An analytical method for time-varying mesh stiffness calculation for straight bevel gears under spalling conditions
Bibliographic record
Abstract
Abstract Tooth spall is a prevalent gear fault that reduces mesh stiffness and adversely affects transmission ability of gear systems. While plenty of research focuses on tooth spall faults in spur and helical gears, few analytical approaches were established to calculate the time-varying mesh stiffness in straight bevel gears, especially those affected by tooth spall. This deficiency can be attributed to the lack of an accurate tooth spall model. This paper proposes an approach for straight bevel gears mesh stiffness calculation with a curved-bottom spall. The spur gear spall model is modified to adapt to the tooth profile in straight bevel gears. The time-varying mesh stiffness calculation formulas are then revised in spall region. Using potential energy, Hertzian contact stiffness is calculated considering load distribution between gear teeth. The foundation stiffness calculation is updated considering practical gear shape. Tooth stiffness caused by axial forces is also considered. Finite element analysis is utilized for the theoretical method verification, which suggests a high consistency of results between two methods. The low error between the proposed approach and finite element approach implies that the proposed method is acceptable for practical use.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".