Dynamic Modeling of Aerostatic Spindle With Shaft Tilt Deformation
Bibliographic record
Abstract
Abstract This paper presents a new dynamic model of aerostatic spindle including the journal and thrust bearings. Reynolds equations are used to model the dynamics of a 4-degree-of-freedom (DOF) aerostatic journal bearing and a 3-DOF aerostatic thrust bearing. Finite element model of the spindle shaft is developed based on the Timoshenko beam theory considering the centrifugal and gyroscopic effects and is coupled with the bearing to construct the dynamic model of the whole aerostatic spindle. The effect of shaft tilt motion due to elastic deformation on the dynamic characteristics of the aerostatic bearing is considered for the first time. The finite difference method is used to determine the load capacity and moments provided by the bearings with changing air film thickness due to shaft vibration, and Newmark-β method is used to obtain the dynamic response of the spindle shaft. The simulated natural frequencies of the aerostatic spindle are verified through impact experiments under static and rotating conditions. Based on the developed model, the effects of tool overhang length, rotating speed, air film thickness, and supply air pressure on the frequency response function of the spindle are investigated comprehensively. The proposed dynamic model of the aerostatic spindle is able to provide useful guidance for structure design and process planning for micro-machining.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".