Torque to linear thrust through lead screw Answered
I am trying to figure out maximum linear force I can produce with an electric motor through use of lead screw and nut. I have come up with an equation which seems correct but resulting forces are way higher than my intuition believes is correct.
I tackled the problem from the perspective of energies:
F' * p = M/r * 2*π*r
linear force * thread pitch = torque / radius [M/r = force at radius] * circumference of lead screw
F = 2*π*M/p * (1-k) //k stands for coefficient of friction between lead screw and nut)
Radius falls out of equation, which seems fine as force is provided by torque, which is radius agnostic. I used a 7€ stepper for source of torque which can provide 0.42 Nm of torque and a lead screw with 8 mm pitch and 4 mm radius, I assumed 15% losses. My equation tells me that such system can provide 280 N of force, which seems wayyy too much for a cheap motor.
I have attached a python code that calculates linear force in case it helps
Can someone tell me if my equation is either correct or flawed?