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Nonlinear modeling for bearing fault diagnosis in non-stationary operating conditions

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Abstract

Bearing failure is one of the most important causes of shutdown in rotating machines. Most bearing diagnostic methods can only be used on machines with steady-state operational conditions. Changes in operating conditions cause changes in the statistical characteristics of the vibrating signals, which causes erroneous alarms related to bearing failure. The statistical index of vibration signals, independent of operating conditions of speed and load, is introduced in this paper to diagnosis bearing fault growth and reduce the rate of incorrect bearing failure alarms. The existing theoretical model is employed to simulate and extract the vibration database under variable operational conditions and finally, to extract the statistical index according to vibration surface plot parameters. Surface plots of acceleration RMS versus speed and load were used for extract statistical index and experimental laboratory data are also used to verify the proposed index.

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Abbreviations

\(k_{{{\text{in}}/{\text{out }}j \cdot r}}\) :

Nonlinear contact stiffness

\(c_{{{\text{in}}/{\text{out }}j \cdot r}}\) :

Linear contact damping

\(m_{0} \cdot m_{b} \cdot m_{i}\) :

Mass of the outer raceway plus the support structure, rolling element, inner raceways plus the shaft

\(\theta_{{{\text{out}} j \cdot r}}\) :

The angle of the vector \(\overrightarrow {{z_{j \cdot r} }}\) with respect to the center of the outer raceway

\(m_{r} \cdot { }k_{r} \cdot { }c_{r}\) :

Spring mass damping system correspond to excitation of the bending modes of the casing, which results in vibrations across the entire casing

\(F_{{{\text{in}}}} \cdot { }F_{{{\text{out}}}}\) :

Total contact forces acting on the inner race and outer race

\(F_{{\text{d in}}} \cdot { }F_{{\text{d out}}}\) :

Total contact damping forces acting on the inner race and outer race

\(k_{s} \cdot { }c_{s}\) :

Stiffness and damping of the support

\(R\left( \varphi \right)\) :

The distance between the outer raceway and the center of the outer raceway at angle \(\varphi = \theta_{{{\text{out}} j \cdot r}} + \psi_{j \cdot r}\)

\(\psi_{j \cdot r}\) :

The angle between the point of the maximum deformation and the vector \(\overrightarrow {{z_{j \cdot r} }}\)

\(\beta_{j \cdot r}\) :

The angle of the deformation location on the rolling element

\(\phi_{j \cdot r}\) :

The angular position of the jth rolling element of the rth row

\(\rho_{j \cdot r}\) :

Generalized coordinates defined for the rolling elements

\(\left\{ {f_{r} } \right\}\) :

Vector with generalized contact forces

\(\overrightarrow {{z_{j \cdot r} }}\) :

Distance of the rolling element from the center of the outer raceway

\(W\) :

Static load

\({m}_{b}\) :

Mass of a rolling element

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

Nominal rotational speed

\(\delta_{{{\text{out}} j \cdot r}}\) :

Deformation toward the center of the outer raceway

\({\delta }_{b j\cdot r}\) :

Deformation perpendicular to the jth rolling element

\({r}_{b}\) :

The rolling element radius

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Acknowledgements

The authors express thanks to Shahid Tondgooyan Petrochemical Company (STPC), Iran National Science Foundation (INSF) under grant 97009084 for financial support and Dr. Somaye Mohammadi for revising the article text.

Funding

The research leading to these results received funding from Shahid Tondgooyan Petrochemical Company and Iran National Science Foundation (INSF) under Grant Agreement No 97009084.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Mohammad Samavatian, Mehdi Behzad & Hamid Mehdigholi

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  1. Mohammad Samavatian
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  2. Mehdi Behzad
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Correspondence to Mehdi Behzad.

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Samavatian, M., Behzad, M. & Mehdigholi, H. Nonlinear modeling for bearing fault diagnosis in non-stationary operating conditions. J Braz. Soc. Mech. Sci. Eng. 46, 323 (2024). https://doi.org/10.1007/s40430-024-04898-8

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