Development of a mathematical model of a stacker crane with regard to energy dissipation
Bibliographic record
Abstract
Stacker cranes are widely used in automated warehouses. The actual task is to increase their energy efficiency and productivity. Simulation mathematical models are used for the solution of this problem at the stage of research and development works. We have developed a mathematical model of a rack stacker crane in long spatial displacements taking into account energy dissipation of linear coordinates of the cart and the cargo carriage. The model is a system of two second-order Lagrange differential equations. Partial derivatives of analytical expressions of kinetic and potential energies of the dynamic stacker crane system as well as dissipative Rayleigh function are used for derivation of the differential equations. Different values of dissipation coefficients for two linear coordinates of the stacker crane can be used. Using SimInTech we develop a simulation model of a conventional stacker crane based on the suggested system of differential equations and represented in the form of a block diagram. The developed simulation model is described and an example of its use is given. A complex model of a shelf stacker crane includes as a constituent part a procedure of determining time intervals of equivalent-accelerated motion of the links. Examples of time dependences of the crane bogie and cargo carriage coordinates, drive forces providing the set coordinate dependences, drives work and total work are given. The developed mathematical model of the stacker-crane can be used for the modelling of the processes of the cargo moving along the rack, its raising to the given height corresponding to the rack target cell, its lowering as well as for the estimation of the energy input of the crane.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".