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Article(id=1228654093296661149, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228654089437901468, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.12.015, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1672502400000, receivedDateStr=2023-01-01, revisedDate=1676304000000, revisedDateStr=2023-02-14, acceptedDate=null, acceptedDateStr=null, onlineDate=1770863563130, onlineDateStr=2026-02-12, pubDate=1735315200000, pubDateStr=2024-12-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770863563130, onlineIssueDateStr=2026-02-12, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770863563130, creator=13701087609, updateTime=1770863563130, updator=13701087609, issue=Issue{id=1228654089437901468, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='12', pageStart='1993', pageEnd='2167', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770863562211, creator=13701087609, updateTime=1770863940325, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228655675413299456, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228654089437901468, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228655675413299457, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228654089437901468, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=2132, endPage=2140, ext={EN=ArticleExt(id=1228654093560902305, articleId=1228654093296661149, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Optimization and experimental analysis of pyramid lattice energy absorption device of energy absorption hydraulic support, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to improve the energy absorption and safety of the energy absorption hydraulic support，a multi-layer lattice energy absorption device is designed. The basic structure of pyramid lattice energy absorption device is designed according to the structure and energy absorption space of energy absorption support column. The maximum energy absorption of the energy absorption device，the maximum mean of the support force within the allowable range，and the minimum fluctuation coefficient of the support force are taken as the optimization objective function，the base diameter and span of the pyramid cell are taken as the optimization design variables，and the constraint conditions are taken as the peak and mean of the support force of the energy absorption device within the allowable range. The Workbench software is used to optimize the structural parameters of the energy absorption device with the pyramid height of 30 mm，40 mm and 50 mm respectively. Three groups of optimization solutions are obtained and the optimal structural parameters are determined by comparative analysis. The single-layer energy absorption device with the optimal parameters reduced in the compression experiment was used for experimental analysis，and the results show that the absorption energy is 4.18716 kJ. The calculated energy absorption energy of the original single-layer energy absorption device is 113.05332 kJ，and the energy absorption energy of the whole energy absorption device is 565.2666 kJ. The relative error between the experimental results and the simulation results is only -9.92%. The energy absorption capacity of the new energy absorption device is at least 50% higher than that of the traditional thin-wall structure energy absorption device，which proves the effectiveness of the optimized design and the high energy absorption capacity of the energy absorption device.

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为提高吸能液压支架的吸能性进而提高其安全性，设计了一种多层点阵吸能构件。根据吸能构件立柱的结构及吸能空间设计了金字塔点阵吸能构件的基本结构。以吸能构件的吸能最大、支撑力均值在允许范围内最大及支撑力波动系数最小为优化目标函数，以金字塔胞体的立足直径和跨度为优化设计变量，以吸能构件的支撑力峰值和支撑力均值在允许范围内为约束条件，利用Workbench软件分别对金字塔高度为30，40，50 mm的吸能构件结构参数进行多目标优化设计，得到三组优化解并通过对比分析确定最佳结构参数。采用压缩试验对等比例缩小的最优参数的单层吸能构件进行试验分析，结果显示其吸能量为4.18716 kJ，计算得到原尺寸单层吸能构件吸能量为113.05332 kJ，吸能构件整体吸能量为565.2666 kJ，与仿真结果相对误差仅为-9.92%。该吸能构件比传统薄壁结构吸能构件的吸能性提高50%以上，证明了优化设计的有效性和吸能构件的高吸能性。

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沈佳兴（1990—），男，博士，副教授。E-mail：。

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沈佳兴（1990—），男，博士，副教授。E-mail：。

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沈佳兴（1990—），男，博士，副教授。E-mail：。

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figureFileSmall=HuU+O2Yj/8zYTASmVMcOlQ==, figureFileBig=sXHAKTw8WkJO2y1x2lTGMw==, tableContent=null), ArticleFig(id=1228654111948730686, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228654093296661149, language=CN, label=图21, caption=吸能曲线, figureFileSmall=HuU+O2Yj/8zYTASmVMcOlQ==, figureFileBig=sXHAKTw8WkJO2y1x2lTGMw==, tableContent=null), ArticleFig(id=1228654112028422467, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228654093296661149, language=EN, label=Tab.1, caption=

Optimization results of cell body parameters

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方案高度h/mm优化结果a/mm优化结果d/mm
13039.713.8
24030.513.7
35034.614.6
), ArticleFig(id=1228654112137474378, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228654093296661149, language=CN, label=表1, caption=

胞体参数优化结果

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方案高度h/mm优化结果a/mm优化结果d/mm
13039.713.8
24030.513.7
35034.614.6
), ArticleFig(id=1228654112212971854, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228654093296661149, language=EN, label=Tab.2, caption=

Dimensional relationship of physical quantities

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物理量符号量纲
材料密度ρρ
弹性模量EρL2T-2
压缩位移δL
压缩时间TT
几何尺寸LL
支撑力FρL4T-2
吸能量QρL5T-2
), ArticleFig(id=1228654112322023763, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228654093296661149, language=CN, label=表2, caption=

物理量的量纲关系

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物理量符号量纲
材料密度ρρ
弹性模量EρL2T-2
压缩位移δL
压缩时间TT
几何尺寸LL
支撑力FρL4T-2
吸能量QρL5T-2
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Dimensional matrix

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指数物理量ρTL
αρ100
bE1-22
cδ001
dT010
eL001
fF1-24
gQ1-25
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量纲矩阵

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指数物理量ρTL
αρ100
bE1-22
cδ001
dT010
eL001
fF1-24
gQ1-25
), ArticleFig(id=1228654112577876319, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228654093296661149, language=EN, label=Tab.4, caption=

π matrix of physical quantities

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指数物理量π1π2π3π4
bE1000
cδ0100
fF0010
gQ0001
αρ-10-1-1
dT2022
eL-2-1-4-5
), ArticleFig(id=1228654112674345314, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228654093296661149, language=CN, label=表4, caption=

物理量的π矩阵

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指数物理量π1π2π3π4
bE1000
cδ0100
fF0010
gQ0001
αρ-10-1-1
dT2022
eL-2-1-4-5
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吸能液压支架金字塔点阵吸能构件优化及试验分析
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沈佳兴 1, 2 , 潘子豪 2 , 冷岳峰 2 , 徐平 2 , 范中海 2
振动工程学报 | 2024,37(12): 2132-2140
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振动工程学报 | 2024, 37(12): 2132-2140
吸能液压支架金字塔点阵吸能构件优化及试验分析
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沈佳兴1, 2 , 潘子豪2, 冷岳峰2, 徐平2, 范中海2
作者信息
  • 1辽宁工程技术大学矿产资源开发利用技术及装备研究院，辽宁　阜新　123000
  • 2辽宁工程技术大学机械工程学院，辽宁　阜新　123000

    • 沈佳兴（1990—），男，博士，副教授。E-mail：。

Optimization and experimental analysis of pyramid lattice energy absorption device of energy absorption hydraulic support
Jia-xing SHEN1, 2 , Zi-hao PAN2, Yue-feng LENG2, Ping XU2, Zhong-hai FAN2
Affiliations
  • 1Research Institute of Technology and Equipment for the Exploitation and Utilization of Mineral Resources， Liaoning Technical University，Fuxin 123000，China
  • 2School of Mechanical Engineering， Liaoning Technical University，Fuxin 123000，China
出版时间: 2024-12-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.12.015
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摘要
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为提高吸能液压支架的吸能性进而提高其安全性，设计了一种多层点阵吸能构件。根据吸能构件立柱的结构及吸能空间设计了金字塔点阵吸能构件的基本结构。以吸能构件的吸能最大、支撑力均值在允许范围内最大及支撑力波动系数最小为优化目标函数，以金字塔胞体的立足直径和跨度为优化设计变量，以吸能构件的支撑力峰值和支撑力均值在允许范围内为约束条件，利用Workbench软件分别对金字塔高度为30，40，50 mm的吸能构件结构参数进行多目标优化设计，得到三组优化解并通过对比分析确定最佳结构参数。采用压缩试验对等比例缩小的最优参数的单层吸能构件进行试验分析，结果显示其吸能量为4.18716 kJ，计算得到原尺寸单层吸能构件吸能量为113.05332 kJ，吸能构件整体吸能量为565.2666 kJ，与仿真结果相对误差仅为-9.92%。该吸能构件比传统薄壁结构吸能构件的吸能性提高50%以上，证明了优化设计的有效性和吸能构件的高吸能性。

吸能支架  /  金字塔结构  /  点阵吸能构件  /  安全性

In order to improve the energy absorption and safety of the energy absorption hydraulic support，a multi-layer lattice energy absorption device is designed. The basic structure of pyramid lattice energy absorption device is designed according to the structure and energy absorption space of energy absorption support column. The maximum energy absorption of the energy absorption device，the maximum mean of the support force within the allowable range，and the minimum fluctuation coefficient of the support force are taken as the optimization objective function，the base diameter and span of the pyramid cell are taken as the optimization design variables，and the constraint conditions are taken as the peak and mean of the support force of the energy absorption device within the allowable range. The Workbench software is used to optimize the structural parameters of the energy absorption device with the pyramid height of 30 mm，40 mm and 50 mm respectively. Three groups of optimization solutions are obtained and the optimal structural parameters are determined by comparative analysis. The single-layer energy absorption device with the optimal parameters reduced in the compression experiment was used for experimental analysis，and the results show that the absorption energy is 4.18716 kJ. The calculated energy absorption energy of the original single-layer energy absorption device is 113.05332 kJ，and the energy absorption energy of the whole energy absorption device is 565.2666 kJ. The relative error between the experimental results and the simulation results is only -9.92%. The energy absorption capacity of the new energy absorption device is at least 50% higher than that of the traditional thin-wall structure energy absorption device，which proves the effectiveness of the optimized design and the high energy absorption capacity of the energy absorption device.

energy absorption support  /  pyramid structure  /  lattice energy absorption device  /  security
沈佳兴, 潘子豪, 冷岳峰, 徐平, 范中海. 吸能液压支架金字塔点阵吸能构件优化及试验分析. 振动工程学报, 2024 , 37 (12) : 2132 -2140 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.12.015
Jia-xing SHEN, Zi-hao PAN, Yue-feng LENG, Ping XU, Zhong-hai FAN. Optimization and experimental analysis of pyramid lattice energy absorption device of energy absorption hydraulic support[J]. Journal of Vibration Engineering, 2024 , 37 (12) : 2132 -2140 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.12.015
正文
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引言
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冲击地压对井下煤炭开采的安全性有重大影响，特别是在发生严重冲击地压时，岩体的破碎、爆裂及振动对矿井支护设备的稳定性及安全性乃至工作人员的生命安全产生严重威胁［1-3］。为解决该问题，国内外学者提出了锚杆-锚索支护、门式液压支架支护、U型钢支撑等方法［3-5］，上述增加支护强度的方法在一定程度上减少了冲击地压事故的发生。但这类方法通过增大巷道支护强度来抑制冲击地压的发生，巷道积聚的能量没有得到及时释放。随着时间推移，冲击地压事故依旧会发生，并且由于积聚的能量更多，发生冲击地压时的危害更大。
为解决这一难题，相关专家提出让位吸能防冲击方法并设计了让位吸能液压支架［6-9］。该方法是在支架的适当位置设置一个强度相对较低但又能起到支撑作用的吸能构件，当冲击地压发生时，吸能构件及时让位变形，吸收冲击能量，且让位吸能的同时吸能构件还能提供合适的支撑力，进而防止设备其他位置的损坏。该方法能够及时吸收冲击地压的能量，防止事故的发生，从根本上解决冲击地压的危害。
吸能构件的结构对其吸能性和支撑力产生关键影响。为提高吸能构件的性能，相关专家提出了许多吸能构形，其中，文献［3，9］提出了曲折棱管吸能结构，姜红星［10］研究了正四边形、矩形、圆形及正六边形截面管体的吸能性，王春华等［11］提出了变梯度薄壁吸能结构，田立勇等［12］研究了多胞薄壁吸能构件的吸能特性，安栋等［13］研究了预折纹自引导吸能装置的吸能特性并通过试验和仿真证明其吸能性，高永新等［14］研究了卡箍式结构的吸能装置并优化了结构尺寸。上述方法均是利用薄壁管体的变形吸收能量，但没有充分利用薄壁管体内部空间来设置吸能装置，因此吸能量有限。为设计具有高吸能性并能提供稳定支撑力的吸能装置，本文设计了一种多层点阵吸能结构，以期利用密集的点阵结构变形来充分吸能进而提高支架的吸能性和支撑力的稳定性。
1　吸能构件关键指标
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吸能构件是支架实现让位吸能的核心结构，描述吸能构件吸能性的指标主要包括：支撑力峰值、总吸能、支撑力均值及支撑力波动系数等。
（1）支撑力峰值Fmax为吸能构件受到冲击载荷作用后吸能构件首次出现的最大支撑力，该力即为液压支架的最大承载力。
（2）总吸能Q为吸能构件在压溃变形过程中吸收的总能量，可以根据支撑力和位移曲线计算得到，表达式为：
式中　 δ为吸能构件的最大让位压缩量；s为吸能构件的瞬时压缩量；F（s）为压缩量为s时的瞬时支撑力。
（3）支撑力均值为吸能构件在压缩过程中的支撑力均值，大小为：
（4）支撑力波动系数为支撑力峰值Fmax与支撑力均值Fmean之比，其反映的是压缩过程中吸能构件的支撑力整体波动性，大小为：
（5）最大让位压缩量δ表示支撑力从支撑力峰值降低后首次达到许用的最大承载力时对应的压缩位移。在支撑力一定的情况下，最大让位压缩量越大，吸能越高。
根据各参数定义可知，吸能构件的总吸能越大，吸能性越好。支撑力峰值需在合适的范围内，支撑力峰值过大则无法让位吸能，从而失去保护液压支架其他结构的作用。支撑力均值也应在合适的范围内、且越大越好。支撑力波动系数越小，表明吸能构件波动性较小，稳定性越好。
2　点阵吸能构件
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让位吸能液压支架的主要原理是利用安装在液压立柱底部的点阵吸能构件的让位变形吸收冲击地压的能量以防止液压支架的其他部件损坏。点阵吸能构件由多层吸能单元构成，每层吸能单元都是由点阵吸能胞体构成，如图1所示。点阵吸能胞体的结构对点阵吸能构件整体吸能特性有关键影响。本文选取点阵吸能胞体结构为金字塔结构，其立足为圆柱体，如图2所示，该点阵吸能构件具有比吸能高、支撑力平稳、胞体结构简单、制造方便等优点。研究的防冲液压支架型号为ZHDF4150/31/40，如图1所示，吸能构件的极限行程长度L为350 mm，吸能构件的缸径D为230 mm，液压立柱的工作阻力为4150 kN，根据通用技术条件中关于液压支架最大承载力的要求可知，吸能构件的最大承载力要在1.2~1.4倍的工作阻力之间［15］，因此点阵吸能构件的支撑力峰值范围为4980~5810 kN。
3　点阵吸能构件优化设计
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3.1　参数优化设计模型
本文采用Workbench软件对金字塔胞体参数进行优化设计。优化时选取金字塔结构的高度h、立足的直径d及立足的半跨度a为设计变量，并利用Workbench软件中的Design Modeler模块建立金字塔点阵吸能构件的参数化三维模型，如图3所示。分析可知，直径d过大导致支撑力过大，直径d过小又不能提供足够的支撑力；半跨度a大小影响每层能够布置金字塔胞体的个数，为保证每层能够布置足够的金字塔胞体个数且又不会因半跨度a过小导致立足之间相互干涉，设计变量d和a的大小应适中。本文初步选取设计范围为：5 mm≤d≤15 mm；20 mm≤a≤50 mm。点阵吸能构件的极限行程长度L为350 mm，因结构的总吸能与吸能单元的层数有关，高度h越小，吸能单元的层数越多，导致每层之间的隔板数量增加，使整体的可压缩位移减小，且层数过多或金字塔胞体个数过多导致计算量几何倍数增加，给优化求解带来困难。因此初设高度h范围为30~50 mm。因为高度h变化会使参数化模型的层数变化，导致参数化模型拓扑结构改变，参数化模型无法自动更新，且若h作为连续变量也会导致优化设计的样本点数翻倍，使计算样本增加过多，难以通过软件求解，为此对高度h进行分级优化，即选取高度h为30，40，50 mm三个等级。然后依次研究立足直径和跨度连续变化情况下的最优结果，最后对比分析各种高度时最优解的吸能性后挑选得到最终最优参数。
根据吸能构件行程长度L和金字塔胞体的高度h设计吸能构件的整体结构。如图4（a）所示，当胞体高度h=30 mm时，吸能单元之间的隔板厚度不能过薄，否则压缩时金字塔结构未压缩变形而隔板先变形导致结构失效，同时为了提高金字塔胞体层数，提高最大吸能，设置隔板的厚度为15 mm，整个吸能构件的金字塔胞体层数为8，吸能构件的高度为345 mm，小于350 mm。当胞体高度h=40 mm时，设置隔板的厚度为20 mm，整个吸能构件的金字塔胞体层数为6，吸能构件的高度为340 mm，小于350 mm。当胞体高度h=50 mm时，设置隔板的厚度为20 mm，整个吸能构件的金字塔胞体层数为5，吸能构件的高度为330 mm，小于350 mm。
优化设计时利用Workbench软件中的显示动力学分析模块对吸能构件的冲击吸能性进行仿真分析。将建立的三维参数化模型导入分析模块中，吸能构件的材料为钢，其密度为7830 kg/m3，通过Johnson Cook本构模型模拟材料硬化属性［16］，该材料的初始屈服应力为792 MPa，硬化常数为510 MPa，硬化指数为0.26，应变速率常数为0.014，热软化指数为1.03［16］。有限元分析模型如图5所示，模型中包含吸能构件和冲击压板两个结构，设置压板为刚体，吸能构件为柔性体，图中网格大小为10 mm，根据文献［3］可知，冲击地压的冲击速度范围为5~15 m/s，为研究最大冲击情况下的安全性，压板竖直向下的冲击速度为15 m/s，在吸能构件底部的底面添加固定约束（如图5所示）。为了提高优化效率，将分析时长设为0.005 s，在软件中添加塑性变形吸能分析选项和支撑力分析选项，再通过插入命令的方式设定支撑力均值与支撑力峰值之比为支撑力波动系数。同时将仿真分析结果的总吸能f1（a，d）、支撑力峰值f2（a，d）、支撑力均值f3（a，d）及支撑力波动系数f4（a，d）设为输出变量。
利用软件的Direct Optimization模块进行优化设计，将该模块与冲击吸能仿真模块关联，设总吸能f1（a，d）、支撑力均值f3（a，d）、支撑力波动系数f4（a，d）为优化目标函数。该优化设计是为寻找使得吸能构件的整体吸能最大且具有较好的支撑效果的最优结构参数，因此f1（a，d），f3（a，d）两个优化目标函数越大越好，f4（a，d）优化目标函数越小越好。结构的支撑力峰值f2（a，d）应在4980~5810 kN范围内，设置f2（a，d）为约束条件。由此可以得到该优化设计的数学模型为：
式中　 F（a，d）为综合优化目标函数，该优化目标取最小值，因此将f1（a，d），f3（a，d）取负值；β1，β2，β3为权重系数，装置总体吸能大小决定能够抵抗冲击地压的强度，因此相对比较重要，所以β1=0.5，β2和β3为0.25。
优化设计时选择优化方法为MOGA（遗传算法），该算法适合多目标多变量优化。设置初始计算样本数为20，最大允许帕累托百分比为70%，候选优化结果个数为1，当高度h为30 mm时，各样本性能如图6和7所示，图中横坐标为每个样本的编号，纵坐标为样本性能。如图7所示，位于蓝色和红色虚线内的样本点是支撑力符合要求的样本，再根据图6就可以确定样本点的吸能大小。
3.2　优化结果
优化软件采用最小二乘法对仿真得到的100个数据样本进行拟合，得到优化目标函数F（a，d）的变化趋势，再利用MOGA算法进行优化求解，得到三种胞体高度时的参数优化结果如表1所示。
4　优化结果性能分析
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根据表1数据对吸能构件建模并进行完整压缩吸能特性仿真分析。仿真时模型的材料参数、网格设置、约束条件及速度载荷与第3节优化时相同。
当高度h为30 mm时，吸能构件的支撑力历程曲线和吸能历程曲线分别如图8和9所示。仿真分析时研究了15 m/s的最大冲击时支撑力的变化，由图8可知，刚压缩时吸能构件瞬时冲击最大，结构的应变率效应影响最明显，产生的支撑力峰值也较大，高达5745.8 kN，之后应变率效应影响迅速减小，支撑力也迅速减小，降为峰值的1/2左右。吸能构件的支撑力峰值位于4980~5810 kN之间，符合要求。随着吸能构件逐渐压缩，支撑力也略微上升，当压缩位移为112.5 mm时，吸能构件开始被压实，支撑力曲线出现拐点，之后支撑力迅速上升。当压缩位移为119.4 mm时，吸能构件支撑力达到5810 kN，达到许用最大支撑力。继续压缩吸能构件会导致支撑力过大、支架其他结构损坏。各典型压缩位移时吸能构件的压缩变形如图8所示。分析可知吸能构件在0~119.4 mm内压缩位移是有效行程，根据图9可知有效行程内的有效吸能大小为296.82 kJ。计算得到该优化结果的支撑力均值为2485.93 kN，支撑力波动系数为2.31。压缩位移为119.4 mm时，吸能构件的应力云图如图10所示。由图10可知，该时刻吸能构件的最大应力为1142 MPa，最大应力主要位于金字塔胞体上，且根据图可以看出，每层金字塔胞体已经完全弯曲变形，金字塔胞体立足已与隔板贴合。
当高度h为40 mm时，吸能构件的支撑力历程曲线和吸能历程曲线分别如图11和12所示。根据图11可知，刚压缩时结构出现支撑力峰值，大小为5255.1 kN，位于4980~5810 kN之间，符合要求。当压缩位移为112.6 mm时支撑力曲线出现拐点，当压缩位移为116 mm时达到最大许用支撑力为5810 kN。各典型压缩位移时吸能构件的压缩变形如图11所示。根据图12可知有效压缩位移内吸能构件的吸能大小为534.78 kJ。计算得到该优化结果的支撑力均值为4610.17 kN，支撑力波动系数为1.14。提取压缩位移为116 mm时吸能构件的应力云图如图13所示，吸能构件的最大应力为1179.2 MPa。
当高度h为50 mm时，吸能构件的支撑力历程曲线和吸能历程曲线分别如图14和15所示。根据图14可知，刚压缩时结构出现支撑力峰值，大小为5755 kN，位于4980~5810 kN之间，符合要求。当压缩位移为128.6 mm时支撑力曲线出现拐点，当压缩位移为150.04 mm时达到最大许用支撑力5810 kN。各典型压缩位移时吸能构件的压缩变形如图14所示。根据图15可知有效压缩位移内吸能构件的吸能大小为627.5 kJ。计算得到该优化结果的支撑力均值为4182.22 kN，支撑力波动系数为1.38。提取压缩位移为150.04 mm时吸能构件的应力云图如图16所示，吸能构件的最大应力为1155.8 MPa。
比较可知，三个方案的支撑力峰值均满足要求。方案二和方案三的支撑力均值均达到4000 kN以上，支撑力波动系数均在1.4以下。比较方案二和方案三的总吸能量可知，方案三比方案二高92.72 kJ。对于吸能构件而言，总吸能大小代表支架能够抵抗冲击地压的强度，因此高吸能性尤为重要，所以方案三为最优方案。最优方案的具体结构为：金字塔胞体高h=50 mm，立足的直径d为14.6 mm，立足的跨度a为34.6 mm，隔板厚度为20 mm，整个吸能构件层数为5层，吸能构件高度为330 mm。
5　试验分析
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5.1　相似比分析
利用3D打印技术制造单层吸能单元模型，采用等比例缩小的方式进行加工，本文的试验模型等比例缩小3倍，打印的实物如图17所示。缩小后模型的尺寸参数为：金字塔胞体高度为16.7 mm；立足直径为4.9 mm；跨度为11.5 mm；胞体直接打印到试件底板上固定，底板与液压机底座接触并固定使其几乎不发生变形，因此制造试验实物时在不影响试验结果的情况下适当减小了底板厚度，底板厚度为3 mm；底板的外径为76.7 mm。
根据相似理论，试验模型应与实际模型几何相似，因此在制造试验模型时点阵结构应该等比例缩小，且打印使用材料与仿真材料相同。
采用量纲分析法研究实际吸能与试验吸能的相似比。分析可知与吸能量Q相关的主要物理量包括：弹性模量E，压缩位移δ，支撑力F，材料密度ρ，几何尺寸L，压缩时间T。取材料密度ρ、几何尺寸L、压缩时间T为基本量纲。则相关物理量的量纲关系如表2所示。
根据π定理可知：
式中　 π为因子；α，b，c，d，e，f，g为指数。
量纲矩阵如表3所示。
由表3可得指数关系方程：
根据方程（6）计算得到π矩阵如表4所示。表4中每一列构成一个π因子，则相似准则表达式为：
，，，，由相似边界条件可知：几何尺寸相似比；因3D打印试件材料内部是密实的，只有个别局部存在气孔，且3D打印使用的原材料为钢粉，与实际钢密度相同，所以实际模型的密度与试验试件密度基本相同，密度相似比；因为实际压缩位移是试验的3倍，所以压缩时间相似比。
根据相似第一定理可知相似因子具有恒值性，因此π4为：
式中　下标“y”表示原始模型相关物理量；下标“s”表示缩小后试验模型相关物理量。
根据式（7）计算得到吸能量的相似比=27。
5.2　试验过程及结果
冲击地压的速度为5~15 m/s，介于高速冲击和准静态之间，霍普金森杆冲击试验机速度太高且对试验试件的形状尺寸有严格要求，该试验试件不满足要求，所以不适合用于该试验。考虑到万能液压机可以适应不同形状尺寸的试件，且能实时记录并储存试件的压缩-位移曲线以便于后续处理，同时经济性也比较好，因此采用万能液压机进行压缩吸能试验。试验时采用液压机的最大压缩速度为5 mm/min。压缩时试件的变形如图18所示，图18（a）为试件初始压缩，图18（b）为试件的金字塔立足已经被压缩弯曲，图19为试件完全压溃后的形貌。
试件的支撑力曲线如图20所示。根据图20可知，其支撑力在压缩后迅速增加，当压缩位移达到2 mm左右时出现明显的平台区，正是由于平台区的出现保证了吸能单元在几乎稳定的支撑力下实现持续的让位吸能，当压缩位移为10 mm时试件被压实，支撑力迅速上升，因此试件的有效压缩位移为0~10 mm。在压缩过程中A点的支撑力略微降低是因为该时刻部分立足与隔板连接断开（如图19所示）导致支撑力减小。比较图20和14可知，图20在刚压缩时没有出现支撑力峰值，这是因为压缩试验为准静态所以没有应变率效应影响，从整体上看两图的变化趋势基本一致，证明了仿真的可靠性。
根据图20的压缩位移-支撑力曲线计算得到吸能单元的总吸能曲线如图21所示，可知试验吸能变化趋势与仿真结果一致，单层吸能单元的有效吸能为4.18716 kJ。
根据吸能相似比可知，原尺寸单层吸能单元的有效吸能为4.18716×33=113.05332 kJ，又因吸能构件为5层，所以整个吸能构件的总吸能为565.2666 kJ，与仿真结果627.5 kJ的相对误差仅为-9.92%。根据图20和21可知，试验试件在10 mm被压实，根据相似比可知原尺寸吸能单元的有效压缩位移为10×3=30 mm，同时考虑到吸能构件为5层，所以原尺寸吸能构件的有效压缩位移为30×5=150 mm，与仿真结果的有效压缩位移基本一致。
分析试验总吸能和仿真总吸能产生误差的原因是由于试验模型是通过金属3D打印制造，其内部的微观组织结构不同于热处理后的工程钢，其强度和韧性要小，进而导致与仿真结果存在误差且试验结果略小，但总体上相对误差较小，证明了仿真和设计的有效性。同时，传统薄壁结构吸能构件的吸能大小在400 kJ左右［7，9，11-12，14］，点阵结构吸能构件的吸能性提高了50%以上，因此证明了该吸能构件的优越性。
6　结论
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（1）针对ZHDF4150/31/40型吸能液压支架设计了金字塔点阵吸能构件，分别优化了高度为30，40，50 mm时金字塔胞体的立足直径和跨度，确定了最佳金字塔胞体结构参数为：高度为50 mm，立足直径为14.6 mm，立足跨度为34.6 mm。
（2）分别通过仿真和试验研究了结构参数最优时的吸能构件吸能性，其中吸能构件的仿真结果为627.5 kJ，试验结果为565.2666 kJ，二者相对误差仅为-9.92%，证明了优化设计的有效性。
（3）金字塔点阵吸能构件比传统薄壁结构等吸能构件的吸能量提高50%以上，支撑力均值大且支撑力波动系数较小，证明了该吸能构件的优越性。
基金
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  • 中国煤炭工业协会科学技术研究指导性计划资助项目(MTKJ2010-290)
文献
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2024年第37卷第12期
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doi: 10.16385/j.cnki.issn.1004-4523.2024.12.015
  • 接收时间：2023-01-01
  • 首发时间：2026-02-12
  • 出版时间：2024-12-28
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  • 收稿日期：2023-01-01
  • 修回日期：2023-02-14
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中国煤炭工业协会科学技术研究指导性计划资助项目(MTKJ2010-290)
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    1辽宁工程技术大学矿产资源开发利用技术及装备研究院，辽宁　阜新　123000
    2辽宁工程技术大学机械工程学院，辽宁　阜新　123000
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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