Proceedings of SerbiaTrib '13

Forces: Fr, Fµr, Fs, Fµs [N]50004000300020001000FrFµrFsFµsFriction force in line contact [N]14001200100080060040020000 5 10 15 20 25Spooling angle [rad]Fµlc00 1 2 3 4 5 6 7Spooling angle [rad]Figure 6. The reaction force of the lower rope layer FR ,friction force between the rope layers FµR , reactionforce on the side FS and friction force on the side FµSdependence on the spooling angleThe friction force between the layers FµR alsohas the increasing character from the beginning ofthe critical spooling and all the way to the pointwhen the rope crosses to the general spooling case,for it is directly related to the force FR by thefriction coefficient µ2, (12). The reaction force onthe side of the drum FS rises up to the spoolingangle of φ ≈ 1,5 [rad], while after reaching theextreme value it decreases to zero. Its value equalszero at φ ≈ 4, 2 [rad]. The friction force on the sideFµS acts similarly, because it is related to thereaction force on the side through the frictioncoefficient µ1, (12). When the forces FµS and FSreach zero, the perpendicular force transfers to thelast spool of the lower spooling layer exclusivelyby the friction force between the rope windings.3.3 General case of rope spoolingGeneral case of rope spooling for multilayeredspooling has the greatest share in the spoolingprocess. Generally, friction force occurs on the tworope inlets on the contact line of the winding beingspooled and the two spools from the previous layer.In this case the total friction force is divided intotwo equal parts, (8). Friction force FµLC in linecontact on the rope inlet gets close asymptoticallyto the half of the nominal value of the pulling force,(Figure 7). In the case of rope spooling onto thehigher layers, the general case, in difference withfirst layer spooling, the friction force carries thetotal tractive force (φ≈12÷15[rad]) between thesecond and the third layer.Figure 7. Friction force Fµ in general case of ropespooling dependence on the spooling angleIn this case a grater friction coefficient value isadopted from the one used for rope spooling ontothe first layer (µ 2 =0,35).3.4 Comparative diagrams for different frictioncoefficient valuesLastly the comparative friction force diagrams(Figure 8) and perpendicular force (Figure 9)diagrams for friction coefficients µ = 0,2 ÷ 0,4(initial parameters are also taken from Table 1) aregiven. For these resulting diagrams the general ropespooling case was used.Friction force in line contact [N]14001200100080060040020000 5 10 15 20 25Spooling angle [rad]µ = 0,20µ = 0,25µ =0,30µ =0,35µ =0,40Figure 8. Friction force Fµ for different frictioncoefficients dependence on the spooling angleIt can be seen from Figure 8 that for all frictioncoefficient values the friction force has the sameinitial value during spooling. As expected, thehighest number of spools for total transfer of pulingforce to friction force is necessary for the highestfriction coefficient (φ > 12 [rad]), while for thelowest friction coefficient the transfer is possibleonly after the third spooling (φ > 19 [rad]).With perpendicular forces the case is slightlydifferent (Figure 9). Perpendicular forces do notexceed the nominal value of the pulling force forthe value of the friction coefficient of 0,3.Perpendicular forces with the friction coefficient of 0,3 do exceed the value of nominal pullingforce.238 13 th International Conference on Tribology – Serbiatrib’13