Mathematical modeling of the vertical load of a hopper-type container placed on a long-base structure of a platform car

Abstract

Higher operational efficiency of container transportation can be achieved by putting into operation hopper containers. The special feature of a container is its inclined end and sidewalls, which makes it possible to self-discharge bulk freight through the discharging hatches forming the floor. The vertical loading of a hopper container placed on the long-base flat car was determined with the mathematical modelling. The mathematical model described the translational movement of a flat car in the vertical plane, i.e. bouncing oscillations. The flat car for the calculation consisted of three bodies: bearing structure loaded with four containers and two 18-100 bogies. The containers were considered as attached masses that completely repeated the movement pattern of the bearing structure of the flat car in the vertical plane. The mathematical model also included the elastic characteristics of the track. The calculation was made for the containers placed on a long-base 13-7024 flat car. The mathematical model was solved with the Runge-Kutta method in MathCad. The initial conditions were equal to zero. It was found that the maximum acceleration in the mass center of the bearing structure of a flat car loaded with hopper containers was 1.28 m/s2, which did not exceed the allowable values. The vertical dynamic coefficient was 0.13. The motion of the flat car was estimated as excellent.The results of the research will be of value for those who are dealing with development of advanced container structures with better operational efficiency for container transportation.Key words: transport mechanics, hopper container, dynamic loading, dynamic characteristics, container transportation.