How to calculate centripetal force in helical movement

[DjoeZty]

Hi there,

I hope you experts can help me out:

I have a braiding process in which a rod is wrapped around with braiding wires.
Pulling the rod is the linear velocity, spinning of the braiding wires around the rod is a circular movement.
Added together they form a helical movement.

The ratio of the circular movement and the linear movement, forms the pitch (angle) of the braiding wires on the rod. Very simple mathematics, so far.

We also can increase wire tension by adjusting brakes at the supply of the braiding wires.
But how to calculate the centripetal force of the braiding wires in the helical movement given on the rod?

In practice we see that at large pitches (big angles) the centripetal force becomes limited.
This is not the same at all diameters of the rod.

Can you help me out with some useful equations that link the centripetal force with the helical movement?

Thanks in advance and best regards,
Joost aka DjoeZty

 

[JBA]

How are you determining that it is specifically the centripetal force that is changing? Are you basing it upon a variance in the required brake load or some other observation?

 

[DjoeZty]

We see that the braided wires around the rod are loose at great er pitch, tension towards the center aka the rod becomes too little. I presume that it has yo do with the centripetal forceren, since it becomes worse at higher circular speed (rpm).

 

[Bandit127]

Your braider is running a circular motion so centripetal force will remain constant for the same rpm.

Your problem increases as the speed of the rod drawn through the braider increases.

Your limits for a constant rpm are:
1. No draw on the rod. Your pitch is zero. You will have good adhesion of the braid to the rod. In fact it will pile up as if on a bobbin. Your braid is 90 deg to the rod.
2. Infinitely fast draw on the rod. Your pitch is infinite. You will have no adhesion to the rod as your braid will effectively be laid along the axis of the rod in a straight line. Your braid is 180 deg to the rod.

I think this problem has more to do with friction vs the angle of the braid than centripetal force. A DOE might be in order. Pitch vs rod diameter is my first guess.

 

[JBA]

I do not have a direct answer to your question; but, I have a suggested approach that may give you a method of determining the relative effect between two different helix angle wraps based upon the tangential stress in the wire due to centripetal force. As I view it, since there is no change in wrap diameter there is no change in centripetal force or stress and strain on the wire due to the helical angle of wrap; however, due to the longer length of wire in each wrap with increase in helical angle there is an increase in the elongation of the wrap.
As a result, It appears that by calculating the tangential stress and resulting strain of the wrap and multiplying this by the longer wire length due the pitch (helix angle) you can determine the total wire wrap elongation and thereby the resulting increase in wire wrap diameter that may be resulting in the looser winds.

If you do not have an equation at hand a good reference for calculating the relative tangential stresses you might consider using the following online calculator or its equations; however, its radius dimension changes will not be accurate due to the added helix wrap length. (I cannot comment as to its accuracy because its stress equations are different from those in the Sigley "Machine Design" reference)

http://www.amesweb.info/StructuralAnalysisBeams/Stresses-Rotating-Rings.aspx

Alternatively, I would suggest Shigley "Machine Design" by McGraw Hill as a source of alternative stress equations for rings.

At this this is the best suggestion I can offer to approaching your problem; and, hopefully there will additional post by other forum members relative to other solutions.

 

[wrobel]

Let $\boldsymbol r(s)$ stand for the radius -vector of a curve fixed in the space; $s$ is the arc-length parameter. A point $M$ moves on the curve by the law $s=s(t)$. Then the acceleration of the point $M$ is given by the formula $\boldsymbol a=\ddot s\boldsymbol T(s)+k(s)\dot s^2\boldsymbol N(s)$. Here $M\boldsymbol T\boldsymbol N\boldsymbol B$ is the Frenet frame and $k=k(s)$ is the curvature of the curve

 

[Nidum]

Helical winding puts a twist in the wire along it's length . This twist induces bending forces in the wire which can in some cases cause loops formed during the winding process to spring away from the mandrel .

 

[DjoeZty]

Thanks for the replies!

We will try to get more practical data to validate the theory.
Come back to you soon :-)