Question 5 of 7: Headframe Design Parameters, Hoist-Rope Engineering and Shaft Hoisting-System Selection

Question 5: Headframe Design Parameters, Hoist-Rope Engineering and Shaft Hoisting-System Selection (15 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

5.1.1 Fleet angle. As introduced in 1.6.1, the fleet angle is the plan-view angle between a hoist rope's actual path across the width of a moving (drum) hoist and the true vertical line through the head sheave; it must stay within a small allowable limit (≈1.5°) to avoid excessive rope/groove wear, and is the parameter that fixes the minimum headframe height.

5.1.2 Sheave-wheel diameter criteria. The sheave diameter is set from a bending-fatigue design ratio between sheave (or drum) diameter and rope diameter — commonly expressed as a minimum D/d ratio specified by the rope manufacturer or governing code for the rope's construction and duty (locked-coil ropes need a larger D/d than round-strand rope for equal fatigue life, and Question 6 uses a drum/rope ratio of 108 for exactly this reason). A larger sheave reduces the cyclic bending stress each outer wire sees every time the rope passes over it, extending fatigue life, at the cost of a taller, more expensive headframe.

5.1.3 Rope diameter basis. The rope diameter is sized from the maximum load the rope must carry — the loaded conveyance plus the full length of suspended rope — divided by the minimum static factor of safety against the rope's rated breaking strength required by the governing hoisting regulation (in BC, the Health, Safety and Reclamation Code for Mines); this is precisely the calculation performed for the 425 m production shaft in Question 6.1.

5.2.1 Testing of hoist ropes. Every new rope is proof-tested against a certified sample/witness-length breaking-strength test before being placed in service. Once in service, ropes undergo scheduled non-destructive electromagnetic (NDT) flaw-detection testing to detect internal wire breaks and loss of metallic cross-section that cannot be seen from the outside, supplemented by regular detailed visual inspection for external broken wires, corrosion, wear and diameter reduction, on an inspection interval set by the governing hoisting regulation.

5.2.2 Safety of hoist ropes. Rope safety is maintained through a mandated minimum factor of safety against breaking strength (applied when the rope is new, with the working factor of safety allowed to decline somewhat with service life under code), a maximum permitted service life or mandatory replacement after a specified number of broken wires within any lay length, and the ongoing NDT/visual inspection programme of 5.2.1 — together these ensure a rope is retired well before its actual residual strength is challenged, rather than being run to failure.

5.2.3 Z, V and Omega strand terms. These describe the cross-sectional profile of the shaped outer wires used in a locked-coil rope's outer layer(s): a Z-strand wire has a Z-shaped profile that interlocks with its neighbours around the rope circumference to form a smooth, sealed outer surface; V-strand (and half-locked/Omega-profile) wires use an alternative interlocking wedge or half-round shape achieving the same goal by a different manufacturing geometry. All three are ways of eliminating the gaps between adjacent outer wires that a plain round-strand rope has, giving the locked-coil rope its higher metallic fill (strength per outer diameter), smooth low-drag surface, and resistance to internal water/corrosion ingress.

5.2.4 Internal lubricants in locked-coil ropes. Lubricant is worked into the rope during stranding (and reapplied periodically in service) for two reasons: it reduces inter-wire friction and fretting wear as the individual wires flex against each other under repeated bending over sheaves and the drum, and, because a locked-coil rope's interlocking outer profile largely seals the core from external inspection, it excludes moisture from the inner wires and inhibits internal corrosion that cannot otherwise be detected visually. The lubricant is typically a corrosion-inhibiting, petroleum- or wax-based grease compound formulated with rust inhibitors and, in many products, a fibrous or waterproofing additive, chosen for good penetration between the wires during manufacture and long-term retention without excessive "bleed" onto the sheaves in service.

5.3.1 Cage-and-counterweight hoisting system. Two configurations are available: a single-drum hoist, with the cage on one rope end and the counterweight on the other so the counterweight balances most of the static (empty-cage) load, minimising the motor power needed for what is primarily a personnel/material duty; or a double-drum (independent) hoist, which can control the cage and counterweight (or two independent conveyances) on separate drums for greater operational flexibility. For this cage-and-counterweight duty the single-drum, counterweighted configuration is recommended: since the counterweight always moves in exact opposition to the cage, the independent-drum flexibility of a double-drum system is not needed, and the simpler single-drum machine is cheaper to install, operate and maintain for a secondary (non-production-tonnage) hoisting duty.

5.3.2 Skip hoisting system. A double-drum hoist is the appropriate choice for the two-skip, two-production-level duty described: the two skips are loaded from two different production levels at different depths, so each drum needs an independently adjustable stopping point — a capability a double-drum machine provides directly through independent clutching/positioning of each drum, whereas a Koepe (friction) hoist is best suited to a single, fixed-depth, exactly counterbalanced duty and cannot easily accommodate two skips loading from different levels. The rope on each drum should be a locked-coil construction (per 1.5 and 5.1.3/5.2), sized by the same static-load/factor-of-safety method used in Question 6.1, with each drum sized against its own drum/rope diameter ratio for fatigue life.