A power screw of 32 mm nominal diameter and 5mm pitch is acted by an axial load of 12 kN with permissible thread bearing pressure is 6 MPa. Considering bearing action between the threads in engagement, what is the number of threads in engagement with the screw.

Explanation:

Concept:

Power screw:

• A power screw is a mechanical component that is used to convert rotary motion into linear motion.
• It uses the helical motion of a screw to transmit the power rather than holding the parts together.
• The screw can be thought of as a wedge or a ramp that has been wound around a shaft. By holding a nut stationary and rotating the shaft, we can have the nut sliding either up or down the wedge in the shaft. In this way, a relatively small moment on the shaft can cause very large forces on the nut.

Bearing stress:

• If force F is to be lifted by the power screw, then bearing pressure on the screw is given by

 \(σ_b = \frac{2\times F}{\pi\times d_n \times n_t \times p}\)

Where, F = force applied, d_n = nominal diameter, n_t = threads engaged, and p = pitch of the thread.

Calculation:

Data given,

σ_b = 6 Mpa, F = 12 kN, d_n= 32 mm, p = 5 mm

\(6 \times 10^6 = \frac{2\times 12 \times 10^3}{\pi \times 32 \times 10^{-3}\times 5 \times 10^{-3} \times n_t}\)

∴ n_t = 7.95 ~ 8

∴ the minimum number of threads engaged shall be equal to or greater than 8 for the safe operation of the power screw.

From the options, the minimum number closest to 8 is 9. Therefore, option B is the right answer.