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Damage Factor Calculation for Condition Monitoring of Rolling Bearings

  • Research Article-Mechanical Engineering
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Abstract

New demands placed on industry make it necessary to improve design, real-time monitoring and failure prediction methods for rolling bearings. This paper presents an approach for assessing how contact surface damage affects the vibration response of rolling bearings and how vibration-based monitoring shows the damage level of rolling element bearings. A new parameter named the damage factor is introduced to quantify the vibration response of rolling bearings. The analytical–numerical method for calculation of this parameter is developed based on nonlinear dynamics postulates. The developed method for damage factor calculation is tested on a particular type of radial deep groove ball bearing, and an experimental verification is performed, showing a maximum deviation of 7% in the results. The conclusions drawn from the obtained results and the potential contributions of the introduced parameters for rolling bearing design are discussed. The chosen polynomial function keeps deviations in relation to the calculated damage factor within 3% for failed areas of different sizes.

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Abbreviations

A d :

Maximum vibration amplitude of a damaged bearing, m/s2

A u :

Vibration amplitude of an undamaged bearing, m/s2

B :

Bearing width, m

C :

Dynamic load capacity, N

C 0 :

Static load capacity, N

C(t):

Damping matrix

C r :

Radial deep groove ball bearing damping, N s/m

D :

Bearing outer race diameter, m

d :

Bearing inner race diameter, m

d 0 :

Average diameter of damages for particular rolling bearing type (obtained empirically), m

d b :

Diameter of bearing rolling elements, m

d c :

Diameter of the dividing axis of the bearing cage, m

d d :

Diameter of damage on a contact surface, m

d i :

Diameter of the inner race, m

d o :

Diameter of the outer race, m

E :

Young's modulus, N/m2

F(t):

Vector of external forces

F :

External load, N

F δ :

Load distributed on the most loaded rolling element, N

f i :

Specific inner ring frequency, Hz

K(t):

Stiffness matrix

K r :

Radial deep grove ball bearing stiffness, N/m

K V :

Damage factor

M(t):

Mass matrix

m red :

Reduced mass of system shaft-bearing-casing, kg

n :

Rotational velocity, rpm

Q(t):

Vector of nonlinearity coefficient

q :

Nonlinearity coefficient, N/m3

r ti :

Inner ring groove radius, m

r to :

Outer ring groove radius, m

t :

Time, s

y(t):

Vector of the generalized displacement

y :

Displacement in radial direction, m

z :

Total number of rolling elements

α :

Bearing contact angle, degrees

γ :

Angular distance between rolling elements, degrees

δ :

Local contact deformation on the most loaded rolling element and raceway surface with damage, m

ε :

Total radial displacement of axis of bearing in radial direction, m

µ :

Friction coefficient in contact zones

µ m :

Poisson’s ratio

ω :

Angular velocity, s−1

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Acknowledgements

We thank the Factory of Rolling Bearings and Cardan Shafts FKL, Temerin, Serbia, for providing the data and producing the samples utilized in this research.

Funding

Parts of the presented research are funded by the Ministry of Education, Science and Technological Development of the Republic of Serbia, through the Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia, and the Faculty of Mechanical Engineering of University of Belgrade.

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Authors and Affiliations

  1. Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000, Belgrade, Serbia

    Ivana D. Atanasovska

  2. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11000, Belgrade, Serbia

    Natasa D. Soldat & Radivoje M. Mitrovic

  3. Department of Mechanical Engineering, Manipal University Jaipur, Jaipur, India

    Santosh S. Patil

  4. Faculty of Mechanical Engineering, University of Montenegro, Dzordza Vasingtona bb, 81000, Podgorica, Montenegro

    Radoslav Z. Tomovic

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  1. Ivana D. Atanasovska
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Correspondence to Ivana D. Atanasovska.

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Atanasovska, I.D., Soldat, N.D., Patil, S.S. et al. Damage Factor Calculation for Condition Monitoring of Rolling Bearings. Arab J Sci Eng 48, 3181–3194 (2023). https://doi.org/10.1007/s13369-022-07126-4

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  • DOI: https://doi.org/10.1007/s13369-022-07126-4

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