Where bending fatigue comes from

When a wire rope bends over a sheave, the wires on the outside are stretched and the wires on the inside are compressed. Every trip around the sheave gives each wire one such stress cycle. Once enough cycles have accumulated, cracks appear at the wire surface and wires eventually break. That is bending fatigue.

A high static breaking force does not mean the rope can carry the same load through repeated bending. Fatigue life depends on the bending stress range, the number of cycles and the surface condition of the wires, and the stress range is set mainly by the D/d ratio.

Bending fatigue is not the same as wear. Wear reduces the wire cross-section bit by bit; fatigue starts cracks where stress concentrates. The two usually act together, but the answers differ: wear is fought with lubrication and groove maintenance, fatigue with a larger D/d or a construction that bends more easily.

What the D/d ratio means

D is the diameter of the sheave or drum and d is the nominal rope diameter, so D/d is the ratio between them. It measures how hard the rope is folded as it bends: the smaller the ratio, the tighter the curvature and the higher the bending strain in the outer wires.

On the same rope, dropping D/d from 20 to 12 nearly doubles the bending strain in the outer wires, and fatigue life usually falls faster than that ratio suggests. That is why ropes on small sheaves always fail sooner.

D/d limits are not set at random by the maker. They usually come from the standard, the mechanism duty class and the rope construction together. Use the equipment manual and the applicable standard for actual values, and do not carry experience from one machine straight over to another.

• Repeated broken wires at the same sheave position.
• Transverse cracks or pressure marks on outer wires.
• The same rope replaced several times, failing at the same wheel.
• Steps, burrs or obvious wear in the sheave groove.

How to read typical values

On general industrial lifting equipment, D/d commonly sits between 16 and 25; machines with a high duty class and frequent lifting take the larger values, while light, slow machines can use the smaller ones. Passenger lifts demand much more, commonly 30 and above, because both safety margin and fatigue life have to be higher.

These numbers are order-of-magnitude references, not a design basis. The real value comes from the duty grouping, load spectrum and safety factor in the standard, checked against the rope construction: at the same D/d, a coarse-wire construction sees higher bending strain than a fine-wire one.

If the existing machine cannot take a larger sheave, the practical answer is usually a construction that bends more easily, not the same rope forced to last longer. Construction options are set out in the wire rope construction guide

Why reverse bending is worse

When a rope passes from one sheave to another and the direction of bend reverses, that is reverse bending. The outer wires are stretched and then compressed within a short length, the stress range is larger, and fatigue damage accumulates faster.

Avoid S-shaped reeving in the layout wherever possible. Where reverse bending cannot be avoided, allow a smaller D/d or a higher safety margin, with the conversion method taken from the applicable standard. Many equipment manuals state a permitted number of reverse bends or forbid the arrangement outright.

Multilayer spooling on a drum is a form of reverse bending as well. A rope moving from one layer to the next may change bend direction, and the layers press on each other. On a multilayer drum, fatigue and deformation are usually more complex than on a single layer. When spooling is untidy, ropes can also cross and press on each other, creating local points of high stress.

The trade-off between fatigue and wear

A construction with many fine wires bends well but wears quickly at the surface; a coarse-wire construction resists wear but strains each wire harder in bending and fatigues sooner. Decide which will happen first: many sheaves and frequent bending put fatigue first; rough grooves, dust and long rubbing distances put wear first.

Compacted and sealed strands raise the metallic cross-section and smooth the surface, so they wear better, but they are less flexible and see higher bending stress at the same D/d. Using them usually means allowing a larger sheave to compensate.

A rotation-resistant rope is a multilayer strand structure with opposite lay directions in the inner and outer layers. Sliding between layers in bending is complex, so it is usually stiffer than a plain six-strand rope of the same diameter and needs a larger D/d. The constructions are described in the rotation-resistant wire rope guide

Sheave grooves and wheel condition

A groove radius that is too small pinches the rope, while one that is too large leaves too little contact area and lets the rope rock in the groove. Both raise local stress and shorten fatigue life. Once the groove bottom wears into a step or picks up burrs, rope damage accelerates visibly. Measure the groove at several points around the circumference; a single reading does not represent the whole wheel.

Sheave material and hardness must match the rope too. A groove that is too soft wears into a channel; one that is too hard can damage the rope. Measuring groove diameter and profile at intervals is cheaper than replacing wheels after the rope has failed.

The fleet angle also needs control. Too large an angle drags the rope against the groove side, adding wear and stress. Take the permitted angle from the equipment and standard, and leave enough straight length in the layout.

Check with data, not by feel

Before fixing D/d, gather three sets of data: the rope's nominal diameter and construction, the actual diameter of the sheave or drum, and the machine's duty class and expected number of cycles. With one set missing, the conclusion is not reliable.

Rope breaking force and metallic area are available in published data, and the groove profile and permitted tolerances come from the wheel maker. Only by aligning the two sides can you judge whether the existing layout is reasonable. Technical data is set out in the steel wire rope data sheet

On site modifications, watch the effective diameter. Once a layer of rope is wound on the drum, the actual bending diameter is the drum diameter plus the rope diameter, so D/d shifts slightly; on small drums that difference cannot be ignored.

• Rope: construction, nominal diameter, lay and core.
• Wheel: actual diameter, groove profile, material and hardness.
• Duty: duty class, cycles per day and expected life.
• Layout: wrap angle, fleet angle and any reverse bending.

One-line rule

The larger the sheave, the lower the bending stress and the longer the fatigue life; the more flexible the construction, the smaller the D/d it can accept. When fixing D/d, read the standard and the machine first, the construction second, then check against the real cycle count. Before changing construction, confirm the sheaves and drums still suit the new rope.

Where broken wires have already appeared early, do not just change the rope. Measure the sheave, check the groove and calculate D/d, or the new rope will fail in the same place again.