Force to Squeeze a Tube

Intuitively, I think the larger diameter roller will take more force to squeeze in, but the force required to move the tube through should then likely be greater for the smaller one. However, I've got a nagging suspicion the wall thickness and stiffness of the tubing may alter the way that works.

Your good questions always get a rating; it's just that such ratings are, like my hair comb, completely meaningless.

Thicker wall tubing takes more pressure.

stiffer tube material takes more pressure.

The key is what is the pressure you must cause to make the fluid enter the process. That back pressure will be what the tube must resist and what the rollers must pump.

if it pumps 1 GMP into 20 PSI the power needed and strength of tubing can be computed as well as the force needed to make a seal.

Usually peristaltic pumps are use for low pressures where positive displacement is needed to meter a known volume per minute into a process stream.

All very true...but doesn't really answer what I asked!

All things being equal...the diameter of the roller will make some difference....but what?.... As it moves to encounter the tube/fluid/back pressure it will have to exert a force to squeeze the system.... Is that higher or lower depending on roller diameter?

Then as the roller moves along having squeezed the tube ...which roller is easier to move ...big or small.

Del

This suggests that the issue of torque is paramount.

This is a fascinating question which would probably much easier to solve experimentally.

If we were to look at it from the side as it happened... you say a tube that is 12.7mm in diameter. Once squeezed, the squeezed part is about (guesstimate here) 6.4mm in diameter. Basically the wheel/roller would be trying to "climb" the "taller" 6.3mm swell ahead of it all the time.

As an example:

Looking at the 6"/152.4mm curb out on the street, which would roll over it easier, a 5"/127mm wheel or one that is 20"/508mm in diameter?

The larger one of course. The larger the wheel/roller, the less of an angle you are needing to overcome, thus less exertion force.

The monster trucks with their 6 foot tires don't have much problem driving over car bodies vs trying to do that with 2 foot diameter tires.

Oh, wait. That is a common sense answer. Scientifically I am probably wrong, but I will stick with what HAS worked for me all my life: bigger wheels roll over things easier. The bigger the wheel/roller is than what you are rolling over, the easier it is... for me. You may not have noticed that, maybe you never drive over curbs or through ditches or over logs and rocks?

You'll have to get someone else to give you a scientific answer, Del.

Ken

Yup, that's pretty much how I figure it...but of course the bigger roller has to compress a larger area when it first makes the squeeze...

So it's a bit of a compromise.... like most thing in life*.

Del (*no extra charge for the philosophy )

Yes it is, but I would take the larger wheel/roller evertime I would think. Humm, something else to think about, that is for sure. I wonder what the ratio of pressure is for holding the tube flat with a small roller vs large roller? I think theoretically the larger roller would take a consistently higher pressure than the smaller roller would, same as we step on the garden hose with our foot and it doesn't squeeze the water off until we use just the sharp edge of our shoe (generating more force on a smaller area).

It's 0100 in the morning here, time for a short nap I think. Can't think quickly at this time of the day for some reason.

Ken

The smaller roller is easier to squeeze clearly. Theoretically both are doing exactly the same amount of work as you push them along (unit distance). If there is any inconsistency in the composition of the fluid the bigger roller will even things out more.

what about the viscosity of item being pumped?a thicker substance would require more force to pump regardless of the size of the rollers pressing it compared to a thinner substance with smaller rollers.

Just thinking out loud, but it would appear to me that the diameter of the roller is not as significant as the width of the roller. A roller of, say, 5mm diameter and 10 mm wide would move the same amount of the tube contents as one that is 10 mm wide and 20 mm diameter. The speed of the rotating smaller roller would have to be greater to move the same amount of contents as the larger one, but that could be accomplished. Two rollers of the same width but differing diameters would each move the same contents but at different rotative speeds.

As for the power to move the contents, it would be reasonable to assume that the roller moving the most product, by whatever method (speed increase or width increase) would be the one that expends the most power..

Here's my vote,

No problem mate.

In the equation, the tube diameter, wall thickness and whats inside are irrelevant. They are the same for both scenarios therefore are crossed out in the equation. Whats left with is the rollers at 5mm and 20mm to do the job of squeezing. The force of either would be the same assuming the weight of the 2 rollers where equal. If the 20mm were heavier, then it would require less force.

Hi Mr Cat,

You always find interesting questions!

I made a sketch of the crushing in order to explain in better way what I think. I want to specify from start that I am not 100% sure of the model but at least I try to find a "mechanical" explanation. Lets' go:

Left you see half of a "small" roller going to the left and right a "big" roller going to the right.

There are several working zones so that the analysis has to be made zone by zone.

Far enough from the roller the tube is still cylindrical. In the neighbourhood the tube is first oval but has not yet a contact with the roller and a 3rd zone appears where the tube is between roller and supporting wall. For sake of simplicity I considered the wall straight although in a pump it is a hollow cylinder.

The combined movement rotation + displacement leads to a relative movement around the IRC so that the forces from the "crushing" only have a direction as the figure shows it. Those forces are dependent of the crushing value "h" and have a direction which depends on the roller diameter. As figure shows it seems that the bigger the radius the more important the moment given by the crushing forces. The local force increases when "h" increases but in a non linear form according to my computations the force grows proportional to the 3rd power of (d-h).

The other resistance is given by the pressure in the crushed tube. It has 2 effects :

one in the region where the tube is deformed but not yet in contact with the tube. This zone will give a force with about same direction as for the crushing itself.

In the region where the tube is in contact with the roller the pressure will act radial and have as effect only the increase of bearing frictions.

According to this analysis it seems that the total displacement resistance will very much depend on the wall thickness relative to the mean diameter of the tube.

It seems that it will increase non linear with the roller diameter.

Since you have a good experience in this field I shall appreciate if my model agrees with what you got as experimental values.

With respect to only the static crushing it seems that a smaller roller will need a lower force to deform the tube. The problem is quite complex so that only a simplified model is for me possible. There are FEA programmes for high deformations but I have not the time to go so far although I have access to such programmes.

Tube wall is generally about half the bore for a good rugged tube with good memory.

eg. 6.3 bore x 3.2 wall although we do use stuff like 6x2 for higher volume lighter load pumping.

My prob' is that I'm an electronics designer with a good but informal mechanical background.
Empirically it probably doesn't make a huge difference as the constraints of the overall design don't allow a huge variation in roller size.

One problem is in a 2 roller design, there is a point where both rollers are squeezing the tube...this ensures that the tube is always sealed and liquid can't flow back the 'wrong way'... this position represents a high load on the motor. A Small diameter roller helps to minimise this, but only by a small amount. A fair amount of 'over squeeze' is designed in to allow a good pumping pressure...say 2-3 bar.

Your diagram and analysis is cool although your comment ....It seems that it will increase non linear with the roller diameter... could do with a little further explanation/clarification. (You must spell it out s l o w l y 'cos I'm a Cat)

Cheers

Del

If it really matters - do a lash-up. It's not Rocket Science .

Grrrr ftttzzzz spitttsss.

As I've said already the constraints of actual pump size blah blah...it's more of a discussion than a life or death question...OK I am designing a new pump, but I will pretty much stich to a proven geometry with a few inovative wheezes to improve ease of tube chaning, minimise tube wear etc.

Now look you've made my tail all fluff out. It takes ages for th hackles to go back down too .

Here I am doing my damndest to entertain with interesting questions and that's the thanks I get...I shall go off in a huff (or maybe a Landau)

Del

It is the second time I send a "reply" and it does NOT appear. I would very much like to understand why. It is a problem with the editing or any limitations from the supervisor?

The answer was the "slow" explanation for non linearity you requested.

By the way it is very interesting that the 1st thought goes in a direction which is not supported by a deeper analysis. It is common to find one self in such position since our qualitative analysis is often based on a not correct model.

Hello Del the cat,

real thought provoking post!

I am not sure, but think you have answered your own question. glad you gave the tube dimensions as, without them it is difficult to know which to choose.

I cannot see how a magnate would help the travel along the tube, though it will of course help the initial 'squeezing' action.................My answer is the same as yours, the large tube + a magnate!

jfmfit

The different answers are a very good example of how we think in "models" and how we can make the wrong model choice, come to the wrong answer although totally sure to have the right thought and with a flawless logic but starting from wrong a wrong base.

Please think again if the comparison between a car going over a border and the crushing of the tube is valid. I would suggest a kind of "mind storm" to bring arguments pro and cons.

Case 491 writes about exercises to maintain our brains active it can be one of those.

Some daring and irresponsible approximations applied to an imprecise geometric rendering of torque as a function of roller diameter indicate, as Del the Cat writes, that the smallest diameter roller needs the least torque.

It seems that the roller diameter cannot be smaller than the tube bore.

Torque increases as approximately the power 2 or 3 of the ratio of roller to tube diameters.

Structural considerations such as gearing ratios, prevention of slippage and rate of liquid delivery obviously predominate.

It seems that the roller diameter cannot be smaller than the tube bore.

Why not? the roller diameter can easily be smaller than the tube bore...

Take a 1mm drill and press it into a 6 mm diameter pipe, it will clamp off the flow through the pipe?!!

John.

You are right of course but my approximations break down for a roller diameter smaller than the tube bore...

" ... indicate, as Del the Cat writes, ... needs the least torque."

Please be careful not to put words in other peoples' mouths. The first reference to "torque" in this thread is from Guest in #11. Yours in #25 are, to date, the only other references.

Most peristaltic pumps clamp a roller at a fixed position relative to the tube. It is the rolling of the roller that moves the squeezed tube or moves along the squeezed tube. Therefore using 'torque' seems to be a fair and legitimate interpretation of Del the Cat's fascinating problem. It is quite true that if this discussion was, say, in a court of law discussing patent rights, meticulous wording quotations should have been adhered to.