應用新型齒廓修整方法改善擺線針輪行星齒輪傳動的負載接觸特性

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卓沛辰(Pei-Chen Cho) 查詢紙本館藏

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機械工程學系

論文名稱

應用新型齒廓修整方法改善擺線針輪行星齒輪傳動的負載接觸特性
(Improvement of Loaded Contact Characteristics of Cycloid Planetary Gear Drives by Applying a Novel Tooth Profile Modification Method)

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摘要(中)

擺線針輪行星齒輪機構因具有高減速比、高嚙合齒數，以及高承載與高衝擊吸收能力等優點，在各產業應用甚廣。在實際應用中，擺線齒輪作為此機構主要元件，擺線齒輪的齒形為研究的發展重點。因擺線齒輪與其他元件受到加工與組裝誤差等影響，使得擺線齒輪與針輪齒對接觸必須存在背隙，始得以補償誤差。一般而言，擺線齒輪之齒廓多採取修形方式來決定齒間背隙。另一方面，由於擺線針輪行星機構在實際傳動時，曲軸軸承必須存在間隙。而軸承間隙的存在也會影響到擺線齒廓與針齒的接觸，使得修形齒廓在設計上更加複雜。然而傳統以移距/等距方法的修整齒廓，會受限於有限數目的的參數，在給定背隙的限制條件下，並不易達成較佳傳動效能。本論文則提出一種新的齒廓修整方式，來改善擺線針輪行星齒輪機構在具有齒廓背隙與曲軸軸承間隙狀況下，各接觸對間的負載狀況；特別是雙齒差擺線齒對在在齒頂處的接觸衝擊問題。本文所提出的齒廓修整方法有別於傳統移距/等距方法，係直接由預定單一擺線齒與針齒嚙合的曲軸轉動角度誤差關係，來設計擺線齒廓。此一方法可以直接將要求背隙納入轉動角度誤差曲線設計之中，並且透過改變此誤差曲線參數來改變各接觸對的受力關係，以滿足傳動需求。由這種修整方式所得到擺線齒廓，也適合使用目前CNC齒輪精加工的成熟技術來製作。本研究曲軸轉動角度誤差曲線係選用對數曲線，並使用考量軸承間隙下的受載接觸分析模型做為分析工具。首先透過有系統分析新型齒廓修整參數對傳動效能的影響，建立參數設計法則。並以此對新式修整方法與傳統等距/移距修整方法所得到的齒廓進行案例分析與比較。分析結果顯示，新型修整的齒廓案例具以下優勢：在單齒差擺線齒輪方面，可以有效提高接觸率，降低各個接觸對最大負載值。在雙齒差擺線齒輪方面，滾子或爪銷接觸對受力無明顯差異，但在擺線/針齒接觸對有較佳受力表現；同時在具有軸承間隙下，齒對接觸範圍可以有效避開齒頂位置，降低了軸承間隙對齒頂撞擊接觸的風險。由研究結果顯示，本論文所提出之新型齒廓修整方式，可以根據設計要求，如背隙、受力大小、傳動誤差等，有系統地調整參數，有效改善擺線針輪行星減速機的傳動性能。

摘要(英)

The cycloid pin-wheel reducer is widely used in various industrial application due to high reduction ratio, large number of engaged tooth pairs, as well as high load capacity and shock absorption ability. In practical applications, the profile of the cycloidal gear, which is the critical component of this mechanism, is the focus of research and development. Because the cycloidal gear and the relevant components are affected by manufacturing and assembly errors, backlash between the contact tooth pairs must be present to compensate these errors. In general, the backlash can be achieved by using profile modification of the cycloidal tooth. However, due to the transmission of a cycloidal-pinwheel planetary mechanism, a clearance must exist in the crankshaft bearing. This clearance also affects the contact between the cycloidal tooth profile and the pin, making the profile design more complex. However, the conventional method of profile modification using the shifting-offset/equidistant-offset modification is limited by a finite number of parameters and does not easily achieve improved transmission while adhering to a given backlash constraint.
This thesis proposes a novel method for tooth profiles modification to enhance the loaded contact characteristics of contact pairs in a cycloidal-pin wheel planetary gear mechanism. The method addresses the issue of backlash in the tooth profile and clearance of the crankshaft bearings, with a focus on the contact impact of the tooth pairs at the tip of the cycloidal in the gear mechanism with tooth number difference of two. The tooth profile modification method proposed in this paper is based on designing a cycloidal tooth profile from the predetermined rotation angle error curve of the crankshaft for the mesh of a cycloid and a pin tooth. This method differs from the conventional shifting-offset/equidistant-offset modification method. This method incorporates the required backlash directly into the design of the rotation angle error curve. By adjusting the parameters of this error curve, the force relationship between the contact pairs can be changed to meet the transmission requirements. The cycloidal tooth profile obtained by this modification method is also suitable for manufacturing using current CNC gear finishing technology.
In this study, the logarithmic curves were used to represent the rotation angle error curves of the crankshaft. The analysis tool used was the loaded contact analysis model with consideration of crankshaft bearing clearances. The influence of the profile modification parameters on the transmission performance was systematically analyzed, and the parameter design rules were also established. A case study was conducted to compare the profiles obtained by the novel profile modification method with those obtained by the conventional method. The analysis results demonstrate the advantages of the modified profile using the proposed method: (a) It is possible to effectively increase the loaded contact ratio and reduce the maximum load value for each contact pair in the case of the cycloidal gear mechanism with a tooth number difference of one. (b) For the cycloidal gear mechanism with a tooth number difference of two, there is no significant difference in the force on the contact pairs of the bearing rollers or the pin shaft with the cycloidal gear. However, there is better force performance on the cycloidal-pin tooth contact pairs. Additionally, when there is bearing clearance, the contact area of the tooth pairs can effectively avoid the position of the tooth tips, reducing the risk of contact impact on the tooth tip due to the bearing clearance.
The study demonstrates that the proposed tooth profile modification method can systematically adjust parameters to meet design requirements, such as backlash, forces acting on the contact pairs, and transmission error, resulting in improved transmission performance of the cycloid planetary gear reducer.

關鍵字(中)

★ 擺線針輪減速機
★ 擺線行星齒輪
★ 雙齒差擺線齒輪
★ 擺線齒廓修整
★ 接觸率
★ 受載接觸分析

關鍵字(英)

★ Cycloid pin-wheel reducer
★ Cycloid planetary gear drive
★ Cycloidal gear with tooth number difference of two
★ Cycloid profile modification
★ Contact ratio
★ Loaded contact analysis

論文目次

摘要 i
Abstract iii
目錄 v
圖目錄 ix
表目錄 xii
符號對照表 xiii
第1章前言 1
1.1 研究背景 1
1.2 文獻回顧 3
1.3 研究目的 4
1.4 論文架構 5
第2章擺線齒輪齒廓基本幾何與運動關係 6
2.1 單齒差擺線齒輪幾何特性 6
2.1.1 擺線齒形的理論輪廓 6
2.1.2 齒廓基本特性 8
2.1.3 行星齒輪機構速比關係 10
2.1.4 齒對接觸角度位置 12
2.1.5 接觸率 13
2.1.6 齒廓修整基本原理 13
2.2 雙齒差擺線齒輪幾何特性 15
2.2.1 雙齒差擺線齒輪輪廓 15
2.2.2 齒廓基本特性—齒頂尖點 16
2.2.3 齒頂圓角 17
2.2.4 行星齒輪機構速比關係 18
2.2.5 齒對接觸角度位置 18
2.2.6 接觸率 19
第3章新型擺線齒形設計方法 21
3.1 等距移距齒廓修整之問題 21
3.1.1 修整齒廓曲軸轉角誤差 21
3.1.2 傳動誤差(Transmission Error) 22
3.1.3 小結 23
3.2 新型齒形修整方法—基於曲軸轉角誤差曲線修整方法 24
3.2.1 新型齒形修整原理 24
3.2.2 曲軸轉角誤差曲線設計方法 25
3.2.3 對數曲線 25
3.3 輪廓修整量曲線轉換 26
3.3.1 修整量計算 27
3.3.2 齒頂、齒底修整量修正 28
3.4 應用於雙齒差齒輪之輪廓修形設計方法 31
3.4.1 自訂曲軸轉角誤差曲線修正 31
3.4.2 齒底修整量修正 32
3.4.3 齒頂尖點圓角 34
第4章考慮軸承間隙之擺線齒輪機構受載接觸分析 37
4.1 軸承間隙下受載接觸分析模型與假設 37
4.2 軸承間隙下接觸分析模型 38
4.3 軸承間隙下的力平衡關係 40
4.3.1 軸承滾子力平衡 41
4.3.2 擺線齒輪力平衡 41
4.3.3 輸出力矩平衡 41
4.3.4 力平衡式與條件 41
4.4 受載迭代收斂計算方法 41
4.4.1 剛性圖法 42
4.4.2 計算迭代方法 43
第5章齒廓修整對雙齒差齒輪受力之影響 45
5.1 個別輪廓參數對齒廓受力之影響 45
5.1.1 曲線比例係數ss調整 45
5.1.2 曲線形狀係數sf調整 46
5.1.3 曲線範圍θrange調整 47
5.1.4 小結 48
5.2 軸承間隙對受力之影響 48
5.3 綜合輪廓參數對受力之影響 49
5.3.1 受力結果整理 49
5.3.2 輪廓參數與受力結果關係 51
5.3.3 不同輪廓之受力比較 51
5.3.4 小結 53
5.4 圓角選擇 53
第6章案例與代號彙整 55
6.1 齒輪參數 55
6.1.1 單齒差齒輪參數 55
6.1.2 雙齒差齒輪參數 55
6.2 修整參數 56
6.2.1 齒廓修整形式比較 56
6.2.2 軸承間隙 56
6.2.3 圓角修整 56
6.3 剛性圖案例比較 57
第7章齒輪之受力分析結果 59
7.1 單齒差齒輪案例分析 59
7.1.1 單一齒廓曲軸誤差(∆φc) 59
7.1.2 傳動誤差(TE) 60
7.1.3 齒廓受載分析 61
7.1.4 其他接觸對受載分析 62
7.1.5 齒廓應力分析 63
7.1.6 實際接觸率 65
7.2 雙齒差齒輪案例分析 66
7.2.1 單一齒廓曲軸轉角誤差 66
7.2.2 傳動誤差(TE) 67
7.2.3 齒廓受載分析 68
7.2.4 其他接觸對受載分析 69
7.2.5 齒廓應力分析 70
7.2.6 實際接觸率 72
第8章結論與展望 73
8.1 結論 73
8.1.1 新型修整設計參數之影響 73
8.1.2 不同修整之受力比較 74
8.1.3 修整之其他問題 75
8.2 未來展望 75
參考文獻 77

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指導教授

蔡錫錚(Shyi-Jeng Tsai)

審核日期

2024-1-29

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