Mathematical modeling of the roller - rope coupling operation in misalignment conditions
The article deals with the results of construction and mathematical modeling of rope - roller coupling in condition of radial misalignment. As a result of modeling, the operation of coupling is revealed in the presence of misalignment of the shafts connected by it. Formulas are obtained that allow to determine the elongation of the rope depending on the magnitude of misalignment, as well as the design parameters of the coupling. The results of the investigations also allow determining the radial load from the coupling on the shafts at any angle of rotation of the coupling. Numerical simulation by the obtained formulas made it possible to establish that coupling is characterized by high compensating ability and low radial stiffness. So, with a radial displacement of 0.5 mm (for a prototype coupling with elastic star allow only 0.25 mm), the rope - roller coupling creates a load of only 5 N on the shafts, with a rope elongation of 5.5 µ m. The dependencies obtained are approved during the design of the coupling, and the results of the calculations on them are checked by comparison with the results of the construction and showed a coincidence. The obtained results can be used in the design of rope - roller couplings.