Development and verification of a mathematical model of straight blade cutting longan branches

Objective To model the process of straight blade cutting longan branches based on material mechanics and elastic foundation beam theory, and to calculate the shearing force of branches from the straight blade cutting using the model.

Method Shixia longan branches were used as test materials. The mechanical parameters of the branches and the coefficient of friction between the branch and blade were measured using a universal material test machine and a custom friction tester. The peak shearing forces were measured by the universal material testing machine and also calculated by the developed model under conditions of different branch moisture contents (M), branch diameters (d) and blade bevel angles (θ). The blade used in the cutting tests had a bevel angle of 10°, 20° or 30°.

Result When M=76%, d=20.4 mm and θ=20°, the calculated curve showed the same trend as the curve derived from the experimental results, and the error of the peak shearing force was around 2.3%. When d=15.3 mm, θ=20° and M >30% which was the fiber saturation point, the peak shearing force increased with the increment of M and calculated values were within the error ranges of the experimental data. When M=76%, d=24.6 mm and θ increased from 10° to 30°, the peak shearing force increased significantly and the calculated values were also within the error ranges of the experimental data.

Conclusion The model can be used to estimate the shearing force and investigate the effects of different mechanical parameters on the peak shearing force. The results will provide theoretical reference for the design and optimization of pruning machines.