Mathematical modelling of the movements of tractor working tools in controlled traffic farming

Abstract

The main index of quality work of wide-span tractors for controlled traffi c farming is the scale of damaging the plants with the working tools. Damaging the plants is considerably dependent on the scope of transversal deviations of the working tools which is conditioned by the movement stability of the wide-span tractor and some deviation from the trajectory of the established controlled traffi c farming and working tools in the fi eld dimension. Therefore, the study of the transversal movement of the working tools of a wide-span tractor and the impact of their deviations on the quality of implementing the technological process requires in-depth re- search and substantiation of constructive and kinematic parameters, which would ensure high quality of their work within the controlled traffi c farming system. Aim. To enhance the work quality of the wide-span tractors using the elaborated mathematical model of transversal deviations of the working tools, which would allow substantiating the constructive and kinematic parameters as well as the scope of the protection zone, based on condition of avoiding damage to the plants. Methods. The methods of building estimated mathematical models for the functioning of agricultural machines and equipment, based on theoretical mechanics, advanced mathematics, and the probability theory were used. Results. The article offers the methods of determining kinematic parameters of wide-span tractors and the probability of damaging plants in a row, which provide for substantiated selection of distances between the kinematic center of the tractor and the center of resistance of the device, used to lay the controlled traffi c farming, and the working tools as well as for selection of the scope of the protection zone with the consideration of their constructive parameters, stability and movement controllability. New mathematical dependences were elaborated, the application of which allows determining permissible thresholds of transversal deviations of the working tools, remarkable for standard deviation in agrotechnical conditions regarding the damage to plants in a row, which takes place while estimating the work- ing indices of wide-span tractors in the controlled traffi c farming. Conclusions. The optimal zone of placing the devices for controlled traffi c and working tools is concentrated on minimally possible longitudinal distance from the kinematic center of the tractor. The factor of deviation difference should be taken into consideration while placing the working tools for wide-span tractors.