Deflection of Rubber Cylinder 1

[smjmitchell]

Hi All,

I have a rubber cylinder 40mm dia (1.57") and 331mm (13.03") long. It is made from natural rubber of duro 50. The rubber is supported from buckling under compressive load by a number of diagaphrams that slide over the rubber and are evenly spaced along the length.

I need to predict the load vs deflection characteristics of the rubber cylinder when subject to a compressive loading directed along the axis of the cylinder. I fully understand that testing is the only way to get accurate results. However before testing I would like to do some calculations to demonstrate that the rubber selection is at least roughly right.

My first question is:

Is there an approximate way to predict the deflection if the rubber under a given load. Max strain would be approx 24% if the rubber hardness and sizes are right.

I am interested in any of the following:

1. Rules of thumb.

2. Approximate analysis methods.

3. Semi Emphirical methods based on published test data.

4. More advanced theoretical methods.

5. FEA modelling. I have access to an FEA code that can model rubber using the Generalised Mooney Rivlin, Mooney Rivlin, Neo-Hookean, Ogden rubber models. However the problem is that I don't have any of the material constants for the material. Is there a source of such constants in the literature ? If such constants were available I would build a simple axisymmetric model. However to be honest I would prefer a non FEA approach - but it would be interesting to check against the FEA.

Unfortunately I have no other information on the rubber except that it is natural rubber of 50 duro.

Question 2:

This rubber cylinder is from the landing gear of a light aircraft. It will be subjected to rapid rates of loading (i.e. landing shocks). Does rubber of this type behave in a similar manner when loaded with a static load and loaded dynamically. i.e. If I know what the maximum dynamic load and deflection are, will I get the same deflection if I load the rubber cylinder with the same load in a static condition ????


BTW I am no expert on rubber: far from it ... this is the first time I have dabbled in the field. Any advice will be greatly appreciated.

Thanks,

Steve

 

[tomaspin]

Steve,

From what you describe, this sounds like quite a strange rubber spring, especially as you are using diaphragms to prevent the rubber cylinder from buckling. This height/diameter ratio is really not best suited for use as a compresseion type spring.

If you are looking for high deflection capability, you could do a lot worse than consider an 'Aeon' spring. These are convoluted tubular rubber springs which are designed to buckle, and can therefore give a much higher deflection than a compression spring of the same height, without needing lateral restraint.
For example, a 5 inch double convolution spring will give up 3 inches total compression!! The downside is that the working dimeter is quite large. 'Aeon' type springs are made by several companies, but try

http://www.timbren.com

for details.

By all means analyse your design, but I think it will take a lot of effort to get it to work reliably. Also because of the extreme diameter to length ratio, none of the standard 'simple' calculation methods will give an accurate answer.

For 50 shore natural rubber, Young's modulus E = 2.0MN/m[sup]2[/sup], and shear modulus G = 0.64MN/m[sup]2[/sup], will be reasonably close in the absence of any other data.

The dynamic stiffness of a rubber part is always higher than the static stiffness - this is due to the hysteresis (internal damping) present in rubber materials. Typically, the dynamic stiffness will be between 20-30% higher than the static stiffness, but this is dependent on the rubber material, and the speed of application of the force.

If you search some of my replies to other threads in this forum, I have posted details of some useful references for rubber spring design, the best one being 'Rubber Springs Design' by E.F.Gobel. This is out of print, but copies do come up for sale from time to time - I paid abour £25 for mine.

I hope this is of help to you, but please let me know how you get on.

Regards

Tom Aspin

 

[smjmitchell]

Well yes I agree .. it is a bit odd. I didn't design it though. It is similar to other designs in widespread use. However I would consider replacing the long cylinder of rubber with cylinders of the same diameter but only approx 2" high. Approx 6-7 of these could be stacked on top of one another and separated by metal diagrams which keep the assembly centred inside the outer steel tube. Would this be a better design ?? (This is also a common design in these types of legs). Presumably the separate smaller cylinders (1.57" dia x 2" Long) would have more damping due to the friction between them and the metal diagrams as the rubber expands laterally under compression. The rubber would not be bonded to the metal but rather centred with a nipple on the diaphram that pushes into a hole in each end of the rubber (I hope this makes sence - hard without a picture). The whole assembly is preloaded to keep everything in place.

I don't think the Aeon spring will work on account of the diameter. However I will have a close look at them for some other projects.

OK WRT analysis .... what is a more typical length diameter ratio for rubber springs (compressive loads are approx 2200 lb at 3 in deflection in this case). Also can you point me in the direction of some reference to the "standard 'simple' calculation methods" that you refer to ??? Some elaboration on these methods would be appreciated.

What is the source the modulus data that you quote ? Is there a standard reference where I could go to get data for other shore hardnesses if I need to start adjusting the hardness to get acceptable deflection characteristics.

Similarly is there a reference you could refer me to for further details and explanation of the effects of loading rate on stiffness ???

I will search your previous posts and will certainly track down a copy of Gobel ...

Thanks your you help.

Steve

 

[tomaspin]

Steve,

The source of the modulus data is a small 40 page book " Engineering Design with Natural Rubber" by P.B Lindley. The updated version is still in print and is published by the MRPRA ( Malaysian Rubber Producers Association) in the UK. The web address is :

http://www.tarrc.co.uk/.

I can thoroughly recommend this book, plus it contains some additional references.
This also contains calculation methods for simple geometry parts, and should be sufficient to allow you to some reasonable calculations

The basic material data is as follows:

Hardness Youngs modulus(MN/m2) Shear Modulus (MN/m2)

30 0.92 0.30
35 1.18 0.37
40 1.50 0.45
45 1.80 0.54
50 2.20 0.64
55 3.25 0.81
60 4.45 1.06
65 5.85 1.37
70 7.35 1.73
75 9.40 2.22

The units are Mega newtons/ meter squared, and are for guidance only.Your test lab or compound supplier should be able to give you accurate data.

The diameter to height ratio for compression parts depends to a certain extent on how the compression load is applied, and whether there is the potential for any misalignment, but normally the diameter of the section should be less than the height.

The assembly you describe sounds like the rubber equivalent of a spring (belville) washer stack, and provided the separate rubber pads can move freely in the axial direction without fretting, then it should work reasonably well. Try to limit the total compression to a maximum of 20% of the working rubber depth - this should give you reasonable durability. I would however make sure that you define the fatigue life of the part, and test to make sure that you can achieve this.

Generally speaking, we consider a rubber part to be fully fatigued when the static stiffness has fallen by 25%, irrespective of the visual condition.

I hope this helps

regards,

Tom

 

[smjmitchell]

Tom,

Thanks again .. invaluable information.

I have tracked down second hand copies of both Gobel and Lindley and should have them within a week. I will read and digest their contents and then post again if I have further questions.

Your help is greatly appreciated.

Steve

 

[tomaspin]

Steve,

Whoops - just re read my last post!

I should have said that the height should be less than the diameter, for stable compression parts.

Sorry, must have been Friday brain fade.

I'm glad you tracked down a copy of Gobel so easily - it took me about 18 months! Just check it's the English version.

Regards

 

[smjmitchell]

Tom,

Yes I figured you had that around the wrong way ... good to have it confirmed though. Thanks.

The copy of Gobel that I have coming is:

Rubber Springs Design
by E. F. Göbel. (Translated and edited by A. M. Brichta.)
New York, Wiley [1974] "A Halsted Press book"
211 p
ISBN 0470308559

Not sure if you meant english in the context of the English language (vs German) or that the publish should be English. I assume the former ...

Thanks again,

Steve

 

[tomaspin]

Steve,

In addition to the references mentioned earlier, I have come across another title which might be of interest:

Engineering with rubber, How to design rubber components, published by Hanser Gardner ($99). If you go to

http://www.hansergardner.com

, go to browse categories and then rubber, you can see some extracts from the book. Click on sample pages, and you get 'Chapter 8: Design of components'in pdf form, plus the preface and table of contents.

I've not read this chapter yet, but you might find it a useful read, before your other books arrive.

Regards

Tom

 

[smjmitchell]

Tom,

Thanks I have just downloaded it.

I will read it tomorrow.

Steve