Question

3. (9 points) 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

a) 49.95 watts

b) The self locking condition is satisfied

Step-by-step explanation:

Given data

weight of the square-thread power screw ( w ) = 100 kg = 1000 N

diameter (d) = 20 mm ,

pitch (p) = 2 mm

friction coefficient of steel parts ( f ) = 0.1

Gravity constant ( g ) = 10 N/kg

Rotation of electric power screwdrivers = 300 rpm

A ) Determine the power needed to raise to the basket board

first we have to calculate T

T = Wtan (∝ + Ф ) *
`(Dm)/(2)` ------------- equation 1

Dm = d - 0.5 ( 2) = 19mm

Tan ∝ =
`(L)/(\pi Dm)` where L = 2*2 = 4

hence ∝ = 3.83⁰

given f = 0.1 , Tan Ф = 0.1. hence Ф = 5.71⁰

insert all the values into equation 1

T = 1.59 Nm

Determine the power needed using this equation

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

= 49.95 watts

B) checking if the self-locking condition of the power screw is satisfied

Ф > ∝ hence it is self locking condition is satisfied