Firmness evaluation of melon using its vibration characteristic and finite element analysis

Firmness evaluation of melon using its vibration characteristic and finite element analysis 1 2 first-author 1 †E-mail:ybying@zju.edu.cn †E-mail:ybying@zju.edu.cn ybying@zju.edu.cn 1 1 1 Department of Biosystems Engineering, Institute of Modern Agricultural Equipment and Automation, Zhejiang University, Hangzhou 310029, China Department of Biosystems Engineering, Institute of Modern Agricultural Equipment and Automation, Zhejiang University, Hangzhou 310029, China Department of Agricultural Engineering, Faculty of Engineering, Sinnar University, Sudan Department of Agricultural Engineering, Faculty of Engineering, Sinnar University, Sudan The “Huang gua” melons were measured for their physical properties including firmness and static elastic modulus. The vibrational characteristics of fruits and vegetables are governed by their elastic modulus (firmness), mass, and geometry. Therefore, it is possible to evaluate firmness of fruits and vegetables based on their vibrational characteristics. Analysis of the vibration responses of a fruit is suggested for measuring elastic properties (Firmness) non-destructively. The impulse response method is often used to measure firmness of fruits. The fruit was excited using three types of balls (wooden, steel and rubber) and the vibration is detected by an accelerometer. The Instron device was used to measure the static elastic modulus of the inner, middle and outer portions of melon flesh. Finite element (FE) technique was used to determine the optimum excitation location of the chosen measurement sensor and to analyze the mode shape fruits. Four types of mode shapes (torsional or flexural mode shape, first-type, second-type spherical mode and breathing mode shape) were found. Finite element simulation results agreed well with experimental results. Correlation between the firmness and resonant frequency ( r 2 =0.91) and between the resonant frequency and stiffness factor ( r 2 =0.74) existed. The optimum location and suitable direction for excitation and response measurement on the fruit were suggested. Melon Sensing Finite element Experimental modal analysis Firmness INTRODUCTION 1 Researchers continue to develop non-destructive methods to evaluate the effect of their impact on agricultural products using high-tech methods. Non-destructive techniques sensing has been applied for obtaining fruit and vegetable quality index. Non-destructive method for measuring firmness using sonic or vibration characteristics applied in previous investigations was recently reviewed by Armstrong ( 1989 1989 ) and Liljedahl and Abbott ( 1994 1994 ). The sonic vibration technique using the resonant frequency of the fruit vibration modes often applied to estimate fruit firmness had been verified to have high correlation to quality and maturity (Chen and Sun, 1991 1991 ; Tollner et al., 1993 1993 ). Early researches found that f 2 m or f 2 m 2/3 ρ 1/3 ( f being the first or second natural frequency of the tested fruit, m being its mass, and ρ being density) could serve as the ‘stiffness coefficient’ or ‘index of firmness’ for fruits and vegetable of spherical shape (Abbott et al., 1968 1968 ; Finney, 1970 1970 ; Cooke, 1972 1972 ). The properties vibrations of some commodities are significantly correlated with firmness and ripeness (Essex and Finney, 1972 1972 ). Acoustic properties of fresh fruits reported were applied in non-destructive quality evaluation (Ying and Cai, 1997 1997 ). The acoustic emission was sensed by microphone and the signal was analyzed using an FFT (Fast Fourier Transform) algorithm to extract the response frequencies of the fruit. The result showed significant correlation between the acoustic parameters of apples and their apparent Young’s modulus and firmness (Yamamoto and Haginuma, 1980 1980 ). Theoretical analysis revealed two-fundamental mode shapes referred to as torsional modes and spherical modes which were found to exist in apples (Cooke, 1972 1972 ; Rosenfeld et al., 1991 1991 ; 1993 1993 ; Huarng et al., 1992 1992 ; Chen and De Baerdemacker, 1993a 1993a ; 1993b 1993b ; Chen, 1993 1993 ). The specific objectives of the work: 1. To determine the physical properties of melon. 2. To analyze the vibration of the mode shape by applying finite element model (FEM). 3. To establish the relationship between melon firmness, stiffness and resonant frequency. 4. To optimize the material of the impactor for detecting the melon. 5. To determine the optimum location of the excitation, to choose measurement sensor and to analyze the mode shape fruits. MATERIALS AND METHODS 1 Materials 2 Thirty “Huang gua” melons of different weight were bought from a supermarket of Hangzhou for the study. Impactor types 2 Three types of impactors, viz. wooden, rubber and steel, with the same diameter (30 mm) were used in the experiment. Experimental determination of the spherical resonant frequency 2 The acoustic response of each melon which was suspended freely was measured by striking the fruit on the equator of its surface with different types of ball the output vibration on the opposite side of the fruit was detected by a made in China accelerometer (CA-YD-126) with sensitivity 0.30 pc/(m·s 2 ), cross-axis sensitivity ratio < 5%, max acceleration (10 5 m/s 2 ). The vibration detected by the accelerometer was transformed into electric signal, which was amplified and filtered by a 3–3000 Hz band processing circuit. The processed signal was sampled at a rate of 10 kHz with a data acquisition board PCL-1800 (Advantech Co. Ltd.). The signals were analyzed using a Fast Fourier Transform (FFT) to extract the resonance frequencies of the fruit. A schematic diagram showing the instrument setup for measuring the acoustic response of each melon is shown in Fig. 1 1 . An automated data acquisition system for the impact characteristic experiments of agricultural materials was developed. The software for the data acquisition was developed on the Advantech’s Genie which is a Windows-based data acquisition, control, analysis and presentation development software package (Wang et al., 2002 2002 ). The schematic diagram of the acquisition system for impact characteristics and the structure of software of data acquisition are shown in Fig. 2 2 and Fig. 3 3 respectively. Firmness measurement 2 The firmness of the melon was tested by parallel plate compression in a Universal Testing Machine (Instron Device 5543). The fruit positioned with their stem horizontal and compressed using 6 mm diameters puncture probe on the equator surface at the same location where the fruit was impacted at speed of 10 mm/s. The displacement curve was recorded. The mass of the melon was measured with a precision balance. The volume was measured by the water method displacement. The melon was cut into halves and the dimensions of the principal axes were recorded (Fig. 4 4 ). The bulk volume of each melon was estimated by the ellipsoid equation from Eq.( 1 1 ) while the stiffness ( S ) was calculated by using Eq.( 2 2 ). V est =1.334π ab 2 S = f 2 m 2/3 Eq.( 2 2 ) was expressed in stiffness units with dimension 10 4 Hz 2 g 2/3 . Experimental determination of static elastic modulus 2 Three cylindrical cores were cut near the equator from one half of each melon, using a cylindrical borer. Each cylindrical core was then cut into three 10 mm long 14 mm diameter samples referred to as outer, middle and inner layer of the flesh, Instron testing machine was used to measure the static elastic modulus. Compression speed of 25-mm/min was selected; the force deformation curve was obtained. Fig. 5 5 shows a force-deformation curve measured at 10 mm-height the melon’s middle layer. The curve appears linear in the initial compression phase and tended to be nonlinear after deforming about 4.5 mm. To calculate the static elastic modulus, the final linear part of the curve was used. At such a range of deformation, no juice was obviously squeezed out yet. Fig. 6 6 shows the variation of young’s modulus in the outer, middle and inner layers of the three samples. Finite element simulation of the dynamic properties of intact melons 2 Finite element models of fruit were first created using ANSYS version 7.0 (SAS IP. Inc.). For the FE model, the melon was considered as an elastic body with a seed cavity. The nonlinear visco-elastic texture of the melon was therefore simplified as linear elastic texture. This simplification was widely used in previous theoretical study on the dynamic properties of the fruit (Cooke, 1972 1972 ; Armstrong et al., 1990 1990 ; Rosenfeld et al., 1991 1991 ; Huarng et al., 1992 1992 ; Chen and De Baerdemacker, 1993a 1993a ; 1993b 1993b ). Good agreement with real fruit was obtained. 3-D 10-node 92 solid elements were used, allowing three translational and three rotational degrees of freedoms at each node. Model ellipsoidal solid was generated using some measuring experimental data in (Table 1 1 ). M mea : Measured mass V mea : Measured volume V est : Estimated volume V flesh : Flesh volume ρ : Density E est : Estimated elasticity Sample (No.) 1 1 M mea (kg) 2 2 V mea (cm 3 ) 3 3 V est (cm 3 ) 4 4 V flesh (cm 3 ) 5 5 ρ (kg/m 3 ) a (cm) b (cm) c (cm) d (cm) 6 6 E est (MPa) 1 1.137 1210 1239 1011 1125 7.5 6.5 5.3 3.2 2.0 2 1.564 1669 1674 1304 1119 7.5 7.3 5.0 4.2 3.4 3 1.535 1550 1563 1207 1271 7.4 7.1 5.1 4.1 4.5 4 1.681 1790 1786 1337 1257 8.0 7.3 5.8 4.3 3.6 5 2.090 2110 2115 1268 1648 8.3 7.8 5.6 4.7 4.0 6 1.560 1666 1672 1170 1282 7.7 7.2 5.2 4.8 4.5 7 1.912 2040 2036 1399 1367 8.2 7.7 6.2 4.9 4.5 8 1.837 2200 2196 1477 1244 8.4 7.9 6.6 5.0 4.6 9 2.062 1949 1956 1367 1508 8.3 7.5 6.1 4.8 3.4 10 2.076 2150 2166 1523 1363 8.5 7.8 5.9 5.1 3.6 11 1.463 1595 1580 1252 1169 7.7 7.0 4.9 4.0 8.2 12 1.468 1560 1539 1214 1121 7.5 7.0 5.1 3.9 5.2 13 1.390 1538 1546 1340 1037 8.1 6.8 6.1 3.0 6.3 14 1.616 1840 1824 1366 1183 8.4 7.2 6.5 4.1 6.9 15 1.626 1720 1735 1354 1201 8.7 6.9 6.3 3.8 7.2 16 1.184 1510 1830 1191 994 8.2 7.3 6.1 5.0 4.3 17 1.433 1610 1595 1292 1109 8.0 6.9 5.9 3.5 8.0 18 1.575 1846 1830 1365 1154 8.2 7.3 6.3 4.2 5.8 19 1.537 1729 1718 1261 1219 7.7 7.3 5.4 4.5 6.6 20 1.621 1898 1808 1371 1574 8.1 7.3 6.2 4.1 4.9 21 1.312 1574 1565 1173 1220 7.9 6.9 5.7 3.8 7.6 22 1.393 1533 1541 1132 1231 7.3 7.1 6.3 4.1 5.8 23 1.456 1548 1539 1325 1099 7.5 7.0 5.3 3.1 6.9 24 1.477 1610 1585 1250 1182 7.3 7.2 5.0 4.0 6.1 25 1.310 1505 1455 1143 1146 7.3 6.9 4.9 3.9 7.3 26 1.177 1488 1413 1044 1127 7.3 6.8 5.0 4.2 4.8 27 1.219 1142 1116 1113 1095 7.2 6.8 4.9 3.7 6.7 28 1.500 1610 1621 1356 1110 9.3 6.5 6.7 3.1 7.3 29 1.031 1128 1244 1043 990 7.9 6.2 5.2 3.1 7.3 30 1.053 1150 1147 944 1120 8.0 5.9 5.2 3.1 4.9 The generated nodes were up to 610. Total nodes were calculated using subspace solver with free boundary conditions. The first six modes represented rigid body modes, and flexible modes started from the seven modes; the melon was aligned with the global coordinated system given in Fig. 4 4 . In this work the model updating technique was used to tune the lowest natural frequency f of each FE model to match that of the corresponding experiment. The modulus of elasticity (MOE) was then estimated without destroying the fruit used for dynamic MOE tests. It is assumed that the system was not damped. The undamped vibration of the nodes was: $$M\ddot x(t) + Kx(t) = f(t)$$ where M is the mass matrix. K is the stiffness matrix, x and $$\ddot x(t)$$ are the displacement and acceleration vectors, and t is the time. In this Finite Element Modal Analysis (FEMA) free vibration is assumed. So no force is applied and correspondingly f ( t )=0. For linear system this vibration will be harmonic of the form: X i = φ i cos ω i t where φ i is the eigenvector representing the i th natural frequency, ω i is the i th natural angular frequency and t is the time. By substituting Eq.( 3 3 ) into Eq.( 2 2 ) yields $$(K - \mathop \omega \nolimits_i^2 M)\mathop \varphi \nolimits_i {\text{ = }}0$$ For a non-trivial solution this corresponds to the following equation. $$(K - \mathop \omega \nolimits_i^2 M){\text{ = }}0$$ This equation represents an eigenvalue problem, which can be solved for n values of ω 2 (eigenvalues) and n eigenvector problems, where n is number of all the degrees of freedom (DOFs). This eigenvalue problem was solved by using ANSYS FE program using subspace iteration method. RESULTS AND DISCUSSION 1 Mode shapes of the melon in vibration 2 This work took advantage of model updating technique to tune the lowest natural frequency of each FE model to match that of the corresponding experiment. The modulus of elasticity (MOE) was then estimated without destruction of the fruit for dynamic MOE tests. All estimated dynamic MOEs were comparable with reference data on melons (Chen et al., 1996 1996 ). It was reported that the dynamic MOEs were also about 2 to 10 times static MOE of melons (Deihl et al., 1979 1979 ). The MOE of FE model was tuned such that the first bending mode frequency matched experimental frequency (Cherng, 2000 2000 ). In the FE simulation, four kinds of mode shapes were obtained: first-type spherical mode, second-type spherical mode, torsional mode, and breathing mode. 1. First-type spherical mode The first-type mode is the oblate-prolate mode. During vibration, the melon model extends in one direction and contracts at the same time in the perpendicular direction. Three such modes were found to exist within a narrow frequency band of 238.75 Hz to 279.22 Hz (Fig. 7 7 ). For each first-type spherical mode, two nodal lines exist. In order to measure the vibration signal of the mode, excitation and response sensors should be placed on the melon surface far away from the nodal lines. Furthermore, the direction of both the excitation and the sensory axis of the response sensors should be in line with the vibration directions. The Y -axisymmetric mode has one nodal line in the upper part and another one in the lower part of the melon. Its vibration signal can be detected at the top, middle or bottom of the melon in the direction normal to the local surface. Most of the spherical modes measurements were made around the equator of the melon. 2. Second-type spherical mode Fig. 8 8 shows the second-type spherical modes with resonant frequencies (of 280.92 Hz to 288.92 Hz) characterized by the out of-phase transverse vibration at the upper and the lower part, little vibration along the longitudinal axis, existence of a nodal line each near the top, the equator, and the bottom. 3. Torsional mode The torsional mode in Fig. 9 9 has resonant frequency of 290.85 Hz to 296.33 Hz, and is characterized by opposite rotation of two hemispheres connected at the equator plane around the Y -axis; their vibration is normal to each other. Fig. 9 9 shows the Y -axisymmetric torsional mode, with tangential displacement in planes vertical to the Y -axis. To measure its vibration signal, excitation and response sensors should be placed in the direction tangential to the upper or lower part of the melon where the most deformation occurs during vibration. 4. Breathing mode The breathing mode in Fig. 10 10 is a pure compression mode with resonant frequency of 306.81 Hz, and characterized by simultaneous expansion or contraction in all radial directions. It is a kind of spherical mode with a node point in the center of the model. Its vibration signal can be measured anywhere on the surface in the radial direction. Table 2 2 summarizes the results of experiment modal analysis. The results of finite element analysis on the selected melons were similar to these obtained by (Cherng, 2000 2000 ; Chen et al., 1996 1996 ). There are six rigid body modes, which can be observed at 0 Hz. Sample No. Measure frequency (Hz) Identification modes Estimated frequency or FE result (Hz) 1 238.75–279.22 First-type spherical mode 145.93–175.62 2 280.92–288.92 Second-type spherical mode 182.47–290.85 3 290.85–296.33 Torsional mode 293.34–298.75 4 306.81 Breathing mode 303.81 Location and direction of force excitation and measurement sensors 2 The resonant frequency of some mode shapes obtained by experiment gives clues on the right locations and directions of the excitation and response measurement sensors. To measure the vibration signal of the mode, excitation and response sensors should be mounted in the region away from nodal lines. To estimate the firmness of the melon by the first-type longitudinal resonant frequency, the middle part of the melon surface is recommended as the location for the force excitation and the response sensors, because there are fewer modes that can be measured in this region. To measure its vibration signal, the excitation and response sensors should be placed in the direction tangential to the upper or lower part of the melon where most of deformation occurs during vibration. For the breathing mode, its vibration signal can be measured in the radial direction anywhere on the model surface. Effect of testing fruit on the equator, with different types of impactor on the natural frequency 2 Fig. 11 11 and Fig. 12 12 show the frequencies versus amplitude curves for three types of impactors. The wooden ball shows the highest peak in the curve compared to the other two types. Relation between the resonant frequency and melon stiffness factor (SF) and firmness 2 Linear regression analysis (LRA) of melon stiffness ( S ) and firmness yields the regression equation coefficient Y =205.25884+39.83976 X and correlation r 2 =91. Fig. 13 13 and Table 3 3 give the relation between the firmness and resonant frequency. The relation indicates the ability to accurately predict the fruit firmness as the quality in fruits and vegetables. Table 4 4 and Fig. 14 14 show the relation between the resonant frequency and stiffness factor (SF) of the fruit, with regression equation coefficient Y =209.83092+6.53524 X , correlation r 2 =0.74. Parameter Value Error Prob > | t | R -square (COD) Adj. R -square Root-MSE (SD) N A 205.25884 3.51833 <0.0001 0.90596 0.9012 6.82804 30 B 39.83976 3.51833 <0.0001 Parameter Value Error Prob > | t | R -square (COD) Adj. R -square Root-MSE (SD) N A 208.66503 10.78405 <0.0001 0.75971 0.74437 10.26613 30 B 6.60899 1.06904 <0.0001 CONCLUSION 1 The Finite Element Model (FEM) for melons was established by FE simulation. Three kinds of mode shapes referred to as the first-type spherical, second-type spherical mode, and the breathing or pure compression mode were found to exist for melon. The breathing mode was found to exist only in melon. The simulation of mode shapes resonant frequencies agreed well with the measured values. The direct measured volume agreed well with the estimated volume, although there were some differences, which were within reasonable range, because there were some sources of errors attributed to the inherently imperfect geometry. The smaller wooden ball 30 mm in diameter had higher amplitudes of higher resonant frequency. The stiffness factor ( f 2 m 2/3 ) obtained by other researchers were also successfully used to evaluate fruit firmness so the stiffness factor has correlation with the resonant frequency, r 2 =0.74. The firmness has better correlation ( r 2 =91) with the resonant frequency of the fruit. The selection of location and direction for the force excitation and the response measurement sensor are most important for detecting a mode. The middle part on the fruit surface is suggested to be used while estimating the fruit firmness by the resonant frequency of the first-type spherical mode. References JA Abbott , GS Bachman , RF Childers , JV Fitzgerald , FT Matusik . Sonic techniques for measuring texture of fruits and vegetables . Food Technology , 1968 . 22 635 - 646 . . Sonic techniques for measuring texture of fruits and vegetables PR Armstrong . Measurement of Apple Firmness Using the Acoustic Impulse Response , 1989 . : East Lansing, Mich Mich, State Univ. , . Measurement of Apple Firmness Using the Acoustic Impulse Response P Armstrong , HR Zapp , GK Brown . Impulsive excitation of acoustic vibrations in apples for firmness determination . Transactions of the ASAE , 1990 . 3 ( 4 ): 1353 - 1359 . . Impulsive excitation of acoustic vibrations in apples for firmness determination H Chen . Analysis of the Acoustic Impulse Resonance of Apples for Non-Destructive Estimation of Fruit Quality , 1993 . : KU Leuven, Belgium . Analysis of the Acoustic Impulse Resonance of Apples for Non-Destructive Estimation of Fruit Quality H Chen , J De Baerdemacker . Modal analysis of the dynamic behavior of pineapples and its relation to fruit firmness . Transactions of the ASAE , 1993 . 35 ( 5 ): 1439 - 1444 . . Modal analysis of the dynamic behavior of pineapples and its relation to fruit firmness H Chen , J De Baerdemacker . Finite element based modal analysis of fruit firmness . Transactions of the ASAE , 1993 . 36 ( 6 ): 1827 - 1833 . . Finite element based modal analysis of fruit firmness P Chen , Z Sun . A review of nondestructive method for quality evaluation and sorting of agricultural products . Journal of Agricultural Engineering Research , 1991 . 49 85 - 98 . . A review of nondestructive method for quality evaluation and sorting of agricultural products H Chen , J De Baerdemacker , V Bellon . Finite element study of the melon for nondestructive sensing of firmness . Transaction of ASAE , 1996 . 39 ( 3 ): 1057 - 1065 . . Finite element study of the melon for nondestructive sensing of firmness PA Cherng . Vibration modes of ellipsoidal shape melons . Transactions of the ASAE , 2000 . 43 ( 5 ): 1185 - 1193 . . Vibration modes of ellipsoidal shape melons JR Cooke . An interpretation of the resonant behavior of intact fruits and vegetables . Transactions of the ASAE , 1972 . 15 ( 6 ): 1075 - 1080 . . An interpretation of the resonant behavior of intact fruits and vegetables K Deihl , D Hamann , J Whitfield . Structural failure in selected raw fruits and vegetables . J Texture Studies , 1979 . 10 ( 4 ): 371 - 340 . . Structural failure in selected raw fruits and vegetables E Essex , JR Finney . Vibration techniques for testing fruit firmness . Journal Texture Studies , 1972 . 3 263 - 283 . . Vibration techniques for testing fruit firmness EE Finney . Mechanical resonance within Red Delicious apples and its relation to fruit texture . Transactions of the ASAE , 1970 . 13 ( 2 ): 177 - 180 . . Mechanical resonance within Red Delicious apples and its relation to fruit texture LD Huarng , P Chen , SK Upadhyaya . Determination of Acoustic Vibration Modes in Apples . 1992 . ASAE Paper, No. c92-65. st. Josph, Mich, ASAE . Determination of Acoustic Vibration Modes in Apples LA Liljedahl , JA Abbott . Change in sonic resonance of Delicious and ‘Golden Deliciou’ apples undergoing accelerated ripening . Transactions of the ASAE , 1994 . 37 ( 3 ): 907 - 912 . . Change in sonic resonance of Delicious and ‘Golden Deliciou’ apples undergoing accelerated ripening DI Rosenfeld , L Shmulevich , G Rosenhouse . Three-Dimensional Simulation of Acoustic Response of Fruit for Firmness Sorting . 1991 . ASAE Paper, No. 91-6046. st. Joseph, Mich, ASAE . Three-Dimensional Simulation of Acoustic Response of Fruit for Firmness Sorting D Rosenfeld , I Shmulevich , G Rosenhouse . Three Dimensional Simulation of the Dynamic Response of Fruit . 1993 . ASAE paper, No. 93-6022. St. Joseph, Mich, ASAE . Three Dimensional Simulation of the Dynamic Response of Fruit EW Tollner , K Brecht , BL Upchurch . RL Shewfelt , SE Prussia . Postharvest Handling a System Approach in Nondestructive Evaluation: Detection of External and Internal Attributes Frequently an Associated with Quality or Damage . Postharvest Handling: A Systems Approach , 1993 . : San Diago, CA, New York Academic Press, Inc , 225 - 255 . . Postharvest Handling a System Approach in Nondestructive Evaluation: Detection of External and Internal Attributes Frequently an Associated with Quality or Damage H Yamamoto , H Haginuma . Acoustic impulse response method for measuring natural frequency of intact fruits and preliminary applications to internal quality evaluation of apples and watermelon . Journal of Texture Studies , 1980 . 11 117 - 136 . . Acoustic impulse response method for measuring natural frequency of intact fruits and preliminary applications to internal quality evaluation of apples and watermelon YB Ying , DP Cai . Acoustic properties of fresh agricultural products and its application in non-destructive quality evaluation . Transaction of the CSAE , 1997 . 13 ( 3 ): 208 - 212 . . Acoustic properties of fresh agricultural products and its application in non-destructive quality evaluation JP Wang , L Gai , J Wang . Development of data acquisition system for experiments of impact characteristics of agricultural materials . Transactions of the CSAE , 2002 . 18 ( 3 ): 150 - 153 . . Development of data acquisition system for experiments of impact characteristics of agricultural materials The authors gratefully acknowledge the help of Professor Wang Jun, Associate Professor Song Huizhi, Dr. Yu Yonghua, and all group members. 10.1631/jzus.2005.B0483 Project supported by the National Natural Science Foundation of China (No. 30370371) and the Natural Science Foundation of Zhejiang Province (No. 301267), China 2004-11-09 2005-01-20 2005-05-22 2022-01-05 Copyright © 2005, Journal of Zhejiang University Science 2005 Journal of Zhejiang University-SCIENCE B (Biomedicine and Biotechnology) 06 6B