Nonlinear Oscillation of Shell Workpiece in High Speed Milling Under 1:2 Internal Resonance Condition
Bibliographic record
Abstract
We aim to study nonlinear dynamics of a shell-shaped workpiece during milling processes in this paper. The shell-shaped workpiece is modelled as a cantilever thin shell subjected to a cutting force with time-delay effects. The formulas of the cantilever shell were derived by the classical shell theory and the von Karman strain-displacement relations. The resulting differential equations are reduced to a two-degree-of-freedom nonlinear system ordinary differential equations by applying the Galerkin’s approach. The method of Asymptotic Perturbation method is used to obtain the averaged equations, which were dealt with the resonance cases of 1:2 internal resonance and principal parametric resonance. Dynamic behaviors are presented based on the numerical solutions. The results show that different time-delay parameters result in periodic motion, multiple periodic motion, and chaotic motion.
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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".