DETERMINATION OF POWER LOSSES DUE TO PERIODIC COMPRESSION-EXPANSION OF THE OIL-AIR MIXTURE BETWEEN THE TEETH OF GEARS. PART 1. MATHEMATICAL MODEL
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Bibliographic record
Abstract
The simultaneous contact of two pairs of teeth between their active profiles creates a closed volume of the oil-air mixture. Reducing this volume leads to the occurrence of such a negative phenomenon as periodic compression and expansion of the oil-air mixture in volume. At high gear rotation speeds, a significant increase in the pressure of the oil-air mixture is observed and, as a result, additional vibration of the gearing occurs. The oil-air mixture outflow rate can reach the speed of sound, which causes additional noise during gear operation, and at high rotational speeds, a hydraulic shock occurs in the space closed between the pinion and gear teeth, resulting in cavitation. By representing the helical gear as a set of spur gears displaced relative to each other in the tangential direction, it simplified the mathematical model to describe thermodynamic processes in a series of isolated cavities. The following variants are considered: a) the first cavity in the direction of engagement is connected to the environment on one side and to the next second cavity on the other side; b) some i-th cavity is connected to the cavities i - 1 and i + 1, respectively; c) the edge cavity N is connected to the previous cavity N - 1 and the environment. Thus, a mathematical model of the periodic compression-expansion of the oil-air mixture in the space closed between the teeth is presented, which considers the cross-sectional areas of the axial and radial flows of the oil-air mixture, the ambient pressure of the space closed between the teeth, the velocity of the radial flow of the oil-air mixture, the instantaneous volume of the elementary cavity closed between the teeth, and the current pressure in the cavity. Keywords: power losses, oil-air mixture, periodic compression-expansion, toothed gears, mathematical model, hydrodynamic model
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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 | 0.001 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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