球面漸開線直傘齒輪修整設計、分析與疲勞測試

劉育豪(Yu-hao Liu)

指導教授 ： 蔡錫錚

國立中央大學/工學院/機械工程學系/碩士(2014年)

摘要

傘齒輪的應用非常廣泛，適用於各種軸交角之傳動上。傳統的製造方式大多使用齒輪專用機進行切削加工，然而不同輪專用機系統所製作的齒形亦有差異，使得所製造之齒輪除不能互通共用外，且設計加工參數多，若要對齒面做修整，相關設計參數之設定會變得相當複雜。因此本論文之研究目的，即提出以球面漸開線做為直齒傘齒輪之齒形，並以雙曲線建構之齒線隆起之齒面修整模式。為確認修整模式之可行性，論文中分別分析修整型傘齒輪對在未受載及受載狀況下之齒面接觸狀況，同時亦製造出測試齒輪，進行齒印量測及疲勞破壞測試。
本論文使用之齒面接觸分析方法，係利用球面漸開線之法向量幾何特性定義傘齒輪對在空間中任一組裝下的接觸條件條件，以簡化嚙合齒面接觸點位置之求解，再以此方法分析修整參數對接觸點位置及傳動誤差於不同組裝誤差下之影響。接觸點位置分析結果顯示，偏位誤差敏感度最大，其次分別為大、小齒輪之軸向誤差，而角度誤差並不會影響接觸點在齒面寬方向之位置，僅在齒形方向做改變。傳動誤差分析結果顯示，傳動誤差曲線在偏位誤差下近似於拋物線，而在大、小齒輪軸向誤差下則為非連續之近似直線，而在角度誤差下並無傳動誤差產生。
嚙合齒對之受負載齒面接觸分析，係使用影響係數法求解修整型傘齒輪對之受載齒面接觸應力、負載分配與受載傳動誤差。接觸應力分析結果可知：(1) 嚙合齒對在接觸開始時接觸應力會偏高，(2) 嚙合齒對在接觸開始與接觸結束位置，因受齒頂邊緣之影響，會發生齒面會有接觸應力集中現象。受載傳動誤差分析結果顯示：(1) 在不同負載下之傳動誤差曲線，會隨著輸入扭力增加而使整體誤差曲線偏移量加大；(2) 在有、無各組裝誤差下之傳動誤差曲線，在單、雙齒對接觸交界處會產生一明顯的段差，同時會隨輸入扭力增加而加大。
組裝誤差下嚙合位置則以齒印量測以及CAD干涉模擬兩種方式進行驗證，驗證結果顯示本研究提出之TCA模型計算結果與上述兩種驗證方式結果相符。
齒輪疲勞測試部分係於功率封閉型的測試平台上進行，對未修整齒輪及修整型齒輪，在不同負載下進行5*10^5週期之疲勞破壞測試，並比較其齒面破壞面積比率。由實驗結果可得知，在相同的負載條件及有限壽命下，修整型傘齒輪齒面破壞程度較未修整型齒輪小。在各疲勞測試中，同時會量測齒輪運轉時的振動，頻譜分析結果可知未修整齒輪邊緣接觸與齒輪不對心狀況對振動的影響，在齒面破壞後會變得嚴重；修整型齒輪齒面的磨損對於振動的影響較為明顯，若將軸變形補償納入測試，修整型齒輪整體的振幅值明顯較其他兩種條件低。

關鍵字

球面漸開線傘齒輪 ； 齒線修整 ； 組裝誤差分析 ； 受載齒面接觸分析 ； 受載傳動誤差分析 ； 傘齒輪疲勞試驗

並列摘要

Bevel gears are wildly applied to angular transmission. Traditionally, bevel gears are manufactured by different dedicated gear machines according to the corresponding gearing system. Consequently, the bevel gears manufactured by different gearing system are not interchangeable due to different gearing parameters. Therefore, the design of flank modification on machined bevel gears will be more complicated. Therefore, the purpose of this research is to propose a lead crowning method with hyperbolic curve for spherical involute bevel gears. This design approach is intuitive and suitable for moulded gears. Loaded and unloaded tooth contact of bevel gear pairs under assemblely errors are analyzed to verify the feasibility of the proposed approach. Finally, test bevel gears are also manufactured for the measurement of tooth contact patterns and the fatigue tests.
The tooth contact analysis (TCA) proposed in the thesis is based on the contact conditions which are determined by the spherical involute geometric characteristics, so as to simplify the solving procedure. With aid of this approach, the influence of the flank modification parameters on the contact positions and transmission errors were analyzed for the gear pairs under different assembly errors. The results show that the contact position of the tooth pair due to the offset error is the most sensitive, the next is due to the mounting distance errors of the gear and the pinion. The shaft angle error does not affect the contact position in the direction of the face-width, but only the direction of the tooth profile. The curve of unloaded transmission error (TE) due to the offset error is similar to parabolic curve, the others due to the mounting distance errors are discontinuous linear curve. The shaft angle error affects no transmission error.
The loaded tooth contact analysis (LTCA) approach is based on the influence coefficient method to determine tooth contact stress, load sharing and loaded transmission errors. The results show that contact stress at the contact begin is the highest, and the concentrated contact stress occurs at the contact begin and the contact end. The loaded transmission error (LTE) will be shifted to a certain lag angle when the input torque is increased. At the inner and outer point of single contact tooth pair, a significant jump of the discontinuous LTE curve is also increased with a larger input torque, independ on presence of assembly errors.
The contact positions under various assembly errors simulated by the proposed TCA model are validated by measurement of contact pattern of test gears and interference analysis in CAD porgram. The results show that the TCA model is in good agreement with the contact pattern measurement and CAD simulation.
The gear fatigue test was conducted on a power close-loop test rig. Two kinds of test gears, each with non-modifided and modifided flanks, were tested under different loads for 5*10^5 cycles. The ratios of the tooth surface damage area of different cases are compared. The experimental results show that pitting damage on modified flanks is less than non-modifided under the same conditions.
Additionally, the vibration of the test gears was also measured during the test. It is found from the analysis results of the frequency spectrum that the vibration of the non-modifided gears due to the edge contact and the eccentric error was more serious after occurrence of the pitting on the flanks. The tooth wear has significant effect on thr vibration of the modified gears. Further more, the total amplitude values of vibration on the modifided gears are significantly lower than other cases, if the compensation of the shaft deformation is considered

並列關鍵字

Spherical involute bevel gear ； Lead modification ； Assembly error analysis ； Loaded tooth contact analysis ； Loaded tranmossion error ； Bevel gear fatigue test

參考文獻

[5] ASNI/AGMA ISO 23509-A08, Bevel and Hypoid Gear Geometry, 2006.

[6] ANSI/AGMA 2005-D03, Deaign Manual for Bevel Gears, 2008.

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[21] Terauchi, Y., Nagamura, K. et al, “Study on Tooth Bearing of Bevel Gears. 2nd Report, Relation between Tooth Bearing and Assembly Error, Shaft Angle Error,” Transactions of the Japan Society of Mechanical Engineers, Series C, Vol. 51, No. 468, pp. 2034-2041, 1985.