Skip hoist rope safety factor after a proposed payload increase
A vertical shaft is 600 m deep and hoists ore in a single-drum skip. The skip payload is 14 t, the empty skip mass is 10 t, and the rope has a linear mass of 7.2 kg/m and a breaking force of 1,350 kN. The winder accelerates at 0.9 m/s² and decelerates at 0.9 m/s²; the worst static load occurs at the start of the wind when the rope is fully extended. The site standard requires a minimum rope safety factor of 6.0 based on the maximum static load. The mine plans to increase skip payload to 16 t to meet a production target and has asked for a rope check. There is no spare headframe capacity and the existing rope is only six months old. The winder brake is rated for the current load but has not been re-certified for a heavier skip.
1. Calculate the static and dynamic rope safety factors at the proposed 16 t payload and at the current 14 t payload. Use g = 9.81 m/s².
Read the worked answer
At 14 t payload, static load = (14 + 10) × 9.81 + 7.2 × 600 × 9.81 = 235.4 + 42.4 = 277.8 kN. Static safety factor = 1,350 / 277.8 = 4.86. At the start of the wind, the dynamic factor for acceleration is (1 + a/g) = 1 + 0.9/9.81 = 1.092. Dynamic load = 277.8 × 1.092 = 303.3 kN, so dynamic safety factor = 1,350 / 303.3 = 4.45. At 16 t payload, static load = (16 + 10) × 9.81 + 42.4 = 255.1 + 42.4 = 297.5 kN. Static safety factor = 1,350 / 297.5 = 4.54. Dynamic load = 297.5 × 1.092 = 324.9 kN, dynamic safety factor = 1,350 / 324.9 = 4.16. Neither case meets the site standard of 6.0, and the existing 14 t duty is already below it. The 16 t proposal makes the deficiency worse.
2. Recommend how to proceed. Include the payload or rope strength needed to meet the standard and discuss the headframe and brake constraints.
Read the worked answer
The rope is not acceptable at either payload against a required static safety factor of 6.0. For 14 t, the maximum allowable static load is 1,350 / 6.0 = 225 kN. The rope plus empty skip accounts for 42.4 + 98.1 = 140.5 kN, leaving only 84.5 kN for payload, or 8.6 t. For 16 t, the maximum allowable static load is still 225 kN, so the allowable payload is even lower. Alternatively, the rope breaking force would need to be at least 6.0 × 297.5 = 1,785 kN for the 16 t static case, and about 1,950 kN if the dynamic load is used for the same margin. A higher-strength rope may require a larger drum and sheave diameter, which the existing headframe may not accommodate. Reducing skip mass or using a balanced two-rope system could help. The brake and headframe must be re-certified for any higher load before the change. The immediate recommendation is not to increase payload; either retain 14 t with a compliant rope and reduced payload, or engineer a complete winding system upgrade.
3. What other checks should be made before accepting a replacement rope of higher breaking strength?
Read the worked answer
Check the complete winding system, not just the rope catalogue strength. Confirm the drum and sheave diameters give an acceptable rope-to-sheave ratio for the new rope construction, and check the rope end attachment and balance rope if fitted. Recalculate the static and dynamic loads including the new rope mass, since a stronger rope may be heavier and reduce the net gain. Check the winder motor, gearbox, brake and emergency brake against the new inertia and load, and confirm the headframe and shaft guides can take the increased loads. Verify the rope fatigue and wear regime, because a higher strength rope may have different bending fatigue performance. Finally, confirm the statutory or site acceptance criteria, inspection intervals and discard criteria for the new rope, and update the operating procedures and load charts before the rope enters service.