轮胎破片冲击机身的非等比例相似模型研究

康煌 王舒 闫文敏 崔海林 郭香华 张庆明

康煌, 王舒, 闫文敏, 崔海林, 郭香华, 张庆明. 轮胎破片冲击机身的非等比例相似模型研究[J]. 爆炸与冲击, 2022, 42(7): 073201. doi: 10.11883/bzycj-2021-0359
引用本文: 康煌, 王舒, 闫文敏, 崔海林, 郭香华, 张庆明. 轮胎破片冲击机身的非等比例相似模型研究[J]. 爆炸与冲击, 2022, 42(7): 073201. doi: 10.11883/bzycj-2021-0359
KANG Huang, WANG Shu, YAN Wenmin, CUI Hailin, GUO Xianghua, ZHANG Qingming. A study of incomplete similar models for tyre fragment impact on fuselage structures[J]. Explosion And Shock Waves, 2022, 42(7): 073201. doi: 10.11883/bzycj-2021-0359
Citation: KANG Huang, WANG Shu, YAN Wenmin, CUI Hailin, GUO Xianghua, ZHANG Qingming. A study of incomplete similar models for tyre fragment impact on fuselage structures[J]. Explosion And Shock Waves, 2022, 42(7): 073201. doi: 10.11883/bzycj-2021-0359

轮胎破片冲击机身的非等比例相似模型研究

doi: 10.11883/bzycj-2021-0359
详细信息
    作者简介:

    康 煌(1995- ),男,硕士,助理工程师,kh1881020@163.com

    通讯作者:

    王 舒(1968- ),男,硕士,正高级工程师,wszdm@163.com

  • 中图分类号: O383

A study of incomplete similar models for tyre fragment impact on fuselage structures

  • 摘要: 为降低机身结构抗冲击性能的实验成本,利用相似理论建立机身的非等比例缩放模型,开展模型实验是行之有效的方法。基于量纲分析的方法,建立Johnson-Cook线性应变率函数的修正关系;鉴于生产制造技术的限制,考虑扭曲厚度的非等比例机身模型对相似性行为的影响,采用指数函数法建立了非等比例模型的相似修正关系。通过对比实验中破片冲击过程的变形形态、靶板的应变时间历程曲线和最终变形轮廓,验证了数值模型的有效性。此外,分析了破片偏航姿态、机身材料、厚度和质量等因素对机身结构抗冲击性能的影响。结果表明:(1) 150 m/s的冲击速度下,破片冲击角度90º和着靶角度180º是最严苛的冲击条件。综合多种因素,分析认为3.5 mm厚的钛合金为机身结构的最佳选择,并以此作为全尺寸原型验证相似模型;另外,提出了一种可以快速获取缩比模型的设计方法。(2)应变率效应对轮胎破片冲击机身结构的影响并不显著,等比例缩放模型与原型结果吻合较好。(3)厚度扭曲的非等比例模型能够有效地预测原型结构的变形行为;虽然,在时间尺度上,模型与原型存在一定的偏差;但是,在空间尺度上,非等比例相似模型能够有效地修正扭曲厚度造成中心最大挠度的预测误差,修正后的最大误差不超过5.1%,这表明该方法能够有效地指导机身结构的相似模型设计。
  • 图  1  高速摄影[2]和数值计算分别得到的橡胶轮胎破片以30º冲击角度和135 m/s的冲击速度撞击铝合金靶板后不同时刻的变形形貌

    Figure  1.  Deformation morphologies of the rubber tire fragment with the initial impact velocity of 135 m/s at the impact angle of 30º after its impacting on an aluminum alloy target at different times obtained by high-speed photography[2] and simulation

    图  2  不同冲击角度下靶板的空间变形轮廓

    Figure  2.  Spatial deformation profiles of target plates at different impact angles

    图  3  中心监测点的应变时间历程曲线

    Figure  3.  Time history of strain at the central point

    图  4  不同姿态的破片冲击靶板的空间位置

    Figure  4.  Spatial positions of the fragments with different attitudes impacting into target plates

    图  5  靶板的最终变形轮廓曲线

    Figure  5.  Residual deformation profiles of target plates

    图  6  靶板中心挠度的时间历程曲线

    Figure  6.  Deflection time history at the center points of target plates

    图  7  轮胎破片正侵彻机身结构的有限元模型

    Figure  7.  The finite element model for a tire fragment impacting the fuselage

    图  8  机身中心点的瞬时最大挠度的时间历程曲线

    Figure  8.  Time histories of the maximum instantaneous deflections at the centers of the fuselages

    图  9  瞬时最大挠度时刻靶板中心的等效应力和有效塑性应变云图

    Figure  9.  Equivalent stress and plastic strain of the fuselage structures at the instant of the maximum transient deformation

    图  10  扭曲厚度模型的修正函数${f_2}$与厚度变化因子${\alpha _x}/\alpha $的理想关系曲线[10]

    Figure  10.  The ideal curve of function${f_2}$and the thickness factor${\alpha _x}/\alpha $[10]

    图  11  相似模型设计流程

    Figure  11.  Design process for the scaled-down model

    图  12  对比未修正的等比例模型和原型的中心变形的时间历程曲线

    Figure  12.  Comparison of deformation-time curves between the uncorrected scaled models and the prototype

    图  13  对比非等比例模型与原型的挠度时间历程曲线

    Figure  13.  Comparison of deformation-time curvesfor the center points of the plates

    图  14  非等比例模型与原型靶板的最大变形时刻的轮廓图

    Figure  14.  The maximum deformation profiles of the plates for the incomplete scaling model and prototype

    表  1  机身材料参数[3-4]

    Table  1.   Material parameters of fuselage[3-4]

    材料$\rho $/(g·cm−3)E/GPaμA/MPaB/MPaNCm
    Al 20242.71 720.332254060.340.0151.0
    Ti-6Al-4V4.451100.418623310.340.0120.8
    下载: 导出CSV

    表  2  靶板中心点最终挠度的实验结果[2]与模拟结果的对比

    Table  2.   Comparison of the residual deformations at the centers of the target plates between experiment[2] and simulation

    破片尺寸靶板尺寸β/(º)v/(m·s−1)靶板中心点的最终挠度
    实验值/mm[2]模拟值/mm相对偏差/%
    30 mm×15 mm×60 mm260 mm×260 mm×1.6 mm301352.9 2.418.6
    30 mm×15 mm×60 mm260 mm×260 mm×1.6 mm301368.610.117.4
    下载: 导出CSV

    表  3  不同冲击条件下方形铝靶板中心的响应参数

    Table  3.   Response parameters at the centers of square aluminum plates under different impact conditions

    β/(º)θ/(º)v/(m·s−1)瞬时最大挠度/mm最终挠度/mm脉宽/ms
    30301507.822.041.028
    1207.283.161.300
    606012.17.801.178
    15014.610.41.420
    909015.010.21.260
    18017.213.61.450
    下载: 导出CSV

    表  4  机身的几何结构及响应参数

    Table  4.   Geometric structure and response parameters of the fuselage

    材料厚度/mm质量/kg瞬时最大挠度/cm
    Al01铝合金4.092.99.35
    5.0116.27.91
    6.0139.46.77
    钛合金3.0113.29.08
    3.5132.07.28
    4.0150.96.24
    下载: 导出CSV

    表  5  对比模型与原型的瞬时最大挠度

    Table  5.   Comparison of the maximum displacement between the model and the prototype

    对比源比例因子靶板厚度/mm原型冲击速度/(m·s−1)靶板挠度/cm挠度相对偏差/%模型修正速度/(m•s−1)
    原型13.5001507.28
    模型1/100.3507.132.06151.9
    1/80.4387.250.41151.7
    1/50.7007.260.27151.4
    1/21.7507.171.51150.6
    下载: 导出CSV

    表  6  不同指数对应的冲击速度和挠度

    Table  6.   Impact velocities and central deflections in relation to different exponents

    nvm/(m·s−1)${\alpha _{ {x_1 } } }=2.0$ $\alpha _{ {x_{2} } }=3.5$
    $\left| { { {\text{δ} }_{ {x_1} } } - { {\text{δ} }_{ {x_2} } } } \right|/{ {\text{δ} }_{ {x_1} } }$/%
    $ {v_{{x_1}}} $/(m·s−1)${ {\text{δ} }_{ {x_1} } }$/cm$ {v_{{x_2}}} $/(m·s−1)${ {\text{δ} }_{ {x_2} } }$/cm
    1.00150279.98.66 463.27.7412
    1.05300.08.88 525.08.208
    1.12310.69.10 558.98.507
    1.15321.59.25595.18.963
    下载: 导出CSV

    表  7  对比原型与模型的靶板瞬时最大挠度

    Table  7.   Comparison of the maximum deflection between the prototype and models

    模型缩放因子扭曲因子 机身板厚/mm冲击速度/(m·s−1)靶板挠度/cm与原型挠度的相对偏差 /%
    原型11.003.5150.07.28
    扭曲非等
    比例模型
    1/82.291.0150.02.1271.9
    2.741.2150.01.6178.9
    3.431.5150.01.0985.0
    修正后的扭曲
    厚度模型
    1/82.291.0329.67.58 4.1
    2.741.2484.27.65 5.1
    3.431.5625.97.13 2.1
    下载: 导出CSV
  • [1] 张建敏. 飞机轮胎爆破模式浅析 [J]. 力学季刊, 2014, 35(1): 139–148. DOI: 10.15959/j.cnki.0254-0053.2014.01.019.

    ZHANG J M. A brief study on damaging effects of Aeroplane tire and wheel failures [J]. Chinese Quarterly of Mechanics, 2014, 35(1): 139–148. DOI: 10.15959/j.cnki.0254-0053.2014.01.019.
    [2] MINES R A W, MCKOWN S, BIRCH R S. Impact of aircraft rubber tyre fragments on aluminium alloy plates: Ⅰ: experimental [J]. International Journal of Impact Engineering, 2007, 34(4): 627–646. DOI: 10.1016/j.ijimpeng.2006.02.005.
    [3] KARAGIOZOVA D, MINES R A W. Impact of aircraft rubber tyre fragments on aluminium alloy plates: Ⅱ: numerical simulation using LS-DYNA [J]. International Journal of Impact Engineering, 2007, 34(4): 647–667. DOI: 10.1016/j.ijimpeng.2006.02.004.
    [4] JIA S Q, WANG F S, YU L J, et al. Numerical study on the impact response of aircraft fuselage structures subjected to large-size tire fragment [J]. Science Progress, 2020, 103(1): 36850419877744. DOI: 10.1177/0036850419877744.
    [5] 杨娜娜, 赵天佑, 陈志鹏, 等. 破片冲击作用下舰船复合材料结构损伤的近场动力学模拟 [J]. 爆炸与冲击, 2020, 40(2): 023302. DOI: 10.11883/bzycj-2019-0019.

    YANG N N, ZHAO T Y, CHEN Z P, et al. Peridynamic simulation of damage of ship composite structure under fragments impact [J]. Explosion and Shock Waves, 2020, 40(2): 023302. DOI: 10.11883/bzycj-2019-0019.
    [6] 陈映秋, 杨永谦. 相似理论在分节驳结构模型试验中的应用 [J]. 中国造船, 1985(4): 56–64.

    CHEN Y Q, YANG Y Q. The application of similitude theory in integrated barge model test [J]. Shipbuilding of China, 1985(4): 56–64.
    [7] 秦健, 张振华. 原型和模型不同材料时加筋板冲击动态响应的相似预报方法 [J]. 爆炸与冲击, 2010, 30(5): 511–516. DOI: 10.11883/1001-1455(2010)05-0511-06.

    QIN J, ZHANG Z H. A scaling method for predicting dynamic responses of stiffened plates made of materials different from experimental models [J]. Explosion and Shock Waves, 2010, 30(5): 511–516. DOI: 10.11883/1001-1455(2010)05-0511-06.
    [8] 沈雁鸣, 陈坚强. 超高速碰撞相似律的数值模拟验证 [J]. 爆炸与冲击, 2011, 31(4): 343–348. DOI: 10.11883/1001-1455(2011)04-0343-06.

    SHEN Y M, CHEN J Q. Numerically simulating verification of the comparability rule on hypervelocity impact [J]. Explosion and Shock Waves, 2011, 31(4): 343–348. DOI: 10.11883/1001-1455(2011)04-0343-06.
    [9] 杨亚东, 李向东, 王晓鸣, 等. 钢筋混凝土结构内爆炸相似模型试验研究 [J]. 南京理工大学学报(自然科学版), 2016, 40(2): 135–141. DOI: 10.14177/j.cnki.32-1397n.2016.40.02.002.

    YANG Y D, LI X D, WANG X M, et al. Experimental study on similarity model of reinforced concrete structure under internal explosion [J]. Journal of Nanjing University of Science and Technology, 2016, 40(2): 135–141. DOI: 10.14177/j.cnki.32-1397n.2016.40.02.002.
    [10] OSHIRO R E, ALVES M. Predicting the behaviour of structures under impact loads using geometrically distorted scaled models [J]. Journal of the Mechanics and Physics of Solids, 2012, 60(7): 1330–1349. DOI: 10.1016/j.jmps.2012.03.005.
    [11] KONG X S, LI X, ZHENG C, et al. Similarity considerations for scale-down model versus prototype on impact response of plates under blast loads [J]. International Journal of Impact Engineering, 2017, 101: 32–41. DOI: 10.1016/j.ijimpeng.2016.11.006.
    [12] KANG H, GUO X H, ZHANG Q M, et al. Predicting the behavior of armored plates under shallow-buried landmine explosion using incomplete scaling models [J]. International Journal of Impact Engineering, 2021, 156: 103970. DOI: 10.1016/j.ijimpeng.2021.103970.
    [13] MAZZARIOL L M, OSHIRO R E, ALVES M. A method to represent impacted structures using scaled models made of different materials [J]. International Journal of Impact Engineering, 2016, 90: 81–94. DOI: 10.1016/j.ijimpeng.2015.11.018.
    [14] 徐坤. 典型结构响应相似律的应变率效应研究 [D]. 北京: 北京理工大学, 2016: 78. DOI: 10.26948/d.cnki.gbjlu.2016.000280.

    XU K. Research on scaling law of typical structure on strain rate effect [D]. Beijing, China: Beijing Institute of Technology, 2016: 78. DOI: 10.26948/d.cnki.gbjlu.2016.000280.
    [15] 苏子星, 何继业. 基于Cowper-Symonds方程的相似理论修正方法 [J]. 爆炸与冲击, 2018, 38(3): 654–658. DOI: 10.11883/bzycj-2016-0308.

    SU Z X, HE J Y. Modified method for scaling law based on Cowper-Symonds equation [J]. Explosion and Shock Waves, 2018, 38(3): 654–658. DOI: 10.11883/bzycj-2016-0308.
    [16] 刘源, 皮爱国, 杨荷, 等. 非等比例缩比侵彻/贯穿相似规律研究 [J]. 爆炸与冲击, 2020, 40(3): 033302. DOI: 10.11883/bzycj-2019-0086.

    LIU Y, PI A G, YANG H, et al. Study on similarity law of non-proportionally scaled penetration/perforation test [J]. Explosion and Shock Waves, 2020, 40(3): 033302. DOI: 10.11883/bzycj-2019-0086.
    [17] 陈材, 石全, 尤志锋, 等. 圆柱形弹药空气中爆炸相似性规律 [J]. 爆炸与冲击, 2019, 39(9): 092202. DOI: 10.11883/bzycj-2018-0255.

    CHEN C, SHI Q, YOU Z F, et al. Similarity law of cylindrical ammunition explosions in air [J]. Explosion and Shock Waves, 2019, 39(9): 092202. DOI: 10.11883/bzycj-2018-0255.
    [18] Livermore Software Technology Corporation. LS-DYNA keyword user’s manual: Volume Ⅱ: material model [M]. Livermore, California, USA: Livermore Software Technology Corporation, 2018.
    [19] NEUBERGER A, PELES S, RITTEL D. Springback of circular clamped armor steel plates subjected to spherical air-blast loading [J]. International Journal of Impact Engineering, 2009, 36(1): 53–60. DOI: 10.1016/j.ijimpeng.2008.04.008.
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出版历程
  • 收稿日期:  2021-11-03
  • 修回日期:  2021-11-30
  • 网络出版日期:  2022-06-06
  • 刊出日期:  2022-07-25

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