渐开线椭圆齿轮齿廓数学建模与图形仿真

doi:10.3696/j.issn.1672-6952.2010.01.018

辽宁石油化工大学学报 ›› 2010, Vol. 30 ›› Issue (1): 63-66.DOI: 10.3696/j.issn.1672-6952.2010.01.018

渐开线椭圆齿轮齿廓数学建模与图形仿真

任芳舒1,2,唐晓初1*

1.辽宁石油化工大学机械工程学院,辽宁抚顺113001;2.齐齐哈尔职业学院,黑龙江齐齐哈尔161000

收稿日期:2009-06-22 出版日期:2010-03-25 发布日期:2017-07-05
作者简介:任芳舒(1983-),女,辽宁北票市,在读硕士。

Mathematical Modeling and Graphics Simulation for Tooth Profile of an Ellipse Involutes Gears

REN Fang-shu^1,2，TANG Xiao-chu^1*^

1.School of Mechanical Engineering，Liaoning Shihua University,Fushun Liaoning 113001, P.R.China; 
2.Qiqihar Vocational College, Qiqihar Heilongjiang 161000，P.R.China

Received:2009-06-22 Published:2010-03-25 Online:2017-07-05

摘要/Abstract

摘要： 提出了一种渐开线椭圆齿轮齿廓造型的新方法。首先,根据对渐开线齿廓形成原理和渐开线齿轮任
意圆上的齿厚公式的分析,建立了插齿刀的渐开线圆柱齿轮齿廓的数学模型。其次,建立插齿刀与椭圆齿轮毛坯即
节曲线在共轭时的几何位置关系,使插齿刀作纯滚动,再用啮合方程将这两个模型结合起来,获得椭圆齿轮齿廓曲
线加工数学模型。第三,在加工过程中,为保证刀具和齿坯之间的范成关系,刀具在齿坯节曲线上滚过的弧长等于
刀具绕其自身回转中心转过的弧长。最后,用计算机图形仿真的方法获得了椭圆齿轮的渐开线齿廓曲线图形,验证
了该数学模型的正确性和有效性。

关键词: 椭圆齿轮 , 渐开线齿廓 , 节曲线 , 范成法 , 图形仿真

Abstract:

A new modeling method of an ellipse gear's profile was proposed. Firstly, according to the analysis of the forming principle of the involutes profile and the tooth thickness of formula, a mathematical model of involutes profile was established. Secondly, a geometric relationship of pinion cutter and pitch curve of an ellipse gears was established, which made pinion cutter do pure rolling. Then the engaging equations of two models were combined and the mathematical model of tooth profile of ellipse gear was established. Third, in processing, the arc length of cutter on the pitch curve was equal to be the length of cutter rotating around its axis in order to guarantee the generating between the pinion cutter and the blank. Finally, an involutes profile of an ellipse gears was formed using the method of computer graphics simulation. The accuracy and the validity of the mathematical model were confirmed by simulation.

Key words: Ellipse gears , , Involutes profile , , Pitch curve , , Generating , , Graphic simulation 

任芳舒,唐晓初. 渐开线椭圆齿轮齿廓数学建模与图形仿真[J]. 辽宁石油化工大学学报, 2010, 30(1): 63-66.

REN Fang-shu，TANG Xiao-chu. Mathematical Modeling and Graphics Simulation for Tooth Profile of an Ellipse Involutes Gears[J]. Journal of Liaoning Petrochemical University, 2010, 30(1): 63-66.

[1]	李静. 非圆齿轮渐开线齿廓数学模型的建立[J]. 辽宁石油化工大学学报, 2009, 29(2): 39-41.
[2]	李静. 渐开线椭圆齿轮造型设计与分析[J]. 辽宁石油化工大学学报, 2009, 29(1): 57-60.

渐开线椭圆齿轮齿廓数学建模与图形仿真

Mathematical Modeling and Graphics Simulation for Tooth Profile of an Ellipse Involutes Gears

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