Reliability Analysis of a Mounted Moldboard Plow Bottom Standard using the FORM Method

Document Type : Original Manuscript


1 Department of Mechanical Engineering of Biosystems, Faculty of Agriculture, Shahrekord University, Shahrekord, Iran

2 Department of Mechanical Engineering of Biosystems, Faculty of Agriculture, Shahrekord University

3 Department of Industrial Design, University of Art, Tehran, Iran

4 Department of Biosystems Engineering, College of Agriculture, Shiraz University, Shiraz, Iran,


Using the reliability index to express a system’s safety, reliability theory is applied to study a structure’s failure probability due to the uncertainty (i.e., randomness) of design and production parameters with (a) variability in working conditions and the environment and (b) direct interaction with the soil, the conventional approach has been based on deterministic design methods. In contrast, using the concept of reliability as a new and useful approach, we develop the industry of design and manufacture of agricultural machinery. In this study, the first-order reliability method (FORM) was used to analyze the reliability of a plow bottom standard. To perform the reliability analysis, the required forces on the standard were determined by simulating the interaction of the plow with the soil using finite element method by Abaqus software. Random variables were considered as longitudinal and vertical forces on the bottom standard, radius of the standard arc, plastic cross-section modulus, and yield stress. The reliability index (β) as a measure of the system’s safety of was determined using reliability analysis whose value was found to be 2.569 for the bottom's standard. Moreover, the failure probability (Pf) of the bottom's standard was calculated as 0.005. In the final step, the results of FORM reliability analysis were compared with the reliability results of the Monte Carlo simulation of the plow bottom’s standard. The results showed that the bottom standard’s probability of failure in the FORM and Monte Carlo methods for the conditions considered—i.e., very compacted soil, plowing depth of 30 cm, and velocity of 3 m s-1—are low and almost low, respectively. Also due to the lack of lateral force FX in the limit state function, the FORM analysis indicated sufficient uncertainty of the bottom standard design; therefore, strengthening or optimizing this part of the moldboard plow chassis seems necessary.

Graphical Abstract

Reliability Analysis of a Mounted Moldboard Plow Bottom Standard using the FORM Method


  • Use of reliability approach in the design of tillage machines.
  • Application of "FORM" method in design of moldboard plow.
  • Calculation the failure probability and reliability index of plow structure.
  • Considering uncertainties in the probabilistic design of plow structure.


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