MATHEMATICAL MODEL OF THE MOTION PALLET PROCESS ON BRAKE MAGNETIC TYPE ROLLER
https://doi.org/10.26518/2071-7296-2020-17-3-364-373
Abstract
Introduction. One of the main elements of the safe operation of gravity roller conveyors used in pallet racks is a brake roller. The most promising design is the brake roller magnetic (eddy current) type. The operation principle of such rollers is based on the laws of electromagnetic induction and involves the braking of a conductor moving in a magnetic field, due to the interaction of eddy currents (or Foucault currents) arising in the volume of the conductor with an external magnetic field. However, in the market of warehouse shelving equipment, brake magnetic rollers are not widely used due to their high cost, which is primarily due to the lack of domestic designs and methods for their calculation. The aim of the work is to develop a mathematical model of the moving pallets process on a magnetic type brake roller.
Materials and methods. The paper presented the theoretical study results on the development of a mathematical model of the moving pallets process on a magnetic type brake roller, described in works on centrifugal friction rollers and eddy current brake devices.
Results. The main parameter determining the functions of the brake magnetic roller and hence the speed of the pallet along the gravity roller conveyor is a magnetic viscosity coefficient. The speed dependence of the pallets on the brake magnetic roller for various values of a magnetic viscosity coefficient is determined, its analysis is carried out.
Conclusions. A mathematical model of the moving pallets process on a brake magnetic roller is developed. The movement speed equation of the pallets on the brake magnetic roller is obtained. For a reasonable choice of the design parameters of the magnetic brake roller, experimental studies are required to determine a magnetic viscosity coefficient.
About the Authors
I. A. Sharifullin
Bauman Moscow State Technical University
Russian Federation
Russian Federation
Ildar A. Sharifullin - a postgraduate of the Lifting and Transport Systems Department
105005, Moscow, 2 Baumanskaia Street., 5, building 1
(499) 263–65–92
A. L. Nosko
Bauman Moscow State Technical University
Russian Federation
Russian Federation
Andrei L. Nosko - Dr. of Sci., Associate Professor, Professor of the the Lifting and Transport Systems Department
Scopus Author ID 6507019256
105005, Moscow, 2 Baumanskaia Street., 5, building 1
(499) 263–65–92
E. V. Safronov
Bauman Moscow State Technical University
Russian Federation
Russian Federation
Evgenii V. Safronov - Cand. of Sci., Associate Professor of the Lifting and Transport Systems Department
105005, Moscow, 2 Baumanskaia Street., 5, building 1
(499) 263–65–92
References
1. N. Boysen, D. Boywitz, F. Weidinger. Deeplane storage of time-critical items: one-sided versus two-sided access // OR Spectrum. 2018; 40, 4: 1141– 1170.
2. D. Boywitz, N. Boysen N. Robust storage assignment in stack- and queue-based storage systems // Comput. Oper. Res. 2018; 100: 189–200.
3. R. Accorsi, G. Baruffaldi, R. Manzini, Design and manage deep lane storage system layout. An iterative decision-support model // Int. J. Adv. Manuf. Technol. 2017; 92 (1-4): 57–67.
4. R. Vujanac, N. Miloradovic, S. Vulovic. Dynamic storage systems // ANNALS of Faculty Engineering Hunedoara – International Journal of Engineering. 2016; 14: 79–82.
5. S. Wu, Ya. Wu, Ya. Wang. A structured comparison study on storage racks system // J. Residuals Sci. Tech. 2016; 13 (8).
6. L. Ghomri, Z. Sari. Mathematical modeling of the average retrieval time for flow-rack automated storage and retrieval systems // J. Manuf. Syst. 2017; 44: 165–178.
7. M. A. Hamzaoui, Z. Sari. Optimal dimensions minimizing expected travel time of a single machine flow rack AS/RS // Mechatronics. 2015; 31: 158–168.
8. Safronov E.V., Sharifullin I.A., Nosko A.L. Ustroystva bezopasnoy ekspluatatsii gravitatsionnykh rolikovykh konveyyerov palletnogo tipa: Monografiya [Devices for safe operation of pallet type gravity roller conveyors: Monograph]. Moscow. Universitetskaya kniga. 2018: 72. (in Russian)
9. Nosko A.L., Safronov E.V. Metodika opredeleniya maksimal’no dopustimoy skorosti dvizheniya poddona na gravitatsionnom rolikovom konveyyere [Methodology for determining the maximum allowable speed of a pallet on a gravity roller conveyor]. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroyeniye. 2017; 8 (689): 33–41. (in Russian)
10. Martynenko U. G. Dvizheniye tverdogo tela v elektricheskikh i magnitnykh polyakh: monografiya [Motion of a solid in electric and magnetic fields: monograph]. Moscow. Nauka. 1988: 368. (in Russian)
11. Ozolin A.U., Skubov D.U., Shtukin L.V. Sposoby tormozheniya padayushchego lifta s pomoshch’yu postoyannykh magnitov [Methods of braking a falling lift with the help of permanent magnets]. Nauchno-tekhnicheskiye vedomosti Sankt-Peterburgskogo gosudarstvennogo politekhnicheskogo universiteta. 2008; 6 (70): 82–86. (in Russian)
12. Nosko A. L., Safronov E. V. Metodika rascheta tormoznogo rolika tsentrobezhnogo tipa primenitel’no k gravitatsionnym rolikovym konveyyeram dlya pallet [Calculation method of the centrifugal type brake roller as applied to gravity roller conveyors for pallets]. Mekhanizatsiya stroitel’stva. 2017; 78; 6: 26–31. (in Russian)
13. E. Simeu, D. Georges. Modeling and control of an eddy current brake // Control Engineering Practise. 1996; 4 (1): 19–26.
14. Ozolin A.U., Skubov D.U., Shtukin L.V. Issledovaniye vikhretokovogo diskovogo tormoza [Research eddy current disc brake]. Nauchnotekhnicheskiye vedomosti Sankt-Peterburgskogo gosudarstvennogo politekhnicheskogo universiteta. 2009; 1 (74): 57–60. (in Russian)
15. Luskan’ O.A. Opredeleniye skorosti transportirovaniya shtuchnykh gruzov na inertsionnom rolikovom konveyyer [Determining the speed of piece goods transportation on an inertial roller conveyor]. Izv. TulGU. Pod”yemno-transportnyye mashiny i oborudovaniye. Tula: TulGU. 2003; 4: 84–89. (in Russian)
16. Zenkov R.L., Ivashkov I.I., Kolobov L.N. Mashiny nepreryvnogo transporta [Continuous transport machines]. Moscow. Mashinostroyeniye. 1987: 431. (in Russian)
17. Luskan’ O.A. Teoreticheskiye osnovy peremeshcheniya gruzov impul’snymi konveyyerami: Monografiya [Theoretical foundations of the goods movement by pulse conveyors: Monograph]. Saratov: Sarat. gos. tekhn. un-t. 2010: 99. (in Russian)
18. Luskan’ O.A. Inzhenernyy raschet impul’snykh konveyyerov: Monografiya [Engineering calculation of pulse conveyors: Monograph]. Saratov: Sarat. gos. tekhn. un-t. 2011: 80. (in Russian)
19. Hollowell, Thomas Culver; Kahl, Justin Tyme; Stanczak, Matthew Don; Wang, Yizhou. Eddy Current Brake Design for Operation with Extreme Backdrivable Eddy Current Motor. Mechanical Engineering Undergraduates. 2010.
20. Andrew H. C. Gosline, Vincent Hayward. Eddy Current Brakes for Haptic Interfaces: Design, Identification, and Control. IEEE/ASME Transactions on Mechatronics. 2008; 13 (6): 669–677.
21. Karakoc Kerem, Suleman Afzal, Park Edward J. Analytical modeling of eddy current brakes with the application of the time varying magnetic fields. Applied Mathematical Modeling, Netherlands. 2015. 1168–1179.
22. Karakoc Kerem, Park Edward J., Suleman Afzal. Improved braking torque generation capacity of an eddy current brake with time varying magnetic fields: A numerical study. Finite Elements in Analysis and Design. Elsevier. 2012; 59: 66–75.
23. K. Lee, K. Park. Modeling eddy currents with boundary conditions by sing Coulomb’s law and the method of images. IEEE Transactions on Magnetics. 2002; 38 (2): 1333–1340.
24. M.A. Heald. Magnetic braking: Improved theory. American Journal of Physics. 1988; 56 (6): 521–522.
25. S. Anwar. A parametric model of an eddy current electric machine for automotive braking applications. IEEE Transactions on Control Systems Technology. 2002; 12 (3): 422–427.
26. Hyeon-Jae Shin, Jang-Young Choi, Han-Wook Cho, Seok-Myeong Jang. Analytical torque calculations and Experimental testing of permanent magnet Axial eddy current brake. IEEE Transactions of Magnetics. 2013; 49 (7): 4152–4155.
Review
For citations:
Sharifullin I.A., Nosko A.L., Safronov E.V. MATHEMATICAL MODEL OF THE MOTION PALLET PROCESS ON BRAKE MAGNETIC TYPE ROLLER. The Russian Automobile and Highway Industry Journal. 2020;17(3):364-373. (In Russ.) https://doi.org/10.26518/2071-7296-2020-17-3-364-373
Views:
674
Email this article 