Experimental and numerical study of an angular contact ball bearing vibration response with spall defect on the outer ra
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O R I G I NA L
Seyed Mohammad Jafari · Rezvan Rohani · Abbas Rahi
Experimental and numerical study of an angular contact ball bearing vibration response with spall defect on the outer race
Received: 10 February 2020 / Accepted: 7 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Angular contact ball bearings are widely used in rotary machines for their combined loads capacity, i.e., simultaneously acting radial and axial loads. Spall defect is one of the most important potential failure modes of the rolling element bearings. The main motivation of this study is to achieve a true perception of the spall defect influence on the angular contact ball bearing to predict bearing failure. In this paper, simulation and experimental analysis are performed for an angular contact ball bearing with a spall defect in the outer race. At first, the bearings without and with outer race defect are modeled, and after extracting the governing equations, they are solved using function ODE45 in MATLAB. This function implements a Runge–Kutta method with a variable time step for efficient computation. Then the vibration response in different conditions of rotating speed and axial preload is simulated. A bearing test bench is designed to perform the experimental tests. The defect is contrived in the outer race of a healthy bearing, and the vibration signals at both conditions (healthy and defective) are collected. The spall defect in the outer race is considered to have a cylindrical shape to close the model to real conditions as much as possible. The results are then presented in the form of time-domain signals and fast Fourier transformations (FFT) graphs. The FFT results showed that defect in the outer race produces dominant peaks with a suitable similarity to each other in both simulations and experimental tests. Keywords Vibration analysis · Ball bearing · Dynamic model · Outer race defect List of symbols Fu Ii Iin Iout Ishaft K in K out mc
Unbalance force Mass moment of inertia of the ith rolling element Mass moment of inertia of the inner race Mass moment of inertia of the outer race Mass moment of inertia of the shaft Stiffness of contact between the inner race and ball Stiffness of contact between the outer race and ball Mass of the cage
S. M. Jafari (B) · A. Rahi Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Daneshju Blvd, Tehran 1983963113, Iran E-mail: [email protected] A. Rahi E-mail: [email protected] R. Rohani Irankhodro Powertrain Company, Tehran, Iran E-mail: [email protected]
S. M. Jafari et al.
mi m in m out Nb p Q q qi qb R r rin rout T Tb Tcage Tin Tout Tr.e. V Vb Vcage Virace Vorace Vr.e. Vspring xin ; yin xout ; yout α˙ i γ˙out δ Xi ωc ωbp θi δ r = 1/ρ FFT rpm
Mass of the rolling elements Mass of the inner race Mass of the outer race Number of balls Empirical constant for a particular geometry Contact force Empirical constant for a particular geometry Radial position of the ith rolling element from the center of the inner race Radius of each rollin
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