Develop and Verify Energy-Based Statistical Linearization Technique to Analysis Nonlinear Stochastic Vibration of a Spur Gear Pair
Bibliographic record
Abstract
Abstract In this article, an energy-based statistical linearization method (SL) is proposed to simulate a nonlinear dynamic model of spur gear pair. The gear pair operates under combined deterministic and random loads, and both backlash and time-varying mesh stiffness are considered in the dynamic model. The equivalent linear function approximates the teeth backlash nonlinearity in the gear model. The energy-based linearization, which minimizes the error in potential energy between the original and equivalent linear systems, is used. Simulations are conducted on a gear pair, and the effect of the input torque on the dynamic response of the gear pair is then examined. The results demonstrate that for high input torque, the system operates in the linear range. For low input torque, the results are not similar to the original because the system became strongly nonlinear. Monte Carlo simulations were carried out to verify the accuracy of the presented method.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".