Purpose

The purpose of this paper is to discuss the asymptotic models of different parts with a pitting fault in rolling bearings.

Design/methodology/approach

For rolling bearings with a pitting fault, the displacement deviation between raceways and rolling elements is usually considered to vary instantaneously. However, the deviation should change gradually. Based on this shortcoming, the variation rule and calculation method of the displacement deviation are explored. Asymptotic models of different parts with a pitting fault are discussed, respectively. Besides, rolling bearing systems have prominent fractional characteristics unconsidered in the traditional models. Therefore, fractional calculus is introduced into the modeling of rolling bearings. New dynamic asymptotic models of different parts with a pitting fault are proposed based on fractional damping. The numerical simulation is performed based on the proposed model, and the dynamic characteristics are analyzed through the bifurcation diagrams, trajectory diagrams and frequency spectrograms.

Findings

Compared with the model based on integral calculus, the proposed model can better reflect the periodic characteristics and fault characteristics of rolling bearings. Finally, the proposed model is verified by the experiment. The dynamic characteristics of rolling bearings at different rotating speeds are analyzed. The experimental results are consistent with the simulation results. Therefore, the proposed model is effective.

Originality/value

(1) The above models are idealized, i.e. the local pitting fault is treated as a rectangle. When a component comes into contact with the fault, the displacement deviation between the component and the fault component immediately releases if the component enters the fault area and restores if the component leaves. However, the displacement deviation should change gradually. Only when the component touches the fault bottom, the displacement deviation reaches the maximum. (2) Due to the material's memory and fluid viscoelasticity, rolling bearing systems exhibit significant fractional characteristics. However, the above models are all proposed based on integral calculus. Integral calculus has some local characteristics and is not suitable for describing historical dependent processes. Fractional calculus can better describe the essential characteristics of the system.

中文翻译：

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基于分数阻尼的点蚀故障滚动轴承动态渐近模型

目的

本文的目的是讨论滚动轴承中具有点蚀故障的不同零件的渐近模型。

设计/方法/方法

对于点蚀故障的滚动轴承，通常认为滚道与滚动体之间的位移偏差是瞬时变化的。但是，偏差应该逐渐改变。针对这一不足，探讨了位移偏差的变化规律和计算方法。分别讨论了具有点蚀断层的不同部位的渐近模型。此外，滚动轴承系统具有传统模型未考虑的突出的分数特征。因此，分数阶微积分被引入到滚动轴承的建模中。提出了基于分数阻尼的不同部位点蚀断层的动态渐近模型。基于所提出的模型进行数值模拟，并通过分岔图分析动态特性，

发现

与基于积分的模型相比，该模型能更好地反映滚动轴承的周期性特征和故障特征。最后，通过实验验证了所提出的模型。分析了滚动轴承在不同转速下的动态特性。实验结果与仿真结果一致。因此，所提出的模型是有效的。

原创性/价值

(1) 上述模型是理想化的，即局部点蚀断层被视为一个矩形。当元件接触到故障时，如果元件进入故障区，元件与故障元件之间的位移偏差立即释放，如果元件离开，则恢复。但是，位移偏差应该逐渐变化。只有当构件接触断层底部时，位移偏差才达到最大值。(2) 由于材料的记忆性和流体粘弹性，滚动轴承系统表现出显着的分数特性。然而，上述模型都是基于积分计算提出的。积分有一些局部性，不适合描述历史相关过程。