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1、第 21 卷第 1 期 2005年1 月农 业 工 程 学 报 Transactions of the CSAEVol. 21 No. 1 Jan. 2005Finite element models of watermelon and their applicationsJamal Nourain1, 2, Ying Yibin1, Wang Jianping1, Rao Xiuqin1(1. College of Biosystems Engineering and Food Science, Zhejiang University, H angzhou 310029, China;2.
2、Agricultural Engineering Department, Sinnar University, Sudan)Abstract: The firmness of watermelon can be nondestructively evaluated by measuring the resonant frequency of thewatermelon.The watermelon was excited by a wooden pendulum ball and the response signal was captured by an accelerometer. The
3、 FE models of watermelons were established and the optimum location of the force excitation and thesuitable response measurement sensor for measuring the resonant frequency of watermelon were determined. The middlepart on the fruit surface was suggested to be used while estimating the fruit firmness
4、 by the resonant frequency of the first- type longitudinal mode. T o measure the flexural mode, the directions of both the exciting force and sensory axis of theresponse measurements sensor should be kept in tangent to the fruit surface. The comparison between experimental resultsand the finite elem
5、ent estimated results confirms that the model is in reasonable agreement with real fruit.It was found that the Youngs modulus was an adequate indicator for firmness, and the high correlation between the resonant frequencyand Youngs modulus existed, R2= 0. 90. The results of this study may be helpful
6、 to develop the non- destructive firmnesssensor for spherical fruits. Key words: watermelon; finite element models; firmness; physical properties; inspectionCLCnumber: TP274; O242. 1 Document code: A Article ID: 1002- 6819( 2004) 06- 0017- 06Received date: 2003-09-24 Revised date: 2004-08-17Foundati
7、on item: T his research was financially supported by the NaturalScience Foundation of China(N o. 30370371) ; Natural Science Foundationof Zhejiang Province (N o. 301267) .Biographies: Jamal Nourain, Ph. D. candidate at Zhejiang UniversityCorrespondence author: Ying Yibin, Ph. D. ,professor,College o
8、fBiosystemsEngineeringandFoodScience,ZhejiangUniversity,Hangzhou 310029, China. Email:ybying zju. edu. cn0 IntroductionNondestructive measurement of fruit firmness has become a worldwide interest in recent times. Based on thephysicalpropertiesofthefruit,many nondestructive techniques have been devel
9、oped for fruit quality evaluation.For example,the resonant frequency of the vibrational modes of the fruit was used to estimate the fruit firmness.The vibration mode and the corresponding resonant frequencies ofwatermelon can be obtained by exciting a watermelon at several points on its surface and
10、detecting the response atsome otherpoints.Yingand Cai 1reported that the acoustic properties of fresh fruits were applied in non-destructive quality evaluation. Yamamoto et al 2measured apple firmness through recording the sounds generated in the fruit by striking it with a wooden pendulum. Armstron
11、g and Brown 3and Armstrong et al 4developed a prototype sonic system for measuring apple firmness and found that the first resonant frequency was a good indicator of fruit firmness. Abbott et al 5reported that the index f22m,withf2representingthesecondresonantfrequency andm the mass of an apple, cou
12、ld be used to represent the firmness of the apple.Chen and DeBaerdemacker 6- 8applied the finite element method to analyze the vibrational modes in apples and other fruits. They reported that three classes of vibrational modes, torsional, the first type spheroidal, and thesecond type spheroidal, sho
13、uld be used, and that for the nonspherical objects such as apples, the stiffnesscoefficient f2m or f2m2 3was a goodindicatorof firmness. T hey observed that results from the finite element simulation of the fruit are compatible with theexperimental results when the elastic modulus was used as the in
14、dicator of the fruit firmness.The objectives of this paper are: 1) To establish the nonsphericalfiniteelementmodels( FEM )ofwatermelon; 2) T o determine the optimum location of theforceexcitationandthesuitableresponse measurementsensorformeasuringtheresonant frequency; 3) T o find out the relationsh
15、ip between thevibrationcharacteristicsofwatermelonandits firmness;4)T o compare the differences between experimental results and FEM estimated results.1 Methods and Materials1. 1 Theory and analysisThe standard formulation for finite element solutionofsolid isthe displacementmethod.The finite elemen
16、t modes of model were created using ANSYS version 7. 0 ( SAS IP, Inc) . T he watermelon model was constructed, and the analysis files were prepared.17The ellipsoid was assumed to be linearly elastic, homogenous, and isotropic. T he Poissons ratio was assigned 0. 3 for all cases. The 3-D 10-node 92 solid element was used, allowing three transnational as well as three rotational degrees of freedoms ( DOFs) ateach node. Model solid for ellipsoidal, was generated using some me
