Answer:
Load force = 31.24kN
Efficiency = 16.67%
Explanation:
It was stated that
Input Power = P,in = 3kW = 3,000W
Speed, S = 1rev/s
Pitch, p = 8mm
Thread frictional coefficient = μt = 0.18
Collar frictional coefficient = μc = 0.09
Friction radius of collar, Rc = 50mm
Step 1, calculate the torque while the load is being lifted in terms of 'F'.
This is determined by using the formula
T = ½FDm[1 + πDmμt]/[πDm - μtp]
By substituton.
T = ½F(40-4)[1 + π(40-4)0.18]/[π(40-4) - 0.18 * 8]
T = 18F(1 + 6.48π)/(36π - 1.44)
T = 3.44F.Nmm
T = 3.44 * 10^-3F Nm
Step 2 is to calculate the torque due to friction from the collar
T = Fμc * Rc
T = F * 0.09 * 50
T = 4.5F. Nmm
T = 4.5 * 10^-3F Nm
Then, we calculate the axial resisting load 'F' by using the the following power input relation.
P,in = Tw
P,in = (T1 + T2) * 2πN
Substitute each value
3,000 = (3.44 + 4.5) * 10^-3 * F * 10^-3 * 2 * π * 2
F = 3000/((3.44 + 4.5) * 10^-3 * 10^-3 * 2 * π * 2
F = 31,247.69N
F = 31.24kN
Hence, the axial resisting load is
F = 31.24kN
Calculating Efficiency
Efficiency = Fp/2πP
Efficiency = 2Fp/P,in
Substitute each value
Efficiency = 2 * 31,247.69 * 8 * 10^-3/3000
Efficiency = 0.166654346666666
So approximately efficiency = 16.67%
