挤压对灵武长枣应力应变影响的有限元分析

高坤 张海红 王娟 马晓艳 王通

高坤,张海红,王娟,等. 挤压对灵武长枣应力应变影响的有限元分析[J]. 食品工业科技,2021,42(20):207−213. doi:  10.13386/j.issn1002-0306.2021020200
引用本文: 高坤,张海红,王娟,等. 挤压对灵武长枣应力应变影响的有限元分析[J]. 食品工业科技,2021,42(20):207−213. doi:  10.13386/j.issn1002-0306.2021020200
GAO Kun, ZHANG Haihong, WANG Juan, et al. Finite Element Analysis of the Influence of Extrusion on the Stress and Strain of Lingwu Long Jujube[J]. Science and Technology of Food Industry, 2021, 42(20): 207−213. (in Chinese with English abstract). doi:  10.13386/j.issn1002-0306.2021020200
Citation: GAO Kun, ZHANG Haihong, WANG Juan, et al. Finite Element Analysis of the Influence of Extrusion on the Stress and Strain of Lingwu Long Jujube[J]. Science and Technology of Food Industry, 2021, 42(20): 207−213. (in Chinese with English abstract). doi:  10.13386/j.issn1002-0306.2021020200

挤压对灵武长枣应力应变影响的有限元分析

doi: 10.13386/j.issn1002-0306.2021020200
基金项目: 国家自然科学基金(31860422)
详细信息
    作者简介:

    高坤(1996−),女,硕士研究生,研究方向:食品加工与安全,E-mail:13139532641@163.com

    通讯作者:

    张海红(1967−),女,博士,教授,研究方向:无损检测,E-mail:nxdwjyxx@126.com

  • 中图分类号: S662.9

Finite Element Analysis of the Influence of Extrusion on the Stress and Strain of Lingwu Long Jujube

  • 摘要: 为了分析灵武长枣在采摘过程中内部应力应变对挤压的响应规律,为采摘机器人的设计提供理论依据,本文利用万能力学试验机在15、20、25、30、35 mm/min五种不同挤压速率下对灵武长枣整果进行了横向和纵向压缩,对力-变形曲线进行拟合,求得长枣在压缩破裂时的刚度及破裂力,并对15和35 mm/min两种横向挤压速率进行了有限元模拟,建立了有限元模型。结果表明:灵武长枣在受到挤压时,其力学性能具有各向异性,横向的抗压能力更强。横向压缩时,整果破裂负载为214.34~266.53 N,弹性模量为14.90~17.05 MPa,相对变形量为20.70%~22.67%;纵向压缩时,整果破裂负载为132.52~185.40 N,弹性模量为4.59~6.07 MPa,相对变形量为13.72%~17.25%。受力点的应力应变在果肉中是最大的,并沿赤道向果核周围延伸,且逐渐减小。压缩速率为15 mm/min的有限元模型的模拟值与其实验值的偏差为14.98%,35 mm/min的偏差为11.06%。运用有限元法对灵武长枣挤压模拟是可行的。
  • 图  1  不同加载方向

    Figure  1.  Different loading directions

    注:a.横向压缩;b.纵向压缩。

    图  2  力-变形曲线

    Figure  2.  Force-deformation curve

    图  3  力-变形拟合曲线

    Figure  3.  Force deformation curve fitting

    注:a~e表示压缩速率15 、20、25、30、35 mm/min。

    图  4  灵武长枣剖面和三维模型

    Figure  4.  Section and 3D model of Lingwu long jujube

    注:左:剖面;右:三维模型。

    图  5  网格划分及加载方式

    Figure  5.  Mesh division and loading method

    图  6  灵武长枣压缩载荷下等效应力应变云图

    Figure  6.  Equivalent stress and strain cloud diagram of Lingwu long jujube under compressive load

    注:a.速率15 mm/min横向受压应变云图;b.速率15 mm/min横向受压应力云图;b.速率35 mm/min横向受压应变云图;d.速率35 mm/min横向受压应力云图。

    图  7  实验与有限元模拟力-变形曲线对比

    Figure  7.  Comparison of experimental and finite element simulation force-deformation curves

    注:a.速率15 mm/min曲线对比;b.速率35 mm/min曲线对比。

    表  1  灵武长枣压缩力学参数

    Table  1.   Compression mechanical parameters of Lingwu long jujube

    压缩方向压缩速率(mm/min)破裂负载(N)弹性模量(MPa)相对变形量(%)
    15214.34±11.5814.92±1.8322.24±1.70
    20255.81±6.0116.45±1.3621.86±1.22
    横向25256.84±8.0717.05±1.7721.01±1.56
    30266.53±7.0614.90±1.9922.67±1.81
    35256.04±13.5015.41±1.9420.70±1.31
    15169.01±13.864.59±1.1816.58±1.32
    20132.52±6.775.32±0.6613.72±1.15
    纵向25185.40±12.845.00±1.1017.25±1.05
    30143.97±9.504.65±0.9014.82±1.18
    35154.51±8.186.07±1.0714.43±1.41
    下载: 导出CSV

    表  2  压缩方向和速率对破裂负载的显著性分析

    Table  2.   Significance analysis of compression direction and velocity to rupture load

    参数III 类平方和自由度均方F显著性
    修正模型192232.883a921359.20928.889**
    截距3005445.55413005445.5544064.969**
    压缩速率25465.13646366.2848.611**
    压缩方向149989.9161149989.916202.867**
    压缩速率×压缩方向16786.55644196.6395.676**
    误差46579.21163739.353
    总计3379366.61373
    修正后总计238812.09472
    注:*为影响显著,P<0.05;**为影响极显著,P<0.01;表3表5同。
    下载: 导出CSV

    表  3  压缩方向和速率对弹性模量的显著性分析

    Table  3.   Significance analysis of compression direction and velocity to elastic modulus

    参数III 类平方和自由度均方F显著性
    修正模型2297.302a9255.25634.061**
    截距7908.76417908.7641055.332**
    压缩速率38.51349.6281.285
    压缩方向2166.85312166.853289.141**
    压缩速率×压缩方向26.2146.5520.874
    误差472.128637.494
    总计11523.39873
    修正后总计2769.4372
    下载: 导出CSV

    表  4  灵武长枣力-变形拟合系数

    Table  4.   Fitting coefficient of force deformation of Lingwu long jujube

    压缩方向压缩速率(mm/min)拟合系数R2刚度(N/mm)破坏能(N·mm)
    α1α2α3d
    1523.242447.80081−0.957452.480360.9974920.36372602.30476
    2021.822658.12784−0.745611.468970.9995742.10692660.30723
    横向25−4.2938728.96514−3.597763.3240.999827.65222542.99942
    3035.46957.00027−0.91664−1.146220.9987528.07828728.11888
    3515.309455.05719−0.40627−0.484410.998113.327131052.62966
    1519.051861.008880.07985−0.465940.9995440.12344450.8926
    2012.758433.75923−0.38387−0.086330.9996115.8224387.7403
    纵向25−19.572319.27209−0.4627710.5640.993840.68274521.28812
    3017.0010.63146−0.06674−0.87890.9994814.15176587.0032
    3527.676860.13727−0.06818−0.932530.9997420.49613583.79502
    下载: 导出CSV

    表  5  横纵向压缩速率、弹性模量、破裂负载、相对变形量、刚度及破坏能间相关性分析

    Table  5.   Correlation analysis between transverse and longitudinal compression rate, elastic modulus, rupture load, relative deformation, stiffness and failure energy

    压缩方向压缩参数压缩速率弹性模量破裂负载相对变形量刚度破坏能
    横向压缩速率1−0.1260.626**0.463**−0.391*0.567**
    弹性模量10.318*−0.653**0.203−0.114
    破裂负载10.276−0.0690.248
    相对变形量1−0.0990.208
    刚度1−0.529**
    破坏能1
    纵向压缩速率10.2960.2510.055−0.413*0.844**
    弹性模量10.06−0.535**0.1200.063
    破裂负载10.712**0.527**0.458**
    相对变形量10.380*0.279
    刚度1−0.047
    破坏能1
    下载: 导出CSV
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  • 收稿日期:  2021-02-26
  • 网络出版日期:  2021-09-15
  • 刊出日期:  2021-10-11

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