DOI QR코드

DOI QR Code

The Effects of Damping on the Limit Cycle of a 2-dof Friction Induced Self-oscillation System

마찰 기인 2자유도계 시스템의 자려진동에 대한 댐핑의 영향

  • 조용구 (한양대학교 대한원 자동차공학과) ;
  • 신기홍 (안동대학교 기계공학과) ;
  • 이유엽 (한양대학교 대학원 자동차공학과) ;
  • 오재응 (한양대학교 기계공학부)
  • Published : 2002.07.01

Abstract

A two-degree of freedom model Is suggested to understand the basic dynamical behaviors of the interaction between two masses of the friction induced vibration system. The two masses may be considered as the pad and the dusk of the brake. The phase space analysis is performed to understand complicated dynamics of the non-linear model. Attractors in the phase space are examined for various conditions of the parameters of the model especially by emphasizing on the damping parameters. In certain conditions, the attractor becomes a limit cycle showing the stick-slip phenomena. In this Paper, not only titre existence of the limit cycle but also the sloe of the limit cycle is examined to demonstrate the non-linear dynamics that leads the unstable state. For the two different cases of the system frequency[(1) Two masses with same natural frequencies, (2) with different natural frequencies] . the propensity of limit cycle Is discussed In detail. The results show an important fact that it may make the system worse when too much damping Is present in the only one part of the masses.

Keywords

References

  1. Ibrahim. R. A. 1994. "Friction-induced Vibration. Chatter, Squeal, and Chaos Part 1: Mechanics of Contact and Friction". Applied Mechanics Review. Vol. 47. No.7. pp. 209-226. https://doi.org/10.1115/1.3111079
  2. Ibrahim. R. A, 1994, "Friction-induced Vibration. Chatter. Squeal, and Chaos Part 2: Dynamics and Modelling". Applied Mechanics Review. Vol. 47. No.7. pp. 227-253. https://doi.org/10.1115/1.3111080
  3. Mclntyre, M. E. and Woodhouse. J.. 1979. "Fundamentals of Bowed-string Dynamics". Acustica, Vol. 43, pp. 94-108.
  4. Capone. G.. D'agostino, V.. Valle, S. D. and Guida. D.. 1992, "Influence of the Vibration Between Static and Kinetic Friction on Stick-slip Instability". Wear, Vol. 161, pp. 121-126. https://doi.org/10.1016/0043-1648(93)90460-4
  5. Capone, G.. D'agostino, V.. Valle, S. D. and Guida. D.. 1992. "Stick-slip Instability Analysis", Meccanica, Vol. 27, pp. 111-118. https://doi.org/10.1007/BF00420589
  6. Ruina, A. 1983, "Slip Instability and State Variable Friction Laws". Journal of Geophysical Research. Vol. 88. No. B12. pp. 10359-10370 https://doi.org/10.1029/JB088iB12p10359
  7. Popp, K. and Stelter. P.. 1990. "Stick-slip Vibrations and Chaos", Phil. Trans. R. Soc. Lond. A, Vol. 332. pp. 89-105. https://doi.org/10.1098/rsta.1990.0102
  8. Bengisu, M. T. and Akay, A., 1999. "Stickslip Oscillations: Dynamics of Frict ion and Surface Roughness", J. Acoust. Soc. Am.. Vol. 105, No. 1. pp. 194-205. https://doi.org/10.1121/1.424580
  9. Berman. A, D.. Ducker. W. A and Israelachvili, J. N, 1996, "Origir. and Characterization of Different Stick-slip Friction Mechanisms", Langmuir. Vol. 12, No. 19. pp. 4559-4563. https://doi.org/10.1021/la950896z
  10. Van De Velde, F. and De Baets, P.. 1996. "The Relationship Between Friction Force and Relative Speed During the Slip-phase of a Stick-slip Cycle". Wear, Vol. 219. pp. 220-226. https://doi.org/10.1016/S0043-1648(98)00213-0
  11. "The Friction Force During Stick-slip with Velocity Reversal", Wear. Vol. 216, pp. 138-149.
  12. You, H. I. and Hsia, J. H., 1995, "The Influence of Friction-speed Relation on the Occurence of Stick-slip Motion". ASME Journal of Tribology, Vol. 117, pp. 450-455. https://doi.org/10.1115/1.2831274
  13. Wiercigroch, M.. 1994. "A Note on the Switch Function for the Stick-slip Phenomenon", Journal of Sound and Vibration. Vol. 175. No. 5, pp. 700-704. https://doi.org/10.1006/jsvi.1994.1559
  14. Awrejcewicz, J.. 1988, "Chaotic Motion in a Nonlinear Oscillator with Friction". KSME International Journal, Vol. 2. No.2. pp. 104-109. https://doi.org/10.1007/BF02953669
  15. Awrejcewicz, J. and Delfs. J., 1990. "Dynamics of a Self-excited Stick-slip Cscillatcr with Two Degrees of Freedom Part II. Slip-stick, Slip-slip. Stick-slip Transitions, Periodic and Chaotic Orbits", European Journa. of Mechanics, A/Solids, Vol. 9. No.5. pp. 397-418.
  16. Galvanetto, U.. Bishop, S. Rand Briseghella, L.. 1995, "Mechanical Stick-slip vibrations", International Journal of Bifurcation and Chaos. Vol. 5, No.3. pp. 637-651. https://doi.org/10.1142/S0218127495000508
  17. Ouyang, H.. Mottershead, J. E.. Cartmell. M. P. and Brookfield, D. J.. 1999. "Friction-induced Vibration of an Elastic Slider on a Vibration Disc", International Journal of Mechanical Sciences, Vol. 41. pp. 325-336. https://doi.org/10.1016/S0020-7403(98)00059-9
  18. Shin. K.. Brennan, M. J.. Oh, J. E. and Harris, C. J., 2002, "Analysis of Disc Brake Noise Using a Two-degree of Freedom Model", Journal of Sound and Vibration, (will be published)
  19. Shin, K., Oh, J. E. and MichaeL J. B., 2002, "Nonlinear Analysis of Friction Induced Vibrations of a Two-degree-of-freedom Model for Disc Brake Squeal noise", JSME, (will be published)
  20. 이재응. 허인호. 이병림. 2000. "Stick-slip 마찰이 있는 비선형 진동 시스템의 규명에 관한 연구", 한국소음진동공학회지, Vol. 10, No.3, pp. 451-456.
  21. 최연선, 배철용, 2001, "정렬 불량을 갖는 마찰 진동계의 3자 유도 비선형 해석", 한국소음진동 공학회 추계학술대회논문집, pp. 79-84.

Cited by

  1. Identification of Damping Characteristics of Free-piston Stirling Engines via Nonlinear Dynamic Model Predictions vol.26, pp.3, 2016, https://doi.org/10.5050/KSNVE.2016.26.3.248