A Study on the Structural Characteristics of Miniature Metal Bellows in Joule-Thomson Micro-Cryocooler

줄-톰슨 마이크로 냉각기용 소형 금속 벨로우즈의 구조적 특성에 관한 연구

  • 이승하 (LIG넥스원(주) 전자광학연구센터) ;
  • 이태원 (금오공과대학교 기계공학부)
  • Published : 2008.09.01

Abstract

A miniature metal bellows is used to minimize the excessive flow of the cryogenic gas in Joule-Thomson micro cryocooler. It is made of metal alloy and its geometry is axisymmetric. The bellows is filled with high pressure gas. It contracts or expands in the axial direction for a wide change of temperature, because the pressure and volume inside the bellows must be satisfied with state equation of the gas. Therefore, in order to design the bellows in Joule-Thomson micro-cryocooler, it is important to evaluate deformation of the bellows under internal pressure exactly. Considering geometric nonlinearity, deformations analysis of the bellows were obtained by a commercial finite element code ANSYS, The bellows was modeled by 3-node axisymmetric shell elements with reduced integration. Experiments were also performed to prove the validity of proposed numerical analysis. The results by numerical analysis and experiments were shown in good agreements.

Keywords

References

  1. Ota, T. and Hamada, M., "On the Strength of Toroidal Shell (1st Report, The Proposition of the Solution)," Bul. JSME, Vol. 29, No. 197, pp. 142-158, 1963. https://doi.org/10.1299/kikai1938.29.142
  2. Clark, R. A., "Symptotic solutions of Elastic Shell Problem, Asymptotic solutions of Differential Equation and Their Applications," John Wiley and Sons, Inc., pp. 185-210, 1964.
  3. Laupa, A. and Weil, N. A., "Analysis of UShaped Expansion Joint," J. Apple. Mech., Vol. 29, No. 3, pp. 15-123, 1962. https://doi.org/10.1115/1.3636449
  4. Koh, B. K., Park, G. J. and Lee, W. I., "Development of a Bellows Finite Element for the Analysis of Piping System," Transactions of the KSME, Vol. 19, No. 6, pp. 1439-1450, 1995.
  5. Koh, B. K and Park, G. J., "Development of Bellows Finite Element Analysis Program and Simplified Formulas of Bellows and Shape Optimization," Transactions of the KSME(A), Vol. 21, No. 8, pp. 1195-1208, 1997.
  6. Kim, D. H. and Choi, M. J., "Vibration Analysis Model for Bellows Using Reduced Degree of Freedom in the Vehicle Exhaust System," KSPE Autumn Conference, pp. 659-663, 2001.
  7. Chien, S. B., Chen, L. T. and Chou, F. C., "A Study on the Transient Characteristics of a Self-regulating Joule-Thomson Cryocooler," Cryogenics, Vol. 36, No. 12, pp. 979-984, 1996. https://doi.org/10.1016/S0011-2275(96)00085-9
  8. Lee, S. E and Lee, T. W., "Deformation Analysis of Self-regulating Bellows in Joule-Thomson Cryocooler," Journal of the KSPE, Vol. 25, No. 4, pp. 100-107, 2008.
  9. Ahmad, S., Irons, B. M. and Zienkiewicz, O. C., "Analsis of Thick and Thin Shell Structures by Curved Element," Int. J. Numer. Methods Eng., Vol. 2, No. 2, pp. 419-451, 1970. https://doi.org/10.1002/nme.1620020310
  10. Zienkiewicz, O. C., Taylor, R. L. and Too, J. M., "Reduced Integration Techniques in General Analysis of Plates and Shells," Int. J. Numer. Methods Eng., Vol. 3, No. 2, pp. 275-290, 1971. https://doi.org/10.1002/nme.1620030211
  11. Hughes, T. J. R., Cohen, M. and Haron, M., "Reduced and Selective Integration Techniques in the Finite Element Analysis of Plates," Nuclear Eng. Desgn., Vol. 46, No. 1, pp. 203-222, 1978. https://doi.org/10.1016/0029-5493(78)90184-X
  12. Stolarski, H. and Belytschko, T., "Membrane Locking and Reduced Integration for Curved Elements," J. Apple. Mech., Vol. 49, No. 1, pp. 172-176, 1982. https://doi.org/10.1115/1.3161961
  13. Stolarski, H. and Belytschko, T., "Shear and Membrane locking in the Curved C0 Elements," Comp. Method in Appl. Mech. and Engrg., Vol. 41, No. 3, pp. 279-296, 1983. https://doi.org/10.1016/0045-7825(83)90010-5
  14. ANSYS, "Online Documentation for ANSYS V11.0," ANSYS Inc., 2007.
  15. Bathe, K. J., "Finte Element Procedures," Prentice-Hall, p. 419, 1996.
  16. Cook, R. D., Malkus, D. S. and Plesha, M. E., "Concepts and Applications of Finite Element Analysis," John Wiley and Sons, pp. 352-357, 1989.