臺灣博碩士論文加值系統

行星齒輪機構是以多顆行星輪分別承受負載分配之方式來傳遞功率，因此有在相同空間下能傳遞較大功率之優勢。然而因加工與組裝誤差以及組件受載變形等因素，造成各行星齒輪間負載不等分配以及嚙合齒面負載不均等問題，因此多會使用均載機構設計來解決此問題。在眾多均載機構中，彈性銷均載機構可藉由其負載變形，使行星齒輪產生浮動以達均載效果。
本論文之研究目的即在以實驗方式量測行星齒輪機構在靜態負載下之負載分配與負載分佈，以探討加工組裝誤差及組件受載變形等因素之影響。在本論文中先以發展之理論，分析各項加工與組裝誤差對負載分配之影響，其誤差種類包括行星輪齒齒厚、銷孔之切向與徑向誤差，還有托架與太陽齒輪偏心誤差等，其中行星輪齒齒厚、銷孔之切向與徑向誤差對負載分配之影響不隨托架轉動角度變化，而托架與太陽齒輪偏心誤差會使負載分配隨著托架旋轉動產生周期性之變化。而各類誤差對負載分配影響中最大的為托架偏心誤差、隨後為太陽齒輪偏心誤差，再來是行星齒輪銷孔位置之切向誤差，然後是行星輪之齒厚誤差，而銷孔位置之徑向誤差對負載分配影響最不明顯。
本論文實驗採用之行星齒輪機構包括太陽固定式行星機構(3顆行星輪)與具彈性銷之行星機構(5顆行星輪)等兩種，實驗方式以背對背且功率封閉之實驗平台進行加載量測，輸入裝置則捨棄電動機，改以蝸輪分度之方式輸入轉動角度來進行量測。量測數據分別量測環齒輪齒根應變與太陽齒輪齒根應變，另外於彈性銷上黏貼應變規量測其應變變形。負載部份則以扭矩200Nm與300Nm分別量測。
由實驗結果分析可知負載分配率隨托架轉動產生激烈變化，可知托架偏心與太陽偏心相對於整體負載分配率變化占有相當之重要角色。而扭力越大，負載分配之高低差值會降低。由負載分佈量測結果可發現，太陽固定式行星機構之負載分佈極度不均，而彈性銷機構則能有效改善齒面負載分佈不均。

Because planetary gear drives transmit power parallel through split-path of multiple planets, they own the advantage of higher power density in comparison of other gear drives. However, uneven load sharing among the planets and uneven load distribution on the engaged flanks occur due to the manufacturing errors and assembly errors as well as the deformation of the components in the planetary gear set. In order to solve this problem of the related component by using flexible element or floating gears. The well known methods are the design with a floating sun gear and with flexible pins.
The aim of this study is to analyze the static load sharing and load distribution in planetary gear sets having manufacturing and assembly errors. The uneven load sharing due to the eccentric error of the carrier and/or the sun gear vary cyclically with carrier rotation, but the invariant load sharing is affected only by the tooth thickness error and pin hole position errors. Among the errors in the planetary gear set, the eccentric error of the carrier affect the load sharing the most. The next is eccentric error of the sun gear. The tangential pin hole position error and the tooth thickness error. The radial pin hole position has the least effect on the load sharing.
Two types of planetary gear sets were tested in the study: a planetary gear set with a fixed sun gear location (three planets), and a planetary gear set with a flexible-pin mechanism (five planets). The loads acting on the teeth were measured on the test rig with close_loop type (“back-to-back” type). A worm gear device is use to set the input rotation angle of the sun gear. Strain gauges were mounted on the tooth roots of the ring gear and sun gear, and also on the flexible pins to acquire the load data. The test torque for the planetary gear set was chosen as 200 Nm and 300 Nm in the study.
The result of the experimental study shows that the load sharing factor varies cyclicaly with the rotation of the carrier. The main influence factor for uneven load sharing are the eccentric error of the carrier and the sun gear, as expected. The larger torque can also reduce the uneven load sharing. The result of the load distribution shows that the design of flex-pin could effectively improve the uneven distributed of tooth surface.

摘要 i
Abstract iii
謝誌 v
目錄 vi
圖目錄 ix
表目錄 xx
符號說明 xxi
第1章 緒論 1
1.1 研究背景 1
1.2 文獻回顧 2
1.3 研究目的 4
1.4 論文架構 4
第2章 研究方法 6
2.1 行星機構誤差種類 6
2.1.1 托架銷孔正位度誤差 7
2.1.2 齒厚誤差 8
2.1.3 托架偏心量、太陽齒輪偏心量與偏位角 10
2.2 行星齒輪機構嚙合關係 10
2.2.1 任意位置下行星機構嚙合關係 11
2.2.2 無誤差無偏心下齒間間隙 13
2.2.3 具誤差無偏心下齒間間隙 14
2.2.4 太陽齒輪、托架偏心且具誤差下齒間間隙 14
2.2.5 各齒對嚙合位置 16
2.3 行星齒輪負載分析 18
2.3.1 行星機構負載模型 18
2.3.2 齒對受負載撓度計算 21
2.4 實驗分析 25
2.4.1 齒根應變與齒面受力的轉換 25
2.4.2 負載分配計算 26
2.4.3 負載分佈計算 26
第3章 行星機構誤差對負載分配影響分析 28
3.1 分析用參數與誤差設計 28
3.2 無偏心情況下負載分配與嚙合剛性情形 29
3.2.1 全無誤差下情形 29
3.2.2 齒厚誤差影響 32
3.2.3 銷孔誤差影響 38
3.3 托架偏心下負載分配與嚙合剛性情形 48
3.3.1 無齒厚、無銷孔誤差下情形 48
3.3.2 齒厚誤差影響 53
3.3.3 銷孔誤差影響 55
3.4 太陽齒輪偏心下負載分配情形 60
3.4.1 無齒厚與銷孔誤差下情形 60
3.4.2 齒厚誤差影響 66
3.4.3 銷孔誤差影響 69
3.5 綜合誤差下負載分配與嚙合剛性情形 74
第4章 實驗設計與規劃 78
4.1 實驗平台 78
4.1.1 實驗平台構成 78
4.1.2 蝸輪蝸桿轉動裝置 82
4.2 太陽固定式行星齒輪組設計 83
4.2.1 參數設計 83
4.2.2 機構設計 85
4.2.3 相關主要設計公差 88
4.3 具彈性銷之行星機構設計 89
4.3.1 機構設計 89
4.3.2 彈性銷機構 91
4.3.3 相關主要設計公差 92
4.4 行星機構誤差量測 93
4.4.1 銷孔中心位置量測 94
4.4.2 齒厚量測 97
4.5 負載規劃 99
4.5.1 行星齒輪組裝 99
4.5.2 扭力負載 99
4.6 受載量測規劃 101
4.6.1 應變規黏貼 101
4.6.2 訊號擷取 109
4.6.3 實驗流程 112
第5章 實驗結果與分析 113
5.1 量測數據彙整與處理 113
5.2 太陽固定式行星機構實驗結果 122
5.2.1 負載分配結果分析與討論 122
5.2.2 負載分佈結果分析與討論 127
5.3 彈性銷軸行星機構實驗結果 129
5.3.1 負載分配結果 129
5.3.2 負載分佈結果分析與討論 142
第6章 結論與未來展望 145
6.1 結論 145
6.2 未來展望 146
參考文獻 147
附錄 A 150

[1] TIMKEN, http://www.timken.com/en-us-Pages/Home.aspx
[2] Hidaka, T., Terauchi, Y., and Dohi, K., “On the relation between the Run Out Errors and the Motion of the Center of Sun Gear in a Stoeckicht Planetary Gear,” Bull. JSME, 22, pp. 748-754, 1979.
[3] Kahraman, A., “Load Sharing Characteristics of Planetary Transmissions,” Mech. Mach. Theory, 29, pp. 1151-1165, 1994.
[4] Singh, A., “Load sharing behavior in epicyclic gears: Physical explanation and generalized formulation,” Mechanism and Machine Theory, 45, pp.511–530, 2010.
[5] Bodas, A., and Kahraman, A., “Influence of Carrier and Gear Manufacturing Errors on the Static Load Sharing Behavior of Planetary Gear Sets,” JSME Int. J., Ser. C, 47, pp. 908-915, 2004.
[6] Terauchi, Y., Nagamura, K., “Study on Deflection of Spur Gear Teeth : 2nd Report, Calculation of Tooth Deflection for Spur Gears with Various Tooth Profiles,” Bulletin of JSME , Vol. 24, No. 188, pp. 447-452, 1981.
[7] Oda, S., Miyachika, K., Shimizu, H., “Practical Formula for Tooth Deflection of Internal Spur Gear,” Bulletin of JSME , Vol. 29, No. 257, pp. 3905-3910, 1986.
[8] 黃冠霖， “具太陽齒輪浮動之行星機構負載分析”。國立中央大學機械工程學系碩士論文，2010。
[9] Tsai, S.-J., Hwang, G.-L., Yeh, S.-Y., “An Analytical Approach for Load Sharing Analysis of Planetary Gear Drives” 13th World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011.
[10] 葉湘羭，“具行星齒輪浮動之行星齒輪機構靜態負載分析”，國立中央大學機械工程學系碩士論文，2011。
[11] Hidaka, T., and Terauchi, Y., “Dynamic Behavior of Planetary Gear¬¬¬－1st Report, Load Distribution in Planetary Gear,” Bull. JSME, 19, pp. 690-698, 1976.
[12] Ligata, H., Kahraman, A., and Singh, A., “An Experimental Study of the Influence of Manufacturing Errors on the Planetary Gear Stresses and Planet Load Sharing” ASME J. Mech. Des., vol.130, 2008.
[13] Hayashi, T., Li, Y. X., Hayashi, I., Endou, K., and Watanabe, W., “Measurement and Some Discussions on Dynamic Load Sharing in Planetary Gear,” Bull. JSME, 29, pp. 2290-2297, 1979.
[14] Boguski, B., Kahraman, A., and Nishino, T., “A New Method to Measure Planet Load Sharing and Sun Gear Radial Orbit of Planetary Gear Sets” Journal of Mechanical Design, Vol.134, 2012.
[15] Meeusen, M., Ceulemans, M., Otto, M., “Load Distribution Measurements on Planetary Gear Systems” VDI BERICHTE, pp. 697-712, 2010.
[16] Tsai, S.-J., Yeh, S.-Y., Yu, Y.-Y., “Design and Analysis of the Planetary Gear Drive with Flexible Pins for Wind Turbines” Proceedings of the EWEA 2012, pp. 16-19, 2012.
[17] 余遠毅， “彈性銷均載機構設計分析與驗證”，國立中央大學機系工程學系碩士論文，2012。
[18] DIN 3960 Concepts and Parameters Associated with Cylindrical Gears and Cylindrical Gear Pair with Involute Teeth,1980.
[19] Tsai, S.-J., Yeh, S.-Y., “Static Load Sharing and Transmission Errors of Planetary Gear Drives in Presence of Manufacturing and Assembly Errors” in preparation for publication, 2014.