International Journal of Agriculture and Crop Sciences. Available online at www.ijagcs.com IJACS/2013/5-16/1739-1744 ISSN 2227-670X ©2013 IJACS Journal
Simulation of a Tomato Sample Using Finite Element Method Mahmood Mahmoodi-Eshkaftaki *1, Ali Maleki1 1.Department of Agricultural Machinery Engineering, Faculty of Agriculture, University of Shahrekord, Shahrekord, Iran. *Corresponding author email:
[email protected] ABSTRACT: The purpose of this study was to investigate deformation behavior of the tomato fruit (hereafter tomato) upon crashing. To achieve this, a 3D simulation was used to generate a model of tomato using finite element method and then compared with experimental results. For finite element modeling with software, some mechanical properties of tomato justly punching from limited sides (head, bottom, two sides, and four sides) must be determined with compression test. To this goal, an apparatus according to Bussinesk method was manufactured. A comparison between experimental data and finite element simulation showed that the two sets of results agree well. Keywords: Elasticity Modulus, Finite element method, Simulation, Tomato. INTRODUCTION Tomato (Lycopersicon esculentum) is classified under subfamily of the Solanaceae. It is a self–fertile vegetable and has 4–6 percent crossbreeding. Tomato is one of the most consuming vegetables used as fresh, dried or processed in human nutrition and is secondary important in its family (Delina Felix and Mahendran, 2009). At present, tomato harvesting and processing are mostly manual while as increased use of tomato in large industries, it is required sufficient knowledge of physical and mechanical properties (MP) of the tomato to design some proper machines for harvesting, grading, cleaning, packaging, and transporting (Perez et al., 2007). Furthermore in these processing, tomatoes are exposed to mechanical loading with impact from different sides. This can lead to puncture injury such as makes a hole in tomato with stem, bruises or cuts, all causing qualitative and quantitative losses (Tianxia et al., 2002; Mazaheri Tehrani, 2007). Researchers have spent a lot of their time and efforts to reduce horticultural losses (Tabatabaeefar and Rajabipour, 2005; Papadopoulou and Manolopoulou, 1990). Thus, by performing studies on MP of tomatoes and effective parameters on them and with aid of obtained information, it can be possible to design mechanical systems for processing tomatoes, therefore by decreasing losses in different process sectors, increase the production output. In order to minimize mechanical damage, the handling stresses must be kept under a certain value. The internal stresses caused by an external force are very difficult to measure. An alternative approach to estimate these stresses is finite element analysis (FEA) (Cardenas and Stroshine, 1991). Presently, the most studies on macroscopic and microcosmic mechanical characteristics and mechanical damages of fruit and vegetables are concentrated on apple and potato (Abbott and Lu, 1996) and several theories of bruising and failure of fleshy fruits have been proposed. Many reports are available in the scientific literature on the FEA and resonant frequencies of various kinds of near-spherical agricultural objects such as apples (Chen and De Baerdemaeker, 1993; Lu and Abbott, 1997), peaches (Verstreken and De Baerdemaeker, 1994), melons (Chen et al., 1996) and tomatoes (Langenakens et al., 1997; Kabas et al., 2008). The researches show that the FEA is a suitable method for calculating the resonance properties of near-spherical solid materials. Tomato is much more susceptible to mechanical damage because of its soft texture. While there are a lot of studies on tomato damages, the number of literatures about the tomato’s compression test studies punching from limited sides by finite element method (FEM) is little; therefore some MP of tomato punching from four sides were measured and then used in FEA to determine the stress and deformation distributions for a tomato model, finally compared the software results with experimentally measured methods.
Intl J Agri Crop Sci. Sci. Vol., 5 (16), ( 1739-17 744, 2013
MATERIALS AND METHODS Five tomato varieties – ‘Kariz’, ‘Darbigo’, ‘Falkato’, ‘Newton’, and ‘Shaqayeq’ – in three ripeness – green, pink, and red – used in this study were obtained from greenhouse of Kesht Nesha Jonoub located at Shahreza, grown at similar conditions. The samples were around full maturity size cleaned manually to remove all foreign matter, dust, dirt, injured samples. Through a completely random factorial design test, test, effects of independent independent factor of tomato varieties and ripeness levels of product at the time of harvesting on MP of tomato were considered. In this experiment, for each test both 48 replications were used and the he tests were carried out at (21±1 21±1) °C and relative humidity of (30±1) % of environment (Papadopoulou Papadopoulou and Manolopoulou, 1990). 1990) Mechanical properties (MP) Fruit stiffness To determine the external stiffness in this research, pressures applied from four concurrent zones – head, bottom, two symmetric sides, and four sides– sides on the fruit skin for each sample. According to the references of fruit stiffness determination, the suitable probe diameter was 8 mm and the penetrating duration for depth of 4–5 4 mm was 2–3 2 s (Mahmoodi, Mahmoodi, 2008). 2008 . To determine the feature, an apparatus was manufactured as shown in Fig. 1 and a 500 N loadcell with 0.001 N precision was fixed on the apparatus by a pawl, furthermore a micrometer was timely used to measure the tomato deformation (Fig. ( 1). ). The loadcell was connected to a PC with a special cable and the data were recorded with its software (Data collection speed of this device was 200 Hz). The equivalent force for penetration of 4–5 4 mm (measured with micrometer) was considered as stiffness index (White White et al., 2005) 2005). Elasticity modulus (E) To determine this feature, the Bussinesk method was used. used. In this method, by pressing the probe cylinder on top of the sample, given the maximum applied force (Fmax) and probe penetration inside the sample (Dp), the fruit E was calculated from Eq. 1 (Abbott Abbott and Lu, 1996). 1996
E=
Fmax (1 − µ 2 ) × Dp 2r
(1)
To determine the the Poisson oisson ratio (µ), (µ after fter measuring the initial length and width of the tomato, it was compressed until deformation occurred on the fruit body, body the µ was calculated by using the following formula after measuring the final diameter and length after deformation (Kabas Kabas et al., 2008): 2008
µ=
∆D Di − D f = ∆L L f − Li
(2)
Where Di is the initial diameter, Df is final diameter, Li is initial length, and Lf is final length of the tomato, in mm (Fig. 2).
Fig Figure 1. Manufactured apparatus to determine the tomato mechanical properties
Figure 2. Definition figure for the Poisson ratio calculation
Finite element simulation To investigate deformation behavior of the tomato samples upon crashing, a 3D simulation was generated for each sample using FEM. The FEM is a numerical technique for solving field problems described by a set of partial differential equations. These types of problem are commonly found in many engineering disciplines, such as machine design, acoustics, acoustics, electromagnetism, soil mechanics, and fluid dynamics (Tianxia Tianxia et al., 2002). 2002 . The FEA
Intl J Agri Crop Sci. Sci. Vol., 5 (16), ( 1739-17 744, 2013
not only is a powerful tool for engineering analysis but also is used to solve problems ranging from the very simple to the very complex (Chen Chen et al., 1996). 1996 Time constraints and limited availability of product data call for many simplifications in the analysis models. On the other hand, specialized analysts implement FEA to solve very advanced problems, such as crash dynamics, material forming or analysis of bio-structures bio structures (Cardenas Cardenas and Stroshine, 1991; Chen and De Baerdemaeker, 1993; Lu and Abbott, 1997; Kabas et al., 2008). 2008 . Today, with the help of advancing technologies, computers and FEA softwares software allow us to use FEM in nearly all disciplines of engineering engineering. The consequent vector which usually applied on a material is FI(t)+FD(t)+FE(t)-R(t)=0, R(t)=0, where FI(t) are the inertia forces, FD(t) are the damping forces, FE(t) are the elastic forces, and R(t) are externally impact forces (The unit of force is N). All of these these forces are time dependent. In static analysis, this equation reduces to FE(t)=R(t) since the inertia and damping forces are neglected due to no velocities and accelerations (Kabas Kabas et al., 2008). 2008 In this research, the effect of the impact on a part or an assembly with a rigid or flexible planar surface was evaluated with a new method. At first a tomato was modeled as a 3D solid by CATIA V5R21 software, and then the simulated tomato was fixed on the rigid plate (No rotations were considered until the initial initial impact occurs). The tomato was assumed to be nearly spherical, solid and with a skin that had the same properties over the entire body. All dimensions, rigid target plane and tomato’s solid model are shown in Fig. 3(a). In the simulation, octree tetrahedral elements were used for the mesh construction of the 3D model of the tomato. After the meshing operation, 9613 total nodes and 5502 total elements obtained (Figure ure 3(b)).
(a) (b) Figure 3. (a) Solid model of tomato and its dimensions in scale of 2, in this case the force have been applied from head; (b) Mesh construction of a 3D model of a tomato Table 1. Comparison of the elasticity modulus and stiffness of four researched side averages averages for the variety traits by Duncan test Head
Bottom
Both sides
Four sides
E (Mpa) 0.1765
c
0.1785
c
0.1085
a
0.1026
a
0.1423
b
0.1798
b
0.1806
b
0.1007
a
0.1059
a
0.1553
b
8.0750
a,b
8.8637
b
7.0100
a
8.4258
b
8.2014
a,b
0.1559
b
0.1507
b
0.0740
a
0.0769
a
0.1353
b
8.0114
Variety
0.1670
c
‘Kariz’
0.1652
c
‘Darbigo’
0.0893
a
‘Falcato’
0.0906
a
‘Newton’
0.1420
b
‘Shaqayeq’
b
7.8743
b
‘Kariz’
8.1162
b
8.1978
b
‘Darbigo’
6.3112
a
6.5709
a
‘Falcato’
7.3990
a,b
7.7797
b
‘Newton’
7.7171
b
7.8134
b
‘Shaqayeq’
Stiffness (N/mm) 7.3994
a
7.6954
a
6.6511
a
7.8951
a
7.6182
a
Averages with similar letters have no significant differences at level of 5%
RESULTS AND DISCUSSION Results of variance analysis showed that the relationship between the tomato E of head, bottom, both sides, and four sides, and variety was statistically significant (P
