Proceedings of SerbiaTrib '13

common for their ability to be installed within thewinch drum.Improvement of the winch drum, as the basicelement of the winch, is based on the examinationof the effect of the forces on the drum,experimentally and using finite element analysis,[8]. Improvement of the drum is done by reducingthe thickness of the material from which the drumis made in noncritical places, while increasing it inthe critical ones, and inserting the requiredstructural stiffeners, [9], [10]. Optimizationmethods are also a possible approach ofimprovement, [11].Improvement of the system for proper windingof the rope around the drum of the vessel winch isbased on its synchronization with the number ofturns of the drum. The synchronization can be donein many ways. Some of the ways are themechanical synchronization with the powertransmission or installing a special driving enginegeneratorfor the system, which is synchronized,with the engine-generator of the winch.In this paper, a mathematical model of windingof a steel rope around the drum is presented. Themathematical model shows the correlation betweenthe friction and pulling forces using geometricalcharacteristics of winding on the winch drum andthe friction coefficient. Following this, the resultsof the algorithm, which are also developed in thispaper, mathematical model as well as comparisoncharacteristics of friction forces for differentcoefficients of friction during winding, are given.Finally conclusions and guidelines for furtherresearch have been presented.2.1 General case of winding of the ropearound the drumIn determining the general case of winding, annth winding on the nth layer is observed. Thewinding lies upon the two windings from theprevious layer (Figure 1).The forces FWR occur as the reaction of therope to the pulling force FW. The friction force Fµalso occurs. Further observation is done on thecross-section where the force FWR acts (Figure 2).In this cross-section, the perpendicular force FNoccurs due to acting of friction force Fµ.Figure 1. General spooling case2. MATHEMATICAL MODEL OF STEELROPE WINDING AROUND THE WINCH-DRUMThe winding of the steel rope around the winchdrum can be single-layered or multilayered. Themathematical model concerns the multilayeredprocess of rope winding, from the first to the lastlayer. The model could be used for defining singlelayeredwinding too, by excluding the upper layersfrom the model. The bevel of the rope due to thewinding is excluded from the mathematical model,because the bevel has an insignificant effect in themajority of winding cases. Also, the assumptionthat during winding the rope acts as an absoluteelastic body is taken, while the wound rope acts asa solid body.Figure 2. Cross-section of ropes in general caseSince the rope is of constant cross-section, thecenters of circumferences, which make the crosssectionof the rope, generally, form an equilateraltriangle. Horizontal component reaction forces ofthe windings of the lower layer FR are annulledbecause of the previous claim. The connectionbetween the perpendicular force FN and thereaction force FR is derived by setting the planarsystem of opposed forces, and the resulting isrelation (3):FN3FR (1)3After determining the reaction, it is necessary todetermine the friction force, which is caused by thetractive force. The friction force was determined by13 th International Conference on Tribology – Serbiatrib’13 235