Question

A square-thread power screw is used to raise or lower the basketball board in a gym, the weight of which is W = 100kg. See the following two figures. For power screws, assume a major diameter d = 20mm, and a pitch of p = 2mm with double threads. The friction coefficient of steel parts is f = 0.1. Gravity constant is g = 10????/kg. (a) (7 points) If the purchased Cordless Electric Power Screwdrivers rotates at 300rpm, determine the power you need to raise to the basket board. (b) (2 points) Check if the self-locking condition of the power screw is satisfied or not.

Answer 1

power = 49.95 W

and it is self locking screw

Step-by-step explanation:

given data

weight W = 100 kg = 1000 N

diameter d = 20mm

pitch p = 2mm

friction coefficient of steel f = 0.1

Gravity constant is g = 10 N/kg

solution

we know T is

T = w tan(α + φ )
`(dm)/(2)` ...................1

here dm is = do - 0.5 P

dm = 20 - 1

dm = 19 mm

and

tan(α) =
`(L)/(\pi dm)` ...............2

here lead L = n × p

so tan(α) =
`(2* 2)/(\pi 19)`

α = 3.83°

and

f = 0.1

so tanφ = 0.1

so that φ = 5.71°

and now we will put all value in equation 1 we get

T = 1000 × tan(3.83 + 5.71 )
`(19* 10^(-3))/(2)`

T = 1.59 Nm

so

power =
`(2\pi N \ T )/(60)` .................3

put here value

power =
`(2\pi * 300* 1.59)/(60)`

power = 49.95 W

and

as φ > α

so it is self locking screw