Semi-analytical model of the interaction of a harrow disc gang with variable-depth soil

   The draft force of a harrow disc gang determines the specific energy cost of tillage. To minimize the cost of determining the draft force of the disc gang in relation to the harrow parameters and soil properties, the author carried out a mathematical modeling of the interaction of the harrow gang with the soil. The semi-analytical model has been built on the assumption of variable depth soil, constancy of depth, forward speed and approach angle of the harrow. It is shown that when the soil is variable only in depth, it can be characterised by two empirical constants and the coefficient of friction of the soil on the disc surface. The kinematic parameter of the disc gang, equal to the ratio of the circumferential speed on the disc blades to the forward speed of the harrow, is determined by the soil properties, the relative depth, equal to the ratio of the working depth to the radius of the discs, and the approach angle of the harrow gang. Based on the analysis of the moments of the soil resistance forces to cutting and friction, the author has shown that when the friction forces in the disc bearings in the variable depth soil are negligibly small, the disc gang of the harrow rotates at an angular speed that provides the minimum possible power of the harrow gang required for tillage. Explicit expressions are obtained for the required power and tractive force of the harrow gang as a function of the number of discs, the angle of approach of the harrow gang, the relative depth, the radius of the discs and the soil properties. Their comparison with published field experiments showed that the maximum relative error in determining the draft of a harrow gang with flat discs was 3.3 % for post-harvest stubble harrowing, and 2.6 % for a harrow gang with spherical discs in a tillage bin.

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