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rotary to screw force calculation

calculate lifting

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malcolm mill05/03/2020 13:11:34
6 forum posts

I suppose the title says it all......

a stepper motor turns in a circular motion with a torque of 1N and shaft diameter 5mm

the motor shaft is then direct coupled to a 8mm x 2mm pitch lead screw

if set vertically with shaft and screw in the same plane what is the lifting force of the screw

Michael Gilligan05/03/2020 13:52:21
16982 forum posts
752 photos

This might help you, Malcolm : **LINK**


malcolm mill05/03/2020 14:06:29
6 forum posts

wonderful link

BUT it means absolutely nothing to me....

I'm 70, I'm on a lot of painkiller and too easily confused and frustrated.

to make it worse... I was an electronics designer to chip gate level and was fluent in 5 computer languages plus binary / boolean.... and find my current lack of accruity very frustrating

thanks anyway michael

Gary Wooding05/03/2020 14:13:54
776 forum posts
196 photos

The torque of the motor = 1N, or 1 Newton at 1 meter (1000mm). The effort, E, provided by the motor is then 2*PI*1000 Newtons for each revolution. For each revolution of the screw the load , L, is lifted through 5mm.

Assuming no loss due to friction, then the effort E must equal load L, so...

2*PI*1000 = L*5, therefore L = 2*PI*1000/5 = 400*PI Newtons, or approx 128 Kg.

If the leadscrew is a ball-screw then friction will be very low and the load should be a little over 100Kg, otherwise friction is likely to be nearer 80% and the load will be reduced to around 35Kg at a guess.

SillyOldDuffer05/03/2020 16:10:19
6643 forum posts
1495 photos

The sort of question makes my brain fizz! Trying to follow Gary's answer, he says "The effort, E, provided by the motor is then 2*PI*1000 Newtons for each revolution." Is that right? I imagine 2N at 500mm, 4N at 250mm etc.

Michael's calculator, making everything zero apart from the pitch and diameter, suggests about 250N for a 1N input. That's about 25kg lift assuming zero friction. With friction assumed to be 80%, about 2kg.

I've no idea if that's right - need more coffee...


Mick B105/03/2020 17:00:56
1799 forum posts
91 photos
Posted by Gary Wooding on 05/03/2020 14:13:54:


For each revolution of the screw the load , L, is lifted through 5mm.


How's that when the stepper's directly coupled to the 2mm pitch leadscrew?

Oh Gordon Bennett, what've I uneashed by asking that... ?? surpriselaugh

John Haine05/03/2020 17:07:29
3521 forum posts
194 photos

It might make it clearer to think in energy terms. So if the motor is exerting 1 newton-metre torque, that's a force of 1 newton (roughly an apple!) at the end of a 1 metre lever. In one revoultion the force moves 2 pi metres, so energy is about 6 joules. If that goes into lifting a weight by 2mm = 0.002 metres, the lifting force must be such as to absorb the same amount of energy. So:

F x 0.002 = 6, or F is ~3000 Newtons. One Kg weight is 9.81, or about 10, Newtons, so maximum lift force is about 300 kg. This assumes no friction in the ball screw.

Gary Wooding05/03/2020 17:52:26
776 forum posts
196 photos

Whoops, I used a pitch of 5mm where it should have been 2mm. So multiply my 128Kg by 5/2 to give 320Kg.

malcolm mill05/03/2020 18:50:28
6 forum posts

THANKS to everybody..... I can now make educated reasoning on motor spec and finish my project...…..

theres nothing more annoying than producing an elegant construction, simply for the motor to start clicking and going nowhere.

I've enjoyed the too and fro between you all...…. the sort of thing I used to love taking part in but, alas, no longer can


Michael Gilligan05/03/2020 19:02:39
16982 forum posts
752 photos
Posted by malcolm mill on 05/03/2020 14:06:29:

wonderful link


BUT it means absolutely nothing to me....



Sorry about that, Malcolm

I was on the ‘bus to Manchester, and I grabbed what I thought looked promising
... But it is a bit heavy, isn’t it !!

Just had another thought though ... which I will throw into the pot:

  • The diameter of the motor shaft is irrelevant, because it’s directly coupled to the screw
  • To a first approximation: The distance travelled in one rotation is the circumference of the screw
  • The linear displacement in one rotation is the pitch of the screw
  • That gives us a ‘gear ratio’

I must leave it to others to do the juggling ... I’m on another bumpy ‘bus ride.



Edit: belatedly reading the last few posts suggests that you’re there already.

Edit: For handy reference: This calculator looks more relevant ...


Edited By Michael Gilligan on 05/03/2020 19:24:49

duncan webster05/03/2020 19:53:02
2927 forum posts
34 photos

work done by motor is torque (N.m) * angular rotation in radians. There are 2*pi radians in one revolution, so work done in one rev is 2*pi*torque

work done by leadscrew in one revolution is force * distance (metres)

In the absence of friction (ballscrew and rolling element thrust bearing) the force is 2*pi*torque/distance.

However OP has quoted torque in N which isn't right, should be Newton.metres,, or

If plain screw and thrust bearing, you'll lose a lot due to friction. The sums get a lot more complicated depending on helix angle of leadscrew, coeff of friction, diameter of thrust bearing, diameter of leadscrew and included angle of thread.

Howard Lewis06/03/2020 17:36:36
4085 forum posts
3 photos

If direct coupled to the Leadscrew, the motor shaft diameter does not come into the calculation,

Effectively, if you unravel a screw thread, it becomes a simple lever.

If you think of the Mechanical Advantage as being Load / Effort , the Effort moves (2 Pi x 8 ) mm to lift the Load 2 mm This is 50.26 mm movement by the Effort to produce 2 mm movement of the Load, so the Mechanical Advantage is 25.13

Neglecting friction, this means that applying a 1N force can exert a force of 25.13N.

Friction will reduce this figure quite markedly..

This overly simplistic, since rather than 8mm it would be more accurate to base calculations on the pitch line diameter.of the thread.

But a screwthread can exert a lot of force, that's why you don't apply much force on the handle, but turn it a lot of times, to jack up your car!


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