Application of harmonic half-waves for automation of high-speed trains control

The emergency braking processes in the European Train Control System (ETCS) of high-speed trains are associated with stepwise regulation of acceleration (deceleration) depending on the braking ability of the train, terrain data and changing weather on the route. These processes are defined in ETCS. The procedure for stepwise regulation of deceleration is carried out by the driver repeatedly in the process of braking until the train stops completely. The beginning of emergency braking and its end, as well as the braking process itself, is accompanied by repeated pulsed operation of the brakes, which leads to jumps in deceleration and, accordingly, to increased wear of the brake system, a decrease in comfort for passengers, which results in the limitation of the maximum allowable speed. The article proposes a new concept and technique for constructing mathematical models of emergency braking curves different from ETCS curves and based on harmonic half-waves. It is shown that the ETCS deceleration curves are described by known second-order power half-waves. Their joint study gives grounds to assert that the application of these curves leads to the obligatory pulsed mode of brake operation. Two new variants of models of emergency braking curves described by harmonic half-waves are proposed. The first option has one pulsed brake application at the end of the braking interval. The second option is free from braking impulses and allows the use of continuous regulation. These models explain the features of ETCS, contain proposals for their elimination, and are applicable to the development of new emergency braking curves that allow smooth control of emergency braking of trains. Efficiency, differences and advantages over ETCS braking curves are shown on the results of mathematical modeling of emergency braking processes.