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Article(id=1228653714681032731, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228653708687377017, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.11.011, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1669392000000, receivedDateStr=2022-11-26, revisedDate=1671379200000, revisedDateStr=2022-12-19, acceptedDate=null, acceptedDateStr=null, onlineDate=1770863472861, onlineDateStr=2026-02-12, pubDate=1732723200000, pubDateStr=2024-11-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770863472861, onlineIssueDateStr=2026-02-12, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770863472861, creator=13701087609, updateTime=1770863472861, updator=13701087609, issue=Issue{id=1228653708687377017, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='11', pageStart='1803', pageEnd='1992', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770863471433, creator=13701087609, updateTime=1770863902026, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228655514792427773, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228653708687377017, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228655514792427774, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228653708687377017, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1906, endPage=1916, ext={EN=ArticleExt(id=1228653714983022627, articleId=1228653714681032731, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Response analysis of transport system based on vehicle-cargo coupling, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Vehicle transport is an important part of logistics transport. It is of great significance to study the response of cargoes in the process of vehicle transport. Considering the coupling effect between cargo and vehicle bottom，an 11-degree-of-freedom vehicle-cargo coupling model is established. The relationship between three-way response is compared，and the influence of different road levels and cargo-related parameters （load，stiffness，damping） on the system response is taken into consideration. The results show that the coupling effect of vehicle-cargo significantly affects the system response. The influence of rotation in transportation cannot be ignored. The vibration response of cargo increases with a decrease of load，stiffness and damping. The worse the road condition is，the bigger the vibration response of cargo and vehicle bottom will be. The research results are of great significance and value for the design of vehicle-cargo transportation system.

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车辆运输是物流运输的重要组成部分，研究车辆运输过程中的货物响应对运输包装设计有着重要意义。考虑货物与车辆底板的耦合作用，建立十一自由度车辆-货物耦合模型，对比三向响应之间的关系，研究不同公路等级及货物相关结构参数（载荷量、刚度、阻尼）对系统响应的影响。结果表明：车辆货物耦合作用显著影响系统响应；运输中转动造成的影响不可忽略；载货量减小、刚度增大、阻尼减小，货物的振动响应随之增加；路况越差，货物及底板的振动响应越大。

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王志伟（1963—），男，博士，教授。E-mail： 。
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黄美琪（1998—），女，硕士研究生。E-mail： 。

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黄美琪（1998—），女，硕士研究生。E-mail： 。

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黄美琪（1998—），女，硕士研究生。E-mail： 。

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Study on random vibration analysis and simulation method of road transport packaging［D］. Guangzhou： Jinan University， 2017., articleTitle=Study on random vibration analysis and simulation method of road transport packaging, refAbstract=null), Reference(id=1228724617334943843, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653714681032731, doi=null, pmid=null, pmcid=null, year=2019, volume=32, issue=6, pageStart=269, pageEnd=277, url=null, language=null, rfNumber=［29］, rfOrder=43, authorNames=BÖRÖCZ P, journalName=Packaging Technology and Science, refType=null, unstructuredReference=BÖRÖCZ P. Vibration and acceleration levels of multimodal container shipping physical environment［J］. 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Component parameters of vehicle system with 11 degrees of freedom

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系统部件参数数值
汽车簧上质量mb/kg3400
座椅与人总质量ms/kg150
额定载货量mhm/kg5000
汽车左前、右前簧下质量mfl，mfr/kg325
汽车左后、右后簧下质量mrl，mrr/kg525
座椅刚度系数Ks/(N·m-1)8000
货物分布刚度系数Kh/(N·m-3)390000，260000，195000
左前、右前悬架刚度系数Kfl，Kfr/(N·m-1)170000
左后、右后悬架刚度系数Krl，Krr/(N·m-1)480000
后轮胎垂向刚度系数Ktr/(N·m-1)1920000
座椅阻尼系数Cs/（N·s·m-1）1000
货物分布阻尼系数Ch/（N·s·m-3）883,8830,17660
左前、右前减震器阻尼系数Cfl，Cfr/（N·s·m-1）7000
左后、右后减震器阻尼系数Crl，Crr/（N·s·m-1）14000
簧上质量绕通过质心的俯仰转动惯量Jp/（kg·m2）11970.8
簧上质量绕通过质心的侧倾转动惯量Jr/（kg·m2）1023
货物绕通过货物质心的俯仰转动惯量Jhp/（kg·m2）8333
货物绕通过货物质心的侧倾转动惯量Jhr/（kg·m2）2733
前轮胎垂向刚度系数Ktf/（N·m-1）960000
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十一自由度汽车系统部件参数

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系统部件参数数值
汽车簧上质量mb/kg3400
座椅与人总质量ms/kg150
额定载货量mhm/kg5000
汽车左前、右前簧下质量mfl，mfr/kg325
汽车左后、右后簧下质量mrl，mrr/kg525
座椅刚度系数Ks/(N·m-1)8000
货物分布刚度系数Kh/(N·m-3)390000，260000，195000
左前、右前悬架刚度系数Kfl，Kfr/(N·m-1)170000
左后、右后悬架刚度系数Krl，Krr/(N·m-1)480000
后轮胎垂向刚度系数Ktr/(N·m-1)1920000
座椅阻尼系数Cs/（N·s·m-1）1000
货物分布阻尼系数Ch/（N·s·m-3）883,8830,17660
左前、右前减震器阻尼系数Cfl，Cfr/（N·s·m-1）7000
左后、右后减震器阻尼系数Crl，Crr/（N·s·m-1）14000
簧上质量绕通过质心的俯仰转动惯量Jp/（kg·m2）11970.8
簧上质量绕通过质心的侧倾转动惯量Jr/（kg·m2）1023
货物绕通过货物质心的俯仰转动惯量Jhp/（kg·m2）8333
货物绕通过货物质心的侧倾转动惯量Jhr/（kg·m2）2733
前轮胎垂向刚度系数Ktf/（N·m-1）960000
), ArticleFig(id=1228724611764908049, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653714681032731, language=EN, label=Tab.2, caption=

Structure parameters of vehicle system with 11 degrees of freedom

, figureFileSmall=null, figureFileBig=null, tableContent=
系统结构参数数值
底板质心到前轴的距离L1/m2.2
底板质心到前左轮的距离L3/m0.82
座椅质心到侧倾轴距离L5/m0.1
货物质心到货物前后边界距离L7/m2
货物质心到底板质心距离L9/m2.1
底板质心到后轴的距离L2/m4.3
底板质心到后左轮的距离L4/m0.815
座椅质心到俯仰轴距离L6/m0.3
货物质心到货物左右边界距离L8/m0.8
), ArticleFig(id=1228724611861377043, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228653714681032731, language=CN, label=表2, caption=

十一自由度汽车系统结构参数

, figureFileSmall=null, figureFileBig=null, tableContent=
系统结构参数数值
底板质心到前轴的距离L1/m2.2
底板质心到前左轮的距离L3/m0.82
座椅质心到侧倾轴距离L5/m0.1
货物质心到货物前后边界距离L7/m2
货物质心到底板质心距离L9/m2.1
底板质心到后轴的距离L2/m4.3
底板质心到后左轮的距离L4/m0.815
座椅质心到俯仰轴距离L6/m0.3
货物质心到货物左右边界距离L8/m0.8
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基于车辆-货物耦合作用的运输系统响应分析
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黄美琪 1, 2, 3 , 王志伟 1, 2, 3
振动工程学报 | 2024,37(11): 1906-1916
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振动工程学报 | 2024, 37(11): 1906-1916
基于车辆-货物耦合作用的运输系统响应分析
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黄美琪1, 2, 3 , 王志伟1, 2, 3
作者信息
  • 1暨南大学包装工程学院，广东　珠海　519070
  • 2暨南大学产品包装与物流广东普通高校重点实验室，广东　珠海　519070
  • 3暨南大学包装工程研究所，广东　珠海　519070

    • 黄美琪（1998—），女，硕士研究生。E-mail： 。

通讯作者:

王志伟（1963—），男，博士，教授。E-mail： 。
Response analysis of transport system based on vehicle-cargo coupling
Mei-qi HUANG1, 2, 3 , Zhi-wei WANG1, 2, 3
Affiliations
  • 1College of Packaging Engineering，Jinan University，Zhuhai 519070，China
  • 2Key Laboratory of Product Packaging and Logistics of Guangdong Higher Education Institutes，Jinan University， Zhuhai 519070，China
  • 3Packaging Engineering Institute，Jinan University，Zhuhai 519070，China
出版时间: 2024-11-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.11.011
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摘要
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车辆运输是物流运输的重要组成部分，研究车辆运输过程中的货物响应对运输包装设计有着重要意义。考虑货物与车辆底板的耦合作用，建立十一自由度车辆-货物耦合模型，对比三向响应之间的关系，研究不同公路等级及货物相关结构参数（载荷量、刚度、阻尼）对系统响应的影响。结果表明：车辆货物耦合作用显著影响系统响应；运输中转动造成的影响不可忽略；载货量减小、刚度增大、阻尼减小，货物的振动响应随之增加；路况越差，货物及底板的振动响应越大。

车辆振动  /  耦合  /  俯仰  /  侧倾

Vehicle transport is an important part of logistics transport. It is of great significance to study the response of cargoes in the process of vehicle transport. Considering the coupling effect between cargo and vehicle bottom，an 11-degree-of-freedom vehicle-cargo coupling model is established. The relationship between three-way response is compared，and the influence of different road levels and cargo-related parameters （load，stiffness，damping） on the system response is taken into consideration. The results show that the coupling effect of vehicle-cargo significantly affects the system response. The influence of rotation in transportation cannot be ignored. The vibration response of cargo increases with a decrease of load，stiffness and damping. The worse the road condition is，the bigger the vibration response of cargo and vehicle bottom will be. The research results are of great significance and value for the design of vehicle-cargo transportation system.

vehicle vibration  /  coupling  /  pitch  /  roll
黄美琪, 王志伟. 基于车辆-货物耦合作用的运输系统响应分析. 振动工程学报, 2024 , 37 (11) : 1906 -1916 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.11.011
Mei-qi HUANG, Zhi-wei WANG. Response analysis of transport system based on vehicle-cargo coupling[J]. Journal of Vibration Engineering, 2024 , 37 (11) : 1906 -1916 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.11.011
正文
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引言
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物联网新时代，物流运输相比以往更为繁忙，车辆已成为产品物流中最主要的运输工具之一，研究产品在车辆上的响应对包装研究具有极为重要的意义。以往车辆工程相关研究主要考虑了以下几个因素：（1）只考虑车辆本身结构系统，如文献［1-10］主要考虑汽车悬架，探究了主动与被动悬架、线性与非线性刚度阻尼对响应的影响，从而得到结构参数优化方案；张立军等［11］和欧健等［12］在建立模型时考虑了悬架柔性体的影响，研究结果表明，刚柔耦合模型会使车身加速度幅值降低，刚柔耦合模型和刚体模型的差异性随车速的增大而增大；胡红元［13］建立了耦合货物的七自由度车辆模型，研究了货物的集中刚度及阻尼对车辆响应的影响，但文章模型仅将货物假设为集中质量置于车厢后端，与实际情况不符。（2）考虑车-桥耦合因素，如文献［14-16］建立了车-桥耦合运动方程，探究车速、车辆数目、位置及车辆结构参数等因素对系统响应的影响。（3）考虑逆子结构法分析产品运输包装耦合系统，WANG等［17-18］结合包装动力学的基本理论，将逆子结构理论引入运输包装领域，发展了产品-包装-运载体的动态逆子结构理论与试验方法。综上所述，以往的研究多是将货物质量计算在车身中或是作为集中质量作用于车厢后端，而没有针对货物-底板之间的耦合作用建立车辆模型。
本文考虑货物与车辆底板之间的耦合作用，建立十一自由度车辆-货物耦合模型，分析相关参数对耦合系统的影响，研究结果对车辆-货物运输系统方案设计具有重要意义和价值。
1　车辆-货物耦合模型
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建立如图1所示的十一自由度车辆-货物耦合模型。相比以往的车辆模型，在车厢后部增加了货物部分，将货物视为一个均布载荷参与系统耦合。
1.1　货物的处理
假定货物的垂向、俯仰、侧倾位移量分别为，汽车底板的垂向、俯仰、侧倾位移量分别为。
将货物简化为一个长方体刚体，货物质心位于底板侧倾轴上，质量均匀分布。假设汽车底板和货物运动状态都为垂向、俯仰和侧倾运动，则货物在右前区域任意点的纵向位移变化量为：
式中　 x，y分别为以货物质心为原点的坐标系的横、纵坐标，以车前进方向为坐标系x轴正方向，左侧为y轴正方向。则货物的总势能为：
同理可得货物总耗散能为：
式中　 Kh与Ch分别为货物的分布刚度与分布阻尼，。
1.2　车辆-货物耦合振动方程
设系统的广义坐标为：Zs，Zh，θhp，φhr，Zb，θp，φr，Zfl，Zfr，Zrl，Zrr共11个，分别为座椅的垂向位移，车厢货物的垂向位移、俯仰角度和侧倾角度，车身（车底板）的垂向位移、俯仰角度和侧倾角度以及四个车轮的垂向位移。输入变量，分别为路面对四轮的左前、右前、左后、右后垂向位移激励信号。
利用拉格朗日方程可得车辆-货物耦合振动方程：
其中，为系统的广义坐标，质量矩阵M为diag（ms，mh，Jhp，Jhr，mb，Jp，Jr，mfl，mfr，mrl，mrr），刚度矩阵K、阻尼矩阵C和外力矩阵Ft分别如下式所示：
其中：
相比以往的车辆方程，增加了货物的三向运动方程，即考虑了货物与汽车底板之间的相互耦合作用。
由耦合方程可知，货物的垂向运动与汽车底板的垂向及俯仰运动耦合，货物的俯仰及侧倾运动则分别与汽车底板的俯仰及侧倾运动耦合。
仿真框架通过MATLAB/Simulink搭建，输出变量设为 。
选用某款东风卡车［13］，相关参数如表1和2所示，货物固定在车厢后部。
2　路面输入
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已有不少学者针对路面不平度的时域仿真进行了研究［19-26］，其中常见的方法为：三角级数合成法、滤波白噪声法、AR法、Poisson法等。本文中将采用滤波白噪声法，假定路面时域信号为均值为0的高斯信号，路面模型各向同性［22］，单轮输入模型为：
式中　 n00为路面空间截止频率，取为0.011 m-1；n0为参考空间频率，取为0.1 m-1；u为车速；为路面不平度系数；W（t）为功率谱为1的白噪声。
左右轮相干函数采用通用相干函数，前后轮利用时间滞后计算传递函数，即可求解出四轮的路面相关性输入矩阵。通过MATLAB/Simulink建立路面仿真模型，限带白噪声模块采样时间设定为0.001 s。需要注意的是，由于Simulink的白噪声模块输出为双边功率谱，因此白噪声功率谱密度设定为0.5。轮距B=1.94 m，轴距L=6 m，车速u=15 m/s，路面不平度Gq（n0）=64×10-6 m3。B级道路的四轮路面输入时域信号q（t）仿真情况如图2所示。
图3显示了四轮仿真路面谱与B级标准路面谱的对比。从图3中可以看到，在车辆振动频率f范围内仿真情况与标准路面情况相符，验证了本文中路面输入仿真信号的正确性。
3　车辆-货物耦合振动分析
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3.1　整体加速度功率谱分析
车辆-货物耦合系统各自由度仿真结果如图4~6所示。可以看到，在耦合系统部件的相互作用下，路面激励信号能量由车轮传递到底板，再传递到货物及座椅（人体）上时，加速度响应减小，车轮的振动能量最大，底板的三向响应及货物的三向响应次之，座椅的三向响应最小。
系统中加入货物的三向耦合后，座椅响应的最高峰值点出现在1 Hz左右；货物与底板垂向响应最高峰值点出现在10 Hz左右；货物转动响应最高峰值点出现在1~3 Hz之间；底板转动响应最高峰值点出现在5~9 Hz之间；四轮响应的峰值点出现在10 Hz左右。底板与货物的垂向响应总体大于座椅的垂向响应，底板的转动响应总体大于货物的转动响应。车辆的振动响应能量（包括货物）主要集中在低频区域，与文献测量结果一致［27-28］。
附录A为文献［27］中厢式卡车仿真与实测信号底板垂向PSD对比，与本文模型中C级道路仿真图像结果大致吻合，但因为实际路况更为复杂且各车辆结构存在差异，因此存在一些偏差。
3.2　系统模态分析
求解出系统的第1~11阶固有频率，结果分别为：1.1437，1.5246，1.6140，2.4478，3.9377，5.6065，8.6197，9.4436，9.4437，10.9644和11.7934 Hz。
11阶振型图见附录B。由振型图分析可得，第1阶振型为座椅的垂向运动；第2阶振型主要为座椅的垂向运动、货物的垂向运动与底板的垂向运动；第3阶振型主要为货物的侧倾运动与底板的侧倾运动；第4，5阶振型主要为货物的垂向、俯仰运动，底板的垂向、俯仰运动与四轮运动；第6阶振型主要为货物的侧倾运动、底板的侧倾与四轮运动；第7阶振型主要为货物的垂向运动，底板的垂向、俯仰运动与四轮运动；第8，9阶振型主要为两个前轮的运动；第10阶振型主要为底板侧倾运动与两个后轮的运动；第11阶振型主要为底板的垂向、俯仰运动与两个后轮的运动。
3.3　三向加速度对比
以往研究车辆响应的文章中，已有一些学者关注到了研究三向响应之间关系的重要性［27-30］。为了对比三向响应之间的关系，在汽车底板上选取两个特殊点P（座椅在汽车底板上的投影点）和Q（底板右后边缘点），在货物上选取特殊点K（货物右后边缘点），将三个特殊点对应的俯仰角加速度和侧倾角加速度分别转化为垂向加速度后进行三向加速度PSD对比，对比情况如图7所示。
在特殊点P处，由图7（a）可以看到，在第二峰群（10 Hz左右）处由俯仰运动造成的能量超过了垂向运动造成的能量，由于该点离侧倾轴距离较近，因此由侧倾转动造成的能量相对较小。
在特殊点Q处，由于该点距离底板质心较远，俯仰转动和侧倾转动所产生的能量更大。由图7（b）可以看到，底板此点处由俯仰转动产生的能量超过了垂向振动产生的能量。
在特殊点K处，由图7（c）可以看出，第一峰群（1~3 Hz）内货物由俯仰转动产生的响应超过了垂向响应，货物由侧倾产生的响应与垂向响应相当。因此通过特殊点的比较，可以直观看出运输过程中转动对货物造成的影响是不可忽略的。
综上所述，俯仰和侧倾的角位移虽然在实际运输中波动很小，但也会在运输过程中对车上的货物产生较大的能量波动，且强度与选定的位置息息相关。若是直接忽略转动方向的影响，将可能由于低估实际物流中的振动强度而造成货物的损坏。
3.4　载货量对耦合系统的影响
分别取载货量mh=1500，3000，5000 kg进行仿真分析，其余的条件参数如表1和2所示。车辆货物和底板的三向加速度PSD对比分别如图8和9所示。
改变载货量对货物的响应有着显著的影响。对应货物的质量增大，货物的转动惯量也增大，货物垂向响应第二振动峰值减小，货物俯仰响应的第二振动峰值减小，货物侧倾响应减小。针对底板的响应进行分析，载货量变化对底板三向响应的影响相对较小。载货量增大，底板垂向响应基本不变；底板俯仰响应第一振动峰值增大，第二振动峰基本不变；底板侧倾响应的第一振动峰值随载货量的增大而减小。
由仿真结果可以发现，载货量的改变对货物本身的响应影响更为明显，当载货量小于车身的质量时，货物的三向响应将会大于底板的三向响应。
3.5　公路等级对耦合系统的影响
对模型输入A，B，C等级的标准路面谱，其余的条件参数如表1和2所示，响应情况如图10所示。由于篇幅限制，文章中只列出货物的三向响应结果，底板的三向响应结果见附录C。
公路等级降低，即路面状况变差，货物与底板的振动强度明显增大，功率谱密度成比例放大。第一峰群内货物的响应水平大于底板的响应水平，第二峰群内则相反。
3.6　货物的刚度与阻尼对耦合系统的影响
货物缓冲垫的在静态压力下的位移量分别取为Δh=2，3和4 cm，则对应的分布刚度分别取为Kh=390000，260000和195000 N/m3。另外，阻尼比ξ分别取为0.01，0.1和0.2，则对应的分布阻尼系数分别取为Ch=883，8830和17660 N·s/m3，其余的条件参数如表1和2所示。货物的三向响应结果分别如图11和12所示，底板的三向响应结果见附录D和E。
由仿真结果可以看出，当货物的刚度减小时，货物垂向响应减小，第二振动峰值减小更为明显，第一振动峰值频率减小；货物转动响应的第二振动峰值下降，第一振动峰值频率减小。针对底板的响应进行讨论，货物的刚度减小，底板垂向响应的第二振动峰值减小；底板转动响应第一振动峰值减小。
当货物的阻尼增大时，对于货物的垂向部分，第二振动峰值迅速减小；对于货物转动部分，各响应峰值都明显下降。针对底板的响应进行讨论，货物的阻尼增大时，底板三向响应均减小，第二振动峰值的减小更为明显。
4　结论
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（1）建立了车辆-货物耦合模型，与以往的文献相比，增加了货物的三向自由度，考虑了货物与车辆底板之间的耦合作用。耦合结果表明，系统第一峰（峰群）频率在1~3 Hz之间，主要由车辆底板、货物及座椅决定；第二峰（峰群）频率在10 Hz左右，主要由四轮决定，与其他文献结果相符，验证了模型的合理性。
（2）车辆垂向振动与车辆转动振动强度相当，因此车辆转动响应不可忽略。运输包装设计中，应将转动振动的影响考虑在内。
（3）通过模型研究了不同公路等级及货物的不同参数（载货量、刚度以及阻尼）对耦合系统振动响应的影响。系统中加入了货物的耦合后，可以得出以下结论：①外界输入激励的变化对底板及货物的影响趋势相同，路面状况越差，底板及货物的响应越大；②载货量显著影响货物响应，载货量增大时，货物的响应减小；③货物刚度显著影响货物的第二振动峰值响应，货物响应总体随着货物刚度的增大而增大，随着阻尼的增大而减小。综上所述，货物参数对系统响应有显著影响，货物运输包装设计必须考虑车辆-货物耦合效应。
附录A
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附录B
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附录C
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附录D
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附录E
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基金
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  • 国家自然科学基金资助项目(50775100)
文献
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2024年第37卷第11期
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doi: 10.16385/j.cnki.issn.1004-4523.2024.11.011
  • 接收时间：2022-11-26
  • 首发时间：2026-02-12
  • 出版时间：2024-11-28
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  • 收稿日期：2022-11-26
  • 修回日期：2022-12-19
基金
国家自然科学基金资助项目(50775100)
作者信息
    1暨南大学包装工程学院，广东　珠海　519070
    2暨南大学产品包装与物流广东普通高校重点实验室，广东　珠海　519070
    3暨南大学包装工程研究所，广东　珠海　519070

通讯作者:

王志伟（1963—），男，博士，教授。E-mail： 。
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