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Influence of contact stiffness of joint surfaces on oscillation system based on the fractal theory

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Abstract

In this paper, in view of microscopic surface topography characteristic, the relationship of microscopic surface topography characteristic and the dynamic characteristic of macroscopic system is established, and the influence of fractal contact stiffness on the stability and nonlinearity of modal coupling system is studied based on microscopic surface topography. According to the fractal characteristic of metal surface machined, the normal and tangential contact stiffness fractal models of joint surfaces are established and verified. In this paper, a critical two-degree-of-freedom modal coupling model is listed, the fractal contact stiffness obtained is embedded into oscillatory differential equation to study the influence of the coupling between friction coefficient and stiffness ratio of joint surfaces and the coupling between natural frequency and stiffness ratio of joint surfaces on the system stability, and the influence of fractal contact stiffness on the limit cycle of system is further analyzed. The above theoretical analysis can provide a reference for the design of suitable surface topography in the engineering.

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References

  1. Majumdar, A., Tien, C.L.: Fractal characterization and simulation of rough surfaces. Wear 136, 313–327 (1990)

    Article  Google Scholar 

  2. Majumdar, A., Bhushan, B.: Fractal model of elastic–plastic contact between rough surfaces. ASME J. Tribol. 113, 1–11 (1991)

    Article  Google Scholar 

  3. Zhang, X., Jackson, R.L.: An analysis of the multiscale structure of surfaces with various finishes. Tribol. Trans. 60, 121–134 (2016)

    Article  Google Scholar 

  4. Zhang, X., Xu, Y., Jackson, R.L.: An analysis of generated fractal and measured rough surfaces in regards to their multi-scale structure and fractal dimension. Tribol. Int. 105, 94–101 (2017)

    Article  Google Scholar 

  5. Ibrahim, R.A.: Friction-induced vibration, chatter, squeal, and chaos—part I: mechanics of contact and friction. ASME Appl. Mech. Rev. 47, 209–226 (1994)

    Article  Google Scholar 

  6. Hunstig, M., Hemsel, T., Sextro, W.: High-velocity operation of piezoelectric inertia motors: experimental validation. Arch. Appl. Mech. 86, 1733–1741 (2016)

    Article  Google Scholar 

  7. Ibrahim, R.A.: Friction-induced vibration, chatter, squeal, and chaos—part II: dynamics and modeling. ASME Appl. Mech. Rev. 47, 227–235 (1994)

    Article  Google Scholar 

  8. Spurr, R.T.: A theory of brake squeal. Proc. Inst. Mech. Eng. Auto. 1961, 33–52 (1961)

    Google Scholar 

  9. Hoffmann, N., Gaul, L.: Effects of damping on mode-coupling instability in friction induced oscillations. ZAMM. J. Appl. Maths. Mech. 83, 524–534 (2003)

    Article  MATH  Google Scholar 

  10. Sinou, J.J., Jézéquel, L.: Mode coupling instability in friction-induced vibrations and its dependency on system parameters including damping. Eur. J. Mech.- A/Solids 26, 106–122 (2007)

    Article  MATH  Google Scholar 

  11. Eriksson, M., Bergman, F., Jacobson, S.: Surface characterisation of brake pads after running under silent and squealing conditions. Wear 232, 163–167 (1999)

    Article  Google Scholar 

  12. Chen, G.X., Zhou, Z.R., Li, H., Liu, Q.Y.: Profile analysis related to friction-induced noise under reciprocating sliding conditions. Chin. J. Mech. Eng. 38, 85–88 (2002)

    Article  Google Scholar 

  13. Okayama, K., Fujikawa, H., Kubota, T., Kakihara, K.: A study on rear disc brake groan noise immediately after stopping. In: 23rd Annual Brake Colloquium and Exhibition. Orlando SAE 2005-01-3917 (2005)

  14. Hammerström, L., Jacobson, S.: Surface modification of brake discs to reduce squeal problems. Wear 261, 53–57 (2006)

    Article  Google Scholar 

  15. Rusli, M., Okuma, M.: Squeal noise prediction in dry contact sliding systems by means of experimental spatial matrix identification. J. Syst. Des. Dyn. 2, 585–595 (2008)

    Google Scholar 

  16. Fuadi, Z., Adachi, K., Ikeda, H., Naito, H., Kato, K.: Effect of contact stiffness on creep-groan occurrence on a simple caliper-slider experimental model. Tribol. Lett. 33, 169–178 (2009)

    Article  Google Scholar 

  17. Fuadi, Z., Maegawa, S., Nakano, K., Adachi, K.: Map of low-frequency stick-slip of a creep groan. Proc. Inst. Mech. Eng. J J. Eng. Tribol 224, 1235–1246 (2010)

    Article  Google Scholar 

  18. Sinou, J.J., Jézéquel, L.: The influence of damping on the limit cycles for a self-exciting mechanism. J. Sound & Vib. 304, 875–893 (2007)

    Article  Google Scholar 

  19. Sinou, J.J., Fritz, G., Jézéquel, L.: The role of damping and definition of the robust damping factor for a self-exciting mechanism with constant friction. J. Vib. Acoust. 129, 297–306 (2007)

    Article  Google Scholar 

  20. Charroyer, L., Chiello, O., Sinou, J.J.: Parametric study of the mode coupling instability for a simple system with planar or rectilinear friction. J. Sound Vib. 384, 94–112 (2016)

    Article  Google Scholar 

  21. Greenwood, J.A., Tripp, J.H.: The elastic contact of rough spheres. J. Appl. Mech. 34, 153–159 (1967)

    Article  Google Scholar 

  22. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)

    Book  MATH  Google Scholar 

  23. Ge, S.R., Zhu, H.: Tribology Fractal. Machinery Industry Press, Beijing (2005)

    Google Scholar 

  24. Liou, J.L., Lin, J.F.: A new microcontact model developed for variable fractal dimension, topothesy, density of asperity, and probability density function of asperity heights. ASME J. Appl. Mech. 74, 603–613 (2007)

    Article  Google Scholar 

  25. Yan, W., Komvopoulos, K.: Contact analysis of elastic–plastic fractal surfaces. J. Appl. Phys. 84, 3617–3624 (1998)

    Article  Google Scholar 

  26. Li, X.P., Yue, B., Zhao, G.H., Sun, D.H.: Fractal prediction model for normal contact damping of joint surfaces considering friction factors and its simulation. Adv. Mech. Eng. 2014, 1–5 (2014)

    Google Scholar 

  27. Li, X.P., Liang, Y.J., Zhao, G.H., Ju, X., Yang, H.T.: Dynamic characteristics of joint surface considering friction and vibration factors based on fractal theory. J. Vibroeng. 15, 872–883 (2013)

    Google Scholar 

  28. Sackfield, A., Hills, D.A.: Some useful results in the tangentially loaded Hertzian contact problem. Strain Anal. 18, 107–110 (1983)

    Article  Google Scholar 

  29. Sheng, X.Y., Luo, J.B., Wen, S.Z.: Prediction of static friction coefficient based on fractal contact. China Mech. Eng. 9, 16–18 (1998)

    Google Scholar 

  30. Wen, S.H., Zhang, X.L., Wen, X.G., Wang, P.Y., Wu, M.X.: Fractal model of tangential contact stiffness of joint interfaces and its simulation. Trans. Chinese Soc. Agric. Mach. 40, 223–227 (2009)

    Google Scholar 

  31. Zhang, X.L., Wang, N.S., Lan, G.S., Wen, S.H., Chen, Y.H.: Tangential damping and its dissipation factor models of joint interfaces based on fractal theory with simulations. ASME J. Tribol. 136, 011704–011710 (2014)

    Article  Google Scholar 

  32. Zhang, H., Yu, C.L., Wang, R.C., Ye, P.Q., Liang, W.Y.: Parameters identification method for machine tool support joints. J. Tsinghua Univ. (Sci. Technol.) 54, 815–821 (2014)

    Google Scholar 

  33. Hultén, J.: Drum brake squeal—a self-exciting mechanism with constant friction. In: SAE Truck and Bus Conference Detroit, pp. 695–706. (1993)

  34. Hultén, J.: Friction phenomena related to drum brake squeal instabilities. In: ASME design engineering technical conferences. Sacramento, pp. 588–596. (1997)

  35. Riebe, S., Ulbrich, H.: Modelling and online computation of the dynamics of a parallel kinematic with six degrees-of-freedom. Arch. Appl. Mech. 72, 817–829 (2003)

    MATH  Google Scholar 

  36. Hua, C., Rao, Z., Na, T., Zhu, Z.: Nonlinear dynamics of rub-impact on a rotor-rubber bearing system with the Stribeck friction model. J. Mech. Sci. Tech. 29, 3109–3119 (2015)

    Article  Google Scholar 

  37. Jiang, H., Jiang, W.: Study of lateral-axial coupling vibration of propeller-shaft system excited by nonlinear friction. Arch. Appl. Mech. 86, 1537–1550 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

The authors greatly appreciate the reviewers’ suggestions and the editor’s encouragement. This work was supported, in part, by a Grant from National Natural Science Foundation of China (Nos. 51275079 and 51575091) and Fundamental Research Funds for the Central Universities (N160306003).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, People’s Republic of China

    Wujiu Pan, Xiaopeng Li, Linlin Wang, Na Guo & Zemin Yang

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  1. Wujiu Pan
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  2. Xiaopeng Li
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  3. Linlin Wang
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  4. Na Guo
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  5. Zemin Yang
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Correspondence to Xiaopeng Li.

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Pan, W., Li, X., Wang, L. et al. Influence of contact stiffness of joint surfaces on oscillation system based on the fractal theory. Arch Appl Mech 88, 525–541 (2018). https://doi.org/10.1007/s00419-017-1325-y

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  • DOI: https://doi.org/10.1007/s00419-017-1325-y

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