Transactions of the Korean Society for Noise and Vibration Engineering (한국소음진동공학회논문집)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
권호 표지
DOI QR코드

DOI QR Code

Vibro-acoustic Characteristics of a Disk Brake Rotor with a Narrow Radial Slot

좁은 반경방향 슬롯을 가진 디스크 브레이크 로터의 소음방사 특성

  • 이형일 (경북대학교 기계자동차공학부)
  • Published : 2009.11.20
Download PDF
⟨ Previous Next ⟩

Abstract

Vibro-acoustic characteristics of a simplified disk-brake rotor containing a narrow radial slot are studied using a semi-analytical procedure. First, modal sound radiations for flexural and radial modes of a generic annular disk having identical key dimension and slot(with free boundaries) are defined using pre-developed analytical solutions based on the modal vibrations from finite element model. The analytical solutions are validated by fully computational methods. Second, sound radiation from a simplified brake rotor simulated using sound radiation solution of the generic disk based on the rotor eigensolutions computed using a finite element code. Predictions by the semi-analytical method matched well numerical calculations using finite element and boundary element method. Finally, sound radiation and vibration characteristics for the example rotor due to a harmonic excitation fixed to the rotor or rotating around the rotor are also obtained.

좁은 슬롯을 포함한 디스크 브레이크 로터의 소음 방사특성을 전산해석과 이론적 계산을 합성한 방법으로 검토하였다. 첫 단계로 로터와 기본 치수가 동일하고 동일한 슬롯을 보유한 후판 환형 디스크의 소음방사 특성을 유한요소해석을 구한 모달 진동 데이터를 바탕으로 기존의 해법을 이용하여 계산하고 수치해석결과로 검증하였다. 다음으로 이 결과를 유한요소해석으로 구한 샘플 로터의 고유진동 특성에 적용, 고유진동으로 인한 소음방사를 계산한 다음 그 결과를 경계요소법을 이용하여 검증하였다. 마지막으로 이 결과를 바탕으로 로터에 고정된 조화가진 및 로터 주위를 회전하는 조화력에 의해 방사되는 소음 및 진동 특성을 검토하였다.

Keywords

References

  1. Murakami, H., Tsunada, N. and Kitamura, T., 1984, 'A Study Concerned with a Mechanism of Disc-brake Squeal,' SAE Technical Paper 841233
  2. Flint, J. and HultÈn, J., 2002, 'Liningdeformation- induced Modal Coupling as Squeal Generator in a Distributed Parameter Disc Brake Model,' Journal of Sound and Vibration, Vol. 254, No. 1, pp. 1-21 https://doi.org/10.1006/jsvi.2001.4052
  3. Hu, Y. K. and Nagy, L. I., 1997, 'Brake Squeal Analysis by Using Nonlinear Transient Finite Element Method,' SAE Technical Paper 971510
  4. Kung, S. W., Dunlap, K. B. and Ballinger, R. S., 2000, 'Complex Eigenvalue Analysis for Reducing Low Frequency Squeal,' SAE Technical Paper 2000-01-0444
  5. Lee, H. and Singh, R., 2004, 'Determination of Sound Radiation from a Simplified Disk Brake Rotor Using a Semi-analytical Method,' Noise Control Engineering Journal, Vol. 52, No. 5, pp. 457-472
  6. McDaniel, J. G., Moore, J., Chen, S. and Clarke, C. L., 1999, 'Acoustic Radiation Models of Brake Systems from Stationary LDV Measurement,' Proc. IMEC 99, Nashville,Tennessee
  7. Fieldhouse, J. D., Steel, W. P., Talbot, C. J. and Siddiqui, M. A., 2004, 'Rotor Asymmetry Used to Reduce Disc Brake Noise,' SAE Technical Papers 2004-01-2797
  8. Mindlin, R. D. and Deresiewicz, H., 1954, 'Thickness-shear and Flexural Vibration of a Circular Disk' ASME Journal of Applied Physics Vol. 25, No. 10, pp. 1329-1332 https://doi.org/10.1063/1.1721554
  9. Mcgee, O. G., Huang, C. S. and Leissa, A. W., 1995, 'Comprehensive Exact Solutions for Free Vibrations of Thick Annular Sectorial Plates with Simply Supported Radial Edges,' International Journal of Mechanical Science, Vol. 37, No. 5, pp. 537-566 https://doi.org/10.1016/0020-7403(94)00050-T
  10. Lee, H. and Singh, R., 2005, 'Acoustic Radiation from Out-of-plane Modes of an Annular Disk Using Thin and Thick Plate Theories,' Journal of Sound and Vibration, Vol. 282, No. 1-2, pp. 313-339 https://doi.org/10.1016/j.jsv.2004.02.059
  11. Irie, T., Yamada, G. and Muramoto, Y., 1984, 'Natural Frequencies of In-plane Vibration of Annular Plates,' Journal of Sound Vibration, Vol. 97, No. 1, pp. 171-175 https://doi.org/10.1016/0022-460X(84)90479-6
  12. Lee, H., 2005, 'Acoustic Radiation from Radial Vibration Modes of a Thick Annular Disk,' Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 9, No. 6, pp. 1210-1217
  13. Yu, R. C. and Mote, C. D. JR., 1987, 'Vibration and Parametric Excitation in Asymmetric Circular Plates under Moving Load,' Journal of Sound and Vibration, Vol. 119, No.3, pp. 409-427 https://doi.org/10.1016/0022-460X(87)90406-8
  14. Shen, I. Y. and Mote, C. D. JR., 1992, 'Dynamic Analysis of Finite Linear Elastic Solids Containing Small Elastic Imperfections: Theory with Application to Asymmetric Circular Plates,' Journal of Sound and Vibration, Vol. 155, No. 3, pp. 443-465 https://doi.org/10.1016/0022-460X(92)90711-6
  15. Honda, Y., Matsuhisa, H. and Sato, S., 1985, 'Modal Response of a Disk to a Moving Concentrated Harmonic Force,' Journal of Sound and Vibration, Vol. 102, No. 4, pp. 457-472 https://doi.org/10.1016/S0022-460X(85)80107-3
  16. Lee, M. R. and Singh, R., 1994, 'Analytical Formulations for Annular Disk Sound Radiation Using Structural Modes,' Journal of Acoustical Society of America, Vol. 95, No. 6, pp. 3311-3323 https://doi.org/10.1121/1.409993
  17. Lee, H. and Singh, R., 2005, 'Comparison of Two Analytical Methods Used to Calculate Sound Radiation from Radial Vibration Modes of A Thick Annular Disk,' Journal of Sound and Vibration, Vol. 285, No. 4-5, pp. 1210-1216 https://doi.org/10.1016/j.jsv.2004.11.002
  18. Gibbs, G. P., Clark, R. L., Cox, D. E. and Vipperman, J. S., 2000, 'Radiation Modal Expansion: Application to Active Structural Acoustic Control,' Journal of Acoustical Society of America, Vol. 107, No. 1, pp. 332-339 https://doi.org/10.1121/1.428307
  19. Bai, M. R. and Tsao, M., 2002, 'Estimation of Sound Power of Baffled Planar Sources Using Radiation Matrices,' Journal of Acoustical Society of America, Vol. 112, No. 3, pp. 876-883 https://doi.org/10.1121/1.1499133
  20. Lee, H. and Singh, R., 2005, 'Self and Mutual Radiation from Flexural and Radial Modes of a Thick Annular Disk,' Journal of Sound and Vibration, Vol. 286, No. 4-5, pp. 1032-1040 https://doi.org/10.1016/j.jsv.2005.01.008
  21. I-DEAS User’s manual Version 11 (UGS Corporation, USA, 2006)
  22. SYSNOISE User’s Manual Version 5.6 (Numerical Integration Technologies N.V., Belgium, 2005)