变双曲圆弧齿线圆柱齿轮修形设计及承载接触分析

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摘要为提高变双曲圆弧齿线(variable hyperbolic circular arc tooth, VHCATT)圆柱齿轮承载能力和改善其动态特性，提出齿面修形设计方法，即齿线方向的刀盘倾斜法和齿廓方向的抛物线修形刀刃法。首先，根据齿轮啮合原理和变双曲圆弧齿线圆柱齿轮修形齿面成形原理，推导修形齿面方程，利用MATLAB和UG实现齿面重构。其次，通过齿轮几何接触分析，计算齿面间隙，同时利用有限元法计算接触点柔度矩阵，进而建立承载接触非线性数学规划模型，获取轮齿承载啮合特性。然后，分析刀盘倾角、抛物线系数与抛物线顶点位置对修形齿面载荷分布与承载传动误差的影响。研究结果表明：取值合理的刀盘倾角和抛物线顶点位置可有效降低齿面载荷与改善系统承载传动误差特性；取值合理的抛物线系数可改善单齿和双齿啮合交替时的载荷突变情况。研究结果为变双曲圆弧齿线圆柱齿轮的动态设计和工业应用提供了理论基础。

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	马登秋1
	2
	刘永平1
	叶振环2
	李大伟1
	魏永峭1

关键词 ：变双曲圆弧齿线圆柱齿轮, 齿面修形设计, 承载接触分析, 齿面载荷分布, 承载传动误差

Abstract：To improve the load-bearing capacity and dynamic characteristics of the variable hyperbolic circular arc tooth trace cylindrical gear (VHCATT cylindrical gear), the modification design method of the VHCATT cylindrical gear’s surface was put forward, that is, the cutter inclination method in the direction of tooth line and the parabola modification blade method in the direction of tooth profile. Firstly, according to the gear meshing principle and the modified tooth surface shaping principle of the VHCATT cylindrical gear, the modified tooth surface equation was derived, and the tooth surface reconstruction was realized by using MATLAB and UG. Secondly, the tooth contact analysis was to calculate the tooth surface clearance. At the same time, the contact point flexibility matrix was calculated by using the finite element method, and the load-bearing contact nonlinear mathematical programming model was established to obtain the load-bearing meshing characteristics further. Then, the influences of cutter inclination angle, parabolic coefficient and parabolic vertex position on load distribution and load transmission error of modified tooth surface were analyzed. The results show that: the reasonable cutter inclination angle and parabolic vertex position can effectively reduce the load of the tooth surface and improve the system load transmission error characteristics. The reasonable parabolic coefficient can improve the sudden change of load in the intermeshing of single tooth and double tooth. The further design and industrial applications of the VHCATT cylindrical gear can be accomplished based on the result.

Key words： variable hyperbolic circular arc tooth trace cylindrical gear tooth surface modification design load tooth contact analysis tooth surface load distribution load transmission error

收稿日期: 2022-07-29 出版日期: 2023-07-28

引用本文:

马登秋1,2，刘永平1，叶振环2，李大伟1，魏永峭1. 变双曲圆弧齿线圆柱齿轮修形设计及承载接触分析[J]. 振动与冲击, 2023, 42(14): 170-179.
MA Dengqiu1,2,LIU Yongping1,YE Zhenhuan2,LI Dawei1,WEI Yongqiao1. Modification design and load tooth contact analysis of a cylindrical gear with variable hyperbolic circular arc tooth trace. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(14): 170-179.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2023/V42/I14/170

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