Modification of the Pitch Curve Design Defect of Non-circular Gear based on Spline Interpolation Method

Liu Qinqin; Lü Gang; Deng Xingqiao

doi:10.16578/j.issn.1004.2539.2018.05.018

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Modification of the Pitch Curve Design Defect of Non-circular Gear based on Spline Interpolation Method

更新时间：2022-10-20

- Modification of the Pitch Curve Design Defect of Non-circular Gear based on Spline Interpolation Method
- Vol. 42, Issue 5, Pages: 90-95(2018)
- 作者机构：
  
  1. 四川大学锦城学院机械工程学院
  2. 浙江大学自贡创新中心机电装备及智能控制研发中心
  3. 西华大学机械工程学院
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2018.05.018
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[1]刘琴琴,吕刚,邓星桥.基于样条插值方法的非圆齿轮节曲线设计缺陷的修正[J].机械传动,2018,42(05):90-95.

Liu Qinqin, Lü Gang, Deng Xingqiao. Modification of the Pitch Curve Design Defect of Non-circular Gear based on Spline Interpolation Method. [J]. 42(5):90-95(2018)
[1]刘琴琴,吕刚,邓星桥.基于样条插值方法的非圆齿轮节曲线设计缺陷的修正[J].机械传动,2018,42(05):90-95. DOI： 10.16578/j.issn.1004.2539.2018.05.018.

Liu Qinqin, Lü Gang, Deng Xingqiao. Modification of the Pitch Curve Design Defect of Non-circular Gear based on Spline Interpolation Method. [J]. 42(5):90-95(2018) DOI： 10.16578/j.issn.1004.2539.2018.05.018.

摘要

针对非圆齿轮节曲线设计中出现的不连续点和尖点问题,依据非圆齿轮节曲线的封闭性条件及其传动比函数,建立了非圆齿轮副节曲线设计缺陷的修正模型,通过引入修正因子,有效避免了节曲线产生不连续点的现象。基于非圆齿轮节曲线上的点与其密切圆之间的几何关系,分别建立了节曲线凸尖点与凹尖点的修正模型。将密切圆上的点作为插值点,密切圆与节曲线的切点为样条插值的边界条件,通过数值插值方法实现了对节曲线尖点的修正。研究结果表明,该算法能快速修正高阶阿基米德螺线齿轮副节曲线的设计缺陷,且算法是有效的。

Abstract

Aiming at discontinuity and cusp problem of pitch curves for non-circular gear pairs,based on the closed condition of pitch curve and transmission ratio function for non-circular gear,modification model of pitch curve design defects for non-circular gear is established. A modification factor is introduced into modification model to avoid effectively discontinuity of pitch curve. Based on geometrical relationship between points lied in pitch curve and its osculating circle,modification models for concave cusp and convex cusp of pitch curve are established respectively. The points lied in osculating circle are considered as interpolation points,the tangency points between osculating circle and pitch curve is boundary conditions of spline interpolation,cusp of pitch curve is modified by using numerical interpolation method. The results indicate that design deficiency such as pitch curve for high-order Achimedean spiral gear pair can be amended quickly by the algorithm,while it is exactly.

关键词

非圆齿轮设计缺陷节曲线修正因子数值插值

Keywords

Non-circular gearDesign defectPitch curveModification factorNumerical interpolation

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