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Article(id=1227614521863368975, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1227614514896634485, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.04.011, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1660060800000, receivedDateStr=2022-08-10, revisedDate=1664899200000, revisedDateStr=2022-10-05, acceptedDate=null, acceptedDateStr=null, onlineDate=1770615709987, onlineDateStr=2026-02-09, pubDate=1714233600000, pubDateStr=2024-04-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770615709987, onlineIssueDateStr=2026-02-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770615709987, creator=13701087609, updateTime=1770615709987, updator=13701087609, issue=Issue{id=1227614514896634485, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='4', pageStart='539', pageEnd='728', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770615708325, creator=13701087609, updateTime=1770795248114, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228367559410512191, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1227614514896634485, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228367559410512192, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1227614514896634485, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=645, endPage=656, ext={EN=ArticleExt(id=1227614522081472796, articleId=1227614521863368975, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Damage analysis of products under logistics non-Gaussian vibration, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

The shock signals in the process of road transportation cause the non-Gaussian characteristics of random vibration process. In order to study the impact of shock on product damage，the measured 8 vibration signals of medium truck and heavy truck are statistically analyzed. The vibration signals are divided into 20% high-intensity non-Gaussian signal，60% medium-intensity Gaussian signal and 20% low-intensity Gaussian signal. The finite element software is used for time-domain vibration analysis to calculate the damage proportion of each signal segment. The results show that the non-Gaussian signal contains high intensity shock signal，which causes the most of damage. The shock amplitude of medium truck vibration data is large and accounts for a small proportion，while the shock amplitude of heavy truck is relatively low and accounts for a large proportion. The higher 5% shock signal for medium trucks caused more than 90% of the damage； The 20% non-Gaussian signal of heavy truck contains 10% higher amplitude vibration besides 10% shock component，and the damage caused by 20% non-Gaussian signal is about 80% or higher. In the whole transport vibration process，the shock signal dominates the accumulation of damage with less content.

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公路运输过程中的冲击信号造成了物流随机振动的非高斯特性。为研究冲击成分对产品损伤的影响，对8条中型卡车和重型卡车实测道路信号进行了统计分析。将振动信号分为20%的高强度非高斯信号、60%的中等强度高斯信号和20%的低强度高斯信号。使用有限元软件进行时域振动分析，计算各信号段的损伤占比。结果表明：振动过程中，非高斯信号蕴含了高强度的冲击信号，造成了绝大部分的损伤。中型卡车振动数据冲击幅值大、占比少，相对而言，重型卡车冲击幅值低、占比多。中型卡车高5%的冲击信号造成了90%以上的损伤；重型卡车20%的非高斯信号中除10%的冲击成分外还包含10%的较高幅值振动，其20%的非高斯信号造成的损伤约为80%或更高。在整个运输振动过程中，含量较少的冲击信号主导了损伤的累积。

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王志伟（1963―），男，博士，教授。E-mail：。
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谢嘉琳（1999—），女，硕士研究生。E-mail：。

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谢嘉琳（1999—），女，硕士研究生。E-mail：。

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谢嘉琳（1999—），女，硕士研究生。E-mail：。

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Guangzhou： Jinan University， 2017., articleTitle=Study on random vibration analysis and simulation method of road transport packaging, refAbstract=null), Reference(id=1227643692702429638, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614521863368975, doi=null, pmid=null, pmcid=null, year=2020, volume=37, issue=6, pageStart=2386, pageEnd=2394, url=null, language=null, rfNumber=［30］, rfOrder=41, authorNames=王志伟, 刘博, 王立军, journalName=应用力学学报, refType=null, unstructuredReference=王志伟， 刘博， 王立军. 基于Grms-N的非高斯加速随机振动理论方法的有限元验证［J］. 应用力学学报， 2020， 37（6）： 2386-2394., articleTitle=基于Grms-N的非高斯加速随机振动理论方法的有限元验证, refAbstract=null), Reference(id=1227643692761149895, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614521863368975, doi=null, pmid=null, pmcid=null, year=2020, volume=37, issue=6, pageStart=2386, pageEnd=2394, url=null, language=null, rfNumber=［30］, rfOrder=42, authorNames=WANG Zhiwei, LIU Bo, WANG Lijun, journalName=Chinese Journal of Applied Mechanics, refType=null, unstructuredReference=WANG Zhiwei， LIU Bo， WANG Lijun. The finite element verification of the non-Gaussian acceleration random vibration theory method based on Grms-N［J］. Chinese Journal of Applied Mechanics， 2020， 37（6）： 2386-2394., articleTitle=The finite element verification of the non-Gaussian acceleration random vibration theory method based on Grms-N, refAbstract=null), Reference(id=1227643692824064456, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614521863368975, doi=null, pmid=null, pmcid=null, year=1982, volume=4, issue=1, pageStart=31, pageEnd=40, url=null, language=null, rfNumber=［31］, rfOrder=43, authorNames=Dowing S D, Socie D F, journalName=International Journal of Fatigue, refType=null, unstructuredReference=Dowing S D， Socie D F. Simple rainflow counting algorithms［J］. 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articleId=1227614521863368975, language=CN, label=图C1, caption=中型卡车和重型卡车选段的重组激励信号, figureFileSmall=6v1sfRo4kij6MR1kZpIJfA==, figureFileBig=bMPf/Ofo8SuGq8eB/FGV3Q==, tableContent=null), ArticleFig(id=1227643687262417240, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614521863368975, language=EN, label=Tab.1, caption=

Basic information of two types of vehicles

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车辆特性中型箱式卡车重型箱式卡车
品牌庆铃，中国庆铃，中国
型号QL5070XHKWRJQL5250XXYDTFZJ
悬吊系统钢板弹簧钢板弹簧
外观尺寸/mm36790×2110×290011700×2500×3990
额定载重/kg382014620
), ArticleFig(id=1227643687333720409, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614521863368975, language=CN, label=表1, caption=

两款车辆基本信息

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车辆特性中型箱式卡车重型箱式卡车
品牌庆铃，中国庆铃，中国
型号QL5070XHKWRJQL5250XXYDTFZJ
悬吊系统钢板弹簧钢板弹簧
外观尺寸/mm36790×2110×290011700×2500×3990
额定载重/kg382014620
), ArticleFig(id=1227643687417606492, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614521863368975, language=EN, label=Tab.2, caption=

Statistical parameters of each segment of 8 measured signals

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信号分段RMS/g峭度K偏度S持续时间/s信号分段RMS/g峭度K偏度S持续时间/s
40%-城市道路-中型卡车原始信号0.210214.50170.0686102040%-高速公路-中型卡车原始信号0.35193.87630.0267600
高20%0.298615.98820.1115204高20%0.52542.6452-0.0132120
中60%0.19543.03780.0175612中60%0.31922.93490.0797360
低20%0.13143.2875-0.0059204低20%0.19372.94390.0221120
0%-城市道路-中型卡车原始信号0.308611.03720.025017400%-高速公路-中型卡车原始信号0.33523.9237-0.0022840
高20%0.47238.92110.0237348高20%0.46243.3020-0.0149168
中60%0.27443.12330.01561044中60%0.31682.96150.0146504
低20%0.16563.37330.0143348低20%0.21693.28940.0064168
60%-城市道路-重型卡车原始信号0.17104.63670.016442060%-高速公路-重型卡车原始信号0.25403.36370.0004660
高20%0.23743.99840.033984高20%0.34262.69390.0080132
中60%0.16063.3016-0.0014252中60%0.24452.8665-0.0001396
低20%0.11193.50590.063584低20%0.16033.1606-0.0115132
0%-城市道路-重型卡车原始信号0.34464.68940.02379600%-高速公路-重型卡车原始信号0.53504.4490-0.0389720
高20%0.51763.23540.0233192高20%0.79453.2638-0.0558144
中60%0.31413.26400.0146576中60%0.48153.0233-0.0051432
低20%0.17283.41460.0274192低20%0.32293.1207-0.0106144
), ArticleFig(id=1227643687501492574, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614521863368975, language=CN, label=表2, caption=

8条道路实测信号各分段的统计参数

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信号分段RMS/g峭度K偏度S持续时间/s信号分段RMS/g峭度K偏度S持续时间/s
40%-城市道路-中型卡车原始信号0.210214.50170.0686102040%-高速公路-中型卡车原始信号0.35193.87630.0267600
高20%0.298615.98820.1115204高20%0.52542.6452-0.0132120
中60%0.19543.03780.0175612中60%0.31922.93490.0797360
低20%0.13143.2875-0.0059204低20%0.19372.94390.0221120
0%-城市道路-中型卡车原始信号0.308611.03720.025017400%-高速公路-中型卡车原始信号0.33523.9237-0.0022840
高20%0.47238.92110.0237348高20%0.46243.3020-0.0149168
中60%0.27443.12330.01561044中60%0.31682.96150.0146504
低20%0.16563.37330.0143348低20%0.21693.28940.0064168
60%-城市道路-重型卡车原始信号0.17104.63670.016442060%-高速公路-重型卡车原始信号0.25403.36370.0004660
高20%0.23743.99840.033984高20%0.34262.69390.0080132
中60%0.16063.3016-0.0014252中60%0.24452.8665-0.0001396
低20%0.11193.50590.063584低20%0.16033.1606-0.0115132
0%-城市道路-重型卡车原始信号0.34464.68940.02379600%-高速公路-重型卡车原始信号0.53504.4490-0.0389720
高20%0.51763.23540.0233192高20%0.79453.2638-0.0558144
中60%0.31413.26400.0146576中60%0.48153.0233-0.0051432
低20%0.17283.41460.0274192低20%0.32293.1207-0.0106144
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Product size of each component and material mechanical property parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
零部件材料尺寸(长×宽×高)/m3厚度/m密度/(kg·m-3)泊松比杨氏模量/1010 Pa切向模量/108 Pa屈服强度/108 Pa
外框铝合金0.2×0.15×0.150.002527700.33
悬臂铝合金0.02×0.01×0.01—27700.33
短柱铝合金0.01×0.01×0.02—27700.33
重块结构钢0.02×0.02×0.01—78500.30
基础结构钢0.4×0.36×0.02—78500.30
), ArticleFig(id=1227643687669264740, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1227614521863368975, language=CN, label=表3, caption=

产品各零部件尺寸及材料力学性能参数

, figureFileSmall=null, figureFileBig=null, tableContent=
零部件材料尺寸(长×宽×高)/m3厚度/m密度/(kg·m-3)泊松比杨氏模量/1010 Pa切向模量/108 Pa屈服强度/108 Pa
外框铝合金0.2×0.15×0.150.002527700.33
悬臂铝合金0.02×0.01×0.01—27700.33
短柱铝合金0.01×0.01×0.02—27700.33
重块结构钢0.02×0.02×0.01—78500.30
基础结构钢0.4×0.36×0.02—78500.30
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Cumulative damage in each signal segment of medium trucks and heavy trucks

, figureFileSmall=null, figureFileBig=null, tableContent=
信号参数原始信号重组信号高5%高10%高20%中60%低20%
40%-城市道路-中型卡车RMS/g0.22840.22840.48320.40440.34210.20330.1413
峭度K10.106210.10627.79728.44008.82883.03323.1149
损伤D/4.35583.58923.55763.58513.58750.0017330.00004
损伤占比/%(82.40)10099.1299.8999.950.0480.002
40%-高速公路-中型卡车RMS/g0.34130.34130.63360.56490.49750.31340.2001
峭度K4.19384.19383.00953.08983.21522.84423.0280
损伤D/1.78632.04141.83841.88441.93830.10150.0016
损伤占比/%(85.72)10090.0692.3194.954.970.08
0%-城市道路-中型卡车RMS/g0.32150.32150.64850.56740.49250.28330.1835
峭度K6.90096.90094.99575.03955.13123.24133.0408
损伤D/2.88552.80272.57062.69992.77430.02820.0002
损伤占比/%(97.13)10091.7296.3398.991.000.01
0%-高速公路-中型卡车RMS/g0.32500.32500.67730.56210.47690.29740.1881
峭度K6.83776.83774.72395.51285.88683.11043.2858
损伤D/1.87422.03042.02232.02602.02730.00300.0001
损伤占比/%(91.67)10099.6099.7899.850.150.001
60%-城市道路-重型卡车RMS/g0.17040.17040.26710.24940.23210.16140.1146
峭度K4.37564.37563.87863.71223.77243.41323.1649
损伤D/1.49721.59010.91781.06301.40890.17600.0025
损伤占比/%(93.80)10057.7266.8588.6011.070.33
60%-高速公路-重型卡车RMS/g0.28520.28520.43140.40700.37490.27490.1982
峭度K3.46333.46333.86203.37443.21922.69962.9961
损伤D/2.32562.10482.03612.03792.10190.00270.0002
损伤占比/%(95.92)10096.7496.8299.860.130.01
0%-城市道路-重型卡车RMS/g0.33470.33470.59550.54950.49380.30800.1786
峭度K4.54894.54892.98833.13433.26383.27023.2087
损伤D/3.78851.69960.36481.12731.33320.36550.0009
损伤占比/%(44.86)10021.4766.3378.4421.510.05
0%-高速公路-重型卡车RMS/g0.45010.45010.66300.62930.58260.43620.3203
峭度K3.38123.38122.70612.83642.93342.98762.9767
损伤D/7.93719.55033.33937.32307.72241.79280.0351
损伤占比/%(79.68)10034.9776.6880.8618.770.37
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中型卡车和重型卡车各信号段的累积损伤

, figureFileSmall=null, figureFileBig=null, tableContent=
信号参数原始信号重组信号高5%高10%高20%中60%低20%
40%-城市道路-中型卡车RMS/g0.22840.22840.48320.40440.34210.20330.1413
峭度K10.106210.10627.79728.44008.82883.03323.1149
损伤D/4.35583.58923.55763.58513.58750.0017330.00004
损伤占比/%(82.40)10099.1299.8999.950.0480.002
40%-高速公路-中型卡车RMS/g0.34130.34130.63360.56490.49750.31340.2001
峭度K4.19384.19383.00953.08983.21522.84423.0280
损伤D/1.78632.04141.83841.88441.93830.10150.0016
损伤占比/%(85.72)10090.0692.3194.954.970.08
0%-城市道路-中型卡车RMS/g0.32150.32150.64850.56740.49250.28330.1835
峭度K6.90096.90094.99575.03955.13123.24133.0408
损伤D/2.88552.80272.57062.69992.77430.02820.0002
损伤占比/%(97.13)10091.7296.3398.991.000.01
0%-高速公路-中型卡车RMS/g0.32500.32500.67730.56210.47690.29740.1881
峭度K6.83776.83774.72395.51285.88683.11043.2858
损伤D/1.87422.03042.02232.02602.02730.00300.0001
损伤占比/%(91.67)10099.6099.7899.850.150.001
60%-城市道路-重型卡车RMS/g0.17040.17040.26710.24940.23210.16140.1146
峭度K4.37564.37563.87863.71223.77243.41323.1649
损伤D/1.49721.59010.91781.06301.40890.17600.0025
损伤占比/%(93.80)10057.7266.8588.6011.070.33
60%-高速公路-重型卡车RMS/g0.28520.28520.43140.40700.37490.27490.1982
峭度K3.46333.46333.86203.37443.21922.69962.9961
损伤D/2.32562.10482.03612.03792.10190.00270.0002
损伤占比/%(95.92)10096.7496.8299.860.130.01
0%-城市道路-重型卡车RMS/g0.33470.33470.59550.54950.49380.30800.1786
峭度K4.54894.54892.98833.13433.26383.27023.2087
损伤D/3.78851.69960.36481.12731.33320.36550.0009
损伤占比/%(44.86)10021.4766.3378.4421.510.05
0%-高速公路-重型卡车RMS/g0.45010.45010.66300.62930.58260.43620.3203
峭度K3.38123.38122.70612.83642.93342.98762.9767
损伤D/7.93719.55033.33937.32307.72241.79280.0351
损伤占比/%(79.68)10034.9776.6880.8618.770.37
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Cumulative damage of 5 typical characteristic signals

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信号参数重组信号高1%高5%高10%高20%中60%后20%
信号1RMS/g0.29540.48470.44450.42330.39260.28150.2110
峭度K3.28022.20972.41782.52030.98762.95792.9876
损伤D/1.61010.06550.16770.45340.83300.75600.0211
损伤占比/%1004.0710.4228.1651.7446.951.31
信号2RMS/g0.30130.93780.61580.51420.43750.27520.1882
峭度K7.40294.38505.88196.52356.79912.97133.0681
损伤D/2.76002.51782.70382.71840.00630.0002
损伤占比/%10091.2297.9698.4999.760.230.01
信号3RMS/g0.32150.89340.64850.56740.49250.28330.1835
峭度K6.90094.42894.99575.03955.13123.24133.0404
损伤D/3.13081.10682.71252.97713.09020.04020.0004
损伤占比/%10035.3286.6495.0998.701.280.02
信号4RMS/g0.30780.68280.60830.55240.47550.26980.1704
峭度K5.62333.31233.39113.53933.88733.15893.2966
损伤D/1.68340.16881.21301.58231.66160.02170.0001
损伤占比/%10010.0372.0693.9998.711.290.001
信号5RMS/g0.37191.72560.99420.79190.63610.29230.1752
峭度K38.66797.487114.325518.080922.04543.37463.1336
损伤D/3.42133.40583.41353.42113.42130.00000.00001
损伤占比/%10099.5599.7799.9999.990.010.001
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5段典型特征信号的累积损伤

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信号参数重组信号高1%高5%高10%高20%中60%后20%
信号1RMS/g0.29540.48470.44450.42330.39260.28150.2110
峭度K3.28022.20972.41782.52030.98762.95792.9876
损伤D/1.61010.06550.16770.45340.83300.75600.0211
损伤占比/%1004.0710.4228.1651.7446.951.31
信号2RMS/g0.30130.93780.61580.51420.43750.27520.1882
峭度K7.40294.38505.88196.52356.79912.97133.0681
损伤D/2.76002.51782.70382.71840.00630.0002
损伤占比/%10091.2297.9698.4999.760.230.01
信号3RMS/g0.32150.89340.64850.56740.49250.28330.1835
峭度K6.90094.42894.99575.03955.13123.24133.0404
损伤D/3.13081.10682.71252.97713.09020.04020.0004
损伤占比/%10035.3286.6495.0998.701.280.02
信号4RMS/g0.30780.68280.60830.55240.47550.26980.1704
峭度K5.62333.31233.39113.53933.88733.15893.2966
损伤D/1.68340.16881.21301.58231.66160.02170.0001
损伤占比/%10010.0372.0693.9998.711.290.001
信号5RMS/g0.37191.72560.99420.79190.63610.29230.1752
峭度K38.66797.487114.325518.080922.04543.37463.1336
损伤D/3.42133.40583.41353.42113.42130.00000.00001
损伤占比/%10099.5599.7799.9999.990.010.001
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物流非高斯振动下的产品损伤分析
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谢嘉琳 1, 2, 3 , 王志伟 1, 2, 3
振动工程学报 | 2024,37(4): 645-656
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振动工程学报 | 2024, 37(4): 645-656
物流非高斯振动下的产品损伤分析
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谢嘉琳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

    • 谢嘉琳（1999—），女，硕士研究生。E-mail：。

通讯作者:

王志伟（1963―），男，博士，教授。E-mail：。
Damage analysis of products under logistics non-Gaussian vibration
Jia⁃lin XIE1, 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: 2024-04-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.04.011
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摘要
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公路运输过程中的冲击信号造成了物流随机振动的非高斯特性。为研究冲击成分对产品损伤的影响，对8条中型卡车和重型卡车实测道路信号进行了统计分析。将振动信号分为20%的高强度非高斯信号、60%的中等强度高斯信号和20%的低强度高斯信号。使用有限元软件进行时域振动分析，计算各信号段的损伤占比。结果表明：振动过程中，非高斯信号蕴含了高强度的冲击信号，造成了绝大部分的损伤。中型卡车振动数据冲击幅值大、占比少，相对而言，重型卡车冲击幅值低、占比多。中型卡车高5%的冲击信号造成了90%以上的损伤；重型卡车20%的非高斯信号中除10%的冲击成分外还包含10%的较高幅值振动，其20%的非高斯信号造成的损伤约为80%或更高。在整个运输振动过程中，含量较少的冲击信号主导了损伤的累积。

随机振动  /  公路运输  /  非高斯  /  疲劳损伤  /  冲击

The shock signals in the process of road transportation cause the non-Gaussian characteristics of random vibration process. In order to study the impact of shock on product damage，the measured 8 vibration signals of medium truck and heavy truck are statistically analyzed. The vibration signals are divided into 20% high-intensity non-Gaussian signal，60% medium-intensity Gaussian signal and 20% low-intensity Gaussian signal. The finite element software is used for time-domain vibration analysis to calculate the damage proportion of each signal segment. The results show that the non-Gaussian signal contains high intensity shock signal，which causes the most of damage. The shock amplitude of medium truck vibration data is large and accounts for a small proportion，while the shock amplitude of heavy truck is relatively low and accounts for a large proportion. The higher 5% shock signal for medium trucks caused more than 90% of the damage； The 20% non-Gaussian signal of heavy truck contains 10% higher amplitude vibration besides 10% shock component，and the damage caused by 20% non-Gaussian signal is about 80% or higher. In the whole transport vibration process，the shock signal dominates the accumulation of damage with less content.

random vibration  /  road transport  /  non-Gaussian  /  fatigue damage  /  shock
谢嘉琳, 王志伟. 物流非高斯振动下的产品损伤分析. 振动工程学报, 2024 , 37 (4) : 645 -656 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.04.011
Jia⁃lin XIE, Zhi⁃wei WANG. Damage analysis of products under logistics non-Gaussian vibration[J]. Journal of Vibration Engineering, 2024 , 37 (4) : 645 -656 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.04.011
正文
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引言
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目前大多数的物流随机振动测试都是基于随机振动服从高斯分布进行的。学者们通过不断深入研究发现：公路运输过程中，包装产品所受的振动为非高斯随机振动［1⁃5］。加速度幅值较大的高水平冲击造成了随机振动过程的非高斯特性，而这些较大幅值的冲击可能在产品累积疲劳损伤时占据了尤为重要的一部分。
在物流冲击信号的分析方面，研究者们对此提出了很多的方法。Young等［6］首次提出“二分法”，将振动信号按照强度大小3∶7进行分离，分别模拟，然后串联得到最终的振动信号。Singh等［7］采用该方法对北美实测道路振动信号进行了分段随机振动测试。随后Wallin［8］采集了不同运输工具的振动数据，将振动信号按照2∶8分离做测试研究。在此基础上，Kipp［9］也提出将信号分成5%的高强度冲击信号、25%的中等强度振动信号和70%的低强度振动信号，分别模拟，串联测试，称之为“三分法”。随后陆续有学者提出了峭度控制法、经验模态分解法、机器学习法等［10⁃13］，Zhou等［14］提出“冲击提取法”，利用十分之一峰值法和移动振幅因子将原始信号中的冲击信号与振动信号精准识别并分离，通过迭代分解将原始信号分解成一系列近似高斯振动段和具有高峭度的冲击段。该方法能够较好地再现运输中的振动信号特征。
在疲劳累积损伤分析方面，安刚等［15］在其研究中讨论了时域疲劳分析方法，该方法计算量比较大，但是精度较高。频域法研究振动由于计算量更小，简单便捷，被广泛研究［16⁃21］。Miles等［22］给出窄带随机载荷激励下的疲劳损伤计算公式，其中应力峰值符合Rayleigh分布，这种基于窄带激励的假设高估了疲劳损伤。Dirlik［23］建立了由两个瑞利函数和一个指数函数组成的高斯稳态宽带激励下雨流幅值的概率密度分布模型，在疲劳损伤寿命估算领域得到广泛运用。Chaudhury［24］基于宽带应力谱的峰值分布给出了宽带激励下的疲劳损伤计算公式。传统的频域疲劳分析方法仅适用于高斯激励，蒋培等［25］利用非高斯概率密度的Hermite多项式渐近展开和三维联合高阶统计特征，推导得到非高斯随机应力载荷下的寿命估计公式，但其计算量非常庞大。袁毅等［26］通过非高斯修正系数建立了非高斯随机过程下的疲劳损伤与高斯随机过程下的疲劳损伤关系，通过估算高斯疲劳损伤得到非高斯疲劳损伤。近年来，众多学者对工程上的疲劳损伤问题进行了诸多研究，陈家焱等［27］针对非高斯随机振动试验控制中功率谱均衡与峭度均衡相互干涉，影响控制精度的问题，提出非高斯随机振动试验并行控制策略。谢树强等［28］基于在位使用时的动应力进行了地铁架构的疲劳损伤分析。
学术界对振动信号的非高斯特性带来的影响越发关注，但对物流非高斯振动信号中冲击和不同等级振动信号成分对产品总体损伤的量化研究仍然较少。本文根据珠三角地区实测物流振动信号的统计参数将振动信号划分为一段包含较大冲击的非高斯信号和两段不同强度的高斯信号；计算各段信号的损伤占比，研究损伤与冲击信号占比之间的变化规律。
1　分离非高斯
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课题组前期采集了珠三角地区5种车型在城市道路和高速公路上以不同载重行驶的15条运输振动信号，发现加速度幅值较大的冲击信号导致了运输工具振动信号的非高斯特性。对其中的中型卡车和重型卡车的8条道路实测信号进行统计分析，两种车型基本信息见表1，具体行驶线路见附录A［5，29］。其中中型卡车与重型卡车各有两个不同的载货量等级，中型卡车的载货量等级分别为40%和0%（空载）；重型卡车的载货量等级分别为60%和0%。为了研究不同强度的冲击或振动信号造成的损伤占比，参考课题组前期将一段非高斯物流振动信号分解成若干段高斯信号和一段冲击信号的思路［14］，本文将整段信号分离成一段包含冲击的非高斯信号与两段不同强度等级的高斯信号，并确定其分段配比。
信号的加速度均方根水平可以在一定程度上代表该段信号的振动强度。采用0.5 s的移动窗宽，计算整段振动信号的移动加速度均方根，按移动加速度均方根的大小将信号重新整合排序得到重组信号。此处以重型卡车空载行驶在高速公路上的信号为例进行说明，图1（a）为整段原始信号。按移动加速度均方根大小将整段信号分成高20%、中60%和低20%的三段信号，为后续研究不同强度的振动信号段造成的损伤提供前期准备工作。图1（b）为排序后的重组信号，图中标注了不同长度信号的区段。分别统计原始信号和各分段信号的均方根、峭度、偏度、持续时间，如表2所示。
通过表2可以看出，中60%的信号和低20%的信号其峭度在3附近，偏度接近于0，可以将其近似认为是高斯信号。经过重组之后高20%的信号包含了较大幅值的冲击，峭度大于3，被划分为非高斯信号。对8条信号的各分段信号进行概率密度分布统计，并使用高斯函数进行拟合。此处以空载重型卡车行驶在高速公路上的信号为例进行说明，如图2所示。发现高斯函数对中60%和低20%的信号拟合程度总体较好。高20%的信号进行高斯拟合后，由于其高幅值的冲击信号占比非常少，在直方图中难以显示，对其尾部进行局部放大，可以看到具有非高斯特性的拖尾现象。在高20%的信号的概率密度图中可以看到低幅值的振动信号仍然存在较大占比，这是因为在重组信号的过程中采用了0.5 s的移动窗宽进行加速度均方根计算并排序，导致实际上高20%的信号中仍然存在一部分低幅值的振动信号。经过分析，其余信号也均存在上述特征。因此，我们可以将一段振动信号根据强度划分为高20%的非高斯信号，中60%和低20%的近似高斯信号。
2　损伤分析
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2.1　有限元分析模型的建立
为了分析物流中冲击和振动对产品造成的损伤，考虑到一般的产品由机体和零部件组成，本文构建的产品模型由一外框结构、一悬臂结构和一立柱结构组成。王志伟等［30］使用该类模型进行了基于Grms⁃N的非高斯随机振动加速理论的有限元验证。外框代表产品的机体，悬臂与立柱结构代表产品的两个关键零部件，其分别连接一质量块，为零部件提供一定的重量，如图3所示。产品各零部件的材料参数见表3。仿真过程中输入的加速度激励为竖直方向，悬臂构件能够评估产品关键件在振动过程中抵抗挠曲的能力，立柱构件能够反应关键件在振动过程中受到的拉、压应力情况。考虑振动测试时将产品固定在振动台上，避免振动过程中发生跳起现象，设置产品与基础振动台之间、产品各零部件之间均为绑定接触。
使用ANSYS Workbench的瞬态结构分析模块进行时域振动分析。为了缩短求解时间，对实测的道路加速度信号进行了节选，选段长为100 s。选段选取了整段信号中的特征区段，加速度均方根和冲击分布情况与整段信号较为接近，8条节选信号的时域图见附录B。对这些选段信号按照0.5 s移动窗宽的加速度均方根由大到小进行排序得到重组信号，使用重组信号作为模型的激励信号进行分析，见附录C。
仿真求解完成后将采集产品关键点的应力变化情况，结合材料的疲劳寿命曲线（图4），使用雨流计数法［31］和Miner线性累积损伤准则计算产品在振动试验中造成的损伤量。并分别计算高20%的非高斯信号、中60%和低20%的近似高斯信号造成的损伤量和其损伤占比。考虑到高20%的非高斯信号中还包含一些相对冲击来说稍低的较大幅振动信号，同时也将计算最高5%、最高10%的冲击信号造成的损伤及其占比。使用ANSYS内置的铝合金的S⁃N曲线数据进行拟合，其数学表达式可以写为：
式中　 S为应力，单位为Pa；N为循环次数。
2.2　结果分析
2.2.1　中型卡车和重型卡车信号造成的损伤分析
仿真求解得到模型在不同道路信号下的Von⁃Mises等效应力云图，观察到产品在振动条件下的应力最大点位于悬臂结构与外框的连接点处，如图5所示，将此处作为产品的关键点，通过后处理提取该关键点的应力响应信息。以空载中型卡车行驶在城市道路上的节选信号为例，其节选信号原始排序如图6所示，重组信号如图7所示；采集原始信号和重组信号分别激励的关键点应力响应情况，分别如图8和9所示。采用雨流计数法得到各信号段应力的雨流幅值分布，如图10所示。采用Miner累积损伤准则计算8条数据各信号段和原始信号的累积损伤，如表4所示。
据表4可知，8条信号的原始信号与重组信号的损伤接近度基本达到80%以上。其中空载重型卡车行驶在城市道路的信号接近度稍差，仅有44.86%，这是由于排序会影响雨流计数过程循环的终止条件，导致雨流幅值有所差异。同时，结合表3中材料的屈服强度，关键点的最大应力情况远小于材料的屈服应力，材料仍然处于线弹性阶段，信号的重新排序对模型的损伤影响较小。
绘制高5%、高10%、高20%信号的累积损伤图，中型卡车数据的损伤变化趋势如图11所示，重型卡车数据的损伤变化趋势如图12所示。
中型卡车的4条信号均在信号前5%处损伤便累计至90%以上，这是由于中型卡车的振动信号中冲击成分占比普遍较少，冲击主要聚集在前5%的信号中。高幅值的冲击造成了整个振动过程绝大多数的损伤。
对于重型卡车，60%载重高速公路信号存在5%左右的远高于整体振动水平的大幅冲击信号，损伤在信号前5%处累积至95%以上。其余3条信号的加速度幅值跨度很大，存在大量低幅值振动，较多的高幅值振动（分布在前20%）。60%载重的城市道路信号存在5%的大幅冲击信号，损伤在信号占比5%处累积到接近60%，随后高幅值振动持续均匀的累积损伤直至接近90%。而空载城市道路、高速公路信号的冲击占比约10%，冲击累积的损伤在70%左右，随后大量的高幅值振动持续均匀累积损伤至接近80%。
整体而言，中型卡车振动信号中的高幅值信号占比较少，约占5%，但其幅值高，可达到3g~4g；中型卡车高5%的信号造成了90%以上的损伤。重型卡车除冲击成分之外还存在大量高幅值信号，其冲击信号幅值较小，在2.0g~2.5g之间，重型卡车20%的非高斯信号造成了约80%或更高的损伤。
2.2.2　5段典型道路信号造成的损伤分析
由上述结果可以看到，选段的冲击成分占比对损伤累积的规律影响较大。不同车型以不同载重在不同的道路上行驶，其采集到的振动信号也会有所差异。为了更清晰地得到振动信号中冲击成分对损伤累积的影响规律，节选了空载中型卡车行驶在城市道路上的5段100 s的典型特征振动信号，如图13所示。信号1~5冲击信号的强度和数量逐渐增大和增多，其中信号5蕴含一个巨大的冲击信号，超过8g。
采用同样的方法得到5段典型道路信号的累计损伤，考虑到某些信号段冲击含量较少，此处增加计算高1%信号的损伤及其占比。表5列出了5段典型特征信号各分段的损伤及其占比，并绘制他们的损伤变化趋势图，如图14所示。
据表5和图13~14可知：信号1不包含较大的冲击信号，整体接近于一个高斯信号，其损伤是缓慢均匀累积的，信号前20%损伤累积达到50%以上；信号2蕴含一个比较突出的冲击信号，冲击信号占比较少，其损伤在信号1%处便迅速累积至90%以上；信号3蕴含相对较多的冲击信号，约占整体信号的5%左右，损伤在前5%处累积至80%以上；信号4蕴含大量的冲击信号，比较均匀地分布在整段信号之间。其冲击信号占比约为10%，损伤在10%处累积至90%以上；信号5的成分包括：一个巨幅冲击信号，达到8g，少量的高幅值振动和大量的低幅值振动。这个巨幅冲击几乎造成了整个振动过程绝大多数的损伤，导致信号前1%处损伤便累积至接近100%。
通过以上分析可以看出由冲击部分造成的损伤基本可以达到80%以上。进一步证明，振动信号对产品造成的损伤是由冲击成分主导的。
3　结论
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本文研究了物流非高斯随机振动对产品造成的损伤规律。按加速度均方根的大小将实测的道路振动信号分成一段非高斯信号和两段近似高斯信号。使用有限元软件进行了时域振动分析，计算了非高斯段和高斯段的损伤。得到如下结论：
（1）通过计算8条中型卡车和重型卡车道路信号不同分段的统计参数，可将运输过程中的随机振动信号根据振动强度划分为20%的蕴含冲击成分的高强度非高斯信号、60%的中等强度高斯信号和20%的低强度高斯信号。
（2）由于运输工具的悬挂系统不同，采集到的运输工具振动信号中的冲击含量和幅值大小有所差异。中型卡车数据冲击信号幅值大，可达到3g~4g，占比约5%。相对而言重型卡车冲击信号幅值低，在2g~2.5g之间，但冲击占比更多。重型卡车20%的非高斯信号中除10%的冲击成分之外还存在约10%的高幅值振动信号，这些高幅值的振动同样造成了较多的损伤。因此重型卡车10%的冲击信号造成的损伤占比相较中型卡车5%的冲击信号造成的损伤占比低。
（3）振动过程中，非高斯信号段蕴含了高强度的冲击信号，造成了绝大部分的损伤，中型卡车高5%的冲击信号造成了90%以上的损伤；重型卡车20%的非高斯信号造成的损伤约80%或更高。
上述结论给出如下两点启示：首先，运输过程中，要通过缓冲结构设计有针对性的降低冲击能量对产品造成的影响；其次，在产品包装实验室评价时，要重点关注冲击部分造成的损伤，对产品运输加速随机振动试验进行改进。
附录A：
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附录B：
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附录C：
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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4期
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doi: 10.16385/j.cnki.issn.1004-4523.2024.04.011
  • 接收时间：2022-08-10
  • 首发时间：2026-02-09
  • 出版时间：2024-04-28
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  • 收稿日期：2022-08-10
  • 修回日期：2022-10-05
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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

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王志伟（1963―），男，博士，教授。E-mail：。
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2种不同金属材料的力学参数
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species		 占总种数比例
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total species (%)		 属
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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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