Model of Inverse Envelope Cutter with Ring-Involute Tooth
Model of Inverse Envelope Cutter with Ring-Involute Tooth
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DOI：
10.1007/s13369-012-0232-3
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发表时间：
2012-05
影响因子：
2.9
通讯作者：
Shyue-Cheng Yang;Chi-Chia Liu;Tsun-Hui Huang
中科院分区：
文献类型：
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作者：
Shyue-Cheng Yang;Chi-Chia Liu;Tsun-Hui Huang
在凹、凸齿轮的加工中，圆锥刀具的设计是一个重要的问题。提出了一种确定齿条刀具数学模型的逆方法。利用所得到的齿条刀具进行了凹、凸齿轮的插齿加工。本文提出的方法解决了齿条刀具的设计问题，用于生成一种新型的凹凸齿轮。以双参数曲面族和直接包络法为基础，以圆锥刀具为展成刀具，根据齿轮理论建立了渐开线环形齿轮的数学模型。给出了所建数学模型的齿轮和小齿轮的冯-米塞斯应力分布等值线。采用数控加工技术，用锥形刀具加工渐开线环形齿轮。基于逆包络原理，利用展开轮齿的数学模型，建立了渐开线环形齿齿条刀具的几何模型和数学模型。为了说明该方法的有效性，一个数值例子来演示齿轮的几何模型与齿轮比为3：2。
The design of a conical cutter is important in the manufacture of concave and convex gears. An inverse method is presented for determining the mathematical model of a rack cutter. The obtained rack cutter was used to generate concave and convex gears. The method proposed in this paper addressed design problems in the rack cutter that were used to generate a new type of concave and convex gears. Based on the two-parameter family of surfaces and direct envelope method, the conical cutter was used as the generating tool for the proposed gear type, and a mathematical model of gears with ring-involute teeth was developed according to gear theory. The contour of von-Mises stress distribution of the gear and the pinion of the proposed mathematical model is presented. Using CNC manufacturing technology, a gear with ring-involute teeth was manufactured by a conical cutter. Based on the inverse envelope concept, the mathematical model of the developed gear tooth was used to determine the geometrical and mathematical models of the rack cutter with ring-involute teeth. To illustrate the effectiveness of the method, a numerical example is presented to demonstrate the geometric model of a gear with a gear ratio of 3:2.