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2 February, 21:19

A single square-thread screw has an input power of 3 kW at a speed of 1 rev/s. The screw has a diameter of 40 mm and a pitch of 8 mm. The frictional coefficients are 0.18 for the threads and 0.09 for the collar, with a collar friction radius of 50 mm. Find the axial resisting load F and the combined efficiency of the screw and collar if the screw is raising the load.

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Answers (2)
  1. 2 February, 21:21
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    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%
  2. 2 February, 21:41
    0
    Axial Resisting Load, F = 31.24kN

    Efficiency = 16.67%

    Explanation:

    Given

    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

    First, we calculate the torque while the load is being lifted in terms of 'F'.

    This is calculated by

    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

    Then we 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

    Efficiency = 16.67%
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