Statistical Linearization of Nonlinear Stiffness Matrix of Planetary Gear Train
Bibliographic record
Abstract
Stochastic dynamic analysis of the planetary gear train is complicated and it becomes more challenging when the nonlinear term is considered in the equation. A backlash between gears’ teeth is one of the nonlinearity sources in the gearbox which changes the equation of random vibration to nonlinear. In this paper, the linearization of the random vibration of multi-degrees of freedom (MDOF) with nonlinear stiffness is examined for planetary gear trains. The method used to treat nonlinearity is the statistical linearization method (SL). At first, to achieve adequate accuracy, the time domain is divided into very small time intervals then SL is utilized in each time step. For each time step an equivalent linear stiffness matrix is calculated and replacs the nonlinear stiffness matrix. The comparison between equivalent stiffness and linear stiffness at each step has shown a good agreement.
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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 | 0.000 |
| 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".