# 벨로우즈에 대한 유한요소해석 프로그램 및 간편식의 개발과 형상최적설계

• Koh, Byung-Kab (Mechanical Engineering Technology Research Center, Hanyang University) ;
• Park, Gyung-Jin (Dept. of Mechanical Engineering, Hanyang University)
• 고병갑 (한양대학교 기계기술연구소) ;
• 박경진 (한양대학교 기계공학과)
• Published : 1997.08.01
• 128 16

#### Abstract

Bellows is a component in piping systems which absorbs mechanical deformation with flexibility. Its geometry is an axial symmetric shell which consists of two toroidal shells and one annular plate or conical shell. In order to analyze bellows, this study presents the finite element analysis using a conical frustum shell element. A finite element analysis is developed to analyze various bellows. The validity of the developed program is verified by the experimental results for axial and lateral stiffness. The formula for calculating the natural frequency of bellows is made by the simple beam theory. The formula for fatigue life is also derived by experiments. The shape optimal design problem is formulated using multiple objective optimization. The multiple objective functions are transformed to a scalar function by weighting factors. The stiffness, strength and specified stiffness are considered as the multiple objective function. The formulation has inequality constraints imposed on the fatigue limit, the natural frequencies, and the manufacturing conditions. Geometric parameters of bellows are the design variables. The recursive quadratic programming algorithm is selected to solve the problem. The results are compared to existing bellows, and the characteristics of bellows is investigated through optimal design process. The optimized shape of bellows is expected to give quite a good guideline to practical design.

#### Keywords

Bellows;Conical Frustum Shell Element;Multiple Optimization Method;Weighting Objective Method

#### References

1. 한국자동차공학회지 v.11 no.2 벨로우즈 문제 해석을 위한 수정 에너지론 이완익;김태완
2. The Finite Element Method Zienkiewicz, O. C.
3. 벨로우즈가 장착된 기계시스템의 상·하향식 설계론 고병갑
4. 有限要素法ハント"フ"ック 鷲律久一郞
5. International Journal of Vehicle Design v.17 no.3 Design of an Automobile Exhaust System using a Top-Down Approach Design Methodology Koh, B. K.;Park, G. J.
6. Introduction to Optimum Design Arora, J. S.
7. Multicriterion Optimization in Engineering with FORTRAN Programs Osyczka, A.
8. IUTAM Symp. on Optimization in Structural Design On the Optimum Shapes of Some Axisymmetric Shells Hamada, M.
9. Asymptotic solutions of Elastic Shell Problem, Asymptotic solutions of Differential Equations and Their Applications Clark, R. A.
10. IDESIGN User's Manual Version 3.5, Optimal Design Laboratory Arora, J. S.;Tseng, C. H.
11. 산업가학연구소논문집 v.35 자동차용 벨로우즈의 설계기준에 관한 연구 이완익;하성규;고병갑
12. 대한기계학회논문집 v.19 no.6 배관시스템 해석을 위한 벨로우즈 유한요소의 개발 고병갑;박경진;이완익
13. Finite Element Programs for Structural Vibrations Ross, C. T. F.
14. Standards of the Expansion Joint Manufacturers Association, Inc.(Sixth Edition) Expansion Joint Manufacturers Association, Inc.
15. ANSYS Engineering Analysis System User's Manual Revision 5.0a Swanson, J.
16. Transaction of the ASME, Journal of Pressure & Vessels Technology v.114 Fatigue and Creep-Fatigue Life Evaluation of U-shaped Bellows Tsukimori, K.(et al.)
17. KSME J. v.9 no.1 Mechanical Behavior of U-shaped Bellows and Shape Optimal Design Using Multiple Objective Optimization Method Koh, B. K.;Park, G. J.;Lee, W. I.
18. 한국자동차공학회논문집 v.3 no.6 U형 벨로우즈의 유한요소해석과 특정강성을 위한 형상최적 설계 고병갑;서용진;박경진
19. M. Thesis, Dept. of Applied Mechanics, IIt Optimum Design of Expansion Bellows for Piping Systems Chakraverti, G.
20. J. Appl. Mech. v.29 no.1 Analysis of U Shaped Expansion Joint Laupa, A.;Weil, N. A.
21. Engineering Optimization v.4 Optimum Design of Flanged and Flued Expansion Joints Bhavikatti, S. S.(et al.)
22. Bul. JSME v.29 no.197 On the Strength of Toroidal shells (1st Report, The Proposition of the Solution) Ota, T.(et al.)
23. ASME Boiler and Pressure Vessel Code for Design by Analysis in Section III and VIII, Division 2
24. The 6th International Pacific Conference on Automotive Engineering v.1 An Optimal Design of the Bellows in the Automobile Exhaust System Lee, W. I;Koh, B. K.;Park, G. J.