Mathematical substantiation of mine locomotive braking efficiency under pulsiting braking torque

Abstract

Purpose. Determination of braking torque parameters that provide high braking performance of a mine locomotive by mathematical modeling of the braking of a mine locomotive by a disc brake that creates a pulsating braking torque. The methods. Forced vibrations of the elements of the wheel-motor unit (WMU) of a mine locomotive in the process of braking with a disc brake are studied by the methods of differential calculus and mathematical modeling. Integration of the system of differential equations is performed by the Runge-Kutt method. Findings. A comparative analysis of a mine locomotive braking by a disc brake, which creates a constant and pulsating sinusoidal braking torque with a different number of sinusoid periods per revolution of the wheel pair, is carried out. It has been proved that the pulsating sinusoidal braking moment generated on the axle of the wheel pair equal to the sum of the constant component and the amplitude of the oscillations of the variable component multiplied by the sine of the product of the number of sinusoid periods per revolution of the wheel pair by its angular coordinate provides higher braking characteristics than the constant braking moment. It is shown that pulsating braking torque reduces the braking time and braking distance of the mine locomotive. The values of the amplitude of oscillations, which depend on the average value of the braking torque, and the number of periods of the sinusoid per one revolution of the wheelset, at which the greatest effect is achieved, are determined. The originality. For the first time, a mathematical model has been developed for braking a mine locomotive by a disc brake, which creates a pulsating braking torque on the axle of the wheel pair, depending on its angular coordinate, taking into account the nonlinear dependence of the adhesion coefficient on relative slip, on the basis of which the efficiency of a disc brake with a multi-sector disc is shown in comparison with a disc brake with a homogeneous disk under various conditions of the rail track. Practical implementation. The research results make it possible to determine the parameters of a disc brake with a multi-sector disc located on the wheelset axle and on the engine shaft, which provide the highest braking efficiency.