Estimating the variability of tillage forces on a chisel plough shank by modeling the variability of tillage system parameters

In this paper, a probabilistic approach is proposed for quantifying the variability of the tillage forces for the shank of a chisel plough with narrow tines and to estimate the failure probability. An existing three-dimensional analytical model of tool forces from McKyes was used to model the interaction between the tillage tools and the soil. The variability of tillage forces was modeled, taking into account the variability of soil engineering properties, tool design parameters and operational conditions. The variability of the soil engineering properties was modeled by means of experimental observations. The dispersion effect of each tillage system parameter on the tillage forces was determined by a sensitivity analysis. The results show that the variability of the horizontal and vertical forces follows a lognormal distribution (μ = 0.872, ξ = 0.449; μ = 0.004, ξ = 0.447) and the relationship between these forces is positive and quasi-linear (ρ(P_H, P_v) = 0.93).This lognormal variability was integrated into the estimation of the failure probability for the shank by using Monte Carlo simulation (MCS) and the first-order reliability method (FORM). The results obtained by these two methods, with the assumption of non-correlation between the horizontal and vertical forces, were almost identical. However, the FORM method was faster and simpler, compared to the MCS technique. Furthermore, the correlation between the horizontal and vertical forces has no significant effect on the failure probability, regardless of the correlation strength. Therefore, it is concluded that the FORM method can be used to estimate the failure probability without considering the correlation between horizontal and vertical forces.