Mathematical substantiation of the limit value of tagential traction force on driving wheels for transport-technological machines

The paper deals with the aspects of determining the ultimate traction force on the driving wheels of land transport and technological machines (LTTM) with 4×2 wheel arrangement. The purpose of the study was to identify the criteria that limit the maximum value of traction force on the driving wheels that can be realized on machines of this type. These criteria are determined by the torque generated by the engine and transformed by the transmission, and are grouped into the following groups: those related to the onset of slipping of the driving wheels and those determining the overturning of the NTTM and the limiting moments for the destruction of the transmission elements. The article presents mathematical dependencies developed to determine the limit values of traction force on the wheels of NTTM. The authors have developed a model that allows conducting numerical experiments to determine the optimal parameters of the engine and transmission. This allows determining the limit thrust force which can be operated with in the further development of the project. These dependencies allow taking into account the influence of various factors in the traction balance equation. The factors affecting the realization of torque are the mass of the machine, including the distribution of mass on the axles and the relative position of the center of mass, the friction coefficient, the angle of inclination of the road and other parameters of interaction with the supporting surface, as well as the characteristics of the transmission that limit the traction capabilities of the machine. After transforming the obtained mathematical expressions, the authors describe the dependence that determines the maximum allowable torque on the crankshaft of the engine. It allows taking into account the engine characteristics when determining the limiting force of traction and provides the possibility of choosing the engine power characteristics for a particular transport-technological machine and transmission ratios.