Simulation of Natural Frequencies of Orange Fruit Using Finite Element Method

Abstract

IntroductionThe growing consumer demand for high-quality products has led to the development of new technologies for assessing the quality of agricultural products. Iran is the 9th largest orange producer in the world. Every year, large quantities of agricultural products lose their optimal quality due to mechanical and physical damage during various operations such as harvesting, packaging, transportation, sorting, processing, and storage. This study is performed to identify the natural frequencies and vibration modes of the Thomson orange fruit using finite element modal analysis by ANSYS software. In addition, physical properties including mass, volume, density, and principal dimensions were measured, and mechanical properties were determined using Instron Texture Profile Analysis. The dynamic behavior of the orange fruit was simulated using the pendulum impact test. Afterward, the obtained impact was applied to the orange fruit by force gauge and three-axis accelerometer sensors in both polar and equatorial directions. The three-dimensional geometric model of the orange fruit was drawn in the ANSYS software. After meshing and applying the boundary conditions, the first 20 modes and corresponding natural frequencies were obtained. Since the objective of this study was to identify the natural frequencies of the orange fruit, it was considered to have free movement and rotation in space. The results showed that the natural frequencies of orange fruit are in the range of 0 to 248.41 Hz. Knowledge of the texture characteristics and dynamic behavior of horticultural products is essential for the design and development of agricultural machinery. Furthermore, the design and development of agricultural machinery are directly related to the biological properties of agricultural products.Materials and MethodsThe Thomson orange variety was used in the present study. The oranges used for the experiments were harvested from the Citrus and Subtropical Fruits Research Institute in Ramsar, Iran, located at coordinates 50° 40′ E and 36° 52′ N. The oranges were subsequently divided into two groups: large (average diameter 82 mm) and small (average diameter 66 mm). Conducting the finite element analysis requires knowledge of the physical and mechanical properties of the flesh and skin of the orange fruit. The physical and mechanical properties of the tested samples include geometric dimensions, modulus of elasticity, Poisson’s ratio, and density. In the present study, the dynamic behavior of the orange fruit under dynamic loads was investigated by performing an impact test using a pendulum. The orange fruit was hung from the ceiling using a thin thread to perform experimental tests and extract the modal parameters. The orange samples were subjected to impact at three angles: 7° (below the yield point), 10° (at the dynamic yield point), and 20° (above the dynamic yield point).Results and DiscussionThe comparison of the experimental (laboratory) natural frequencies and simulation validates the simulation results. The experimental natural frequencies of the first, second, and third modes in the large-group oranges are 125.4, 146.9, and 180.4 Hz, respectively. Additionally, the simulation (modal) frequencies are 133.80, 146.16, and 196.66 Hz for the first three modes, respectively. The lowest and the highest differences were observed in the second (0.5%) and third (9.01%) modes, respectively. In the small-group oranges, the first, second, and third modes have experimental natural frequencies of 152.2, 188.8, and 242.2 Hz, respectively, and simulation frequencies are 167.79, 187.50, and 248.30 Hz. The second and first modes exhibited the smallest and largest disparities between experimental and simulated natural frequencies, respectively, at 0.68% and 10.24%.ConclusionWhile there are certain limitations, it is undeniable that Computer Aided Engineering (CAE) applications are advantageous for predicting the natural frequencies and vibration modes of spherical fruits such as oranges. Utilizing the obtained frequencies, especially the resonance frequency and the vibrational mode shape, enables us to avoid the resonance frequency in the actual transportation of oranges. This is possible through the implementation of suitable packaging and transportation methods, thereby mitigating the deterioration of fruit quality and ensuring an accurate prediction of its shelf life.

Keywords

• dynamic behavior modeling
• modal analysis
• vibration modes