Calculating Frictional Losses in Belleville Springs by Geometrical Interpolation
Bibliographic record
Abstract
Abstract The use of Belleville springs has been proven to be beneficial in tackling the problems related to elastic interaction, creep, differential thermal expansion or in the isolation of seismic vibrations in bolted joints. Because of its high and easily variable spring rates, the use of these springs can also be observed in passive vibration assisted rotary drilling (VARD) tools. Because of relative movement of spring with respect to supporting surfaces and the mating spring surfaces, frictional losses in the spring take place during each compression and relaxation cycle leading to a slightly different load-deflection curve from what has been defined in the literature. The geometry of the spring combined with different stacking configurations complicate the study of frictional losses in these kinds of springs. This work presents a new method to calculate the displacement of different points of Belleville springs during its loading and unloading using geometrical interpolation method. The results of spring displacement are then used to develop a model to calculate frictional load as a function of spring deflection, which is used to analyse load-deflection curves of springs with different dimensional and frictional parameters. The developed methodology is used to plot and understand characteristics curves of four different kind of Belleville springs; High Load, Standard, Force Limiting and Force Adjusting Belleville springs by plotting the graphs for different free-height to thickness and diameter ratios. In the later section of the paper, the proposed methodology has been used to visualize the load-deflection characteristics of Belleville springs used in the p-VARD tool of the Large Drilling Simulator, one of the state-of-the-art drilling simulators at Memorial University of Newfoundland. Results show that understanding of the characteristic curves of different spring configuration helps to plan to drill with desired WOB using a p-VARD tool.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".