Mathematical Model and Tooth Contact Analysis of Helipoid Gears Cut by Shaper Cutters
|關鍵字:||Helipoid 齒輪;刨齒刀;數學模式;傳動誤差;接觸齒印;有限元素法;接觸應力;Helipoid Gear;Shaper cutter;Mathematical model;Transmission error;Contact pattern;Finite element method;Contact Stress|
|摘要:||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﹚。戟齒輪有高負載和高接觸率的優點，因此大量地使用在需要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特殊的專用機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，因此成本較戟齒輪低許多。但是由於交錯軸螺旋齒輪具有較小的負載能力以及接觸率，使得其可應用的範圍受到很大的限制。
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 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. A hypoid gear set can obtain good contact patterns and contact locations only with appropriate machine-tool settings. 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 lower. However, the load capability and the contact ratio are also lower. A new type of gear, named the helipoid gear, is proposed herein 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. A helipoid gear, like a helical gear, can be produced by two conventional gear manufacturing methods, hobbing and shaping methods. Thus, the manufacturing cost of the helipoid gear is similar to that of the helical gear and far less than that of the hypoid gear. In this paper, based on the theory of gearing the mathematical model for helipoid gears cut by a shaper cutter is developed. According to this mathematical model and the tooth contact analysis technique, transmission errors of the helipoid gear set are investigated. Furthermore, the gear set contact pattern is simulated by applying the contact surface topology method and the stress analysis software developed by applying the finite element method is also adopted for the tooth contact stress analysis. Besides, the relationships among the tooth numbers of the shaper cutter, helical angles and contact patterns and transmission errors are also investigated.