Understanding the Friction Forces in Power Screws

[ehabmozart]

Hello

So at the moment, I am reading through Shigley's Mechanical Engineering Design book. I've come, at, last, to the first application chapter. Screws, Fastners.. etc. Since I lack experience, what I am trying right now is to visualize every single diagram in this chapter and move through equations slowly. Attached to this post is an image. It is written in the book as follows 'First, imagine that a single thread of the screw is unrolled for exactly a single turn. One edge of the thread will form the hypotenuse o a right triangle whose base is the circumference of the mean-thread diameter and whose height is the lead' To be honest, I've tried hard visualizing this and searched all over the web, but I have no clue. I can't imagine it. Can someone give me a hand over here?? I think if we unwrap one turn the hypotenuse would be the circumference??... Moreover, in the attached picture, what is F (the load we want to push up or down)?? and why is the nut stationary and is it stuck to the bolt.. Why is there F/2 on the each side if we only have ONE nut?? I will be very interactive in this post because I had very hard time to understand it and look through the internet.

Thanks A LOT to whoever contributes with an answer no matter how small. Thanks in advance and sorry for the long post.

MERRY CHRISTMAS!

 

[Bystander]

I think if we unwrap one turn the hypotenuse would be the circumference??...

Nerp. Think "perpendicular."

 

[billy_joule]

Why imagine it when you can wrap a right triangle of paper around a pencil and see it action.

 

[ehabmozart]

Thanks a lot to both of the replies. Mmmm.. Well, for the first reply. Can you be more precise here?? I mean how can I think 'perpendicular'... For the second reply.. If i wrap a right triangle around the pencil. Fine. Now I unwrap it and the surface of the paper is the ramp. Where did the base of the triangle come from?? Why is it still pi.dm?? Can I have a bit of elaboration please.. Thanks a lot anyway to both of you.!

 

[CWatters]

Lets say you are driving a screw into a block of wood or into nut one turn. If you were to mark a point on the screw with paint you would see that it moves in two ways at the same time..

1) It moves around the screw one turn, which is a distance equal to the circumference = pi * D
and at the same time..
2) It moves parallel to the axis of the screw a distance equal to the pitch of the thread.

These two motions are perpendicular to each other. 2) is parallel to the axis of rotation 1) is perpendicular to the axis of rotation.

If each of these two distances are drawn out on paper perpendicular to each other as shown below then the hypotenuse represents the distance that the point travelled.

When/if you have studied vectors you will recognise this as the head to tail method of adding two vectors.

 

[CWatters]

I tried to draw the triangle wrapped around a cylinder that represents the screw...

 

[ehabmozart]

I tried to draw the triangle wrapped around a cylinder that represents the screw...
View attachment 93645

Sir, I OWE YOU BIG TIME.. Your reply was just like a Christmas gift. Thanks a lot. Check this link. I was about to post it. It has the visualization as well but yours is way better now. Check it out "http://www.cadcamengineering.net/pitch-diameter-lead-or-helix-angle-and-percent-of-threads/".

I hope you just give me a hand in the rest of my doubts if you don't mind and ofcourse if you are willing to by any chance.

Now, in the attachment I had up in the post, what does F represent? Why is F/2 the reaction by the nut. I mean why not a single F for instance since the nut a hollow circle. In short, what is the power screw trying to do and when we simplify it to a triangle, where does it act exactly?? One one single thread??

You may ask me as much questions as you want if you don't understand any of my questions. I'll reply ASAP.. Once again, thanks a lot!

 

[CWatters]

There are two forces shown acting on the nut each f/2 making a total force of f. I think the only reason they did this was because the drawing is a cross section that makes the nut appear to be in two parts, one on the left and one on the right. There isn't a bit of nut in the middle on which they could show a single force f acting.

 

[CWatters]

The force f depends on the application. In a car jack it depends on the weight of the car and the geometry of the jack. In a bolt an nut it depends on how tight you do up the nut.

What matters more is the strain rather than the force. Strain = force/area. The maximum strain allowed is a property of the material the screw and bolt are made of.

The force is transferred from screw to bolt via the thread. I'm not sure what you mean by "On one single thread" as there is only one thread (at least there is only one thread on the diagram in post #1. On some screws they have twin threads like a double helix but perhaps let's not go there just yet). The point is that the load is carried by the whole length of the thread inside the nut.

 

[ehabmozart]

The force f depends on the application. In a car jack it depends on the weight of the car and the geometry of the jack. In a bolt an nut it depends on how tight you do up the nut.

What matters more is the strain rather than the force. Strain = force/area. .

. Well, i thought stress is the force/area. I still don't get your point here. Now the F/2 doubt is solved. Thanks. My question here is let's say there is car at the top which exerts F. How when we draw the right triangle, we speak about the torque to raise F. The triangle represents one turn of the nut so it would be able to raise a part of F and not the entire force?? You get my question? In other words, why does the right triangle we figured out supports the entire force?? Thanks a lot once more!

 

[CWatters]

Yes sorry I meant stress not strain.

A power screw converts torque into a force. The equations that relate the two are given on this page...

https://en.m.wikipedia.org/wiki/Leadscrew

The equation they give takes into account friction. You can simplify it by assuming friction is zero (mu=0).

 

[CWatters]

I don't understand what you mean by the triangle supporting the entire force. You can't equate a torque and a force because for one thing the units are different.

 

[ehabmozart]

I'll explain what exactly do I mean. Now there is an a force from up (let us say the weight of the car). This exerts the F which points downward as shown in the picture. Fine. Now, we are after the torque required to raise the car up. Yes? Fine. So what have the done is calculating the P (pointing to the left) and drawing the triangle as if we are trying to push a body of weight F up a ramp. (This P will then be multiplied by the mean radius to get the torque) Right? Anyway, my question is when we try to raise up a load. When we draw a FBD of the triangle. What is the F which points downward. Oh btw, I attached a new picture which shows exactly how did they analyze it using the triangle. They equated to find the F push and eventually multiply it with the mean radius. Again, why does one triangle which represents one turn of a nut holds the ENTIRE F (load). Moreover, this triangle is 2D. Do you know how would it look like in 3D. I mean there is a 3D of how the triangle looks in ACME threads. I can;t see how different the triangle could be between square thread and ACME. Once more sir, I owe you BIG time. Merry Christmas!

 

[CWatters]

The force required to push an object up a hill depends on the slope of the hill NOT the length of the slope. It's the same with the power screw. The torque is the same regardless of how many turns or fractions of a turn you make. If you made the triangle bigger it could represent 2,3,4...n turns but the pitch angle would stay the same.

 

[CWatters]

If raising a load of mass m the force f will be equal to m*g and all of that has to be lifted even if the nut is only turned a fraction of a degree. The torque required will be as per the equation in that link.

 

[ehabmozart]

Allright.. I think that was a valuable point. Now my question regarding the 3D image of the triangle. I attached a screenshot from a youtube vid which shows the 3D triangle of an ACME thread. Now, this is just mind blowing. How did he get the alpha and more precisely if it was a square what would the 3D triangle be? alpha is zero, I suppose.. But how??

 

[CWatters]

The shape of the thread doesn't change the shape of the triangle. That's because the circumference and pitch are the same or could be the same for all thread profiles. However the thread shape will change how the effect of friction is taken into account. I've never tried to do the maths for that.

Actually some thread profiles are stronger than others so that might allow a different diameter screw to be used but that's a side issue. If the diameter and pitch are the same then the triangle is the same.

 

[ehabmozart]

I forgot to attach the screenshot :S

 

[ehabmozart]

Now for the previous post (where I attach the image) Check how alpha influences the calculations. Intact, I'll show you another screenshot of where F acts exactly according to my book. Can you see the attached picture. Where does F act? I can;t still visualize it. Fill me up with your considerations.

 

[CWatters]

F in the latest screen shot is not the same as f in the earlier drawings.

In the earlier drawings f is the load force. In the new drawing P is the load force.

 

[ehabmozart]

Oh yes, that's true and I totally understand each screenshot. It just a convention. Back to our discussion, can you explain to me the second last attachment and the existence of the 3D triangle and the effect of ACME thread having an angle alpha on the drawing. Moreover, how does this relate to the leftmost part of the last screenshot?? I totally understand that F and P are mixed but I know what each one refers to in each screenshot. Bottom line, all what I wan to understand now is the last two screenshots. I know this may have taken a bit a some extra time but I totally appreciate your replies and thanks for your effort and time.

 

[alw34]

To complement the above discussion, also consider searching Wikipedia...

it has several separate discussions on screws...such as:

https://en.wikipedia.org/wiki/Screw_(simple_machine)

https://en.wikipedia.org/wiki/Mechanical_advantage_device#Screws

 

[CWatters]

Bottom line, all what I want to understand now is the last two screenshots

Ok so this is the difference between a square thread and an ACME thread. I'll use the notation on the FBD for ACME thread (eg load = P).

The simplest to understand is the square threads. These have a bearing surface that only slopes in one direction = pitch=λ. They are flat in the other direction so α=0. Now the pitch λ is usually small and Cos(λ)≈1 so the normal force used to calculate friction is approximately equal to the load force P.

With an ACME thread the bearing surface slopes in two directions (pitch λ and thread angle α). If you assume λ is small then the normal force N ≈ P/Cos(α) or N ≈ P*Sec(α). Now Sec(α) > 1 so the friction force is increased compared to a square thread.