Question 1

1. a) For the following winding conditions determine if a rope with a minimum breaking force of 10 MN gives a satisfactory factor of safety for the winding of ore?

Depth of wind = 775m

Mass of skip and attachments = 10 tonne

Mass of ore wound per wind = 20 tonne

Height of sheaves above skip top when skip unloading at shaft top = 20m

Mass of rope/100m = 750 kg/100m

Note for ore hoisting using a drum winder minimum factor of safety = 7.0

1. b) If the maximum winding speed for the wind described in part (b) is 18 m/s and acceleration = deceleration = 0.6 m/s2 (assume linear change of speed during acceleration and deceleration) determine:

• Accelerating period

• Decelerating period

• Distance travelled by skip in accelerating period

• Distance travelled by skip during decelerating period

• Time travelling at maximum speed

• Distance travelled at maximum speed.

• Total cycle time assuming a 10 s rest period between winds

• Number of cycles per hour

• Capacity of the system per hour

Plot a speed-time graph for this situation.

1. c) The system described in parts (a) and (b) are for an unbalanced hoisting system employing a drum winding system. Determine variation of the tractive force at the circumference of the drum and the total torque required at the drum to drive the system. Rope diameter is 50mm, minimum drum diameter = 100 x rope diameter, diameter of sheaves = 5 m. Skip hoisting system, so k = 1.15. Friction resistance between skip and guides, air resistance, bending resistance etc. = k x mass of loaded skip.

2. d) Determine the variation of the power at the drive shaft for this system assuming a constant radius of coiling of the rope on the drum (hint do this for each element within the cycle and plot on a torque/power time graph)

3. e) Determine the rms torque and power for this system.