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# Calculating linear/thrust force from a linear ball screw and motor combinaton

## Calculating linear/thrust force from a linear ball screw and motor combinaton

(OP)
I Have been trying to find a good source of information on this problem for years. The information that is always given is the simple equation of
F= 2πT/L ×η but when you use this, the force output is unrealistically high. And I always end up just buying something I think will work as a starting point and then iterate from there with testing. But, I would like to be smarter.

For example

Let's say you have a stepper motor with a torque of 2 Nm, and you're using a ball screw with a lead of 5 mm (0.005 m) and an efficiency of 90% (0.9).
The linear force exerted by the ball screw, driven by a stepper motor with a torque of 2 Nm, is approximately 2262 Newtons.

But when you look online for pre-built systems, they force output is no where near this value.

Has anyone got any real-world experience where they have applied this equation and it produces something useful?

### RE: Calculating linear/thrust force from a linear ball screw and motor combinaton

Buckling length of the screw will affect the allowable force. Desired life will affect allowable force. Also, if these are commercial ball screw units, the torque being transmitted through the input shaft will affect the allowable input torque (and thus force). See Duff-Norton literature attached.

### RE: Calculating linear/thrust force from a linear ball screw and motor combinaton

(OP)
awesome thanks for this

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