算分析結果…………………………………77 5.2.1 馬達運動速度分析結果……………………………77 5.2.2 振動子致動軌跡之分析結果………………………84 5.2.3 馬達運動特性分析計算結果………………………86 5.3 實驗結果…………………………………………………87 5.3.1 馬達速度實驗結果…………………………………88 5.3.2 馬達運動特性之實驗結果…………………………107 5.4 計算與實驗結果之比較…………………………………108 5.5 與文獻之比較……………………………………………112 第六章 計算與實驗結果之討論…………………………………116 6.1 振動子與滑動子垂直方向位移計算結果之探討………116 6.2 運動特性計算分析結果之探討…………………………119 6.2.1 馬達運動速度分析結果之探討……………………119 6.2.2 振動子致動軌跡分析結果之探討…………………120 6.2.3 馬達運動特性分析計算結果之探討………………121 6.3 實驗結果之探討…………………………………………122 6.3.1 馬達速度實驗結果之探討…………………………122 6.3.2 馬達運動特性實驗結果之探討……………………123 6.4 計算與實驗結果比較之探討……………………………123 6.5 與文獻比較之探討………………………………………126 第七章 結論與建議……………………………………………130 參考文獻…………………………………………………………133 附錄A 馬達振動方程式之推導………………………………A.1 附錄B 數值方法之表示式……………………………………B.12014520 bytesapplication/pdfen-US超音波馬達振動壓電致動器ultrasonic motorvibrationpiezoelectric actuatorthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/61369/1/ntu-95-R92522630-1.pdf