臺灣博碩士論文加值系統

行進波式超音波馬達主要是利用定子在通電後產生的逆壓電效應所產生的形變與轉子間產生摩擦力來帶動轉子的轉動，以達到驅動的效果。本文主要針對增加定子與轉子間的最大介面扭矩來縮短轉子啟動的時間。藉由最佳化設計方法，使得馬達在受到相同的外在扭矩時，可以利用更短的時間帶動轉子轉動並驅動目標物。
本文訂定了兩個單目標函數，分別為轉子與定子間的最大扭矩及轉子在穩態時的穩定轉速。前者主要目的是縮短轉子的啟動時間；後者則是使系統可因較快轉速而縮短完成工作的時間。本文所使用的最佳化方法為序列二次規劃法(Sequential Quadratic Programming)及遺傳基因演算法(Genetic Algorithm)來搜尋兩個單目標函數的最佳值。
由最佳化設計後的結果顯示，序列二次規劃法會因給定的初始值不同而明顯影響其最佳化結果;而遺傳基因演算法則因初始值的隨機搜尋而可以得到比序列二次規劃法更好的結果。由最佳化設計後的結果可發現，在受到與原系統相同的外加扭矩下，能以更短的時間啟動轉子。系統在穩態時較快的轉速下，可花費比原系統較短的時間達到相同位置。

In order to make the rotor move around, the ultrasonic motor makes use of the friction between the rotor and the deformation produced by inverse piezoelectric effect caused by the electrified stator. This study is primarily aimed at increasing the maximum interface torque between the rotor and the stator to shorten the time of the rotor starting to move around. With optimum methods, we can reduce the time of making the rotor move around and then drive the object when the motor bears equal external torque.
This study defines two single objective functions. One is the maximum interface torque between the rotor and the stator and the other is the stable angular velocity of the rotor. The main purpose of the former function is to shorten the time of the rotor starting to move around. And the latter function reduces the whole work time by a larger angular velocity. The optimum methods chosen in this study are Sequential Quadratic Programming Method (SQP) and Genetic Algorithm (GA), which are used to get the optimum solutions to these two single purpose functions as mentioned.
The data of the optimization show that numerical results will greatly differ because of different initial values given with SQP. However, GA provides better numerical results by electing initial values randomly than SQP does. Furthermore, the rotor starts to move around in a shorter time when the system bears equivalent applied torque as the original system. Besides this, it takes less time to reach the same position with higher stable angular velocity of the rotor. It means that the system can complete its task by shorter time.

CH.1 INTRODUCTION
1-1 Motivation of Research 1
1-2 Literature Review 2
1-3 Outline 3

CH.2 THE EQUATION OF MOTION OF SYSTEM
2-1 The Basic Structure of Ultrasonic Motors 5
2-2 The Piezoelectric Phenomenon 6
2-2-1 The Piezoelectric Effect 6
2-2-2 Piezoelectric Materials 6
2-3 Piezoelectric Equation 7
2-4 Modeling of the ultrasonic motor 10
2-4-1 Stator Model 10
2-4-2 Interface Model 14
2-4-3 Rotor Model 16

CH.3 DYNAMIC ANALYSIS
3-1 Dynamic Analysis 22
3-2 The Numerical Result and Discussions 24

CH.4 OPTIMUM DESIGN OF ULTRASONIC MOTOR
4-1 The Optimization Problem Statement 31
4-2 Sequential Quadratic Programming (SQP) 33
4-3 Genetic Algorithms 35
4-3-1 Linear Fitness Scaling 37
4-3-2 Execution Procedures 38
4-4 The Optimum Result And Discussion 39

CH.5 CONCLUSIONS AND FUTURE STUDIES
5-1 Conclusions 62
5-2 Future Studies 63

REFERENCES 64

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