Abstract：Corrugated sleeves are cylindrical shells with a special bulge in the central region, which are also called corrugated sleeves in automotive engineering. Both ends of the corrugated sleeve are straight. Corrugated sleeves have a distinct flat region in their axial force-compressive displacement curves. Corrugated sleeves with this axial load characteristic are used to preload bearings and absorb energy. Therefore, the axial characteristics are quite important in many designs. The axial compression of a corrugated sleeve was simulated here using the finite element method in ABAQUS with the results verified against tests. The axial force-displacement curves were predicted for various parameters to analyze the influence of the geometric parameters on the axial load characteristics. The FEA results were then used with multi-objective optimization to minimize the maximum equivalent plastic strain and maximize the platform width using the Non-dominated Sorting Genetic Algorithm Ⅱ. This method can be used to optimize the designs of corrugated sleeves for various conditions.
[1] LIU Y, MONKABA V D. Forming simulation and stiffness prediction of a rear axle pinion bearing collapsible spacer[J/OL]. (2001-11-12)[2017-04-26]. http://papers.sae.org/2001-01-2803/. [2] QI Y M, ZHU X Z, DENG S P, et al. Research on spindle bearing pretightening based on spacer sleeve adjustment[J]. Applied Mechanics and Materials, 2014, 488-489:1087-1090. [3] 陈家瑞. 汽车构造(下册)[M]. 3版. 北京:机械工业出版社, 2009.CHEN J R. Automative structure (Part 2).[M]. 3rd ed. Beijing:Machiary industry Press, 2009. (in Chinese) [4] 钱伟长, 郑思梁. 轴对称园环壳的复变量方程和轴对称细环壳的一般解[J]. 清华大学学报(自然科学版), 1979(1):27-47.QIAN W Z, ZHENG S L. Equattions of symmetrical ring shells in complex quantities and their general solutions for slender ring shells[J]. Journal of Tsinghua University (Science and Technology), 1979(1):27-47. (in Chinese) [5] 钱伟长. 半圆弧波纹管的计算——细环壳理论的应用[J]. 清华大学学报(自然科学版), 1979(1):84-99.QIAN W Z. Calculation for semi-circular arc type corrugated tube-applications of the theory of slender ring shells[J]. Journal of Tsinghua University (Science and Technology), 1979(1):84-99. (in Chinese) [6] 朱卫平, 黄黔. 中细柔性圆环壳整体弯曲的一般解及在波纹管计算中的应用(Ⅳ)-型波纹管的计算[J]. 应用数学和力学, 2002, 23(10):1035-1040.ZHU W P, HUANG Q. General solution of the overall bending of flexible circular ring shells with moderately slender ratio and applications to the bellow(IV)-calculation for U-shaped bellow[J]. Applied Mathematics and Mechanics, 2002, 23(10):1035-1040. (in Chinese) [7] 王连东, 彭加耕, 刘助柏, 等. 汽车波形套复合缩径-胀形变形分析与求解[J]. 机械工程学报, 2002, 38(5):149-152.WANG L D, PENG J G, LIU Z B, et al. Deformation analysis and calculation of automobile corrugated sleeve by combined sinking-bulging technology[J]. Chinese Journal of Mechanical Engineering, 2002, 38(5):149-152. (in Chinese) [8] 王连东, 邱兰芳, 刘敏. 波形套工作特性的理论与试验研究[J]. 机械工程学报, 2005, 41(11):184-188.WANG L D, QIU L F, LIU M. Theoretical and experimental research on corrugated sleeve's working characteristics[J]. Journal of Mechanical Engineering, 2005, 41(11):184-188. (in Chinese) [9] SINGACE A A, EL-SOBKY H. Behaviour of axially crushed corrugated tubes[J]. International Journal of Mechanical Sciences, 1997, 39(3):249-261. [10] GHAZIJAHANI T G, DIZAJI H S, NOZOHOR J, et al. Experiments on corrugated thin cylindrical shells under uniform external pressure[J]. Ocean Engineering, 2015, 106:68-76. [11] 余显忠, 黄平辉, 揭钢, 等. 弹性隔套设计与仿真分析[J]. 现代制造工程, 2010(3):1-4.YU X Z, HUANG P H, JIE G, et al. Design and simulation analysis of the elastic sleeve[J]. Modern Manufacturing Engineering, 2010(3):1-4. (in Chinese) [12] 张平, 马建, 那景新. 波纹管耐撞性的多目标优化[J]. 振动与冲击, 2015, 34(15):12-16.ZHANG P, MA J, NA J X. Multi-objective optimization for crashworthiness of corrugated tubes[J]. Journal of Vibration and Shock, 2015, 34(15):12-16. (in Chinese) [13] WU S Y, LI G Y, SUN G Y, et al. Crashworthiness analysis and optimization of sinusoidal corrugation tube[J]. Thin-Walled Structures, 2016, 105:121-134. [14] YANG Z X, YAN J, CHEN J L, et al. Multi-objective shape optimization design for liquefied natural gas cryogenic helical corrugated steel pipe[J]. Journal of Offshore Mechanics and Arctic Engineering, 2017, 139(5), 051703. [15] ANDRIANOV I I, AWREJCEWICZ J, DISKOVSKY A A. Optimal design of a functionally graded corrugated cylindrical shell subjected to axisymmetric loading[J]. Archive of Applied Mechanics, 2018(7):1-13. [16] 桂良进, 范子杰, 王青春. 泡沫填充圆管的动态轴向压缩吸能特性[J]. 清华大学学报(自然科学版), 2004, 44(5):709-712.GUI L J, FAN Z J, WANG Q C. Energy-absorption properties of foam-filled circular tubes subjected to dynamic axial crushing[J]. Journal of Tsinghua University (Science and Technology), 2004, 44(5):709-712. (in Chinese) [17] 桂良进, 范子杰, 王青春. 泡沫填充圆管的轴向压缩能量吸收特性[J]. 清华大学学报(自然科学版), 2003, 43(11):1526-1529.GUI L J, FAN Z J, WANG Q C. Energy-absorption properties of foam-filled circular tubes subjected to axial crushing[J]. Journal of Tsinghua University (Science and Technology), 2003, 43(11):1526-1529. (in Chinese) [18] 刘文卿. 试验设计[M]. 北京:清华大学出版社, 2005.LIU W Q. Test design[M]. Beijing:Tsinghua University Press, 2005. (in Chinese) [19] FRENCH M. Fundamentals of optimization[M]. New York:Springer, 2018. [20] DEB K, PRATAP A, AGARWAL S, et al. A fast elitist multiobjective genetic algorithm:NSGA-Ⅱ[J]. IEEE Transactions on Evolutionary Computation, 2000, 6(2):182-197. [21] DEB K, AGRAWA R B. Simulated binary crossover for continuous search space[J]. Complex Systems, 1994, 9(3):115-148.
2019, Vol. 59 
