АНАЛІЗ ПРУЖНИХ ХВИЛЕУТВОРЕНЬ У КАНАТАХ ВАНТАЖОПІДЙОМНИХ КРАНІВ

Abstract

In the article the boundary value problem on the elastic longitudinal waves motion in the load lifting cranes and mine mechanisms variable length ropes is considered. Solutions of the Cauchy problem, which describe longitudinal oscillations propagation in the ropes (flexible suspensions) as in areas with moving boarders, are found. Displacements and stresses dynamic fields in variable length steel ropes of the specified load lifting mechanisms are investigated. Usually the ropes are balanced, and the main rope carries concentrated stress which before the systems movement was at the main ropes lower end. Dynamic forces in perfectly elastic variable length steel ropes estimation is shown, that only when lifting ropes without end loads under non-integrated boundary conditions, their efforts do not increase. However, practical experience shows that this phenomenon is not observed at moderate lifting speeds due to the fact that along with the dynamic forces amplitudes increase. Due to the decrease in length there is a simultaneous decrease in the amplitudes of their oscillations. The object of analysis refers to a wide range of variable length oscillations one-dimensional objects. A classical mathematical model to describe oscillations and waveforms is used. When studying wave fields in areas with moving boundaries the reflection of pulses from such boundaries is established. Elastic type waveforms in variable length rods (rope models) taking into account the fact that these rods have circular cross section of variable (length of rope/rod) area (rods are cylindrical, rotational paraboloids form, conical rods) is considered. Method based on the possibility of constructing wave equation from waves reflected from fixed and moving given boundaries of a semi-infinite domain solutions is applied.