Question

A square power screw has a mean diameter of 30 mm and a pitch of 4 mm with single thread. The collar diameter can be assumed to be 35 mm. The screw is to be used to lift and lower a load of 7 kN. A coefficient of friction of 0.05 is to be used for friction at the thread and at the collar. Determine the following: (i) Torque required to raise the load, TR, (Equation 8.1) (ii) Torque required to lower the load, TL, (Equation 8.2) (iii) A conservative estimate of self locking condition is to set TL in equation 8.2 to zero and calculate the minimum coefficient of friction to ensure self locking. What is the minimum coefficient of friction to ensure self locking

Answer 1

i) The torque required to raise the load is 15.85 N*m

ii) The torque required to lower the load is 6.91 N*m

iii) The minimum coefficient of friction is -0.016

Step-by-step explanation:

Given:

dm = mean diameter = 0.03 m

p = pitch = 0.004 m

n = number of starts = 1

The lead is:

L = n * p = 1 * 0.004 = 0.004 m

F = load = 7000 N

dc = collar diameter = 0.035 m

u = 0.05

i) The helix angle is:

`tan\alpha =(L)/(\pi *d_(m) ) =(0.004)/(\pi *0.03) \\\alpha =2.43`

The torque is:

`T=F(d_(m) )/(2) ((\pi *u*d_(m)+L )/(\pi *d_(m)-uL ) )+(u_(c) F+(d_(2) )/(2) )=7000*(0.03)/(2) ((\pi *0.05*0.03+0.004)/(\pi *0.03-0.05*0.004) )+(0.05*7000*(0.035)/(2) )=15.85Nm`

ii) The torque to lowering the load is:

`T=7000*(0.03)/(2) ((\pi *0.05*0.03-0.004)/(\pi *0.03+0.05*0.004) )+(0.05*7000*(0.035)/(2) )=6.91Nm`

iii)

`T=F(d_(m) )/(2) ((u*\pi *d_(m)-L)/(\pi *d_(m)+uL) )+u_(c) *F*(d_(c))/(2)\\ 0=F(d_(m) )/(2) ((u*\pi *d_(m)-L)/(\pi *d_(m)+uL) )+u_(c) *F*(d_(c))/(2)\\F(d_(m) )/(2) ((u*\pi *d_(m)-L)/(\pi *d_(m)+uL) )=-u_(c) *F*(d_(c))/(2)\\(d_(m) )/(2) ((u*\pi *d_(m)-L)/(\pi *d_(m)+uL) )=-u_(c) *(d_(c))/(2)\\\\(0.03)/(2) ((u*\pi *0.03-0.004)/(\pi *0.03+u*0.004) )=-0.05*(0.035)/(2)`

Clearing u:

u = -0.016