Dynamic asymptotic model of rolling bearings with a pitting fault based on fractional damping

Abstract

PurposeThe purpose of this paper is to discuss the asymptotic models of different parts with a pitting fault in rolling bearings.Design/methodology/approachFor 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.FindingsCompared 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.