How Does the Action-Reaction Principle Apply to a Screw Fastener and Nut?

[Mark2020]

A screw fastener advances into a nut. Assuming there are no frictional forces (or negligible):

a) Is the action force tangential to the male helical thread (screw) and the reaction tangential (in opposite direction to action) to the female helical thread (nut)
b) or does the action-reaction pair appears along the length of the screw (while advancing into the nut)?

According to my understanding, (a) justifies screw's motion (helical) and should be the answer, otherwise the screw wouldn't be able (due to screw threads) to advance into the nut.

Could someone help me understand the above? (a drawing would be very welcome!)

 

[jbriggs444]

A screw advances into a nut. Assuming there are no frictional forces (or negligible):

a) Is the action force tangential to the male helical thread (screw) and the reaction tangential (in opposite direction to action) to the female helical thread (nut)
b) or does the action-reaction pair appears along the length of the screw (while advancing into the nut)?

According to my understanding, (a) justifies screw's motion (helical) and should be the answer, otherwise the screw wouldn't be able (due to screw threads) to advance into the nut.

Could someone help me understand the above? (a drawing would be very welcome!)

You are trying to characterize a force that exists all up and down and around the threads of a screw and nut and treat it as if it were a single force applied in a single direction?

That's what vector sums are for.

I have a pet peeve about classifying forces as "action" and "reaction". Those are empty adjectives. They mean nothing.

 

[sophiecentaur]

Assuming there are no frictional forces (or negligible):

If there were no friction forces, all you'd be doing is giving the nut angular and linear acceleration. There will be a force / couple pushing the nut along / around and there will be a reaction force / couple against the wrench. This is exactly the same principle (it always is) at work when you push a block across a flat, horizontal and frictionless table.

As @jbriggs444 implies, first deal with your concerns about what's action and what's reaction (arbitrary choice really) then get to solving any problem with a Forces diagram.

 

[Mark2020]

@sophiecentaur,
Certainly, there has to be a wrench (or something else) to initiate nut's motion, however my question points to where the action-reaction pair appears between the male and female threads.

So, If I understood correctly from your answer, does what I marked as (a) is the correct answer?

 

[jbriggs444]

If there is no friction, how would the force end up being tangential?

 

[Mark2020]

Just to make the question clearer for all of us: I just would like to know in terms of the action-reaction principle, if the nut has to go around the screw thread over an action force (tangential to helix trajectory) then in order this motion to occur is required a reaction (tangential to helix trajectory) force (a pushing back) on screw's thread. Is this correct?

 

[Lnewqban]

@sophiecentaur,
Certainly, there has to be a wrench (or something else) to initiate nut's motion, however my question points to where the action-reaction pair appears between the male and female threads.

So, If I understood correctly from your answer, does what I marked as (a) is the correct answer?

A screw-nut system is equivalent to an inclined plane wrapped around a cylinder.
It is still a simple machine to do work with.
Just replace the weight of the sliding block with axial load.
Friction is what prevents actual systems from unscrew themselves under axial load.

This is the case of your problem:
https://en.wikipedia.org/wiki/Inclined_plane#Frictionless_inclined_plane

 

[Mark2020]

If there is no friction, how would the force end up being tangential?

I am speaking about an ideal situation where there are no energy losses due to friction. That was my initial thought.

 

[jbriggs444]

I am speaking about an ideal situation where there are no energy losses due to friction. That was my initial thought.

The question remains. We have a bolt that is freely rotating as it advances into a nut. There is no friction. Why would you expect any tangential force? Why would you expect any force at all?

When you say "tangential", which direction is that? Along the helical track of a thread? Or around a circle at a fixed radius from the center line?

[In the U.S. dialect at least, the distinction between a "screw" and a "bolt" is that screws are self-threading. A "screw" does not use a nut. It cuts or squishes into the material (typically wood, plastic or sheet metal) making the threads with which it meshes. Bolts, by contrast use nuts or pre-threaded ("tapped") holes. This fact is reflected in the design attributes of the two fasteners. "Screws" tend to have pointed tips. "Bolts" tend to have flat tips.]

 

[Mark2020]

The question remains. We have a bolt that is freely rotating as it advances into a nut. There is no friction. Why would you expect any tangential force? Why would you expect any force at all?

[The distinction between a "screw" and a "bolt" is that screws are self-threading. A "screw" does not use a nut. It cuts into the material (typically wood, plastic or sheet metal) making the threads with which it meshes. Bolts, by contrast use nuts or pre-threaded ("tapped") holes]

You are right, I messed it up a little. What I am speaking about is an ideal situation where there are no energy losses due to friction and we have a screw fastener and a nut. The initial thought was about a frictionless mechanical advantage. It sounds it contradicts in principle since the screw and the nut work based on frictional forces. Just for the sake of the argument we keep these frictional forces at play but without consuming energy. I just would like to know if what I share on Comment #6 is correct.

When you say "tangential", which direction is that? Along the track of a thread? Or around a circle at a fixed radius from the center line?

Along the track of the thread.

 

[jbriggs444]

Along the track of the thread.

Then the absence of friction means the absence of tangential force.

Now you have to decide whether there is tension on the screw/bolt.

 

[Mark2020]

Then the absence of friction means the absence of tangential force.

Now you have to decide whether there is tension on the screw/bolt.

And with tension what is the result?

 

[jbriggs444]

And with tension what is the result?

Still no tangential force. But what about the normal force?

 

[Mark2020]

Then what I wrote in Comment #6 should hold over the normal force or not? The nut has in a way to push the screw fastener (or vice versa) in order to advance. But the normal force would be perpendicular to the track of the thread, right?

 

[jbriggs444]

Then what I wrote in Comment #6 should hold over the normal force or not? The nut has in a way to push the screw fastener (or vice versa) in order to advance. But the normal force would be perpendicular to the track of the thread, right?

Right. The normal force at any point along the thread is perpendicular to the track of the thread. It has a non-zero component parallel to the axis of the bolt.

Picture a bolt inserted through this spring and threaded into the nut.

 

[Mark2020]

If the normal force is perpendicular to the track of the thread then, how the nut may push the screw fastener (or vice versa) in order to advance? This is the reason what I shared on my first post that the action and reaction forces should tangential to the threads of the nut and the screw fastener. Otherwise, motion cannot occur.

 

[jbriggs444]

If the normal force is perpendicular to the track of the thread then, how the nut may push the screw fastener (or vice versa) in order to advance? This is the reason what I shared on my first post that the action and reaction forces should tangential to the threads of the nut and the screw fastener. Otherwise, motion cannot occur.

Motion does not need force. Acceleration needs force. You provided the force to cause the initial acceleration when you started the bolt spinning. In the absence of friction and tension, that is all that is needed. The nut can spin onto the bolt indefinitely with no further force required.

Now we need to work through the consequences of tension and normal force.

 

[Mark2020]

Motion does not need force. Acceleration needs force.

In order the screw fastener to advance into the nut (with frictions but we assume they consume negligible energy), a continuous force is required. Stopping the action (or the wrench), the screw fastener will stop advancing. In this particular case force is associated with motion.

 

[jbriggs444]

In order the screw fastener to advance into the nut (with frictions but we assume they consume negligible energy), a continuous force is required. Stopping the action (or the wrench), the screw fastener will stop advancing.

Either it is negligible energy and no force is required or it is non-negligible energy and a force is required.

Pick one. You cannot have it both ways.

 

[Mark2020]

OK, I pick the second one.

 

[jbriggs444]

OK. So you have friction and you need a tangential force. So you need a wrench. What's the problem?

 

[Mark2020]

OK. So you have friction and you need a tangential force. So you need a wrench.

Does it mean what I write in Comment #6 is correct?

 

[Dale]

A screw fastener advances into a nut. Assuming there are no frictional forces (or negligible):

a) Is the action force tangential to the male helical thread (screw) and the reaction tangential (in opposite direction to action) to the female helical thread (nut)
b) or does the action-reaction pair appears along the length of the screw (while advancing into the nut)?

I also am having a hard time wrapping my mind around a bolt and a nut without friction. So I will simply answer with regards to an ordinary bolt and nut that do have friction under normal fastening conditions.

The threads of the bolt and nut form a pair of inclined planes that are in contact all along their length. So you don't have a force per-se but rather a force density. The technical term is a stress. There are components of the stress directed perpendicular to the inclined plane surface and components of the stress directed parallel to the inclined plane section.

If you take an arbitrary section of the nut thread surface then you can integrate the stress over that section to get the force acting on that section of the nut thread surface. By Newton's third law there will be a corresponding section of the bolt thread surface, and if you integrate the stress over that section of the bolt thread surface then you will find that the force is equal and opposite the corresponding nut thread force.

I don't know how to translate that to a frictionless case, but there it is for the usual case.

 

[jbriggs444]

Does it mean what I write in Comment #6 is correct?

Yes, the "action reaction principle" holds for every incremental section where screw thread contacts nut thread. The tangential/frictional force of the one on the other is equal and opposite to the tangential/frictional force of the other on the one.

In practical terms, this means that you need two wrenches. One to drive the screw and one to hold the nut.

 

[jbriggs444]

I also am having a hard time wrapping my mind around a bolt and a nut without friction.

Most easily visualized for me as a wing-nut on a smooth bolt. Give that wing nut a good flick and it'll spin a long ways down the bolt.

 

[Mark2020]

@jbriggs444. Thank you very much for your confirmation. I was really confused as you saw.

An interesting observation on the above (your confirmation) is: Seeing the screw fastener and the nut from a distance, let us say the screw and nut threads are not visible (from a naked eye): Along the length of the screw fastener there is not any rectilinear reaction but just a "virtual" rectilinear action force (nut advances over the screw fastener or vice versa) that as seen from a distance pushes the nut (or the screw fastener) to one direction. Is this true or false?

 

[jbriggs444]

@jbriggs444. Thank you very much for your confirmation. I was really confused as you saw.

An interesting observation on the above (your confirmation) is: Seeing the screw fastener and the nut from a distance, let us say the screw and nut threads are not visible (from a naked eye): Along the length of the screw fastener there is not any rectilinear reaction but just a "virtual" rectilinear action force (nut advances over the screw fastener or vice versa) that as seen from a distance pushes the nut (or the screw fastener) to one direction. Is this true or false?

I do not know what a "virtual rectilinear action force" is. The momentum of the advancing nut is unchanging over time. It needs no force to allow it to advance.

However, if there is resistance from friction and if the nut continues to advance with unchanging momentum then it follows that there must be a matching "second law partner force" that counters that resistance: A wrench applied to the nut. [Be very wary of using the phrase "second law partner" in public]

Newton's second law says that $\sum F = ma$. If we know that $ma$ is zero, it follows that $\sum F = 0$. If there are just two forces $F_1$ and $F_2$ then it is clear that $F_1=-F_2$. These two forces might be ironically called "second law partners"​

We might examine the tangential frictional force in more detail. It has a component in the direction of a circle around the bolt's center axis. It has a component in the direction parallel to the bolt's center axis. Along the length of the thread it will have a net that is in the axial direction together with a torque about that axis. Yet we counter both net effects with just a wrench. No axial force required. How can that be?

You need to consider the normal force as well.

 

[Mark2020]

However, if there is resistance from friction and if the nut continues to advance then it follows that there must be a matching "second law partner force" that counters that resistance: A wrench applied to the nut.

I speak about the quoted part, above. By "virtual rectilinear action force" I mean the advancing of nut (or screw fastener) is not caused by e.g. contact force (like directly pushing the nut or the screw fastener along its length) but through a "virtual" rectilinear force (as seen from distance without noticing the screw threads) that essentially is an induced force (not a contact force). Something similar to electromagnetic induction. Would that be a valid description of what we observe?

 

[jbriggs444]

I speak about the quoted part, above. By "virtual rectilinear action force" I mean the advancing of nut (or screw fastener) is not caused by e.g. contact force (like directly pushing the nut or the screw fastener along its length) but through a "virtual" rectilinear force (as seen from distance without noticing the screw threads) that essentially is an induced force (not a contact force). Something similar to electromagnetic induction. Would that be a valid description of what we observe?

Again, there is no change in momentum. No net force needed to advance the nut.

The net force from screw threads on nut threads is most definitely a contact force. If you want to summarize it as a net linear force plus a net torque, that is fine. [One can always summarize a set of forces acting on a rigid body into a single linear force plus a single torque that will produce the same effect. The calculation process is straightforward. The result is uniquely determined].

But labeling this net force as "virtual" and then making an analogy to electromagnetic induction. That strikes me as unnecessary.

 

[Mark2020]

jbriggs444 said:
Again, there is no change in momentum. No net force needed to advance the nut.

But didn't we say a real world screw fastener and nut with frictions, requires a constant wrench force in order the nut to advance or not?

jbriggs444 said:
The net force from screw threads on nut threads is most definitely a contact force. If you want to summarize it as a net linear force plus a net torque, that is fine.

I don't speak about what happens between the threads. You perfectly clarified that and thank you! I am just addressing the following situation. I will express it in a series of short statements:
1.Fastener screw advances into a nut because of force coming through a wrench
2.Imagine (1) as a picture without the wrench in it (however is still acting)
3.Imagine (2) from a large distance where the screw and the nut threads are not visible (due to distance)
4.Because of (3) the observer (from a distance) sees a screw fastener advancing into a nut or vice versa
5.We know what happens between the threads, when we are very close to the fastener screw-nut system
6.Because of (3) the observer (from a distance) has the impression that a rectilinear contact force applies along the rotation axis of the screw fastener or along the rotation axis of the nut. This happens because he cannot see the screw threads from that distance. Or simply we cover the threads from the naked eye and we stay close to the screw fastener and nut.

Is it clear up to now or am I wrong somewhere in between?

to be continued...