How to calculate required stepper pushing force?

Hello! I got 3 NEMA 17 Stepper Motors along with 3 DRV8825s, an arduino & Capacitors to drive them.How can we calculate the required pushing force for them to be able to lift up an object that's 9Kg heavy using threaded rods? Is there any formula? Is there any gearbox needed and if yes how can we calculate the needed ratio?

Steppers specs:
12V, 1.5A max current, 0.31 Nm max torque

How many motors and how many threaded rods are connected to the weight? What quality of threaded rod? Are you using a nut on the rod or some other design? What are you using to support the threaded rods? Do you need thrust bearings? There are no formulas unless you can measure the friction using the threaded rods.
This is something you need to build before thinking about powering it. Then you can measure the forces required and go from there. Start your project from the bottom, not the top.

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Agree, there are no formulas for such vague specifications. Do some experiments.

the required pushing force for them to be able to lift up an object that's 9Kg

Slightly over 9 kgf.

3 Motors and 3 threaded rods will be connected to it. They are M8 rods with inserted nuts in the lifting frame yes, they're in a triangular shape trying to lift the object.

As for how they will be mounted on the bearing I was thinking of making a PETG 3d-printed holder with 2 tightly screwed nuts at the very bottom of the rod (note: the nuts would have their own place where they would fit tightly too in the printed holder). As of how it will be connected to the shaft, there will be a screw to lock it on its flat side and the 3d printed hole size will be almost exactly the same as the shaft itself.

Ok. When you get it done and moving, you can measure the torque required on each of the threaded rods and then you will know the torque required of the driving mechanism.

i.e. you build the mechanism without the motors fitted, then measure the requirements to lift the platform.

Note the result may not be NEMA 17 steppers, and will also introduce the rate of lift once you have the thread pitch determined.

Question then would be, over what period of time, as that is the missing requirement for an overall answer.
You already have the motor max torque rating.

Does the motor turn the screw or the nut? What is the thread pitch?

Per this bolt calculator: Bolt Torque, Axial Clamp Force, Bolt Diameter Calculator a motor could torque a to 193N preload. For three: 193N*3 /(9.8N/kgf) = 59 kgf.

It should work.

Use a block and tackle (a combination of pulleys and a rope) and the following calculator... you will "pull" the rope by turning a shaft that winds the rope attached to the mass, threaded through your block-and-tackle, and onto the shaft.

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