在邁入工業自動化時代的今日，以工業機器人來執行危險度較高的工作、節省人力支出、提升製程彈性及縮短作業時間，為產線自動化與工廠智慧化發展之一大趨勢，而為達成工業機器人的高重複定位精度、運作時的低噪音與低震動等性能需求，其關節部位的動力傳輸機構多使用擁有高減速比、角度傳動精度高、背隙量小、摩擦力低、輸出扭矩高、體積小重量輕等優點的諧波齒輪。
然而，使用諧波齒輪做為減速傳動機構的工業機器人，不論是在開發階段的測試機台上，還是量產後的實機裝配流程中，各主從部位的零件加工誤差以及輸入馬達本身的同心度誤差皆會在裝配後必然產生一累計同心度偏差量，此偏差量在過高的情況下將導致諧波齒輪運轉嚙合時，柔輪輪齒的齒面等效應力激增，傳動精度降低，進而使工業機器人運作時產生嚴重的噪音與震動、定位時的重複定位精確度不佳、諧波齒輪壽命降低等弊端。
本文目的即利用線性尺寸鏈公差分析方法計算出諧波齒輪與機器人裝配後所產生的最高同心度偏差量，再利用有限元素分析方法進行偏差狀態下的嚙合模擬運算，在齒面等效應力低於柔輪材質的疲勞強度且傳動精度降幅在10%以內的情況下，算出介於零偏差量與最高偏差量之間所容許的最大同心度誤差，並藉由尺寸鏈關係圖回推各零件的中加工誤差量，期能透過定義零件加工公差之規範，或是針對裝配流程進行改善以控管實機裝配流程所累計的同心度偏差量數值。

Today, in the era of industrial automation, industrial robots are used to perform high-risk work, saving manpower expenditure, improving process flexibility and shortening operation time, which is a major trend in the development of production line automation and factory intelligence. The high repeatability of industrial robots, low noise and low vibration during operation, the power transmission mechanism of the joints has a high reduction ratio, high angular transmission precision, small backlash, low friction, and output torque. Harmonic gears with advantages of high volume, light weight
However, industrial robots using harmonic gears as the reduction gears, whether in the development stage of the test machine or in the actual machine assembly process after mass production, the machining errors of the parts of the main and slave parts and the concentricity of the input motor itself The degree error will inevitably produce a cumulative concentricity deviation after assembly. When the deviation is too high, the harmonic gear will be meshed, the equivalent stress of the tooth surface of the flex wheel teeth will increase sharply, and the transmission accuracy will be reduced. In addition, industrial robots generate severe noise and vibration during operation, poor positioning accuracy during positioning, and reduced harmonic gear life.

The purpose of this paper is to use the linear dimensional chain tolerance analysis method to calculate the highest concentricity deviation generated by the harmonic gear and the robot after assembly, and then use the finite element analysis method to perform the meshing simulation operation under the deviation state, and the equivalent stress on the tooth surface is low. In the case of the fatigue strength of the flexible wheel material and the reduction of the transmission accuracy within 10%, calculate the maximum concentricity error allowed between the zero deviation amount and the highest deviation amount, and push back the parts by the dimensional chain relationship diagram. The amount of machining error can be determined by defining the specification of the machining tolerance of the part or by improving the assembly process to control th

摘要.......................................i
Abstract..................................ii
誌謝......................................iv
目錄.......................................v
表目錄....................................vii
圖目錄....................................viii
符號和簡稱................................xi
第一章 緒論...............................1
1.1研究動機與目的.........................1
1.2研究方法...............................2
1.3文獻回顧................................4
第二章 諧波齒輪傳動原理及同心度尺寸鏈分析.....5
2.1諧波齒輪結構與其傳動原理..................5
2.1.1諧波齒輪核心結構部件....................5
2.1.2諧波齒輪的傳動原理.....................6
2.1.3諧波齒輪傳動速比計算...................10
2.1.4諧波齒輪傳動優缺點......................11
2.1.5諧波齒輪實機裝配情形.....................13
2.2 同心度偏差量成因與尺寸鏈分析................15
2.2.1裝配同心度偏差成因........................15
2.2.2線性尺寸鏈公差分析方法求解最大同心度偏差量.....18
2.3 本章小結...................................23
第三章 有限元素模型建立及前處理設定................24
3.1諧波齒輪的有限元素模型建立......................25
3.1.1柔輪與剛輪的齒型定義與有限元素模型建立.......25
3.1.2波發生器有限元素模型建立....................27
3.1.3總組合干涉分析檢查立.......................28
3.1.4諧波齒輪有限元素模型簡化...................29
3.1.5 簡化後的諧波齒輪部件裝配................32
3.2 HyperMesh離散化網格劃分...................33
3.2.1剛輪與柔輪有限元素模型的等角切割...........33
3.2.2柔輪網格劃分.............................34
3.2.3剛輪網格劃分............................35
3.2.4波發生器網格劃分.........................36
3.2.5 諧波齒輪整體網格建立.....................39
3.3 LS-Dyna有限元素分析法--HyperMesh前處理.....40
3.3.1元素性質的選擇...........................41
3.3.2 創建資料集合器.........................41
3.3.3材料機械性質設定.........................42
3.3.4座標系設定.............................45
3.3.5拘束條件設定...........................45
3.3.6初始條件設定...........................48
3.3.7接觸面的定義...........................48
3.3.8沙漏模態.................................49
3.3.9LS-Dyna主程式處理.........................49
第四章 有限元素分析結果..........................50
4.1 最大齒面等效應力網格擷取方法..................51
4.2各同心度偏差量中的齒面等效應力比較..............54
4.2.1最大齒面等效應力界線值.......................54
4.2.2裝配同心度最差及最佳之齒面等效應力............54
4.2.3 最大容許同心度偏差量求解....................55
4.3傳動精度曲線.................................57
4.3.1角度傳動精度基礎理論.......................57
4.3.2傳動精度曲線的擷取.........................58
第五章 同心度誤差改善方法........................62
5.1將最大容許同心度偏差量代回尺寸鏈關係圖..........62
5.2裝配順序與公差調整建議.......................63
第六章 結論與未來研究方向......................64
6.1結論......................................64
6.2未來研究方向...............................64
參考文獻......................................65
Extended Abstract.............................67

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