Modal properties of coffee plants via numerical simulation

Highlights

• Dynamic behavior and modal properties of coffee plants in coffee fruits harvesting.

• Agricultural mechanization for an effective harvesting of coffee fruits.

• Simulations of models of coffee plants via finite element method.

Abstract

Mechanized coffee harvesting is performed by machines that use the principle of mechanical vibration to detach the fruit. In this type of harvest, the machines transmit kinetic energy to the plant. Numerical simulations attached to representative models have been shown to be a viable tool for understanding the coffee harvesting process. In this sense, this study aimed to evaluate the dynamic behavior of coffee plants. For this purpose, a previously developed coffee plant model was used in numerical simulations to extract the modal properties and thus enable a better understanding of the dynamic behavior of coffee plants. The frequencies extracted from the simulations were validated with frequencies observed in laboratory tests. The frequencies found in the laboratory tests were concentrated between 10 Hz and 30 Hz. The validation of the model indicated that there is a correlation between the studied variables.

Introduction

The scarcity of manpower for harvesting coffee leads to the need to increase the efficiency of the equipment used in mechanical and semimechanical harvests to reduce operational costs because harvesting is one of the most expensive stages in the coffee production chain (Silva et al., 2014). According to Santinato et al. (2015), the use of harvesting machines at a certain speed and vibration level can cause severe damage to plants. Thus, it is important to study the aspects of harvesting that involve mechanical vibrations in the machines (Silva et al., 2014) and in the interactions with the plant (Souza et al., 2018).

Mechanized coffee harvesting is performed by machines that use the principle of mechanical vibration to detach the fruits. In this type of harvest, the machines transmit kinetic energy to the plant. For an efficient harvest with the lowest damage to plants, it is necessary to adjust the machines according to the parameters of frequency, amplitude and vibration time (Coelho et al., 2015).

A vibration system can be analyzed using mathematical modeling to represent the important aspects of the real physical system without making it excessively complex. The simulation process consists of obtaining the governing equations, solving the equations and interpreting the results. The equations that describe the vibration of the system are derived from the model previously created. The solutions of these equations result in the response of the vibration system, including the displacement, velocity and acceleration values of the various parts of the system (Segerlind, 1984, Rao, 2008). One of the numerical methods employed in the analysis of static and dynamic systems is the finite element method (FEM), which is commonly used in the analysis of engineering problems; this method can be used to solve mathematical models of physical systems through simulations with a significant degree of reliability (Marques et al., 2015).

The FEM is widely used because it can be applied to problems such as fluid mechanics, electromagnetism, heat transfer, electric fields and acoustics as well as classical problems in elastic-linear structural mechanics. In agricultural engineering, the FEM has been applied in several fields, such as agricultural mechanization, processing of agricultural products and soil mechanics (Velloso et al., 2018). More specifically, the FEM is commonly used for numerical simulations in coffee beans (Sachak-Patwa et al., 2019, Fadai et al., 2019).

Ciro (2001) performed modeling of the fruit-stem system of the Colombia coffee cultivar and considered scenarios with one and two degrees of freedom and different ripening stages. In that study, data on the geometry, mass, specific mass and elastic constant of the stem were used as inputs for the simulations, and the studied models were considered highly dependent on these parameters. In addition, it was observed that achieving a selective harvesting process by changing only the working frequencies of the machines would be difficult.

Tinoco, 2017, Tinoco and Peña, 2017 performed simulations that considered representative models at each stage of fruit ripening. In Tinoco et al. (2014), each mode of vibration was analyzed for the first 20 natural frequencies, and at certain stresses concentrated at the fruit-stem interface, fruit detachment was facilitated.

Santos et al. (2015) studied the fruit-stem system of the Catuaí Vermelho and Mundo Novo cultivars and considered different stages of fruit ripening. The authors analyzed the pendular, torsional and counterphase vibration modes and found that the latter is the most indicated for harvesting because it has higher natural frequencies and can be used in selective harvesting processes.

Coelho et al. (2016) studied the fruit-stem-branch system of the Catuaí Vermelho coffee cultivar. In that study, models with one, two and three fruits were analyzed using stochastic finite element analysis. The overlaps of the frequencies found for the unripe and ripe ripening stages demonstrated that selective coffee harvesting by changing only the parameters related to vibration may not be viable.

Carvalho et al. (2016) studied the coffee plant to obtain a representative model of the real system using reverse engineering. For this purpose, parts of the trunk and branches of a whole plant were scanned to obtain a finite element model, which was validated by experimental tests that reproduced the simulations. The authors recommended that the mechanical properties of the coffee plant be better studied to improve the simulations using the same model developed.

Numerical simulations attached to representative models have been shown to be a viable tool for understanding the coffee harvesting process to support decision-making based on accurate information. Further, these simulations obviate the need for field experiments. In this sense, the main objective of this study is to evaluate the dynamic behavior of coffee plants based on an in-depth study of the mechanical properties of coffee plants to determine the natural frequencies using numerical simulations.