Effect of Gear Backlash Function on the Dynamics Characteristic of Helical Gear

Wang Xin; Kang Boqiang

doi:10.16578/j.issn.1004.2539.2015.12.004

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Effect of Gear Backlash Function on the Dynamics Characteristic of Helical Gear

更新时间：2022-10-20

- Effect of Gear Backlash Function on the Dynamics Characteristic of Helical Gear
- Vol. 39, Issue 12, Pages: 17-23(2015)
- 作者机构：
  
  1. 兰州交通大学机电工程学院
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2015.12.004
  CLC：
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[1]王昕,康博强.齿侧间隙函数对斜齿轮动力学特性的影响[J].机械传动,2015,39(12):17-23.

Wang Xin, Kang Boqiang. Effect of Gear Backlash Function on the Dynamics Characteristic of Helical Gear. [J]. 39(12):17-23(2015)
[1]王昕,康博强.齿侧间隙函数对斜齿轮动力学特性的影响[J].机械传动,2015,39(12):17-23. DOI： 10.16578/j.issn.1004.2539.2015.12.004.

Wang Xin, Kang Boqiang. Effect of Gear Backlash Function on the Dynamics Characteristic of Helical Gear. [J]. 39(12):17-23(2015) DOI： 10.16578/j.issn.1004.2539.2015.12.004.

摘要

考虑斜齿圆柱齿轮的齿侧间隙、时变啮合刚度和综合啮合误差等非线性因素,建立三自由度单级斜齿圆柱齿轮轴-扭耦合非线性动力学模型。以直齿圆柱齿轮传动中采用的"分段线性"齿侧间隙函数为基础,经高次拟合得到适合斜齿圆柱齿轮啮合特点的齿侧间隙函数。采用变步长Rungekutta法数值求解所建立的斜齿圆柱齿轮系统动力学方程,得到系统在两种不同齿侧间隙函数下的非线性动态响应结果。综合运用分岔图、最大Lyapunov指数、相图、Poincaré映射图和FFT频谱图分析了两种不同齿侧间隙函数下频率对系统分岔与混沌特性的影响。经对比分析,高次拟合得到的齿侧间隙函数更符合斜齿圆柱齿轮传动系统的特点。

Abstract

A three- degree- of- freedom shaft- torsion coupling nonlinear dynamics model of a single-stage helical cylindrical gear transmission system is established,which included the nonlinear factors such as gear backlash,time- varying stiffness,transmission error and so on. A gear backlash function suitable for the helical cylindrical gear system is obtained by high order fitting the piecewise linear gear backlash function using in the spur cylindrical gear system. The results of the nonlinear dynamic response under two different gear backlash functions are obtained by employing the established dynamics equation of helical cylindrical gear system with variable step- size Runge- kutta method numerical solution. The influences of frequency on the bifurcation and chaotic characteristics under two different gear backlash functions are analyzed by using bifurcation diagrams,top Lyapunov exponent（ TLE） diagrams,phase portraits,Poincaré maps and FFT spectrums. The gear backlash function obtained by high degree fitting is more suitable for helical gear system by analyzing and comparing.

关键词

斜齿轮齿侧间隙高次拟合分岔混沌

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