| 摘要: | 在設計高速比、體積緊湊之齒輪箱時，若採用業界常見之多階串聯式行星齒輪機構會無法有效縮小機構體積。而本論文為達到前述設計目標，提出兩種小模數之兩階複合式行星齒輪機構進行研究，分別為3K型不思議與差速分流式行星齒輪機構。在考量齒輪箱須承受最大輸入轉速3000 rpm與最大扭矩50 Nm等變動負載條件，及達到特定有限壽命的要求，本研究亦進行性能與疲勞測試來驗證齒輪箱的傳動表現是否符合設定目標。
本論文在設計與分析研究內容包括兩階式行星齒輪系的傳動特性分析、齒輪強度計算及實例設計。首先建立矩陣計算式以求解行星齒輪系轉速、扭矩與效率，得到齒輪之齒數與速比變化關係、元件扭矩分配及內部功率流向等特性。同時針對需求之機構總速比選定初步參數。並於分析機構傳動效率與內部功率流動時，3K型不思議行星齒輪機構因內部功率會產生回流現象，導致齒輪對之嚙合效率變化對機構整體傳動效率影響極為敏感，甚至在為增速機使用時，可能會發生機構自鎖現象。而差速分流式行星齒輪箱則是以功率與基本速度間關係，將差速階與減速階之扭矩分配設計為約25 %與75 %，因此可在減速段齒輪組減少約25 %的負載，藉此降低其體積。
而在進行3K型不思議行星齒輪系的齒形設計時，因僅承受特定旋轉方向之負載，故採用非對稱齒形設計來增強齒輪的強度性能。但由於3K型不思議行星齒輪機構之行星齒輪係在同中心距下與兩相異的環齒輪嚙合，若使用傳統基準齒形搭配移位之方法進行設計，會使設計過程較為繁瑣複雜。本研究因此採用直接齒形設計法來簡化流程。在給定中心距下，以齒輪齒頂高與齒厚作為設計參數，建立漸開線齒輪嚙合與幾何限制關係式，繪製參數選用圖表來決定合適的齒形參數。而差速分流式行星齒輪箱則使用傳統齒形移位法進行設計。
本研究所設計之齒輪為小於1.0 mm 之小模數，然而齒輪強度計算的國際標準(如ISO-6336)，係以模數大於2 mm齒輪所發展的。因此若使用相應計算方法來分析小模數齒輪的強度時，可能會導致誤判與錯估的結果。故本研究以修正尺寸係數及等效負載係數，代入齒輪計算軟體中分析齒輪強度。3K型不思議與差速分流式行星齒輪兩案例的分析結果顯示，齒面承載能力接近齒輪強度臨界點。
在性能測試中，本研究以傳動效率作為主要之性能評估依據。檢驗結果顯示，3K型不思議行星齒輪箱效率表現低於差速分流式齒輪箱，且有30 %以上的差距，並且在作為增速機使用時會產生自鎖現象。而差速分流式齒輪箱則在減速與增速運轉時皆未產生機構自鎖，並在減速時的傳動效率達到80 %以上。基於此結果，不將3K型不思議行星齒輪箱進行疲勞測試。
在差速分流式齒輪箱的疲勞測試結果為：第一版齒輪箱因輸入端太陽齒輪強度不足而導致提早損壞。第二版本之測試樣本一於疲勞測試後齒輪元件保持完好齒形，但經拆解後發現內部有一組銷軸產生斷裂破壞。樣本二齒輪箱則於疲勞測試過程中提早損壞，經拆解後可得知是因銷軸強度不足與軸孔間隙過小而導致卡死破壞。而樣本三之齒輪箱則有嚴重的齒輪齒面磨耗與齒輪的銷軸孔擴孔等損耗狀況，並且於實驗過程中發生機台聯軸器斷裂的情形。在經分析，發現其原因可能為測試過程發生過載，導致齒輪產生較嚴重的損壞與聯軸器破壞，同時疲勞測試使用的負載設定為原始設計值的1.3倍。由上述測試結果顯示各測試樣本齒輪箱之齒輪元件表現與強度計算結果相近。而第二版本齒輪箱之樣本一與二結果因銷軸強度不足，樣本三則受到機台負載設定問題等，而產生較嚴重損壞。在經專家綜合評估後，認定本研究之齒輪強度設計應屬足夠，後續將更改機台負載設定與校正，並確保齒輪表面硬度與行星齒輪銷軸強度。
由研究成果顯示，本論文在3K型不思議直接齒形設計法與差速分流式行星齒輪機構之傳動特性分析法之成果可供設計者在設計複合式行星齒輪機構時的參考依據。而從精度性能測試結果，可確知3K型不思議齒輪箱效率表現與理論分析結果一致，具有低傳動效率與增速自鎖的特性，差速分流式齒輪箱則是與理論計算相近，具有高傳動效率的表現。疲勞壽命實驗之測試樣本損壞狀態更顯示差速分流式齒輪箱之第二版本的齒形修整與參數設計可以符合齒輪傳動有限壽命設計條件下之臨界強度的要求。
;While designing a compact gearbox with a high speed ratio, the multi-stage tandem planetary gear drive, which is common in the practice, could not effectively reduce the size of the gearbox. In order to obtain the planetary gearboxes with high speed ratio and small size, two-stage compound planetary gear train is designed and tested in this study where two types of gearboxes, 3K-type and differential type gearbox are considered repectively. Since these gearboxes are subjected to variable load conditions with maximum input speed of 3000 rpm and maximum torque of 50 Nm, and with a specific load spectrum, performance and fatigue tests were conducted to verify the transmission performance of the gearbox prototypes.
The design and analysis of the compound two-stage planetary gear drives include the analysis of transmission performance, gear strength calculation, and the design of gearbox prototypes. At first, a set of matrixes for calculation of the speed, torque, and efficiency of planetary gearboxes is established with which the relation of the speed ratio with the tooth numbers of the gears, the torque distribution between the two stages and the power flow within the gearbox. Afterwards preliminary design parameter can be determined for the required speed ratio of the gearbox from these analysis results.
While in the analysis of transmission efficiency and internal power flow of the planetary gearbox, a part of the power flow circulates within the 3K-type paradox planetary gearbox, and it results that the overall efficiency of the gearbox is very sensitive to the mesh efficiency of the gears, and this mechanism might be even self-locked in oprating as a speed increaser. While in designing the two-stage differential type planetary gearbox, the torque distribution between the differential stage and the deceleration stage is designed as 25% and 75% respectively, which is based on the relation of the power and speed ratio of each planetary stage. As a result, a smaller-sized gearbox can be obtained to meet the limited space requirements due to the reduction of the maxmum torque in the deceleration stage.
While designing gearbox prototypes, the tooth profile of the differential type gearbox is based on the standard profile with profile-shifting. The 3K-type paradox planetary gearbox, on the other hand, was designed with asymmetric tooth profile to enhance the tooth strength by considering that the gearbox is loaded under a specific direction of rotation. However, because the planet gears engage two diffrernt ring gears with the same center distance, the direct gear design method is used to avoid the complex design process as using the standard tooth profile. And, the addendum and the tooth thickness are selected, and a design chart for selection of appropriate profile parameters is established based on the equations for gear meshing and geometrical limits.
In general, the load capacity calculation of gears in the standard, ISO-6336, is based on the verified results of gears with module greater than 2 mm. The size factor is thus modified for the strength calculation of the proposed gearboxes with the module 0.5 mm. From the analysis results of the gear strength, it was found that the tooth surface durability of both type of the gearbox is close to the maximum limit of load capacity.
It is shown from the results of performance test that the transmission efficiency of the differential type planetary gearboxes is between 70% and 80% , and the efficiency of 3K-type gearbox is only 40% to 50%. Because the transmission efficiency is the major evaluating criterion for gearbox performance and the slef-locking of the 3K-type gearbox can not be avoided, the 3K-type gearbox is not used in the fatigue test.
The results of fatigue test show that the gearbox sample 1 and 2 of the 2nd version of differential type planetary gearbox are failed due to the broken planet pins, but the teeth of the gears remain good condition. the sample 3 were damaged severely due to the over-loading and unstable loding conditions of the test bench. After discussion with the experts, the designed tooth strength of the gearbox prototypes is enough to meet the required specificatiom. The subsequent test will proceed by controlling carefully the surface treatment and hardness of the teeth and the calibration and setting of the fatigue test machine.
The research results show that the direct gear design method of 3K-type paradox planetary gear drive and the transmission analysis method of the differential type planetary gear drive can be used as a reference for designers when designing compound planetary gear drives. From the gearbox performance test results, it can be confirmed that the efficiency performance of the 3K-type paradox planetary gear drive has the properties of low efficiency and self-locking for speed increasing, and the differential type planetary gear drive has the higher transmission efficiency as the theoretical analysis results show. The damage of the samples of the fatigue life test shows that the tooth profile modification and parameter design of the second version of the differential type gearboxes can meet the requirements of the critical strength under the limited life design conditions of the gear transmission. |
