# 3차원 프린팅에 의한 경량 밸브 디스크 제조를 위한 위상최적화 기반의 형상 설계

• Kim, Taehyung (Department of Aeronautical and Mechanical Engineering, Cheongju University)
• 김태형 (청주대학교 항공기계공학과)
• Received : 2018.10.26
• Accepted : 2018.12.12
• Published : 2018.12.31

#### Abstract

In this study, the lightweight design of butterfly valve disc component for power plant based on topology optimization was performed. Here, commercial finite element (FE) analysis software was used. The external shape of the basic disc model was not deformed, and the internal element density was removed to make it lightweight. Optimal design was performed each other after the disc plate and two brackets attached on the surface of the disc were separated. Once the optimal shapes were selected, they were assembled to build up the 3-D lightweight valve disc model. After applying pressure to this model, FE analysis was performed to confirm the structural safety.

본 연구에서는 위상최적화에 기초한 발전설비용 버터플라이 밸브 디스크 부품의 경량설계가 수행되었다. 이때 상용 유한요소해석 소프트웨어가 사용되었으며 기존 상용 밸브 디스크의 외형을 유지시키면서 내부의 불필요 공간을 제거하여 경량구조를 갖도록 하였다. 먼저 밸브 디스크의 원판과 브라켓을 분리하여 각각 최적설계 하였다. 최적의 형상이 선정되면 이들을 조립하여 3차원 경량 밸브 디스크 모델을 완성하였다. 이후 이 모델에 설계 압력을 적용하여 유한요소해석 후 구조적 안전성을 확인하였다.

#### Keywords

Fig. 2. Definition of internal element density for lightweight design of valve disc

Fig. 1. Butterfly valve disc

Fig. 3. Optimal shapes of the disc after FE analysis based on topology optimization

Fig. 4. First optimal shape of the disc thickness after FE analysis based on topology optimization

Fig. 5. Second optimal shape of the disc plane after FE analysis based on topology optimization

Fig. 6. Third optimal shape of the disc plane after FE analysis with topology optimization

Fig. 7. Third optimal shape of the disc plane after FE analysis with topology optimization

Fig. 8. Optimal three dimensional lightweight model after topology optimization

Fig. 9. FE model for structural analysis of the optimal valve disc and boundary conditions

Fig. 10. Effective stress and deformation after FE analysis of optimal 3-D valve disc model

Fig. 11. Optimal butterfly valve disc printed by 3D printer

#### Acknowledgement

Supported by : 청주대학교

#### References

1. Michell, A. G. M., 1904, The limits of economy of material in frame structures, Philosophical Magazine, Vol. 6(8), pp. 589-597.
2. Prager, W., Rozvany, G. N., 1977, Optimization of the structural geometry. In Bednarek A. R., Cesari, L.(Eds.), Dynamical systems, Proceedings of International Conference on Gainsville Florida, New York, pp. 265-293.
3. Bendsoe, M. P., Kikuchi, N., 1988, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, Vol. 71, pp. 197-224. https://doi.org/10.1016/0045-7825(88)90086-2
4. Dassault Systems, 2016, Topology and shape optimization with ABAQUS
5. NX8.0 Documentation, 2012
6. Hans, A. E., Niels, O., 2001, Topology optimization of continuum structures: A review, Applied Mechanics Reviews, Vol. 54(4), pp. 331-390. https://doi.org/10.1115/1.1388075
7. Stolpe, M., Svanberg, K., 2001, An alternative interpolation scheme for minimum compliance topology optimization, Structural Multidisciplinary Optimization, Vol. 22, pp. 116-124. https://doi.org/10.1007/s001580100129
8. Sigmund, O., Clausen, P. M., 2007, Topology optimization using a mixed formulation: An alternative way to solve pressure load problems, Computer Methods in Applied Mechanics and Engineering, Vol. 196, pp. 1874-1889. https://doi.org/10.1016/j.cma.2006.09.021
9. James, K. A., Hansen, J. S., Martins, J. R. R. A., 2009, Structural topology optimization for multiple load cases using a dynamic aggregation technique, Engineering Optimization, Vol. 41(12), pp. 1103-1118. https://doi.org/10.1080/03052150902926827
10. Martine, P. B., Niels, O., John, E. T., 1983, A variational formulation for multiciteria structural optimization, Journal of Structural Mechanics, Vol. 11, pp. 523-544. https://doi.org/10.1080/03601218308907456
11. KS D4101, 2011, Carbon steel castings, pp. 1-14.
12. Dassault Systems, 2017, ABAQUS User Manual.