Helipoid齒輪之接觸分析

Abstract

目前戟齒輪及交錯軸螺旋齒輪已被廣泛地應用於交錯軸的動力傳遞。戟齒輪雖然接觸比大且可承受負載較大，但必須仰賴專用機及有經驗之製造工程師，經過多次嘗試調整各項機器刀具設定值，才可製造出接觸齒印及位置良好的齒輪，因此戟齒輪之製造成本高昂；而交錯軸螺旋齒輪雖然生產成本較低廉，但缺點是接觸比和負荷能力較低。有鑑於此，日本工業大學榮譽教授長田重慶提出一新型的交錯軸齒輪，暫命名為Helipoid齒輪，並利用五軸CNC滾齒機之多自由度創成運動，滾削出此Helipoid齒輪。Helipoid齒輪可以說是從標準交錯軸螺旋齒輪變化而來，其負荷能力較交錯軸螺旋齒輪大、製造成本較戟齒輪低，特性介於戟齒輪與標準交錯軸螺旋齒輪之間。 本論文以齒條刀創成方式，推導Helipoid齒輪之齒型數學模式，再依據所推導Helipoid齒輪齒面方程式，分析其運動誤差特性。在齒輪分析時是假設齒面塗佈經丹，依據接觸齒面外型法進行剛體齒面之接觸齒印分析。此外，為了驗證剛體齒印分析結果的正確性，吾人亦使用有限元素法分析軟體的電腦模擬，探討Helipoid齒輪齒面於負載變形下的接觸情形，以及應力的分佈狀況。 本篇論文係探討Helipoid齒輪齒面數學模式、運動誤差分析及接觸齒印特性分析。最後並依據分析所提結果配合最佳化方法，在考量齒輪組最小運動誤差及最大負荷能力限制條件下，將Helipoid齒輪之運動誤差降至可接受範圍內，而仍保持較大齒面負載能力。

Hypoid gears and crossed-axes helical gears are widely used in crossed-axes power transmissions. Hypoid gears have larger contact ratio and load capability, however, gears must be generated with special machines and experienced enginced engineerss. Therefore, the manufacture cost of hypoid gears is high. Compared with hypoid gears, crossed-axes helical gears have lower manufacture cost, while contact ratio and load capability are smaller. To improve the above-mentioned disadvantages, Japan Industrial University honor professor Nagata proposed an new type of crossed-axes gearing, named Helipoid gear. This novel gear is generated by CNC machines with multi-degree of freedom. Helipoid gears are improved from crossed-axes helical gears, and the manufacture cost is cheaper than that of the gypid gear and the load capability is larger than that of the crossed-axes helical gears. In this paper, the tooth mathematical model of Helipoid gears is developed based on the imaginary rack-cutter generation method.According to the mathematical model, kinematic errors of the helipoid gear set is investigated. The gear set contact pattern is simulated by applying the contact surface topology method whice assumes that the gear set is a rigisd body motion. In order to verify the correctness of the analysis model, the finite element method is also applied to investigate the tooth contact pattern under loads, and the corresponding stress and strain distributions on the gear contact surface are also investigated. Tooth mathematical model, kinematic error and tooth contact pattern of the helipoid gear are investigated in this paper. Based on the results of the above-mentioned analyses, optimization analysis is also studied. The kinematic error of helipoid gear set is reduced to an acceptable level and load capability is still kept.