库尔勒香梨振动模态的有限元分析及坚实度评估

Finite element analysis of vibration mode and firmness evaluation for Korla pear

为了实现香梨坚实度的可靠评估,该文采用有限元法对香梨振动模态分析,以明确库尔勒香梨果形对固有频率的影响,并建立更适于香梨坚实度评价的指标。研究结果表明:香梨梗端和萼端是振动信号激励和感测的适宜位置,其扭转模态、弯曲模态、拉压模态的固有频率可用于香梨坚实度评估;采用香梨固有频率、质量m、密度ρ及描述果形的纵横比q建立的公式2m2/3ρ1/3qt能够有效评估香梨坚实度,各模态的固有频率对应的t值分别为:扭转模态时,t=1.19;弯曲模态时,t=1.47;拉压模态时,t=0.47。这可为香梨内部品质的振动检测提供研究依据和实践指导。

The firmness of fruits can be estimated with measurement of its natural frequency （f）. Considering the effects of mass （m） and density （ρ） on natural frequency of fruits, the different firmness indexes f2m, f2m2/3 and f2m2/3ρ1/3 were proposed. Nevertheless, some studies showed that the natural frequency of fruit was also affected by fruit shape. Consequently, the calculated values of these indexes （e.g. f2m2/3ρ1/3） were inaccurate for firmness evaluation of fruit. However, little information is reported on the firmness index considering the fruit shape. Because the finite element modal analysis has been widely used to obtain natural frequency and mode shapes of fruits and vegetables, so in this work it was applied to provide data of natural frequencies of Korla pear with different shapes and the new firmness index including the fruit shape factor was then established. The roundness ratio （q） of longitudinal cross section was employed to describe the fruit shape of Korla pear quantitatively. It is expressed as q=a/b, where a, b are the major axis （longest intercept） and intermediate axis （longest intercept normal to a） of longitudinal cross section. The previous index f2m2/3ρ1/3 was transformed into f2m2/3ρ1/3qt introducing the power function of roundness ratio qt. The outline of a real Korla pear was determined using the ＂Spline＂ option and the 3D solid model was created by rotating the half contour plane around the major axis. Assuming Korla pear as linear elastic and isotropic material, the model was free meshed using 3D tetrahedral structural solid element with 10 nodes （SOLID 187） in ANSYS Workbench 14.0. The first 20 natural frequencies and mode shapes were extracted from the free modal analysis results. In this work, range ratio （R.R） and coefficient of variation （C.V） were used to analyze the variation of the calculated values of the firmness index. The optimal values of t for different vibration modes, which were corresponding to the maximum of range ratio, were calculated through polynomial fitting the data of the range ratio. Large excitation energy could cause the Korla pears to be damaged, so the first three vibration modes with relative lower natural frequency were selected for analysis, namely torsion mode, bending mode and oblate-prolate mode. The largest deformation appeared at the stem end and the calyx end for selected mode shapes in the finite element modal analysis, so both ends of the Korla pear were suitable positions to excite and detect vibration signal. The results of ANOVA showed that the roundness ratio （q） describing Korla pear shape had significant effect on natural frequencies of these modes. For the new firmness index f2m2/3ρ1/3qt, the optimal values of t for different vibration modes were 1.19 for torsion mode, 1.47 for bending mode and 0.47 for oblate-prolate mode. Compared with index f2m2/3ρ1/3, the range ratio of index f2m2/3ρ1/3qt was larger and the coefficient of variation was smaller obviously. Taking bending mode for example, the value of range ratio increased from 55.08% to 96.18%, whereas the coefficient of variation reduces from 21.97% to 0.61%. As a result, it indicated that the index f2m2/3ρ1/3qt could replace with the index f2m2/3ρ1/3 to accurately evaluate the firmness of Korla pear. Furthermore, this firmness index can provide a theoretical basis and practical guidance for vibration detection of internal quality of Korla pear.