Prediction of Machine’s Centre of Gravity Dislocation with Monte Carlo Simulation

Abstract

The estimation of machine‘s centre of gravity (COG) dislocation is presented in this article. Various types of agricultural tractors‘ parameters were analysed. Their parameters such as track width in the range of 〈1222 mm, 1900 mm〉 and COG height in the range of 〈830 mm, 1340 mm〉 are known from the reports of OECD tests. The static stability of the machine is defined by the critical angle of labile equilibrium or critical overturning angle in static disposition, which is determined from measurement on the tilt table. The critical overturning angle can be calculated from the known parameters of COG dislocation. The critical overturning angle for each analysed machine can be evaluated from the obtained dataset. The mean and standard deviation of parameters were used as input parameters into Monte Carlo simulation (MCS). The MCS method was used for the estimation of the critical overturning angle and height of COG for 2500 data. Simulation was performed using a Mathcad® Prime 9.0 software. The basic statistical analysis was performed using a Spyder software in the Python language. The polynomial approximation equation was set up, and then COG heights were calculated. The critical overturning angle was calculated from the real and simulated parameters. The functions of the critical overturning angle were compared, and the fit of approximation was evaluated by the R2 parameter. The designed model was verified by the F-distribution test.

Keywords

• mathematical modelling
• random dataset
• approximation
• data estimation