Theoretical analysis of the spatial variability in tillage forces for fatigue analysis of tillage machines

This paper presents a new theoretical model to describe the spatial variability in tillage forces for the purpose of fatigue analysis of tillage machines. The proposed model took into account both the variability in tillage system parameters (soil engineering properties, tool design parameters and operational conditions) and the cyclic effects of mechanical behavior of the soil during failure ahead of tillage tools on the spatial variability in tillage forces. The stress-based fatigue life approach was used to determine the life time of tillage machines, based on the fact that the applied stress on tillage machines is primarily within the elastic range of the material. Stress cycles with their mean values and amplitudes were determined by the rainflow algorithm. The damage friction caused by each cycle of stress was computed according to the Soderberg criterion and the total damage was calculated by the Miner's law. The proposed model was applied to determine the spatial variability in tillage forces on the shank of a chisel plough. The equivalent stress history resulted from these forces were calculated by means of a finite element model and the Von misses criterion. The histograms of mean stress and stress amplitude obtained by the rainflow algorithm showed significant dispersions. Although the equivalent stress is smaller than the yield stress of the material, the failure by fatigue will occur after a certain travel distance. The expected distance to failure was found to be df=0.825×106km. It is concluded that the spatial variability in tillage forces has significant effect on the life time of tillage machines and should be considered in the design analysis of tillage machines to predict the life time. Further investigations are required to correlate the results achieved by the proposed model with field tests and to validate the proposed assumptions to model the spatial variability in tillage force

Reliability-based design optimization of shank chisel plough using optimum safety factor strategy

Reliability integration into tillage machine design process is a new strategy to overcome the drawbacks of classical design approaches and to achieve designs with a required reliability level. Furthermore, design optimization of soil tillage equipments under uncertainty seeks to design structures which should be both economic and reliable. The originality of this research is to develop an efficient methodology that controls the reliability levels for complex statistical distribution cases of random tillage forces. This developed strategy is based on design sensitivity concepts in order to determine the influence of each random parameter. The application of this method consists in taking into account the uncertainties on the soil 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 different developments and applications show the importance of the developed method to improve the performance of the soil tillage equipments considering both random geometry and loading parameters. The developed method so-called OSF (Optimum Safety Factor) can satisfy a required reliability level without additional computing time relative to the deterministic design optimization study. Since the agricultural equipment parameters are extremely nonlinear, we extended the OSF approach to several nonlinear probabilistic distributions such as lognormal, uniform, Weibull and Gumbel probabilistic distribution laws

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(PH,Pv)=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 f

Reliability Based Design Optimization for Multiaxial Fatigue Damage Analysis Using Robust Hybrid Method

The purpose of the Reliability-Based Design Optimization (RBDO) is to find the best compromise between safety and cost. Therefore, several methods, such as the Hybrid Method (HM) and the Optimum Safety Factor (OSF) method, are developed to achieve this purpose. However, these methods have been applied only on static cases and some special dynamic ones. But, in real mechanical applications, structures are subject to random vibrations and these vibrations can cause a fatigue damage. So, in this paper, we propose an extension of these methods in the case of structures under random vibrations and then demonstrate their efficiency. Also, a Robust Hybrid Method (RHM) is then developed to overcome the difficulties of the classical one. A numerical application is then used to present the advantages of the modified hybrid method for treating problem of structures subject to random vibration considering fatigue damage