Analysis and rationale of TOW units for tractors with massive towed objects

Abstract

The most difficult stage in the operation of a tractor with massive towed objects is the starting mode. This is due to the need to overcome the static friction force, which significantly exceeds the motion friction force. As a solution to this problem, we can consider the use of the initial kinetic energy of the tractor, which can be developed when using limited elastically deformable tow units. To optimize the mathematical model, the following assumptions are made: traction force F on the hook of the tractor is a constant value; the inertial masses of the tractor and towed objects are the same and equal m. The dynamics of a tractor and massive towed objects is described by means of theoretical mechanics, taking into account the elastic deformation of tow units. The composed systems of linear homogeneous differential equations with right-hand sides are solved by the method of elimination of functions with increasing of exponential order, as a result of which differential equations of the fourth and sixth power are formed. Initial conditions at t = 0: since the tow unit is not deformed and no force is applied to the towed object. The periods t2 and t3 are determined, during which the tow units will undergo maximum deformation. To assess the effectiveness of the use of elastically deformable tow units, the results obtained should be compared with similar results corresponding to absolutely rigid tow units. Comparison of displacements, speeds and energy testifies to the high efficiency of the elastically deformable tow units. The use of elastically deformable tow units makes it possible to accumulate the initial kinetic energy of an aircraft tow tractor, which makes it possible to overcome the static friction force and ensure the starting of heavy towed objects. Comparison of the kinematic and dynamic parameters of the tractor with towed objects for options with absolutely rigid and elastically deformable tow units shows that the efficiency of using the latter increases with an increase in the number of towed objects. Elastically deformable tow units can cause oscillations of the tractor-towed objects system. To prevent them, the tow units must be blocked at the moment of their maximum deformation.