Mathematical model of brush seals for gas turbine engines: A nonlinear analytical solution
Bibliographic record
Abstract
Presented herein is a mathematical model employing differential equations formulation for brush seals used in gas turbine engines. These components are used to seal the bearing chamber from the environment and reduce the loss of lubricant in the atmosphere, ensuring a MTBR long enough to have required the change the seals only during the engine overhaul operation. The model assumes a single curved bristle loop in the form of a curved-bridge beam subjected to the influences of complex external loads (static and dynamic). Further, a model for clustered bristles is proposed. Specifically, the static forces acting on the curved-bridge beam include the weight of the oil capillary attached to the beam, the weight of the beam itself, the capillary force developed between the surfaces of the bristles in the brush and the temperature gradient. The dynamic forces include the leakage oil pressure and the rotation of the shaft. This complex loading induces a nonlinear large deflection on the curved-bridge beam. Also, the temperature gradient present on the bristles during the gas turbine engine operation generates a change in the geometry of the beam and in the magnitude of the forces acting on the bristles modeled as beams. In the present model, the weights are assumed as uniformly distributed forces on the surface of the beam while the capillary forces and the force generated by the rotating shaft are considered to be non-uniform. The equation expressing the curvature of the beam under general loading force is developed and one can choose the appropriate method of solving the generated differential equation after the expression of the general force is defined. Hence, the ordinary differential equation describing the nonlinear large deflection of the curved-bridge beam will be derived using general nonlinear elasticity theory.
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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".