The changes in curvature in single and double helices as they are bent into circular arcs are derived from first principles. This analysis is applied to wire ropes to examine the bending strains in the wires of a frictionless rope as it is bent over a sheave. It is shown that the free bending strains in the wires in the innermost layer of a strand in a rope taken as an example are higher than those in the outer layer wires, while the second wire layer has the lowest bending strains.
The relative movements between the centre-lines of the strands of a wire rope during bending are analysed, as are the movements between the individual wires forming those strands. The formulae are applied to an example, and used to identify the position of greatest relative movement (slip). This position coincides with the most common location of wire failures in bend-over-sheave fatigue testing, suggesting that such slip calculations may form a valuable input to wire rope fatigue predictions.
The frictional behaviour of heavily loaded wire ropes bent over relatively small sheaves has been investigated with 6 x 36,28 mm and 35 mm diameter, IWRC (independent wire rope core) and FC (fibre core), bright and galvanized ropes being tested, over sheaves with D/d ratios between 12 and 20. The groove profiles used were plain U and undercut U, with groove diameters 2.5 per cent smaller than the rope nominal diameter. Some pilot studies were also run on high-strength synthetic fibre ropes. The measurements showed that the effective friction coefficient increased with decreasing line tension and increasing sheave diameter for unused surfaces but became almost constant for used surfaces. It was shown that the undercut U groove had a higher frictional hold than the plain U groove but gave rise to early erratic slip. Galvanized rope had a lower friction coefficient while increased speed of sliding decreased friction.
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