分数阶阻尼在滚动轴承故障诊断中的应用  

Application of Fractional Damping in Fault Diagnosis of Rolling Bearings

作　　者：李云龙 李志农[1] LI Yun-long;LI Zhi-nong(Key Laboratory of Nondestructive Testing(Ministry of Education),Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]无损检测技术教育部重点实验室(南昌航空大学),南昌330063

出　　处：《南昌航空大学学报（自然科学版）》2019年第4期39-44,100,共7页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(51675258,51261024);重庆大学机械传动国家重点实验室(SKLMT-KFKT-201514)。

摘　　要：由于分数阶微积分具有计算精度高和速度快的优势,因此将分数阶微积分的相关理论应用到滚动轴承故障诊断中,建立了分数阶阻尼滚动轴承内圈动力学模型,并利用分数阶傅里叶变换的四阶中心距确定分数阶的最优阶次,分析了分数阶阻尼滚动轴承内圈故障的动力学响应特性。仿真结果表明,随着分数阶阶次的增加,滚动轴承内圈的轴心轨迹由混沌逐渐变为稳定的周期运动;仿真分数阶频谱图更符合实验频谱图。分数阶阻尼模型比整数阶阻尼模型更能反映滚动轴承故障的振动特性,可取得比传统的整数阶阻尼更好的效果。Fractional calculus has the advantage of high computational precision and fast speed. Therefore, the theory of fractional calculus is applied to the fault diagnosis of rolling bearings. A dynamic model of rolling bearingswith a fault in the inner ring based on fractional damping is established. And the dynamic response characteristic of rolling bearings at optimal order, which isdetermined by the fourth-order center distance of the fractional Fourier transformation, is analyzed. The simulationresults show that the axis motiontrajectory of the inner ring gradually changes from chaotic to stable periodic motionwith the increase of fractional order. And the simulation frequency spectrogram at optimal order is more in line with that of the experiment. The fractional damping model can better reflect the vibration characteristics of rolling bearingswith a fault than the integer damping model and can achieve better results than the traditional integer damping.

关 键 词：分数阶微积分 滚动轴承 故障诊断 最优阶次 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3