A train air brake force model: Car control unit and numerical results
Bibliographic record
Abstract
This and a companion paper focus on the integration of a model of a train’s air brake and a non-linear model of a train’s dynamics based on the use of trajectory coordinate formulations. The forces developed by the air brake depend on various system components, including the automatic brake valve, the brake pipe and the car control unit (CCU). The developed braking forces, which depend on the position of handle of the automatic brake valve, are applied to the wheels using the CCU located along the brake pipe and enter into the formulation of the non-linear dynamic equations for the train in addition to other external forces. In order to develop an efficient computational procedure, simplified valve models, with more straightforward operation modes, are considered in order to reduce the computational overhead. The CCU used in this research has a control valve connected to three main pneumatic components: the auxiliary reservoir, the emergency reservoir and the brake cylinder. The reservoirs are the main storage area of the pressurized air, while the brake cylinder transmits the brake force to the wheels using the mechanical components of the CCU, including the brake rigging and the brake shoes. The communications between different parts connected to the control valve are controlled by its slide valve that can be positioned in the brake application, brake release and lap positions. It is also assumed that the CCU modeled in this study has the emergency portion that enables it to apply emergency braking, including the effect of the CCU’s emergency vent valve. In this paper, a mathematical model for the CCU is developed, while the locomotive automatic brake valve and brake pipe models are developed in a companion paper. The relationship between the main components of the air brake system and the train dynamics is discussed, and the final set of differential equations that includes the two models is presented. Furthermore, different computer simulation scenarios are considered in this paper in order to investigate the effect of the air brake forces on the train’s longitudinal dynamics for cases of different braking modes. The numerical results, obtained in this study, are compared with experimental results published in the literature.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.003 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".