Torque Drum
Torque Drum
what will be the maximum uniform speed of the lift?
lift of mass 900kg is connected to a rope which passes to over a drum of 1m diameter,and a balance mass of 450kg is attached to the other end of the rope. the moment of inertia of the drum is 100kg-m^2 and it is driven by a motor through a reduction gear(25 to 1) of 90% efficiency. neglecting the inertia of the gears, calculate the motor torque for a lift accelation of 3m/s^2. if the maximum output of the motor is 15kw.
The net load being moved upwards is given by
Net Load = Mg - mg = 450*9.8 = 4410 N
Since the maximum power is 0.9*15 kw, the maximum uniform speed will be
P = F V = 4410 * V = 15000*0.9
solving for V we get
V = 0.9*15000/4410 = 3.06 m/s
The second part of this problem requires the following equations, I hope you recognize them
T1 - Mg = Ma
mg - T2 = ma
T1 d/2 - T2 d/2 = Total torque
where T1 and T2 and M and m are the tensions in the ropes for the lift and counterweight. respectively. Solving for T1 and T2 into the expression for the total torque we get
Total Torque = d/2(M-m) g + d/2(M+m)a
where d, M,m,g and a are all known. Since you have a reduction of 25 in the gears, the actual torque produced by the motor is the total torque calculated above divided by 25.
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