Influences of Fractional Order Damping on Nonlinear Dynamics of Cracked Rotor

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Influences of Fractional Order Damping on Nonlinear Dynamics of Cracked Rotor

更新时间：2025-07-09

- Influences of Fractional Order Damping on Nonlinear Dynamics of Cracked Rotor
- Vol. 46, Issue 1, Pages: 76-80(2012)
- 作者机构：
  
  西安交通大学智能仪器与监测诊断研究所,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： TH113
- Online First：10 January 2012，
  
  Published：2012
- 稿件说明：
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Influences of Fractional Order Damping on Nonlinear Dynamics of Cracked Rotor[J]. 2012, 46(1): 76-80.
DOI：

Influences of Fractional Order Damping on Nonlinear Dynamics of Cracked Rotor[J]. 2012, 46(1): 76-80. DOI：

摘要

为了有效地提高转子系统特性的分析精度

使其能够准确地进行故障诊断

以Jeffcott转子模型为基础

建立了带有分数阶阻尼和横向呼吸裂纹故障的转子系统的动力学模型.采用4阶龙格库塔法和10阶连分式欧拉法对转子系统的动力学方程进行数值仿真计算

利用轴心轨迹图、Poincare截面映射图和分岔图等

研究了阻尼的分数阶次、转速和裂纹深度对裂纹转子动态特性的影响

并通过实验对理论分析结果进行了验证.分析结果表明:在半临界转速附近

由于裂纹的存在

转子的轴心轨迹呈现明显的双环型(或称内8字形)

因此响应中的2倍频分量占主导地位.随着分数次阻尼阶次的增加

转子系统依次经历混沌、准周期和周期运动

同时裂纹深度、不平衡量以及转速对转子系统的动态特性具有明显影响.

Abstract

Nonlinear dynamics of cracked rotor system with fractional order damping is investigated with a response-dependent breathing crack model. The fourth order Runge-Kutta method and tenth order continued fraction expansion Euler(CFE-Euler)method are introduced to simulate the proposed system equation of fractional order cracked rotors. The effects of derivative order of damping

rotating speed ratio

crack depth

orientation angle of imbalance relative to the crack direction and mass eccentricity on the system dynamics are demonstrated by bifurcation diagram

Poincare map and rotor trajectory diagram. The results show that the rotor system gets chaotic

quasi-periodic and periodic as the fractional order increases. It is also found that the imbalance eccentricity level

crack depth

rotational speed

fractional damping and crack angle all exert considerable influence on the nonlinear behaviors of cracked rotor system.

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references

GASCH R. A survey of the dynamic behaviour of a simple rotating shaft with a transverse crack [J]. Journal of Sound and Vibration,1993,160(2):313-332.

DARPE A K, CHAWLA A, GUPTA K. Analysis of the response of a cracked Jeffcott rotor to axial excitation [J]. Journal of Sound and Vibration, 2002, 249(4): 29-45.

PADOVAN J, SAWICKI J T. Nonlinear vibrations of fractionally damped systems [J]. Nonlinear Dynamics, 1998(16): 32-36.

CAO Junyi, MA C, XIE H, et al. Nonlinear dynamics of Duffing system with fractional order damping [J]. Journal of Computational and Nonlinear Dynamics, 2010,5(4): 041012-041018.

TENREIRO M J A, SILVA M F. Some applications of fractional calculus in engineering [J]. Mathematical Problems in Engineering, 2010(2010): 639801-34.

ROSSIKHIN Y A, SHITIKOVA M V. Application of fractional calculus for dynamic problems of solid mechanics: novel trends and recent results [J]. Applied Mechanics Reviews, 2010, 63(1): 1-52.

高建民, 朱晓梅. 转轴上裂纹开闭模型的研究 [J]. 应用力学学报, 1992, 19(1): 108-112.

GAO Jianmin, ZHU Xiaomei. Study on the model of the shaft crack opening and closing [J]. Chinese Journal of Applied Mechanics, 1992, 19(1):108-112.

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