Soil reaction forces on agricultural disc implements

Abstract

Theoretical models for the prediction of the performance of wide cutting blades have been in existence for some time. These models characterise the soil as a rigid-plastic Mohr-Coulomb material and depend on advanced mathematical techniques developed for the solution of the complex equations of equilibrium of soil elements in two-dimensional plane-strain failure. Less rigorous techniques have been employed for developing mathematical models for the behaviour of deep narrow tines. In both cases the soil-implement contact boundary is assumed to be a plane surface of simple geometrical shape. The extension of these methods to deal with three-dimensional failure generated by curved loading boundaries is of comparatively recent origin. The soil failure patterns associated with disc soil cutting implements fall into this category. The thesis describes the development of a mathematical model for predicting the performance of such implements. The method employed follows the technique used by Godwin et al for reducing three-dimensional failure into two-dimensional components. The present analysis caters for discs implements having both inclination and disc angles. Soil contact in such implements takes place on complex curved surfaces and the geometry of these were analysed. These surfaces were approximated by plane elements which were then assumed to generate two-dimensional failure in planes parallel to the direction of translation of the disc. The rupture geometry and the forces acting on these elements are then computed using the Newcastle adaptation of Sokolovski's rigorous solution to soil failure. The force acting on the soil contact surface is then obtained by a version of the method of slices used for analysing slip surfaces. The model developed can predict the quasi-static soil reactions on disc implements from a knowledge of the disc geometry, soil properites and depth of cut. The computer programme was used to investigate the sensitivity of the input parameters to the final predicted results and this information was used to develop a set of non-dimensional force coefficients which can be used in a simple additive algebraic equation to predict the three orthogonal force components acting on the disc. Empirical correction factors have been devised to cater for deviations between these and computed valus and prediction to within 5 percent of the computer prediction are possible by this relatively simple method. In order to check the performance of this theoretical model a special dynamometer rig was designed and built to assess all three orthogonal force components acting on a disc tool. A single plough disc was tested in a loam soil and the computer prediction was in good agrement with experimental values. The model was also used to check other published experimental results and once again the prediction was good.