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A methodological approach for evaluating a priori the stability of agricultural vehicles equipped with different mounted implements and operating on sloping hillsides is shown here. It uses a Matlab simulator in its first phase and, subsequently, the Response Surface Modelling (RSM) to evaluate the coefficients of a set of regression equations able to account for the Type-I and Type-II stability of the whole vehicle (tractor + implement with known dimensions and mass). The regression equations can give reliable punctual numeric estimations of the minimum value of the Roll Stability Index (RSI) and can verify the existence of a Type-I equilibrium without the need of using the simulator or knowing any detail about the model implemented in it. The same equations can also be used to generate many intuitive graphs (“equilibrium maps”) useful to verify quickly the possible overturning of the vehicle. A case-study concerning a 4-wheel drive articulated tractor is then presented to show the potential of the approach and how using its tools. The tractor has been studied in three scenarios, differing on where the implement has to be connected to the tractor (1: frontally; 2: frontally-laterally; 3: in the back). After performing a series of simulations, a set of polynomial models (with 6 independent variables) has been created and verified. Then, these models were used, together with the related equilibrium maps, to predict the stability of 8 implements for scenario 1, 7 implements for scenario 2, and 3 implements for scenario 3, evidencing in particular the danger of using a lateral shredder with a mass greater than 245 kg. The proposed approach and its main outcomes (i.e., the regression equations and the equilibrium maps) can give an effective contribution to the preventive safety of the tractor driver, so it could be useful to integrate it in the homologation procedures for every agricultural vehicle and to include the resulting documentation within the tractor logbook.

A parametric approach for evaluating the stability of agricultural tractors using implements during side-slope activities