Granular Matter

, Volume 16, Issue 4, pp 485–498 | Cite as

Optimal numerical design of bucket elevators using discontinuous deformation analysis

  • J. L. Pérez-Aparicio
  • R. Bravo
  • J. J. Gómez-Hernández
Original Paper


Bucket elevators are efficient machines to transport granular materials in industrial and civil engineering applications. These materials are composed of hundreds, thousands or even more particles, the global behavior of which is defined by contact interactions. The first attempts to analyze the transportation of granular materials were treated by very simple continuum methods that do not take into account these interactions, producing simulations that do not fit the experimental results accurately. Given the internal discontinuity nature of granular media, it is reasonable to use numerical methods to model their behavior, such as discontinuous deformation analysis (DDA)—a member of the discrete element method family that started to be used in the 90s to analyze similar problems. The version of DDA used in the current work treats grains as rigid circular particles with friction, damping and eventually cohesion with the objective of simulating and analyzing in detail the discharge of granular materials with bucket elevators. A deterministic computer code has been implemented and validated against simplified analytical formulae and experimental results taken from the literature. This computer code is then used to obtain optimum two-dimensional bucket geometries under specific working conditions. The optimization aims to maximize transport distance and to minimize remaining material, taking into account bucket velocity and the properties of the grains. The resulting geometries are discussed and compared against standard designs.


Discontinuous deformation analysis Bucket elevators discharge Numerical contact Penalty method Golden section algorithm Bezier curves 



J.L. Pérez-Aparicio, R. Bravo were partially supported by the MFOM I+D (2004/38), both by MICIIN \(\#\)BIA 2008-00522 and the first also by Polytechnic University of Valencia under grant PAID 05-10-2674. J.J. Gómez-Hernández was partially supported by MICIIN \(\#\)CGL 2011-23295.

Supplementary material

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Supplementary material 1 (eps 1040 KB)
10035_2014_485_MOESM2_ESM.eps (1 mb)
Supplementary material 2 (eps 1035 KB)


  1. 1.
    Rademacher, F.: Non-spill discharge characteristics of bucket elevators. Powder Technol. 22(2), 215–241 (1979)CrossRefGoogle Scholar
  2. 2.
    Koster, K.: Bulk material discharge of bucket elevators, especially high-capacity bucket elevators. [zum schuettgutabwurf bei becherwerken, insbesondere bei hochleistungsbecherwerken]. Aufbereitungs-Technik 25(8), 450–463 (1984)Google Scholar
  3. 3.
    Koster, K.: Use of high-capacity bucket elevators in the cement industry. [zum einsatz von hochleistungsbecherwerken in der zementindustrie]. Zement-Kalk-Gips 33(3), 116–119 (1980)Google Scholar
  4. 4.
    Koster, K.: Development and state of the art in heavy-duty bucket elevators with central chains—part 2 [entwicklung und stand der technik von hochleistungs-becherwerken mit zentralkette—teil 2]. ZKG Int. 49(4), 173–187 (1996)Google Scholar
  5. 5.
    Koster, K.: Centrifugal discharge of bucket elevators. Bulk Solids Handl. 5(2), 449–460 (1985)Google Scholar
  6. 6.
    Koster, K.: Problem of complete emptying of high-speed elevator buckets. Aufbereitungs-Technik 27(9), 471–481 (1986)Google Scholar
  7. 7.
    Korzen, Z.: Mechanics of gravitational discharge of cell-less bucket wheels in reclaiming machines. Bulk Solids Handl. 7(6), 801–812 (1987)Google Scholar
  8. 8.
    Korzen, Z., Dudek, K.: Mathematical model of the operational efficiency of a multibucket centrifugal discharge wheel [model matematyczny wydajnosci roboczego procesu kola wieloczerpakowego z odsrodkowym wysypem]. Politechnika Warszawska Prace Naukowe Mechanika 1(121), 187–199 (1989)Google Scholar
  9. 9.
    Shi, G., Goodman, R.: Two dimensional discontinuous deformation analysis. Int. J. Numer. Anal. Methods Geomech. 9(6), 541–556 (1985)ADSCrossRefMATHGoogle Scholar
  10. 10.
    Pérez-Aparicio, J., Bravo, R.: Discrete Elements, vol. 2, pp. 41–77. Consorcio TCN (2006)Google Scholar
  11. 11.
    Shi, G.: Discontinuous Deformation Analysis: A New Model for the Statics and Dynamics of Block Systems. Ph.D. thesis, University of California, Berkeley (1988)Google Scholar
  12. 12.
    Moosavi, M., Grayeli, R.: A model for cable bolt-rock mass interaction: integration with discontinuous deformation analysis (DDA) algorithm. Int. J. Rock Mech. Min. Sci. 43(4), 661–670 (2006)Google Scholar
  13. 13.
    Pérez-Aparicio, J., Bravo, R., Ortiz, P.: Refined element discontinuous numerical analysis of dry-contact masonry arches. Eng. Struct. 48, 578–587 (2013)CrossRefGoogle Scholar
  14. 14.
    McBride, W., Sinnott, M., Cleary, P.: Discrete element modelling of a bucket elevator head pulley transition zone. Granul. Matter 13(2), 169–174 (2011)CrossRefGoogle Scholar
  15. 15.
    Kruggel-Emden, H., Sudbrock, F., Wirtz, S., Scherer, V.: Experimental and numerical investigation of the bulk behavior of wood pellets on a model type grate. Granul. Matter 14(6), 681–693 (2012)CrossRefGoogle Scholar
  16. 16.
    Walton, O., Moor, C., Gill, K.: Effects of gravity on cohesive behavior of fine powders: implications for processing lunar regolith. Granul. Matter 9(5), 353–363 (2007)CrossRefGoogle Scholar
  17. 17.
    Gao, Y., Muzzio, F., Ierapetritou, M.: Optimizing continuous powder mixing processes using periodic section modeling. Chem. Eng. Sci. 80, 70–80 (2012)CrossRefGoogle Scholar
  18. 18.
    Shmulevich, I.: State of the art modeling of soil-tillage interaction using discrete element method. Soil Tillage Res. 111(1), 41–53 (2010)CrossRefGoogle Scholar
  19. 19.
    Moon, T., Oh, J.: A study of optimal rock-cutting conditions for hard rock tbm using the discrete element method. Rock Mech. Rock Eng. 45(5), 837–849 (2012)ADSGoogle Scholar
  20. 20.
    Makokha, A., Moys, M., Bwalya, M., Kimera, K.: A new approach to optimising the life and performance of worn liners in ball mills: experimental study and DEM simulation. Int. J. Miner. Process. 84(1–4), 221–227 (2007)Google Scholar
  21. 21.
    Balevičius, R., Kačianauskas, R., Mroz, Z., Sielamowicz, I.: Discrete element method applied to multiobjective optimization of discharge flow parameters in hoppers. Struct. Multidiscip. Optim. 31(3), 163–175 (2006)CrossRefGoogle Scholar
  22. 22.
    Hu, L.: Gradual deformation and iterative calibration of Gaussian-related stochastic models. Math. Geol. 32(1), 87–108 (2000)CrossRefGoogle Scholar
  23. 23.
    Bravo, R., Pérez-Aparicio, J., Laursen, T.: An energy consistent frictional dissipating algorithm for particle contact problems. Int. J. Numer. Methods Eng. 92(9), 753–781 (2012)CrossRefGoogle Scholar
  24. 24.
    Belytschko, T., Liu, W., Moran, B.: Nonlinear Finite Elements for Continua and Structures. Wiley, New York (2000)MATHGoogle Scholar
  25. 25.
    Beckert, R., Föll, R.: Untersuchung der abwurfverhältnisse an kettenbecherwerken. Förden Heben 1(15), 833–836 (1966)Google Scholar
  26. 26.
    Jaskulski, A.: Engineer-to-order approach to high speed bucket elevator design in a small-enterprise. Appl. Eng. Agric. 24(5), 545–557 (2008)CrossRefGoogle Scholar
  27. 27.
    Beverley, G.: Mechanics of High Speed Bucket Elevator Discharge. Ph.D. thesis. University of Newcastle (1986)Google Scholar
  28. 28.
    Beverley, G., Roberts, A., Hayes, J.: Mechanics of high speed elevator discharge. Bulk Solids Handl. 3(4), 853–859 (1983)Google Scholar
  29. 29.
    Korzen, Z., Dudek, K.: Reclaiming with a high-speed bucket wheel with centrifugal discharge. Bulk Solids Handl. 11(3), 615–626 (1991)Google Scholar
  30. 30.
    Bravo, R., Pérez-Aparicio, J., Laursen, T.: An enhanced energy conserving time stepping algorithm for frictionless particle contacts. Int. J. Numer. Methods Eng. 85(11), 1415–1435 (2011)CrossRefMATHGoogle Scholar
  31. 31.
    Jaskulski, A.: Methodology of Multi-Criteria Optimization of Appliances for Vertical Grain Transportation. Ph.D. thesis. Warsaw University of Technology (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • J. L. Pérez-Aparicio
    • 1
  • R. Bravo
    • 2
  • J. J. Gómez-Hernández
    • 3
  1. 1.Department of Continuum Mechanics and Theory of StructuresUniversitat Politècnica de ValènciaValenciaSpain
  2. 2.Department of Structural Mechanics and Hydraulic EngineeringUniversity of GranadaGranadaSpain
  3. 3.Research Institute of Water and Environmental EngineeringUniversitat Politècnica de ValènciaValenciaSpain

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