A new method for determining load distributions among rollers of bearing with manufacturing errors
Bibliographic record
Abstract
A new method is presented in this article to determine loads on all rollers in a cylindrical roller bearing. By introducing a pair of nonlinear springs for contact of each roller with its inner and outer races, the equations of equilibrium of the multi-component system are established by means of the virtual work principle. A set of linear complementary equations are deduced and solved using the Lemke algorithm for gaps and contact forces between all potentially engaged components. An iterative scheme is employed to effectively deal with the nonlinearity of the Hertzian contact between non-conforming bodies. Numerical results for a 19-roller cylindrical bearing, having various combinations of roller sizes, show that the proposed method is convergent and accurate. With this method, effects of uneven roller sizes caused by manufacturing errors, on load distributions can be accurately and efficiently determined. The proposed method can be extended to deal with other types of manufacturing errors such as uneven roller angular spacing, eccentricity, ovality, friction, etc., which are of significant interest to the bearing manufacturers.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".