A 2-ton hoist on a jib crane needed a new rope every six months. The rope was 8 mm diameter, 6×19 construction, the standard for this hoist. It failed with broken wires on the crown of the rope, right at the sheave. The wire breaks were distributed along the rope, not at one point, and the rope was stiff and “set” — it kept the curl of the sheave even when unloaded. The customer tried a more expensive rope, then a different brand. Same six-month life. The rope wasn’t the problem. The sheave was too small.
What D/d means and why it matters
D/d is the ratio of the sheave diameter (D, measured at the rope centerline) to the rope diameter (d). It’s the single most important number in rope life. Every time the rope bends around a sheave, the wires on the outside stretch and the wires on the inside compress. The smaller the sheave, the more severe the bending strain, and the faster the wires fatigue.
This hoist had a sheave with a rope-centerline diameter of about 112 mm, so D/d = 14. The manufacturer’s recommendation for a 6×19 rope on a crane hoist is a minimum D/d of 20, and 25 is better for continuous duty. The sheave was under the minimum. At D/d = 14, the bending fatigue life is roughly a third to a quarter of the life at D/d = 20. Six months of life was exactly what the math predicted.
The relationship is not gentle
Rope bending fatigue life doesn’t fall linearly as D/d drops. It falls steeply. A practical rule from the rope handbooks: rope life is roughly proportional to (D/d) raised to a power between 2 and 3, depending on rope construction. Going from D/d = 20 to D/d = 14 cuts life by roughly two-thirds. That matched the six-month replacement interval against the two-year interval the same rope gives on a properly sized hoist.
What made it worse here: the rope was 6×19, which has relatively thick wires and is more sensitive to bending fatigue than a 6×36 or 8×19 construction with thinner wires. A flexible-construction rope (more strands, finer wires) survives small sheaves better. The tradeoff is a softer rope that wears faster on the drum and is less resistant to abrasion. In this application, a 6×36 rope would have gained some life, but the real fix was the sheave.
What we changed
The sheave was replaced with one at D/d = 24 (rope-centerline diameter about 192 mm). The rework needed a slightly bigger sheave housing on the jib, which was simple. The rope life went from six months to about two years. The rope also stopped taking a permanent set, which made inspection easier — a rope that keeps the sheave curl is a rope that’s being over-bent, and it’s a visible warning you should act on before it fails.
Two other things checked at the same time:
- Fleet angle. The angle between the rope and the sheave’s plane, as it winds off the drum, was 3 degrees — fine. Above 4 degrees the rope scrubs the sheave flanges and wears the sides. Keep fleet angle under 2 degrees for grooved drums, under 4 degrees for plain.
- Sheave groove radius. The groove was measured at 4.3 mm radius for an 8 mm rope. Correct is about 0.53 x d = 4.2 mm, so the groove was right. A worn, too-wide groove pinches the rope and shortens life too. Worth measuring while the rope is off.
The selection rule
For wire rope in bending applications (hoists, cranes, reeving), the practical minimums:
| Duty | Minimum D/d |
|---|---|
| Light duty, occasional use | 18 |
| Normal industrial hoist | 20 |
| Continuous or severe duty | 25-30 |
| High-flex constructions (8×19, 6×36) | Can go lower, verify with data |
If the machine’s sheave is already built and the D/d is marginal, the practical moves are: switch to a more flexible rope construction, or reduce the rope diameter if the hoist’s capacity calculation allows it, which is rarely the case. Usually the honest answer is a bigger sheave. The customer here tried two rope upgrades before accepting that the sheave was the issue. The sheave was the issue.
D/d below 20 shortens rope life faster than any lubricant or brand choice can compensate for. The six-month rope wasn’t cheap rope. It was a 14:1 sheave asking a rope built for 20:1 to do a job it couldn’t. Check the sheave size before you switch rope suppliers. Rope life is a geometry problem first.
