小齒數比之錐形齒輪對設計、分析與應用;Conical Gear Drives with Small Gear Ratio: Design, Analysis and Application.

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题名:	小齒數比之錐形齒輪對設計、分析與應用;Conical Gear Drives with Small Gear Ratio: Design, Analysis and Application.
作者:	魏健宇;Wei,Chein-yu
贡献者:	機械工程學系
关键词:	割草機;受載齒面接觸分析;小齒數比;影響係數法;粉末冶金;組裝誤差;鉋切錐形齒輪;Assembly errors;Influence coefficient method;Loaded tooth contact analysis;Powder metallurgy;Shaped conical gear;Small gear ratio
日期:	2013-03-19
上传时间:	2013-06-19 15:27:37 (UTC+8)
出版者:	國立中央大學
摘要:	?鉋切錐形齒輪對之組合為正齒輪與錐形齒輪，因組裝精度要求較低，而且藉由模具方式製作粉末冶金齒輪方式，更有低成本的優勢，因此在大軸交角傳動之應用場合具有取代傘齒輪之潛力。目前鉋切錐形齒輪多應用於大減速比之場合，但對小減速比之錐形齒輪傳動，因受尖齒與根切之限制而使有效齒面寬不足，另一方面在以鉋齒刀少齒差之小齒輪組合所形成之點接觸設計，亦會因接觸點的位置幾乎靠近錐形齒輪小端，易造成邊緣接觸，因而在應用上受到限制。因此本研究之目的即在提出一錐形齒輪對非標準設計方法，並對容許之組裝誤差、接觸應力與承載能力加以分析與驗證。?在錐形齒輪設計部分，以非標準基準齒條之設計方法來增大錐形齒輪齒面寬，同時對鉋齒刀與小齒輪對則透過非等模數非等壓力角之概念來調整接觸點位置。面對複雜參數關係，本論文提出以設計圖表方式進行設計，如此可以有效地在小齒輪正移位的要求條件下，除得到較大錐形齒輪齒面寬，並能調整接觸點位置於齒面中央。藉由齒輪嚙合幾何關係推得之齒面方程，則利用CAD軟體Inventor之API所撰寫之程式模組以產生錐形齒輪3D實體模型，除可用於以CNC銑製的方式製造出錐形齒輪，亦可在CAD程式環境下利用干涉分析，模擬錐形齒輪對在受負載下組裝誤差對於接觸點之影響。組裝誤差影響分析亦以實驗方式進行，結果證明利用CAD軟體模擬之正確性；分析結果也顯示在鉋齒刀與小齒輪齒差愈大的情況下，組裝敏感度愈低，但也愈接近點接觸的型態。?為確認錐形齒對承載能力，則利用影響係數法進行嚙合齒對齒面受負載接觸分析，探討齒對在整個嚙合過程接觸應力變化以及在接觸開始、接觸結束兩特定位置之應力分佈狀況。分析結果顯示，在接觸開始與接觸結束處會發生接觸應力集中之現象，因此在本研究中亦同時針對正齒輪齒頂具圓角、短齒頂/齒根修整、平滑化短齒頂/齒根修整三種型式進行分析。分析結果顯示，齒頂圓角與短齒頂/齒根修整在修整起始位置仍會產生應力集中現象，而平滑化短齒頂/齒根修整雖可有效降低劇增之應力，但齒對在齒頂修整區域嚙合時會形成非赫茲接觸，因此在正齒論進齒頂修整對整個齒對嚙合過程的應力變化改善效果有限，所以接觸應力改善，必須從錐形齒輪齒面修整著手。?在論文最後則以所發展之設計分析方法，以粉末冶金齒胚製作一組錐形齒輪對，實際安裝於割草機中，以割草牛筋敲擊塑鋼棒方式模擬割草時的狀況，進行10^6週期負載實驗。實驗結果顯示，在以實驗設計之嚴苛條件下，齒面只產生輕微之拋光磨損，並無其他破壞損傷，由此證明所發展之錐形齒輪對設計可應用於割草機的操作環境。?Conical gear drives, composed of a spur gear and a shaped conical gear, has the potential to replace the bevel gear for the transmission with a large shaft angle, because of lower required assembly accuracy and low-cost advantage (especially manufactured by powder metallurgy). Conical gear drives have been used most in transmission with a large gear ratio. But in the case of the conical drives with a small gear ratio (smaller than 2), the effective face-width of the conical gear is not enough due to the geometrical limit of tooth pointing and undercutting. On the other hand, the bearing contact between the pinion and the conical gear is localized by selecting the tooth number of the spur gear less than that of the shaper. In such a design, edge contact ocurrs likely due to the contact point locates nearby the undercut limit. Those problems restrict the application of conical gear drives with a small gear ratio in the practice. The purpose of this paper is thus to propose a nonstandard design approach and also to analyze and to validate the assembly error, contact stress and load capacity for the mentioned conical gear drives.?At first some concepts are developed for designing conical gears. The face-width of the conical gear is enlarged by using nonstandard basic rack and the location of the contact point is adjustable by using the concept of the unequal module/unequal pressure angle to design the pinion and the corresponding shaper. Under consideration of the complex relations of the design parameters between the conical gear, the pinion and the shape, design charts are constructed in this paper to obtain a larger effective face-width of the conical gear, and to adjust the location of the contact point near the middle of the face-width. For the purpose of manufacturing on CNC-milling machine, 3D solid models of the conical gearing are generated by using Inventor API program based on the mathematical equations of the tooth surface derived from relations of gear geometry. The generated 3D model are also applied to simulate the location of loaded contact points of conical gear pairs influenced by assembly errors by using interference analysis option of the CAD program. The influence analysis of assembly errors on the location of contact points is also carried out experimentally, and the results validate the feasibility of CAD simulation. The results of analysis showed that the greater the difference of the tooth number between the shaper and the pinion is, the lower the assembly sensitivity is. Moreover, the contact pattern will be much closer to the type of point contact.?To confirm the load capacity of the designed conical gear drive, tooth contact stress is analyzed by using influence coefficient method. The change of contact stress during gear meshing and the distribution of contact stress of engaged teeth at the position of contact begin and conatc end, respectively, are investigated. The analysis results showed that the contact stress is concentrated at the position of contact end and contact begin. Besides, pinions with tip rounding, short linear tip relief and smooth short linear tip relief, respectively, are also considered for loaded tooth contact analysis in the paper. From the analysis results stress concentration can be found at the begin of profile modification of the pinion with tip rounding and short linear tip relief. The pinion with smooth short linear tip relief can reduce the stress concentration, but non-Hertz contact occurs still in the contact region of profile modification. Therefore, the concentrated contact stress can be improved only by applying the tip relief on the conical gear.?Finally, a set of powder metallurgy conical gear pair is mounted it in a gearbox of mower for running test according to the design approach proposed in the paper. The working condition of the mower is simulated by using trimmer line to beat a POM rod. The total load cycle is 106. It is explored from the experiment results that the tooth surfaces of both gears have only slight polishing wear under such a strict load conditions. It can be thus concluded that the proposed design approach for conical gear drives with a small gear ratio can meet the requirements of application for power transmission.
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