Optimization method of bevel gear reliability based on genetic algorithm and discrete element

Sun, Kangkang; Wang, Guoqiang; Lu, Yanpeng

doi:10.17531/ein.2019.2.2

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Tytuł artykułu

Optimization method of bevel gear reliability based on genetic algorithm and discrete element

Autorzy

Sun Kangkang , Wang Guoqiang , Lu Yanpeng

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DOI

10.17531/ein.2019.2.2

Warianty tytułu

Metoda optymalizacji niezawodności przekładni stożkowej z zastosowaniem algorytmu genetycznego i elementów dyskretnych

Języki publikacji

Abstrakty

Gear transmission is the most basic transmission component in mechanical transmission system. Many scholars have done a lot of research on gear reliability. When the variation coefficient is used to calculate and optimize the reliability of bevel gear, in order to calculate the reliability of bevel gear, it is often assumed that the gear works under constant torque, that is, the coefficient of variation (COV) is zero, but this is not the case in practice. In this paper, a gear reliability method based on discrete element simulation is proposed. The purpose of this method is to simulate the actual working conditions of gears, calculate more accurate coefficient of variation in the real world, and improve the accuracy of gear reliability design. Firstly, the real working conditions of the bevel gear transmission are simulated by discrete element method (DEM), and in the transmission system, the tangential force COV of the bevel gear is proved to be equal to the torque COV of the crusher central shaft. Secondly, the multi-objective function model of the gear transmission system is established based on the double tooth roll crusher (DTRC). The optimal volume and reliability of the bevel gear transmission are taken as the objective function, and the teeth number, module and face width factor of basic parameters of gear are optimized by genetic algorithm (GA). Finally, the accuracy of the optimization results is verified by Monte Carlo method. The main purpose of the manuscript is to analyse the effect of actual conditions (DEM simulation) on the optimization results. The results show that the COV of nominal tangential load of bevel gear is about 0.65 under actual working conditions, so in order to guarantee the same reliability, total volume need to be increased by 34.4%. This method is similar to the selection of gear safety factor. In practical production, the selection of safety factor is often based on experience. This paper provides a new method to optimize the reliability of bevel gear, combining with DEM simulation, which provides theoretical guidance for optimal design of bevel gear.

Przekładnia zębata to podstawowy element mechanicznego układu napędowego. Niezawodność przekładni jest przedmiotem wielu badań. Przy obliczeniach i optymalizacji niezawodności przekładni stożkowej z wykorzystaniem współczynnika zmienności, często przyjmuje się, że przekładnia pracuje w warunkach stałego momentu obrotowego, t.j. że współczynnik zmienności wynosi 1. Sytuacja taka jednak nie występuje w praktyce. W niniejszej pracy zaproponowano metodę optymalizacji niezawodności przekładni opartą na symulacji metodą elementów dyskretnych. Celem tej metody jest zasymulowanie rzeczywistych warunków pracy przekładni, dokładniejsze obliczenie rzeczywistego współczynnika zmienności oraz poprawa dokładności projektowania niezawodności przekładni. W pierwszej kolejności, na przykładzie kruszarki podwójnej, wyznaczono model działania układu przekładni stożkowej wykorzystujący wielokryterialną funkcję celu. Optymalną objętość i niezawodność przekładni stożkowej przyjęto jako funkcje celu. Następnie, za pomocą metody elementów dyskretnych, symulowano rzeczywiste warunki pracy przekładni. Wyznaczono moment obrotowy przekładni stożkowej i współczynnik zmienności siły wypadkowej, a podstawowe parametry koła zębatego: liczbę zębów, moduł zęba i współczynnik szerokości zębów, zoptymalizowano za pomocą algorytmu genetycznego. Trafność wyników optymalizacji weryfikowano metodą Monte Carlo. Wyniki pokazują, że badana metoda może skutecznie poprawiać niezawodność przekładni stożkowej.

Słowa kluczowe

bevel gear reliability discrete element method Monte Carlo simulation double tooth roll crusher

przekładnia stożkowa niezawodność metoda elementów dyskretnych symulacja Monte Carlo kruszarka podwójna

Wydawca

Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne

Czasopismo

Eksploatacja i Niezawodność

Rocznik

2019

Tom

Vol. 21, no. 2

Strony

186--196

Opis fizyczny

Bibliogr. 49 poz., rys., tab.

Twórcy

autor

Sun Kangkang

szpsunkk@163.com

College of Mechanical & Aeronautics & Astronautics Engineering Jilin University, Changchun, 130025, P. R. China

autor

Wang Guoqiang

College of Mechanical & Aeronautics & Astronautics Engineering Jilin University, Changchun, 130025, P. R. China

autor

Lu Yanpeng

College of Mechanical & Aeronautics & Astronautics Engineering Jilin University, Changchun, 130025, P. R. China

Bibliografia

1. Boemer D, Ponthot J. A generic wear prediction procedure based on the discrete element method for ball mill liners in the cement industry. Minerals Engineering 2017; 109: 55-79, https://doi.org/10.1016/j.mineng.2017.02.014.
2. Chong T H, Lee J S. A Design Method of Gear Trains Using a Genetic Algorithm. International Journal of Precision Engineering & Manufacturing 2000; 1(1): 62-70, http://pdfs.semanticscholar.org/3460/f3437791bde00fa9f5e21c98e5836980a17a.pdf.
3. Chong T H, Bae I, Park G J. A new and generalized methodology to design multi-stage gear drives by integrating the dimensional and the configuration design process. Mechanism & Machine Theory 2002; 37(3): 295-310. https://doi.org/10.1016/S0094-114X(01)00078-7.
4. Chong T H, Bae I, Kubo A. Multiobjective Optimal Design of Cylindrical Gear Pairs for the Reduction of Gear Size and Meshing Vibration 2002; 44(1): 291-298, https://doi.org/10.1299/jsmec.44.291
5. Corotis RB, Nafday A M. Structural system reliability using linear programming and simulation. Journal of Structural Engineering ASCE 1989; 115(10): 2435–2447, https://doi.org/10.1061/(ASCE)0733-9445(1989)115:10(2435)
6. Delaney G W, Morrison R D, Sinnott M D, et al. DEM modelling of non-spherical particle breakage and flow in an industrial scale cone crusher. Minerals Engineering 2015; 74: 112-122, https://doi.org/10.1016/j.mineng.2015.01.013.
7. Deb K, Jain S. Multi-Speed Gearbox Design Using Multi-Objective Evolutionary Algorithms. Journal of Mechanical Design 2003; 125(3):609-619, http://link.aip.org/link/?JMDEDB/125/609/1.
8. Ditlevsen O, Madsen HO. Structural reliability methods. Chichester, UK: JohnWiley & Sons; 1996.
9. Ditlevsen O, Bjerager P. Plastic reliability analysis by directional simulation. Journal of Engineering Mechanics ASCE 1989; 115(6): 1347–1362, https://doi.org/10.1061/(ASCE)0733-9399(1989)115:6(1347).
10. Freudenthal AM, Garrelts JM, Shinozuka M. The analysis of structural safety. Journal of Structures Division, ASCE 1966; 92: 267–325.
11. Gallego-Calderon J, Natarajan A, Dimitrov N K. Effects of Bearing Configuration in wind Turbine Gearbox Reliability. Energy Procedia 2015; 80 (Pt2): 392-400, https://doi.org/10.1016/j.egypro.2015.11.443.
12. Grimmelt M, Schueller GI. Benchmark study on methods to determine collapse failure probabilities of redundant structures. Structural Safety 1982;1:93–106.
13. Golabi S, Fesharaki J J, Yazdipoor M. Gear train optimization based on minimum volume/weight design. Mechanism & Machine Theory 2014; 73(2): 197-217, https://doi.org/10.1016/j.mechmachtheory.2013.11.002.
14. Hao L. The probabilistic analysis and optimal design of a bevel gear transmission system with failure interaction. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2017; 19(2): 220-228, http://dx.doi.org/10.17531/ein.2017.2.9.
15. Huang X, Hu S, Zhang Y, et al. A method to determine kinematic accuracy reliability of gear mechanisms with truncated random variables. Automotive Engineering 2015; 92: 200-212, https://doi.org/10.1016/j.mechmachtheory.2015.04.017.
16. Karamchandani A. Structural system reliability analysis methods. Report no. 83. Department of Civil Engineering, Stanford University; 1987.
17. Kim, D., et al., System reliability analysis using dominant failure modes identified by selective searching technique. Reliability Engineering & System Safety 2013; 119: 316-331, https://doi.org/10.1016/j.ress.2013.02.007
18. Li M, Xie L, Ding L. Load sharing analysis and reliability prediction for planetary gear train of helicopter[J]. Mechanism & Machine Theory, 2017,115:97-113.https://doi.org/10.1016/j.mechmachtheory.2017.05.001
19. Lee YJ, Song J. Finite-element-based system reliability analysis of fatigueinduced sequential failures. Reliability Engineering & System Safety 2012; 108: 131–41, https://doi.org/10.1016/0167-4730(82)90018-2.
20. Lee JS. Basic study on the reliability analysis of structural systems. Journal of Ocean Engineering and Technology 1989; 12: 145–57.
21. Li Y F, Valla S, Zio E. Reliability assessment of generic geared wind turbines by GTST-MLD model and Monte Carlo simulation. Renewable Energy 2015; 83: 222-233, https://doi.org/10.1016/j.renene.2015.04.035.
22. Marjanovic N, Isailovic B, Marjanovic V, et al. A practical approach to the optimization of gear trains with spur gears. Mechanism & Machine Theory 2012; 53(7): 1-16, https://doi.org/10.1016/j.mechmachtheory.2012.02.004.
23. Melchers RE. Structural reliability: analysis and prediction. 2nd ed New York,NY: John Wiley; 1999. ISBN:0471987719
24. Melchers RE. Structural system reliability assessment using directional simulation. Structural Safety 1994; 16: 23–37, https://doi.org/10.1016/0167-4730(94)00026-M.
25. Mendi F, Boran F E. Optimization of module, shaft diameter and rolling bearing for spur gear through genetic algorithm. Expert Systems with Applications An International Journal 2010; 37(12): 8058-8064, https://doi.org/10.1016/j.eswa.2010.05.082.
26. Moses F, Stahl B. Reliability analysis format for offshore structures. In: Proceedings of the 10th annual offshore technology conference, 1978; Paper 3046. DOI: 10.4043/3046-MS
27. Moses F, Fu G. Important sampling in structural system reliability. Fifth ASCE EMD/GTD/STD specialty conference on probabilistic mchanics; 1988, http://cedb.asce.org/CEDBsearch/record.jsp?dockey=0056556.
28. Moses F. System reliability developments in structural engineering. Structural Safety 1982; 1: 3–13, https://doi.org/10.1016/0167-4730(82)90011-X.
29. Murotsu Y, Okada H, Taguchi K, Grimmelt M, Yonezawa M. Automatic generation of stochastically dominant failure modes of frame structures.Structural Safety 1984; 2: 17–25, https://doi.org/10.1016/0167-4730(84)90004-3.
30. Nejad A R, Gao Z, Moan T. On long-term fatigue damage and reliability analysis of gears under wind loads in offshore wind turbine drivetrains. International Journal of Fatigue 2014, 61(2): 116-128, https://doi.org/10.1016/j.ijfatigue.2013.11.023.
31. Nikolaidis E, Ghiocel DM, Singhal S. Engineering design reliability handbook.Boca Raton, FL: CRC Press; 2005, https://doi.org/10.1201/9780203483930.
32. Rashedi MR. Studies on reliability of structural systems. Department of Civil Engineering, Case Western Reserve University; 1983
33. Savage M, Brikmanis C, Lewicki D G, Coy J J. Life and reliability modeling of bevel gear reductions. Journal of Mechanisms, Transmissions, and Automation in Design 1988; 110(2): 189-196, https://doi.org/10.1115/1.3258925.
34. Savsani V, Rao R V, Vakharia D P. Optimal weight design of a gear train using particle swarm optimization and simulated annealing algorithms. Mechanism & Machine Theory 2010; 45(3): 531-541, https://doi.org/10.1016/j.mechmachtheory.2009.10.010.
35. Savage M, Paridon C A, Coy J J. Reliability Model for Planetary Gear Trains. Journal of Mechanical Design 1983; 105(3): 291-297, https://doi.org/10.1115/1.3267359
36. Shao S, Murotsu Y. Approach to failure mode analysis of large structures.Probabilistic Engineering Mechanics 1999; 14: 169–177, https://doi.org/10.1016/S0266-8920(98)00028-9.
37. Shetty NK. Selective enumeration method for identification of dominant failure paths of large structures. In: Proceedings of OMAE conference, vol. II. ASME. Safety and Reliability 1994: 381–391, https://www.osti.gov/biblio/55808.
38. Swantner A, Campbell M I. Topological and parametric optimization of gear trains. Engineering Optimization 2012, 44(11): 1351-1368, https://doi.org/10.1080/0305215X.2011.646264.
39. Thoft-Christensen P, Baker MJ. Structural reliability theory and its applications. Springer-Verlag; 1982, https://doi.org/10.1007/978-3-642-68697-9_11.
40. Thoft-Christensen P, Murotsu Y. Application of structural systems reliability theory. Berlin: Springer-Verlag; 1986, https://link.springer.com/book/10.1007%2F978-3-642-82764-8.
41. Thompson D F, Gupta S, Shukla A. Tradeoff analysis in minimum volume design of multi-stage spur gear reduction units. Mechanism & Machine Theory 2000; 35(5): 609-627, https://doi.org/10.1016/S0094-114X(99)00036-1.
42. Wang H, Wang H P. Optimal engineering design of spur gear sets. Mechanism & Machine Theory 1994; 29(7): 1071-1080, https://doi.org/10.1016/0094114X(94)90074-4.
43. Wang Y. Optimized tooth profile based on identified gear dynamic model. Mechanism & Machine Theory 2007; 42(8): 1058-1068, https://doi.org/10.1016/j.mechmachtheory.2006.02.011
44. Xiao Q, Mahadevan S. Fast failure mode identification for ductile structural system reliability. Structural Safety 1994; 13(4): 207–26, https://doi.org/10.1016/0167-4730(94)90029-9.
45. Xie L, Wu N, Qian W. Time domain series system definition and gear set reliability modeling. Reliability Engineering & System Safety 2016;155: 97-104, https://doi.org/10.1016/j.ress.2016.06.009.
46. Yang Q J. Fatigue test and reliability design of gears. International Journal of Fatigue 1996; 18(3): 171-177, https://doi.org/10.1016/0142-1123(95)00096-8.
47. Zhang G, Wang G, Li X, et al. Global optimization of reliability design for large ball mill gear transmission based on the Kriging model and genetic algorithm. Mechanism & Machine Theory 2013; 69(6): 321-336, https://doi.org/10.1016/j.mechmachtheory.2013.06.003.
48. Zhou D, Zhang X, Zhang Y. Dynamic reliability analysis for planetary gear system in shearer mechanisms. Mechanism & Machine Theory 2016; 105: 244-259, https://doi.org/10.1016/j.mechmachtheory.2016.07.007.
49. Zolfaghari A , Goharimanesh M , Akbari A A . Optimum design of straight bevel gears pair using evolutionary algorithms. Journal of the Brazilian Society of Mechanical Sciences & Engineering 2017; 39(6): 1-9, https://doi.org/10.1007/s40430-017-0733-9.

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bwmeta1.element.baztech-94ee0ff8-d6a7-4881-a8ea-53ebe2ab9984