Study On Vibration Modal Analysis And Firmness Evaluation Of Irregular Shapes Pear

Pear is the third largest fruit,next only to apple and orange,in China.The industrial development of pear has great significance in enriching fruit farmers.The grading of pear quality can improve the commodity value of pear.Firmness is one of the important indicators for the internal quality evaluation of fruit,and the traditional firmness index is only applicable to evaluate the firmness of sphere-shaped fruit and vegetable.For irregularly shaped pears,traditional firmness index cannot accurately evaluate the firmness.Therefore,a firmness index can be established for fruit with an irregular or a larger variation of fruit shapes.In this study,the Fourier descriptor as a reliable shape descriptor was used to represent complex and irregular pear shape,and the effect of fruit shape on the natural frequency was analyzed using the experimental modal method combined with the finite element（FE）method.Finally,established firmness evaluation index for irregular shapes pears based on Fourier descriptor and resonance frequency.The main conclusions of this paper are as follows:（1）There are three modes including bending mode,compression mode and breathing mode.The vibration deformation of the bending mode was larger at the stem shoulder,and almost no vibration deformation occurred at the calyx shoulder.The maximum vibration deformation of the compression mode occurs at the equatorial region.The vibration deformation of breathing mode was larger at the stem and calyx shoulder of pear.When the uniaxial acceleration sensor is used to detect the resonance frequency of pear,the vibration signal should be sensed at the equatorial region of pear.（2）The experimental tested results of pear were used to correct the FE calculation results,and the error between the frequency of FE and the experimental tested frequency was less than 3.25%.The FE modal analysis results of pear were effective,so the FE method could be used to analysis the vibration characteristics of pear.（3）Information of pear mainly concentrated in the Fourier descriptor in the amplitude of the larger descriptor,with 15 Fourier descriptors reconstruction of pears and pears original outlines have high inosculation.The complex shapes of pear can be described by first 15 Fourier descriptors.（4）The firmness index S_Ewas constructed based on the resonance frequency（f _C）of compression mode and Fourier descriptor F₁,which could eliminate the influence of fruit shape on the evaluation of pear firmness.By comparison,the firmness sensitivity of the new index with a value of 75.81%was mostly close to that of M-T penetration test（79.36%）.（5）Among the four frequency firmness evaluation indexes,the sensitivity of dual-frequency firmness indexS_{f1 f2} for the firmness evaluation of Korla pear has higher firmness sensitivity than that of other frequency indexes.The sensitivity of firmness index S_Efor Korla pear was 74.69%,and it was also suitable for the evaluation the firmness of Korla pear,but it was not as accurate as the dual-frequency indexS_{f1 f2}.In this study,the vibration modal method was used to analysis the influence of Fourier descriptors on the resonance frequency.The firmness of irregular pear can be accurately evaluated by The firmness evaluation index,which established by Fourier descriptor and resonance frequency.The research results can provide reference for the firmness evaluation of irregular pear.