The main interest of designers is not only to determine the amplitudes of tillage forces but also the type of their distributions under different soil mechanical properties with object of achieving reliable designs. Whereas, the deterministic design approach consists in achieving designs without considering the randomness of the design parameters that may lead to non reliable designs. In this work, we establish a statistical study on the randomness of the soil properties in collaboration with Cranfield University. This new study can be considered as a useful database for agricultural equipment design fields. Here, we take into account the uncertainties of soil mechanical properties that have big effects on tillage forces. The tillage forces are calculated in accordance with analytical model of McKyes and Ali with some modifications to include the effect of both soil-metal adhesion and tool speed. The distributions of soil-tool forces are next established to design soil tillage equipments such as shank chisel plow. The reliability index is then calculated using two deferent methods (Monte Carlo method and Hasofer and Lind approach). The Hasofer and Lind approach provides the structural reliability level with a low computing time relative to the Monte Carlo approach.
probabilistic design, reliable design, reliability index, soil-tillage forces
1- Introduction
Accurate prediction of soil-tool forces is of great value to the designers of soil tillage equipments [1]. However, there are many soil cutting models available that could be used to predict the forces acting on the tillage tool [2]. Analytical and numerical methods are proposed to achieve this aim. The soil-tool forces in the analytical methods are function of three categories of variables, 1) soil mechanical properties, 2) tool parameters, and 3) parameters of tillage operating. In these models, the soil mechanical parameters are taken as constants, and the researchers attempted to accomplish the relationships between the soil-tool forces on the one hand, and the tool and tillage operating parameters on the other hand [3]. While the researchers worked to simulate soil material behavior under loading of tillage tools, in the finite elements methods, two various theoretical bases have been introduced, namely the curve-fitting technique and the elastic-perfectly plastic assumption. The two FEM modeling methods have considered Young's modulus of elasticity and Poisson's ratio as constants.
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