Empirical Models for Estimating Draught and Vertical Reaction Forces of a Duckfoot Tool in Compacted Soil: Effects of Moisture Content, Depth, Width, and Speed

This paper presents the development of empirical mathematical models of draught force, Fx, and vertical force, Fy, acting on duckfoots attached to the tines with different stiffness and working in various soil conditions. The models consider technical variables such as stiffness, k, tool depth-to-width ratio, d/w, tool movement speed, v, and soil moisture content, MC, which have not been thoroughly analysed in the literature. The correlation coefficients for predicting Fx and Fy values were 0.4996 and 0.6227, respectively. Statistical analysis confirmed the significant effect of these parameters on the forces acting on the tools, with the variables d/w and v having the most critical impact on Fx and Fy. The SLSQP (sequential least squares programming) optimisation method was used to determine the optimal values of technical variables. The maximum value of Fx was 438.55 N, and the minimum was 98.98 N, with variable values at the edges of the studied ranges. Similarly, Fy values of 135.25 N and −84.55 N, respectively, were obtained. The optimisation results showed good fitness with experimental results, and the negative relative errors (from −1.72% do −4.81%), indicating overestimating, confirmed the accuracy of the model’s predictions. The justification of the research results allowed us to conclude that there is no basis for rejecting the explanatory hypotheses. The developed models have a generalisable value in the analysed ranges, and further research should focus on creating more universal, theoretical models of soil–tool interactions.