Differential equation model for durability of the tractor's engine with application to the model Massey Ferguson 8160

Abstract

A novel mathematical model for the tractor engine durability, based on the appropriate differential equation and conditions, is formulated and presented in this paper. Its practical applicability is experimentally verified for the tractor type Massey-Ferguson 8160. The probability density function of the engine's lifespan, as long as the overhaul is needed, is established and approximated by normal Gaussian function. Fitting coefficients are evaluated through the non-linear fitting of empirical data by Levenberg-Marquardt numerical algorithm.