Assessment of Two Harmonic Balance Method-Based Numerical Strategies for Blade-Tip/Casing Interactions: Application to NASA Rotor67
Bibliographic record
Abstract
Abstract The study presented in this paper focuses on the analysis of rubbing interactions — including unilateral contact and dry friction — between a rotating fan blade and a rigid casing by frequency domain methods. Two previously published Harmonic Balance Method-based methodologies are assessed: 1) an approach relying on augmented lagrangians and 2) a second method using a regularized penalty law combined with a Lanczos σ-approximation filter. Asa reference point for this comparison, a time-domain numerical strategy relying on a Lagrange multiplier-based contact treatment is considered. All computations are run with the NASA rotor 67 fan blade, an open industrial blade geometry. As it undergoes structural contacts, this blade features an intricate dynamics response, thus making it a challenging case study for nonlinear iterative solvers. The contact scenario is chosen to be an ovalization of the casing with no external forcing. This scenario induces highly nonlinear reponses of the blade and complex phenomena such as isolated frequency response curves. The results presented underline a very good agreement of the different strategies with the reference time marching approach. An in-depth comparison is made with an emphasis on nonlinear frequency response curves and time signals. In order to investigate further onto the frequency domain strategies, a comparative analysis is carried out on isolated nonlinear frequency response curves, referred to as isolas. Finally, a physical analysis of these isolas is presented through an in-depth investigation of the main modal contributions for each computed solution. In the end, this paper provides new qualitative elements allowing for a better understanding of rubbing interactions that may not be efficiently obtained with time marching procedures.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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".