The centrifugal load of aeroengine turbine disks is a typical design-dependent load. The difficulties in variable density topology optimization with design-dependent loads involve the material attachment effect of low density elements, the non-monotonicity behaviour of the objective function, and other difficulties. This study first uses the Exponential Approximation of Material Properties (EAMP) to avoid the material attachment effect and improve the convergence speed. A new gray suppression method is then proposed to reduce the gray scale of the topological structure, and a load sensitivity suppression algorithm presented to solve the topology optimization problem. Numerical examples show the effectiveness of the proposed algorithm, with small overall element gray units and fast convergence speed. In the topology optimization of the radial section of the turbine disk, discussion of the load sensitivity suppression coefficient reveals the evolution law and intrinsic links between the topological structure of single-web turbine disks and twin-web turbine disks.
YAN Hao
,
WU Xiaoming
. Topology optimization and structure evolution of turbine disks based on load sensitivity suppression[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022
, 43(5)
: 225295
-225295
.
DOI: 10.7527/S1000-6893.2021.25295
[1] BRUYNEEL M, DUYSINX P. Note on topology optimization of continuum structures including self-weight[J]. Structural and Multidisciplinary Optimization, 2005, 29(4):245-256.
[2] 高彤, 张卫红, 朱继宏. 惯性载荷作用下结构拓扑优化[J]. 力学学报, 2009, 41(4):530-541. GAO T, ZHANG W H, ZHU J H. Structural topology optimization under inertial loads[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(4):530-541(in Chinese).
[3] 张晖, 刘书田, 张雄. 考虑自重载荷作用的连续体结构拓扑优化[J]. 力学学报, 2009, 41(1):98-104. ZHANG H, LIU S T, ZHANG X. Topology optimization of continuum structures subjected to self weight loads[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(1):98-104(in Chinese).
[4] YANG X Y, XIE Y M, STEVEN G P. Evolutionary methods for topology optimisation of continuous structures with design dependent loads[J]. Computers & Structures, 2005, 83(12-13):956-963.
[5] HUANG X, XIE Y M. Evolutionary topology optimization of continuum structures including design-dependent self-weight loads[J]. Finite Elements in Analysis and Design, 2011, 47(8):942-948.
[6] LEE E, MARTINS J R R A. Structural topology optimization with design-dependent pressure loads[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 233-236:40-48.
[7] 易垒, 文毅. 惯性载荷作用下火箭橇结构拓扑优化设计[J]. 应用力学学报, 2013, 30(1):80-85, 148. YI L, WEN Y. Topology optimization of rocket sled structure under inertial loads[J]. Chinese Journal of Applied Mechanics, 2013, 30(1):80-85, 148(in Chinese).
[8] CAIRO R R. Twin-web rotor disk:US5961287[P]. 1999-10-05.
[9] 董少静, 申秀丽, 康滨鹏, 等. 高推质比双辐板涡轮盘结构研究及光弹试验验证[J]. 航空动力学报, 2015, 30(1):114-120. DONG S J, SHEN X L, KANG B P, et al. Structureresearch and photoelastic test verification of twin-web turbine disk with high thrust-weight ratio[J]. Journal of Aerospace Power, 2015, 30(1):114-120(in Chinese).
[10] 张乘齐, 黄文周, 刘学伟, 等. 低惯量涡轮转子结构设计与优化[J]. 燃气涡轮试验与研究, 2013, 26(4):33-36, 50. ZHANG C Q, HUANG W Z, LIU X W, et al. Design and optimization of low inertia turbine rotor structure[J]. Gas Turbine Experiment and Research, 2013, 26(4):33-36, 50(in Chinese).
[11] RINDI A, MELI E, BOCCINI E, et al. Static and modal topology optimization of turbomachinery components[J]. Journal of Engineering for Gas Turbines and Power, 2016, 138(11):112602.
[12] XU H Y, GUAN L W, CHEN X, et al. Guide-Weight method for topology optimization of continuum structures including body forces[J]. Finite Elements in Analysis and Design, 2013, 75:38-49.
[13] 陆山, 赵磊. 双辐板涡轮盘/榫结构优化设计方法[J]. 航空动力学报, 2014, 29(4):875-880. LU S, ZHAO L. Structural optimization design method of twin-web turbine disk with tenon[J].Journal of Aerospace Power, 2014, 29(4):875-880(in Chinese).
[14] SIGMUND O. A 99 line topology optimization code written in Matlab[J]. Structural and Multidisciplinary Optimization, 2001, 21(2):120-127.
[15] 张昆鹏.变密度法拓扑优化插值模型及求解方法改进研究[D] 厦门:厦门大学,2016:22-24. ZHANG K P.Research on modified interpolation and solving of topology optimization based on variable density method.[D].Xiamen:Xiamen University,2016:22-24(in Chinese).
[16] FÉLIX L, GOMES A A, SULEMAN A. Topology optimization of the internal structure of an aircraft wing subjected to self-weight load[J]. Engineering Optimization, 2020, 52(7):1119-1135.
[17] Integrated High Performance Turbine Engine Technology (IHPTET)[R]. U.S. Department of Defense, 2006.
[18] BURGE J C. Gas turbine compressor spool with structural and thermal upgrades:US6267553[P]. 2001-07-31.
[19] HARDING B R, CURTISS D H. Contoured disk bore:US7241111[P]. 2007-07-10.
[20] VASILYEV B, SALNIKOV A, SEMENOV A, et al. Twin-web turbine discs:Part 1-design and analysis of their efficiency[C]//Proceedings of ASME Turbo Expo 2018:Turbomachinery Technical Conference and Exposition. New York:ASME, 2018.
[21] LI L, TANG Z H, LI H L, et al. Convective heat transfer characteristics of twin-web turbine disk with pin fins in the inner cavity[J]. International Journal of Thermal Sciences, 2020, 152:106303.
[22] YAO Q, ZHANG M C, LIU Y S, et al. Life reliability assessment of twin-web disk using the active learning kriging model[J]. Structural and Multidisciplinary Optimization, 2020, 61(3):1229-1251.
[23] JAIN N, SAXENA R. Effect of self-weight on topological optimization of static loading structures[J]. Alexandria Engineering Journal, 2018, 57(2):527-535.
[24] 徐燊, 朱顺鹏, 郝永振, 等. 基于临界面-损伤参量法的高压涡轮盘多轴疲劳寿命预测[J]. 航空学报, 2018, 39(9):221937. XU S, ZHU S P, HAO Y Z, et al. Multiaxial fatigue life prediction of an HPT disc based on critical plane-damage parameter[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(9):221937(in Chinese).
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