三階差速分流式行星齒輪機構傳動誤差與負載分析

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姓名

莊啓佑(Qi-You Zhuang) 查詢紙本館藏

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機械工程學系

論文名稱

三階差速分流式行星齒輪機構傳動誤差與負載分析
(Load and Transmission Error Analysis of a Differential Type Three-stage Planetary Gear Drive)

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摘要(中)

由於全球氣候變遷的影響，再生能源的開發與使用日顯重要，特別是離岸風電已是風電發展的主流。而台灣海峽是全球離岸風電的最佳地點之一，然而風機的增速齒輪箱在設計上必須滿足重量輕、體積小、速比高等特性，因此在各種不同的齒輪機構中，以三階差速分流式行星齒輪機構為最佳解決方案之一。
本論文之目的係探討三階差速分流式行星齒輪機構在誤差與摩擦影響下，各階內部與階間負載分配狀況以及增速齒輪箱的傳動誤差。使用之研究方法則將單階漸開線行星齒輪機構解析分析模型，擴展成可應用於三階差速分流式行星齒輪機構之分析模型。在分析模型中除考慮銷孔位置誤差、齒厚誤差等時變誤差外，也納入非托架與太陽齒輪偏心等時變誤差。在齒輪嚙合分析模型中，則以漸開線齒輪幾何關係建立在齒輪任意位置下，各齒輪齒對之嚙合位置，並據以推導出納入各誤差之齒隙與傳動誤差關係式。另一方面，除應用齒對撓度法，建立各嚙合齒對負載下變形與位移關係，也將各接觸齒對摩擦力等影響納入各元件負載平衡關係中。將此兩種關係式，可建立一線性矩陣數學式，以求得各階各齒對之負載以及各元件位移。再以此分析模型對各個行星齒輪段以及整體機構，有系統地探討摩擦與各種誤差對傳動誤差、階內負載分配、階間負載分流以及傳動效率的影響。
傳動誤差研究結果顯示，在相同偏心誤差下，僅考慮單一行星齒輪時，托架偏心所造成的傳動誤差振幅值大於太陽齒輪偏心的影響。但納入多個行星齒輪的影響，因不同嚙合相位角作用下，機構整體的傳動誤差的振幅值受到太陽齒輪偏心影響最大，托架偏心誤差反而產生較小。銷孔切向位置誤差會使間隙曲線發生偏移，與不同偏心誤差組合時，會改變變化曲線型態以及振幅值。當第一階與第三階同時具有誤差時，傳動誤差振幅值以及變化週期皆會加大。
負載分流分析結果方面，在理想狀態下，階間分流僅受各階速比的影響，而階間負載分配則受到嚙合剛性與相位角影響。摩擦力對階間負載分流的影響較階內分配大。偏心誤差則造成階內負載分配出現類似正弦曲線般的週期性變化，但在托架固定狀況下，並無影響。
由研究結果顯示，本研究所提出的解析計算模型，可以針對多階差速分流式行星齒輪機構在具加工、組裝誤差與摩擦下，有效率分析傳動誤差與不同負載分流狀況，提供此類型行星齒輪機構基本設計之參考。

摘要(英)

Due to the impact of global climate change, the development and use of renewable energy are more important today. In particular, offshore wind power is the main development direction of wind power generation. The Taiwan Strait is one of the best locations for offshore wind power in the world. However, the gearbox of the wind turbine must fulfill the design requirements, such like light weight, small volume and high gear ratio. Therefore, three-stage differential type planetary gear drive is one of the best solutions among various types of gear mechanisms
The purpose of this paper is to investigate the internal and external load distribution as well as the transmission error of a third-stage differential type planetary gear drive under the influence of errors and friction. A developed analytical model of a single-stage involute planetary gear drive is extended to an analysis model for the third-stage differential type planetary gear drive. In the analysis model, not only the time-invariant errors, e.g., the pin-hole position errors and tooth thickness error, are considered, but also the time-variant errors, such as eccentric errors of the carrier and the sun gear. In the gear meshing analysis approach, the meshing position of each gear pair at any position of the gear is established by using the geometric properties of the involute gear. The relation between the backlash and the transmission error is thus also derived. On the other hand, not only the loaded deformation-displacement relations of each engaged teeth are derived based on the tooth compliance method, but the load equilibrium equations of the related components considering the friction are also developed. With combination of these two types of relations, a linear matrix equation can be established to determine the loads acting on each tooth pair and the displacements of the related component. The effects of friction and various errors on the transmission error, internal and external load sharing, as well as the efficiency are then systematically investigated for each stage and the total of the planetary gear drive by using the developed analysis model.
The results from the analysis of transmission error show that only considering a single planetary stage, the amplitude of the transmission error due to the eccentric error of the carrier is greater than that due to the sun gear under the same value of eccentric error. However, because of different meshing phase angle of multiple planet gears, the amplitude of the total transmission error is greatly affected by the eccentric error of the sun gear eccentricity, but the effect due to the eccentric error of the carrier is less. The pin-hole tangential position error will shift the clearance curve if no other time-variant errors exist, and will change the type and the amplitude value of the transmission curve if combined with different eccentric errors. When the two planet stages with non-fixed carrier have errors in the study case, the amplitude and the period of the transmission error curve will increase.
As the results of load sharing analysis show, the external power split in the ideal case is only affected by the speed ratio of each stage, while the load sharing within the planet stage is affected by the meshing stiffness and the phase angle. The effect of friction on the external load sharing is larger than the internal load sharing. When the carrier is not fixed, the eccentric errors result in a cyclical sinusoidal variation, but have no effect with a fixed carrier.
The results show that the analytical calculation model proposed in this study can analyze efficiently the transmission error and the load sharing for multi-stage differential type planetary gear drives with consideration of machining, assembly errors and friction. This computerized approach can serve as an efficient tool for basic design of the gearbox.

關鍵字(中)

★ 差速式行星齒輪組
★ 偏心誤差
★ 負載分配
★ 傳動誤差
★ 傳動效率

關鍵字(英)

★ Differential Type Planetary Gear Drive
★ Eccentric Errors
★ Load Sharing
★ Transmission Errors
★ Efficiency

論文目次

摘　　　要 i
Abstract iii
謝　　　誌 v
目　　　錄 vi
圖　目　錄 ix
表　目　錄 xi
第 1 章緒論 1
1.1 研究背景 1
1.2 文獻回顧 4
1.3 研究目的 4
1.4 論文架構 5
第 2 章結構特性 6
2.1 多階分流式行星齒輪機構之構成原理 6
2.2 速度、扭矩和功率關係 8
2.2.1 增速比 8
2.2.2 扭矩關係 9
第 3 章行星齒輪組嚙合關係 11
3.1 單階基本幾何關係 11
3.2 誤差對行星齒輪組配置幾何關係的影響 16
3.3 偏心托架旋轉對行星齒輪相對位置變化的影響 17
3.3.1 誤差角度 17
3.3.2 中心距與壓力角變化 18
3.3.3 托架轉動對間隙的影響 19
3.4 傳動誤差分析 21
3.4.1 單一行星齒輪條件下的傳動誤差 21
3.4.2 多個行星齒輪條件下的傳動誤差 25
3.5 齒輪接觸點位置 26
3.6 多階行星齒輪機構嚙合關係 29
第 4 章行星齒輪組負載分析模型LTCA 31
4.1 單階接觸齒對負載分析 31
4.1.1 基本模型 31
4.1.2 變形-位移方程式 34
4.1.3 包含摩擦力之負載平衡方程式 36
4.1.4 計算分析模型 38
4.2 多階行星齒輪機構接觸齒對負載分析模型 41
4.2.1 基本模型 41
4.2.2 階間位移連接關係 42
4.2.3 階間負載平衡方程式 43
4.2.4 計算分析模型 44
第 5 章案例概述 45
第 6 章傳動誤差 47
6.1 誤差對單階行星齒輪組傳動誤差之影響 47
6.1.1 托架偏心誤差之影響 47
6.1.2 太陽齒輪偏心誤差之影響 48
6.1.3 切向銷孔誤差之影響 49
6.2 多階行星齒輪組之傳動誤差 52
6.2.1 各單階之傳動誤差 52
6.2.2 任兩階具誤差組合下之傳動誤差 55
6.2.3 綜合誤差下之整體傳動誤差 58
第 7 章負載分配與效率 59
7.1 理想狀況下之負載分配 59
7.1.1 階間分流扭矩分配 59
7.1.2 階內各行星輪間負載分配 59
7.2 具誤差狀況下之負載分配 61
7.2.1 階間分流扭矩分配 61
7.2.2 階內各行星輪間負載分配 61
7.3 傳動效率 64
第 8 章結論與未來展望 66
8.1 結論 66
8.2 未來展望 67
參考文獻 69

參考文獻

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指導教授

蔡錫錚(Shyi-Jeng Tsai)

審核日期

2018-1-29

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