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Experimental and numerical study of an angular contact ball bearing vibration response with spall defect on the outer race

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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.

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Abbreviations

\(F_{\mathrm{{u}}}\) :

Unbalance force

\(I_{\mathrm{{i}}}\) :

Mass moment of inertia of the ith rolling element

\(I_{\mathrm{{in}}}\) :

Mass moment of inertia of the inner race

\(I_{\mathrm{{out}}}\) :

Mass moment of inertia of the outer race

\(I_{\mathrm{{shaft}}}\) :

Mass moment of inertia of the shaft

\(K_{\mathrm{{in}}}\) :

Stiffness of contact between the inner race and ball

\(K_{\mathrm{{out}}}\) :

Stiffness of contact between the outer race and ball

\(m_{\mathrm{{c}}}\) :

Mass of the cage

\(m_{\mathrm{{i}}}\) :

Mass of the rolling elements

\(m_{\mathrm{{in}}}\) :

Mass of the inner race

\(m_{\mathrm{{out}}}\) :

Mass of the outer race

\(N_{\mathrm{{b}}}\) :

Number of balls

p :

Empirical constant for a particular geometry

Q :

Contact force

q :

Empirical constant for a particular geometry

\(q_{\mathrm{{i}}}\) :

Radial position of the ith rolling element from the center of the inner race

\(q_{\mathrm{{b}}}\) :

Radius of each rolling element

R :

Radius of the outer race

r :

Radius of the inner race

\(r_{\mathrm{{in}}}\) :

Position of the mass center of the inner race

\(r_{\mathrm{{out}}}\) :

Position of the mass center of the outer race

T :

Kinetic energy of the bearing system

\(T_{\mathrm{{b}}}\) :

Kinetic energy of the balls

\(T_{\mathrm{{cage}}}\) :

Kinetic energy of the cage

\(T_{\mathrm{{in}}}\) :

Kinetic energy of the inner race

\(T_{\mathrm{{out}}}\) :

Kinetic energy of the outer race

\(T_{\mathrm{{r.e.}}}\) :

Kinetic energy of the rolling elements

V :

Potential energy of the bearing system

\(V_{\mathrm{{b}}}\) :

Potential energy of the balls

\(V_{\mathrm{{cage}}}\) :

Potential energy of the cage

\(V_{\mathrm{{i}}_{\mathrm{{race}}}}\) :

Potential energy of the inner race

\(V_{\mathrm{{o}}_{\mathrm{{race}}}}\) :

Potential energy of the outer race

\(V_{\mathrm{{r.e.}}}\) :

Potential energy of the rolling elements

\(V_{\mathrm{{spring}}}\) :

Potential energy of the springs

\(x_{\mathrm{{in}}} ; y_{\mathrm{{in}}}\) :

Center of the inner race

\(x_{\mathrm{{out}}} ; y_{\mathrm{{out}}}\) :

Center of the outer race

\(\dot{\alpha }_{\mathrm{{i}}}\) :

Angular velocity of the inner race

\(\dot{\gamma }_{\mathrm{{out}}}\) :

Angular velocity of the outer race

\(\delta \) :

Deformation at the point of contact at inner and outer race

\(X_{\mathrm{{i}}}\) :

Small run-out of the cage, mm

\(\omega _{\mathrm{{c}}}\) :

Angular velocity of cage relating to the cage

\(\omega _{\mathrm{{bp}}}\) :

Ball passage frequency

\(\theta _{\mathrm{{i}}}\) :

Angular position of rolling element

\(\delta \) :

deformation at the point of contact at inner and outer race

\(r=1/\rho \) :

radius of rolling element

FFT:

Fast Fourier transformation

rpm:

Revolution per minute

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Acknowledgements

This research was supported by Irankhodro powertrain company (IPCO). We thank all persons who provided insight and expertise that greatly assisted the research.

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Authors and Affiliations

  1. Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Daneshju Blvd, Tehran, 1983963113, Iran

    Seyed Mohammad Jafari & Abbas Rahi

  2. Irankhodro Powertrain Company, Tehran, Iran

    Rezvan Rohani

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  1. Seyed Mohammad Jafari
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Correspondence to Seyed Mohammad Jafari.

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Jafari, S.M., Rohani, R. & Rahi, A. Experimental and numerical study of an angular contact ball bearing vibration response with spall defect on the outer race. Arch Appl Mech 90, 2487–2511 (2020). https://doi.org/10.1007/s00419-020-01733-z

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