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The self-synchronous theory of a dual-motor driven vibration mechanism without shimmy

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Abstract

The paper focuses on the self-synchronous motion and stabilizing conditions of a vibration mechanism driven by dual-motor, which can eliminate the shimmy. The differential equations of motion of the vibration mechanism are derived by applying Lagrange’s equation and the dimensionless coupled equations of the exciters with a modified average small parameter method are obtained. The condition of existence for zero solution of the dimensionless coupled equation is used to derive the condition for the self-synchronous motion of the vibration mechanism. The stability condition of self-synchronous motion is obtained according to the Routh–Hurwitz criterion. Afterward, the numerical simulations are carried out to verify the results of the theoretical analysis. The results are concluded that increasing the mass ratio of the two exciters and decreasing the frequency ratio along the vertical direction, the angle of the resonant excitation and the mass ratio of the inner rigid body against the vibration system are all able to enhance the ability of self-synchronization of the vibration mechanism. The simulation results are finally validated by experiments.

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References

  1. Huygens C.: Horologium Oscillatorium. France, Paris (1673)

  2. Rayleigh J.: Theory of Sound. Dover, New York (1945)

    MATH  Google Scholar 

  3. Blekhman I.I., Fradkov A.L., Nijmeijer H., Pogromsky A.Y.: On self-synchronization and controlled synchronization. Syst. Control Lett. 31(5), 299–305 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  4. Blekhman I.I., Yaroshevich N.P.: Extension of the domain of applicability of the integral stability criterion (Extremum Property) in synchronization problems. J. Appl. Math. Mech. 68(6), 839–864 (2004)

    Article  MathSciNet  Google Scholar 

  5. Blekhman I.I., Fradkov A.L., Tomchina O.P., Bogdanov D.E.: Self-synchronization and controlled synchronization: General definition and example design. Math. Comput. Simul. 58(4), 367–384 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Blekhman I.I.: Synchronization in Science and Technology. ASME Press, New York (1988)

    Google Scholar 

  7. Blekhman I.I.: Synchronization of Dynamical Systems. Nauka, Moscow (1971) (in Russian)

    Google Scholar 

  8. Blekhman I.I.: Vibrational Mechanics. World Scientific, Singapore (2000)

    Book  Google Scholar 

  9. Blekhman I.I.: Selected Topics in Vibrational Mechanics. World Scientific, Singapore (2004)

    MATH  Google Scholar 

  10. Sperling L.: Selbstsynchronisation statisch und dynamisch unwuchtiger vibratoren. Teil I Grundlagen. Technische Mechanik. 14(1), 61–76 (1994) (in German)

    Google Scholar 

  11. Sperling L.: Selbstsynchronisation statisch und dynamisch unwuchtiger vibratoren. Teil II Ausführung und Beispiele. Technische Mechanik. 14(2), 85–96 (1994) (in German)

    Google Scholar 

  12. Ragulskis K.M.: Mechanisms on the Vibrating Base. Lithuanian Academy of Sciences, Kaunas (1963) (in Russian)

    Google Scholar 

  13. Ragulskis K.M., Vitkus I.I., Ragulskiene V.L.: Self-Synchronization of Systems. Self-Synchronous and Vibro-shock Systems. Mintis, Vilnius (1965) (in Russian)

    Google Scholar 

  14. Khodzhaev K.Sh.: Synchronization of the mechanical vibrators related to the linear oscillatory system. Izv. AN SSSR. MTT. 4, 14–24 (1967) (in Russian)

    Google Scholar 

  15. Nagaev R.F.: Dynamics of Synchronizing Systems. Berlin. Heidelberg: Spriger. (2003) (Engl. transl. of the Russian issue. Quasiconservative Synchronizing Systems. St. Petersburg: Nauka, 1996).

  16. Kononenko V.O.: Vibrating System With Limited Power Supply. Illiffe, London (1969)

    Google Scholar 

  17. Balthazar J.M., Felix J.L.P., Reyolando M.L.R.: Short comments on self-synchronization of two non-ideal sources supported by a flexible portal frame structure. J. Vib. Control 10(12), 1739–1748 (2004)

    Article  MATH  Google Scholar 

  18. Balthaza J.M., Felix J.L.P., Brasil R.M.: Some comments on the numerical simulation of self-synchronization of four non-ideal exciters. Appl. Math. Comput. 164(2), 615–625 (2005)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, China

    He Li, Dan Liu, Ye Li, Chun-Yu Zhao & Bang-Chun Wen

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  1. He Li
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  2. Dan Liu
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  3. Ye Li
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  4. Chun-Yu Zhao
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  5. Bang-Chun Wen
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Correspondence to He Li.

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Li, H., Liu, D., Li, Y. et al. The self-synchronous theory of a dual-motor driven vibration mechanism without shimmy. Arch Appl Mech 85, 657–673 (2015). https://doi.org/10.1007/s00419-014-0978-z

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  • DOI: https://doi.org/10.1007/s00419-014-0978-z

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