Nonlinear Dynamics

, Volume 93, Issue 4, pp 2213–2232 | Cite as

Dynamic and stability analysis of the vibratory feeder and parts considering interactions in the hop and the hop-sliding regimes

  • Xiangxi KongEmail author
  • Changzheng Chen
  • Bangchun Wen
Original Paper


In this paper, the interactions of a translational vibratory feeder and the parts in the hop and the hop-sliding regimes are studied by means of an improved multi-term incremental harmonic balance method. It is an effective approach analyzing the interactions by introducing an analytical model of the motion of the feeding parts to the solution procedure. A generalized time-varying piece-wise linear dynamic model of the vibratory feeder is established to conduct a comprehensive investigation on the interactions, where the friction and the impact from the parts are included. The results indicate the dynamic response of the vibratory feeder affects the motion of the parts largely and the motion of the parts also affects the dynamic response in turn. The influences of the mass of the parts, the vibration angle, the installation angle, and the friction coefficient on the interactions of the vibratory feeder and the parts are discussed. The interactions are very important and not ignored.


Vibratory feeder Parts Interactions Hop and hop-sliding regimes Multi-term IHBM 



This study was funded by National Natural Science Foundation of China (Grant No. 51705337, 51375080, 51675350) and China Postdoctoral Science Foundation (Grant No. 2017M611258)

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Ashrafizadeh, H., Ziaei-Rad, S.: A numerical 2D simulation of part motion in vibratory bowl feeders by discrete element method. J. Sound Vib. 332(13), 3303–3314 (2013)CrossRefGoogle Scholar
  2. 2.
    Mucchi, E., Di Gregorio, R., Dalpiaz, G.: Elastodynamic analysis of vibratory bowl feeders: Modeling and experimental validation. Mech. Mach. Theory. 60, 60–72 (2013)CrossRefGoogle Scholar
  3. 3.
    Suresh, M., Narasimharaj, V., Arul Navalan, G.K., Chandra Bose, V.: Effect of orientations of an irregular part in vibratory part feeders. Int. J. Adv. Manuf. Technol. 94(5), 2689–2702 (2018)CrossRefGoogle Scholar
  4. 4.
    Sadasivam, U.: Development of vibratory part feeder for material handling in manufacturing automation: a survey. J. Automat. Mob. Robot. Intell. Syst. 9(4), 3–10 (2015)Google Scholar
  5. 5.
    Ramalingam, M., Samuel, G.L.: Investigation on the conveying velocity of a linear vibratory feeder while handling bulk-sized small parts. Int. J. Adv. Manuf. Technol. 44(3–4), 372–382 (2008)Google Scholar
  6. 6.
    Kobari, Y., Nammoto, T., Kinugawa, J., Kosuge, K.: Vision based compliant motion control for part assembly. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 293–298 (2013)Google Scholar
  7. 7.
    Han, I., Lee, Y.: Chaotic dynamics of repeated impacts in vibratory bowl feeders. J. Sound Vib. 249(3), 529–541 (2002)CrossRefGoogle Scholar
  8. 8.
    Reinhart, G., Loy, M.: Design of a modular feeder for optimal operating performance. CIRP J. Manuf. Sci. Technol. 3(3), 191–195 (2010)CrossRefGoogle Scholar
  9. 9.
    Lim, G.H.: Vibratory feeder motion study using Turbo C++ language. Adva. Eng. Softw. 18(1), 53–59 (1993)CrossRefGoogle Scholar
  10. 10.
    Lim, G.H.: On the conveying velocity of a vibratory feeder. Comput. Struct. 62(1), 197–203 (1997)CrossRefGoogle Scholar
  11. 11.
    Kong, X., Xing, J., Wen, B.: Analysis of motion of the part on the linear vibratory conveyor. J. Northeast. Univ. 36(6), 827–831 (2015)Google Scholar
  12. 12.
    Wen, B., Zhang, H., Liu, S., He, Q., Zhao, C.: Theory and techniques of vibrating machinery and their applications. Science Press, Beijing (2010)Google Scholar
  13. 13.
    Kong, X., Zhang, X., Li, Q., Wen, B.: Dynamical analysis of vibratory feeder and feeding parts considering interactions by an improved increment harmonic balance method. P I Mech. Eng. C.-J. Mech. 229(6), 1029–1040 (2015)CrossRefGoogle Scholar
  14. 14.
    Vilán Vilán, J.A., Segade Robleda, A., García Nieto, P.J., Casqueiro Placer, C.: Approximation to the dynamics of transported parts in a vibratory bowl feeder. Mech. Mach. Theory 44(12), 2217–2235 (2009)CrossRefzbMATHGoogle Scholar
  15. 15.
    Han, I., Gilmore, B.J.: Multi-Body Impact motion with friction–analysis, simulation, and experimental validation. J. Mech. Design. 115(3), 412–422 (1993)CrossRefGoogle Scholar
  16. 16.
    Lau, S.L., Zhang, W.S.: Nonlinear Vibrations of piecewise-linear systems by incremental harmonic balance method. J. Appl. Mech. 59(1), 153–160 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Duan, C., Singh, R.: Super-harmonics in a torsional system with dry friction path subject to harmonic excitation under a mean torque. J. Sound Vib. 285(4–5), 803–834 (2005)CrossRefGoogle Scholar
  18. 18.
    Kim, T.C., Rook, T.E., Singh, R.: Super- and sub-harmonic response calculations for a torsional system with clearance nonlinearity using the harmonic balance method. J. Sound Vib. 281(3–5), 965–993 (2005)CrossRefGoogle Scholar
  19. 19.
    Duan, C., Singh, R.: Dynamic analysis of preload nonlinearity in a mechanical oscillator. J. Sound Vib. 301(3–5), 963–978 (2007)CrossRefGoogle Scholar
  20. 20.
    Sen, O.T., Dreyer, J.T., Singh, R.: Envelope and order domain analyses of a nonlinear torsional system decelerating under multiple order frictional torque. Mech. Syst. Signal Process. 35(1–2), 324–344 (2013)CrossRefGoogle Scholar
  21. 21.
    Teng, J.G., Lou, Y.F.: Post-collapse bifurcation analysis of shells of revolution by the accumulated arc-length method. Int. J. Numer. Meth. Eng. 40(13), 2369–2383 (1997)CrossRefzbMATHGoogle Scholar
  22. 22.
    De Souza Neto, E.A., Feng, Y.T.: On the determination of the path direction for arc-length methods in the presence of bifurcations and ‘snap-backs’. Comput. Method. Appl. M. 179(1–2), 81–89 (1999)CrossRefzbMATHGoogle Scholar
  23. 23.
    Leung, A.Y.T., Chui, S.K.: Non-linear vibration of coupled duffing oscillators by an improved incremental harmonic balance method. J. Sound. Vib. 181(4), 619–633 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Barrios, G.K.P., de Carvalho, R.M., Kwade, A., Tavares, L.M.: Contact parameter estimation for DEM simulation of iron ore pellet handling. Powder Technol. 248, 84–93 (2013)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringShenyang University of TechnologyShenyangChina
  2. 2.School of Mechanical Engineering and AutomationNortheastern UniversityShenyangChina

Personalised recommendations