# Ball screw Gear Ratio?

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#### Sanghak

Does anyone knows about gear ratio of Ball-Screw?
When I'm modeling the motor & transmission dynamics, there I must calculate effective mass of motor and there is ball-screw in transmission.

'motor' - gear(1:4) - 'ball-screw'

To know about the effective mass, I must know the gear ratio of ball screw. But through ball-screw, torque is converted into force which tansformation I can not calculate gear ratio.
Is it the (rev/m)? or (ball-screw diameter/lead)?

I wish somebody can help me.

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#### Rich G

Been dealing with ballscrews a long time and have never heard it refered to as a gear ratio. The load to torque calculation is Load (pounds) times lead (inches) divided by 5.65 gives you torque in inch-pounds. The diameter of the screw has no bearing on it's mechanical advantage. One rev of a 1" dia with a 1/4" lead screw is going to take the same torque as a 2" dia with a 1/4" lead (not considering added mass of the larger screw).

I hope this helps because I don't know of a "gear-ratio" to throw at you.

Good Luck.

Rich
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#### George Younkin

In working with ball screws you refer to the lead of the screw as [in/rev].

To reflect the machine slide inertia to the motor use:
J of slide @ motor=W * (L/N)^2 x 0.0000656= (lb-in-sec^2)
N= Drive ratio

To calculate the reflected inertia of the ball screw to the motor use:
J of the screw @ mot.=[DIA^4xLGTHx7.2x10^-5]/N^2 = [lb-in-sec^2]
DIA= Screw diameter [in]
LGTH= Screw length [in]
N= Drvie ratio

Regards
George Younkin, P.E.
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#### Martin Davenport

I think "gear ratio" could mean that if you have a pitch of 5mm of a single start screw on a thread diameter of 25mm would give a ratio or mechanical advantage of (25xPi)/5 so 15.71:1

This could be useful to calculate the conversion of say motor torque referred at the nut and also to work out referred inertia (15.71)^2.

Or am I missing a trick and there is an easier way to arrive at these useful values amongst others.

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• KristianM1