## Hand Tools

Subject:
Re: Sorta yes....
Response To:

Chris Scholz
Equal torque is generally going to mean equal force.

Yes, but you need to include friction in your calculation.

M = W r tan(theta_s + alpha)

W is the force that you apply to your work piece, r is the radius of your screw, theata_s is the friction angle and alpha the thread pitch. (tan [.] is a trigonometric function of course).
The friction angle can be expressed as tan theta_s = mu

In your scenario (wood screw vs. steel screw), W is the same, alpha is the same, substituting and solving:

r_steel/r_wood = tan(Atan [mu_steel - alpha])/tan(Atan [mu_wood - alpha]).

I understand that a motion screw has a thread angle alpha of 29 degree or so. The coefficient of friction for greased steel on steel is about 0.16, wood on wood is highly variable usually somewhere between 0.5 to 0.2.

Putting this all together the radios of your wooden screw needs to be anywhere between twice as large up to 15 times as large as a steel screw to transmit the same force.

This all assumes you are in the 'elastic' region of the materials, i.e. far away from bending or breaking your vise.

Hope this is useful.

Chris

Resources:
Screw friction https://engineeringstatics.org/Chapter_09-screw-friction.html
Coefficient of friction tables: https://www.engineersedge.com/coeffients_of_friction.htm
Motion screws: https://www.linearmotiontips.com/examining-screws-three-different-angles/