以螺旋型刮刨刀創成Helipoid齒輪之齒面數學模式與接觸分析

Abstract

目前工業上廣泛使用在交錯軸動力傳遞的齒輪主要有交錯軸螺旋齒輪﹙Crossed-axis helical gears﹚以及戟齒輪﹙Hypoid gears﹚。戟齒輪因具有高負載和高接觸率的優點，而被廣泛地使用在需要傳動較大扭力之交錯軸動力傳遞的機械上。然而，由於戟齒輪之齒面複雜，製造時通常需要使用專用的機器以及有經驗之工程人員來操作，因此戟齒輪的生產成本較高。相較而言，交錯軸螺旋齒輪只要使用傳統的滾齒加工或是刨齒加工就能得到良好的成品，因此其製造成本較戟齒輪低許多，但是交錯軸螺旋齒輪的負載能力以及接觸率較小。 Helipoid齒輪是一種新型的齒輪，其概念係由日本工業大學的長田重慶教授所提出，主要是設計來滿足成本與性能之間的平衡，也就是期望能以接近交錯軸螺旋齒輪的製造成本來達成戟齒輪的高負載特性，創造出一個能結合兩者之優點的齒輪。 本論文利用齒輪原理與電腦輔助設計技術，依據以螺旋型刮刨刀創成Helipoid齒輪的概念，推導出Helipoid齒輪之齒面數學模式，並進一步進行齒輪對的齒面接觸分析。同時，本論文也根據齒面接觸分析之結果探討創成Helipoid齒輪的螺旋型刮刨刀之齒數、螺旋角與齒面差異以及齒面接觸情形間的關係。

Crossed-axis helical gears and hypoid gears are two common types of crossed-axis power transmission devices. Hypoid gears offer a high load capability and a high contact ratio, and are widely used for rear-axle transmission in automobiles. However, hypoid gears should be manufactured by special machines with various machine-tool settings due to complex tooth surface geometries. Accordingly, the manufacture of hypoid gear sets requires experienced and well-trained engineers. Therefore, the production and maintenance costs of a hypoid gear are relatively high. The manufacture of helical gears, however, requires only easily operated and conventional machines, and the production cost is relatively lower. However, the load capability and the contact ratio are also lower. A new type of gear, named the helipoid gear, is conceptually proposed by Nagata, eminent professor of Nippon Instittude of Technology, in an attempt to achieve a better balance between gear performance and manufacturing cost than that of hypoid and crossed-axis helical gears. Helipoid gears are designed to exhibit the advantages of both hypoid and helical gears ─ higher load capability and contact ratio than those of a helical gear, and a lower manufacturing cost than that of a hypoid gear. In this research, a mathematical model for the helipoid gears cut by the helical type shaving cutters is developed based on the theory of gearing and the technique of computer aided design. According to this mathematical model and the tooth contact analysis technique, transmission errors of the helipoid gear set are investigated. Besides, the relationships among the tooth numbers and the helical angles of the helical type shaving cutter, the tooth surface deviations and tooth contact conditions are also investigated.