Optimization of a Citrus Canopy Shaker Harvesting System: Properties and Modeling of Tree Limbs

Abstract

<abstract> <b><sc>Abstract.</sc></b> This article presents a part of the research work for the design and optimization of a fruit tree harvesting system using numerical methods. The analytical framework for the optimization is formulated based on a continuous canopy shaker that harvests citrus crops, primarily Valencia oranges (). Tree limbs are modeled analytically in the numerical based design optimization of a shaker that requires information regarding the limb configuration and properties. The objective of this study is to formulate a mathematical model to predict the configuration of primary limbs and to determine the properties of citrus wood. The tree limbs, thus proposed, are statistical prototypes or representations that account for the 5th, 25th, 50th, 75th, and 95th percentiles of actual tree limbs from random individual citrus trees. Polynomial response surface models were developed to predict sectional properties of the statistical model of the tree limbs. The distributions of the secondary branches and fruits were also predicted to model their effect on the dynamic response of the tree limbs. A three-point bending test, specific gravity test, moisture content test, and damping test were conducted on freshly cut samples of citrus wood. An elastic modulus of 8.5 GPa and modulus of rupture of 67.3 MPa were calculated from a load-deflection curve, and a density of 1450.8 kg m^-3, moisture content of 42%, and damping ratio of 10.78 were measured. Although the proposed methodology was developed for a canopy shaker, it could be easily implemented for other vibratory harvesters, such as limb shakers, foliage shakers, and over-the-row harvesters.