<b>Simulation of the dynamic behavior of the coffee fruit-stem system using finite element method

Abstract

ABSTRACT. Mechanical harvesting can be considered an important factor to reduce the costs in coffee production and to improve the quality of the final product. Coffee harvesting machinery uses mechanical vibrations to accomplish the harvesting. Therefore, the determination of the natural frequencies of the fruit-stem systems is an essential dynamic parameter for the development of mechanized harvesting system by mechanical vibrations. The objective of this study was to develop a three-dimensional finite element model to determine the natural frequencies and mode shapes of the coffee fruit-stem systems, considering different fruit ripeness. Moreover, it was carried out a theoretical study, using the finite element three-dimensional model, based on the linear theory of elasticity, for determining the generated stress in a coffee fruit-stem system, during the harvesting process by mechanical vibration. The results showed that natural frequencies decrease as the ripeness condition of the fruit increases. Counter-phase mode shape can provide better detachment efficiency considering the stress generation on coffee fruit-stem system during the harvesting by mechanical vibrations and presented a difference greater than 40 Hz between the natural frequencies of the green and ripe fruit.Keywords: coffee harvesting, mechanization, mechanical vibrations.Simulação do comportamento dinâmico do sistema fruto-pedúnculo do café empregando o método de elementos finitos RESUMO. A colheita mecanizada pode ser considerada como um importante fator na redução de custos de produção e na obtenção de café de qualidade. Um dos princípios mais difundidos e empregados em máquinas colhedoras de frutos é o de vibrações mecânicas. Logo, a determinação das frequências naturais dos sistemas fruto-pedúnculo é requisito básico para o desenvolvimento de sistemas de colheita por vibrações mecânicas. O objetivo desse trabalho foi o desenvolvimento de um modelo tridimensional em elementos finitos do sistema fruto-pedúnculo, para a determinação das frequências naturais e modos de vibração para os diferentes graus de maturação do sistema frutopedúnculo. Adicionalmente, foi realizado um estudo teórico para a determinação dos esforços gerados em um sistema fruto-pedúnculo quando submetido a vibrações mecânicas. Os resultados mostraram que as frequências naturais diminuem à medida que o grau de maturação dos frutos aumenta. O modo de vibração em contra-fase pode proporcionar melhor eficiência de derriça por gerar níveis de tensões mais acentuados na união entre o fruto e o pedúnculo, pela sua configuração geométrica. Para o modo de vibração em contra-fase o intervalo entre as frequências naturais para os graus de maturação verde e cereja foi superior a 40 Hz.Palavras-chave: colheita de café, mecanização, vibrações mecânicas.

<b>Determination of modal properties of the coffee fruit-stem system using high speed digital video and digital image processing

“…A significant difference was found in the natural frequency between the green ripening stage (13.29 Hz) and the red ripening stage (11.62 Hz), confirming the literature (Ciro, 2001;Tinoco et al, 2014;Santos et al, 2015). On the other hand, no difference was found for stem length between the ripening stages ( Table 3), indicating that the observed difference between the natural frequencies is associated with the mechanical properties, such as elasticity modulus of stems.…”

“…Santos, Queiroz, Valente, and Coelho (2015), Tinoco, Ocampo, Peña, and Sanz-Uribe (2014) and Espinosa, Rodríguez, and Guerra (2007) employed the finite element method for determining mode shapes and natural frequencies, and sought resonance bands favoring selective detachment of coffee fruit.…”

<b>Dynamic test for determining the elastic modulus of coffee fruit-stem-branch system

“…In this study, no significant differences were detected, but higher natural frequencies were found in the green fruit-stem system relative to the ripe system. This finding was also verified by Ciro (2001) and Santos et al (2015), and can be explained by the higher elastic modulus of the system at the green stage (Castro & Marraccini, 2006).…”

“…Using an analytical method, Ciro (2001) determined that the natural frequencies of the fruitstem system at the green and ripe stages for the first mode shape were 26.97 and 25.10 Hz, respectively. Santos, Queiroz, Valente, and Coelho (2015) determined the natural frequencies for the fruit-stem system using the finite element method and reported values of 23.2 and 19.9 Hz for the green and ripe stages, respectively. The differences between the results obtained by Santos et al (2015) and Ciro (2001) can be explained by the variations in the geometric, physical, and mechanical properties of the system and the methods applied.…”

“…Santos, Queiroz, Valente, and Coelho (2015) determined the natural frequencies for the fruit-stem system using the finite element method and reported values of 23.2 and 19.9 Hz for the green and ripe stages, respectively. The differences between the results obtained by Santos et al (2015) and Ciro (2001) can be explained by the variations in the geometric, physical, and mechanical properties of the system and the methods applied. In this study, no significant differences were detected, but higher natural frequencies were found in the green fruit-stem system relative to the ripe system.…”