Abstract
A new methodology based on full factorial design (FFD) for the prediction of the size of the spalls on the rolling contact surfaces of thrust ball bearings and its remaining useful life is presented in this research work. The FFD is used to analyse the effect of the following factors: rotational speed, load, spalling size, position of the sensors and frequency range on the vibrations level and the interaction effects between these factors. Data collected from vibratory signals generated by thrust ball bearings operating in the fatigue test rig are used. Statistical analyses show that the full factorial model with sixteen coefficients leads to more precise spalling size estimates. Analysis of variance showed that these results were statistically significant [P value is less than 0.0001 where significance level \(\alpha \) (\(\alpha = 0.05\))]. A modified exponential model used in the prediction of the remaining useful life shows its efficiency and applicability.
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Abbreviations
- ANOVA:
-
Analysis of variance
- CF:
-
Crest factor
- CV:
-
Crest value
- DF:
-
Degree of freedom
- DPH:
-
Defective phase
- FFD:
-
Full factorial design
- FFM:
-
Full factorial model
- FFM11:
-
Full factorial model with 11 coefficients
- FFM16:
-
Full factorial model with 16 coefficients
- FFM32:
-
Full factorial model with 32 coefficients
- FME:
-
Fitted model to experimental data
- F value:
-
Fischer’s ratio
- MS:
-
Mean squares
- NDPH:
-
Non-defective phase
- RMS:
-
Root mean square
- RMSacc:
-
Root mean square of acceleration
- \(\hbox {RMS}_{\mathrm{FFM16}}\) :
-
RMSacc calculated using FFM16 model
- \(\hbox {RMS}_{\mathrm{FME}}\) :
-
RMSacc calculated using FME model
- RMSE:
-
Root mean square Error
- RT:
-
Running time
- RUL:
-
Remaining useful life
- SS:
-
Sum of squares
- TBB:
-
Thrust ball bearing
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Acknowledgements
The authors would like to thank Professor Jean Paul Dron and the team of laboratory MAN/GRESPI of Reims University, France, for collaborating and conducting experiments on the fatigue test rig.
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Boumahdi, M., Rechak, S. & Hanini, S. Analysis and Prediction of Defect Size and Remaining Useful Life of Thrust Ball Bearings: Modelling and Experiment Procedures. Arab J Sci Eng 42, 4535–4546 (2017). https://doi.org/10.1007/s13369-017-2550-y
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DOI: https://doi.org/10.1007/s13369-017-2550-y