How Much Torque is Needed to Lift a 1000 lb Load with a Power Screw?

[orangeincup]

Homework Statement

A power screw with a pitch of 1 mm is directly coupled to a stepper motor rotating at 60 rpm. If
the efficiency of the power screw is 35%, what is the stepper motor torque required to raise a
4450 N (1000 lb) load?

Homework Equations

P=τ*ω
τ=F*r

The Attempt at a Solution

60rpm*2∏/60=6.28 rad/s
τ=4450*(.0005)=2.22 N-m (I assume this is wrong)

The answer is suppose to be 2.023 N-m

 

[billy_joule]

Yes, your answer is wrong.

You need to use all the given data; the pitch to get mechanical advantage and the efficiency to account for torque loss.

 

[orangeincup]

I think torque efficiency is just dividing my torque by .37 once I have solved the torque required? I really have no idea how to get torque though...

 

[billy_joule]

Yes, that method will work for the torque loss.

τ=4450*(.0005)=2.22 N-m (I assume this is wrong)

Where did 0.0005 come from?

You don't need T=Fr to solve this.

Do you know how to calc. the velocity of the load? via the velocity ratio of a screw thread?

Once you know how fast the load is being lifted you calc. the power required (via P=Fv) then finally the torque.

 

[orangeincup]

Yes, that method will work for the torque loss.
Where did 0.0005 come from?

You don't need T=Fr to solve this.

Do you know how to calc. the velocity of the load? via the velocity ratio of a screw thread?

Once you know how fast the load is being lifted you calc. the power required (via P=Fv) then finally the torque.

I thought the pitch was diameter, so I divided by 2 to get radius. And no I don't think I know how to do that, I just started power screws and I mostly only know about how gears work.

 

[billy_joule]

No, pitch is not diameter.

You need to study power screws before attempting exercises on them.
They are just like an inclined plane which you should have covered in physics.
Good luck!

 

[orangeincup]

4450=(2pi*0.35*T)/.001
T=2.028 N-m

Is this correct?

 

[billy_joule]

No.
It looks like you are plugging numbers into random equations and hoping for the right answer, that calc. doesn't include the motor speed so how could it be right?

Do you know what pitch is yet? Can you calculate the speed of a power screw from an angular velocity and a pitch?

Do it step by step:

Calc velocity of the load.
calc power required to lift the load at that velocity.
calc torque required (and account for losses) for the calculated power and given angular velocity.

You need to include all units.

 

[CWatters]

Do it step by step:

Calc velocity of the load.
calc power required to lift the load at that velocity.
calc torque required (and account for losses) for the calculated power and given angular velocity.

I agree but would suggest breaking as follows...

Calc. velocity of the load.
Calc. power required to lift the load at that velocity.
Calc. the power required after accounting for losses (aka efficiency)
Calc. torque required for the calculated power and given angular velocity.

 

[orangeincup]

How do I calculate velocity based off pitch and angular velocity? I can't find any information on it.

Would it just be v=(pitch*angular velocity)/2pi?

v=(.001*6.28)/2*pi
=.001
(.001*4450/.35)/6.28= 2.023

 

[CWatters]

How do I calculate velocity based off pitch and angular velocity? I can't find any information on it.

Would it just be v=(pitch*angular velocity)/2pi?

v=(.001*6.28)/2*pi
=.001
(.001*4450/.35)/6.28= 2.023

No... or at least it might be but I don't get 2.023 as the velocity.

I refer you to Billy's post. Specifically...

It looks like you are plugging numbers into random equations and hoping for the right answer..

and

You need to include all units.

The values in the problem (eg 1mm pitch and 60rpm) appear to have been chosen to make things easy.

For example 60rpm = 1rps. If the pitch is 1mm how far does the load move per revolution or per second?

 

[orangeincup]

That is my calculation for Torque. My calculation for velocity is below. I'm not sure if it's right. I'll write it more clearly.

Pitch=.001
60*2pi/60=6.28 angular velocity

Solving for velocity...

V=(.001*6.28)/2*pi
V=.001

 

[billy_joule]

I'll write it more clearly.

We still don't know what any of those numbers represent...You need to include units.

You have the right number but any professor of mine would give zero marks.
is it 0.001 Ω? furlongs/fortnight? cubits/afternoon? what about all the other figures?

 

[CWatters]

What Billy said. You must state the units.

In addition...

If the screw is rotating at one revolution per second and the pitch is 1mm then seems rather obvious (eg no need for equations) that the load will move at 1mm per second.