Isaac Scientific Publishing

Journal of Advances in Applied Mathematics

Comparative Analysis of Friction in Vibration-Driven System and Its Dynamic Behaviors

Download PDF (1161.5 KB) PP. 23 - 42 Pub. Date: January 1, 2017

DOI: 10.22606/jaam.2017.21003

Author(s)

  • Sainan Wang
    School of Aerospace Engineering and Applied Mechanics, Tongji Univerisity, Shanghai, People’s Republic of China
  • Xiong Zhan
    School of Aerospace Engineering and Applied Mechanics, Tongji Univerisity, Shanghai, People’s Republic of China
  • Jian Xu*
    School of Aerospace Engineering and Applied Mechanics, Tongji Univerisity, Shanghai, People’s Republic of China

Abstract

Numerical simulations and experimental investigations of single module vibration-driven system with friciton have been stuidied in this paper. Friction models can be divided into two classes, namely static and dynamic models. Thus, we just compare the anisotropic Coulomb friction and that of the LuGre model. Through numerical simulations, one can find the LuGre model ha has a good agreement with the experimental data from both qualitative and quantitative viewpoints. Moreover, through changing the physical parameters of the system, the vibration-driven system with the LuGre model can dispaly lots of dynamic behaviors expect for the four types movement forms, such as quasi-periodic motion and periodic two motion.

Keywords

Coulomb friction model, LuGre model, vibration-driven system, stick-slip, dynamic behavior.

References

[1] F. L. Chernous.Ko, "On the motion of a body containing a movable internal mass," Doklady Physics, vol. 50, no. 11, pp. 593-597, 2005.

[2] N. N. Bolotnik, N.N., T. Y. Figurina and F. L. Chernous Ko," Optimal control of the rectilinear motion of a two-body system in a resistive medium," Journal of Applied Mathematics and Mechanics, vol. 76, no. 1, pp. 1-14, 2012.

[3] N. N. Bolotnik, et al., "Dynamics of controlled motion of vibration-driven systems," Journal of Computer and Systems Sciences International, vol. 45, no. 5, pp. 831-840, 2006.

[4] N. N. Bolotnik, and T. Y. Figurina, "Optimal control of periodic motions of vibration-driven systems," IFAC Proceedings, vol. 40, no. 14, pp. 142-147, 2007.

[5] F. L. Chernous Ko, "Analysis and optimization of the motion of a body controlled by means of a movable internal mass," Journal of Applied Mathematics and Mechanics, vol. 70, no. 6, pp. 819-842, 2006.

[6] A. G. Egorov, and O. S. Zakharova, "The optimal quasi-stationary motion of a vibration-driven robot in a viscous medium," Russian Mathematics, vol. 56, no. 2, pp. 50-55, 2012.

[7] H .B. Fang, and J. Xu, "Dynamic analysis and optimization of a three-phase control mode of a mobile system with an internal mass," Journal of vibration and control, vol. 17, no. 1, pp. 19-26, 2011.

[8] H. B. Fang, and J. Xu, "Stick-slip effect in a vibration-driven system with dry friction: sliding bifurcations and optimization," Journal of Applied Mechanics, vol. 81, no. 5, pp. 1-10, 2014.

[9] H. B. Fang, and J. Xu, "Dynamics of a mobile system with an internal acceleration-controlled mass in a resistive medium," Journal of sound and vibration, vol. 330, no. 16, pp. 4002-4018, 2011.

[10] C.H.Y. Hu, C.E. Kreuzerand, and F. L. Chernousko, "Dynamics of a body controlled by internal motions," in Iutam Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty: Proceedings of the IUTAM Symposium held in Nanjing, China, pp. 227-236, 2006.

[11] A. G. Yegorov, and O. S. Zakharova, "The energy-optimal motion of a vibration-driven robot in a resistive medium," Journal of Applied Mathematics and Mechanics, vol. 74, no. 4, pp. 443-451, 2010.

[12] H.B. Fang, and J. Xu, "Controlled motion of a two-module vibration-driven system induced by internal acceleration-controlled masses," Archive of Applied Mechanics, vol. 82, no. 4, pp. 461-477, 2012.

[13] K. Zimmermann, et al., "Dynamics of a two-module vibration-driven system moving along a rough horizontal plane," Multibody System Dynamics, vol. 22, no. 2, pp. 199-219, 2009.

[14] H.B. Fang, and J. Xu, "Dynamics of a three-module vibration-driven system with non-symmetric Coulomb's dry friction," Multibody System Dynamics, vol. 27, no. 4, pp. 455-485, 2012.

[15] K. Zimmermann, et al. "An approach to the modelling of worm-like motion systems with finite degree of freedom– first steps in technical realization," in Proceedings of the Fourth International Conference on Climbing and Walking Robots, Karlsruhe, pp. 561-568, 2001.

[16] R.A. Ibrahim, "Friction-induced vibration, chatter, squeal, and chaos—Part II: dynamics and modeling," Applied Mechanics Reviews, vol. 47, no. 7, pp. 227-253, 1994.

[17] Jedynak R., M. Sulek, 'Numerical and experimental investigation of plastic interaction between rough surfaces, ' Arabian Journal foe science and engineering, vol. 30, pp. 4165-4177, 2014.

[18] L.L. Liu,et al, "An overview of friction models in mechanical systems," Advances in Mechanics, vol. 8, no. 2, pp. 201-213, 2008.

[19] Q. Ding, H.M. Zhai, "The advance in researches of friction dynamics in mechanical system," vol. 43, no. 1, pp. 112-131, 2013.

[20] Pennestrì E., Valerio Rosssi, Salvini P, Valentini P., 'Review and comparison of dry friction force models,' Nonlinear dynamics, vol. 83, pp. 1785-1801, 2016.

[21] J. Swervers, et al., "An integrated friction model structure with improved presliding behavior for accurate friction compensation," IEEE Transactions on Automatic Control, vol. 45, no. 4, pp. 675-686, 2000.

[22] K. Johanastrom, C. Canudas de Wit, "Revisiting the LuGre friction model," IEEE Control Systems, vol. 28, no. 6, pp. 101-114, 2008.

[23] N. Barahanov, R. Ortega, "Necessary and sufficient conditions for passivity of the LuGre friction model," IEEE Transactions on Automatic Control, vol. 45, no. 4, pp. 830-832, 2000.

[24] Y. Wang, Z.He and G.X. Wang, "A practical friction model," vol. 15, no. 8, pp. 59-63, 2011.

[25] J. Awrejcewicz, D. Grzelczyk and Y. Pyryev. "On the stick-slip vibrations continuous friction model," in Proceedings of the 9th Conference on Dynamical Systems–Theory and Applications, Poland, pp. 113-120, 2007.

[26] A.Saha, et al., "A modified LuGre friction model for an accurate prediction of friction force in the pure sliding regime," International Journal of Non-Linear Mechanics, vol. 80, pp. 122-131, 2016.

[27] A.Wijata, et al., "Mathematical model for two-dimensional dry friction modified by dither," Mathematics and Mechanics of Solids, pp. 1-14, 2016.

[28] N.N. Bolotnik, F.L. Chernousko and T.Y. Figurina, "Optimal control of a two-body system moving in a viscous medium," IFAC Proceedings, vol. 43, no. 14, pp. 1308-1313, 2010.

[29] F.L. Chernous Ko., "The optimal periodic motions of a two-mass system in a resistant medium," Journal of Applied Mathematics and Mechanics, vol. 72, no. 2, pp. 116-125, 2008.

[30] N.N. .Bolotnik, and T.Y. Figurina, "Optimal control of the rectilinear motion of a rigid body on a rough plane by means of the motion of two internal masses," Journal of Applied Mathematics and Mechanics, vol. 72, no. 2, pp. 126-135, 2008.

[31] F.L. ChernousKo, "The optimum rectilinear motion of a two-mass system," Journal of Applied Mathematics and Mechanics, vol. 66, no. 1, pp. 1-7, 2002.

[32] A. Preumont, Vibration Control of Active Structures, Springer, 2011.