A Neural Network-Assisted Boussinesq pressure bulb model for load assessment of cylindrical rolling element bearings
Bibliographic record
Abstract
• A NN-assisted pressure bulb model was proposed for load assessment of roller bearings. • The accuracy of the Boussinesq pressure bulb model was investigated. • Two NNs were integrated into the model to enhance accuracy. • High accuracy was validated through simulations and experiments. The accurate assessment of contact forces and radial load is critical for the performance and reliability of the cylindrical rolling element bearings. The current theoretical models based on Hertzian theory are challenging since the deformation is relatively small to measure, and installing sensors on the contact area is difficult. This paper introduced the Boussinesq pressure bulb model for bearing load assessment and found that the original model had a maximum of 33% error because it did not consider the boundary effects and material properties. To improve accuracy, a Neural Network-assisted Boussinesq model is proposed by integrating two Neural Networks (NNs) with the original Boussinesq model. The first NN accurately transfers strain measurements from Fiber Bragg Grating (FBG) optical sensors into stresses at the point of interest, while measuring strain is easier in practical applications. The second NN provides an accurate tuning factor to address errors in the original model. The NN-assisted Boussinesq model greatly outperforms the original model and shows an error below 3.73%. The performance of the proposed model is validated through simulations and experiments. In simulations, errors were below 1% when the outer race and housing were made of the same material, 6.7% for a GCr15 steel outer race with a spheroidal graphite iron housing, and 11.6% for a GCr15 steel outer race with a grey cast iron housing; the latter remains acceptable for non-precision applications. In experiments, radial load estimation errors were below 3% in static tests and 4.6% in dynamic tests. All these simulations and experiments demonstrated the superiority of the proposed method. Moreover, it is practical and easy to implement in real-time bearing stress and load measurements.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".