Which is stronger?

[nerdsforprez]

I am not an engineer. Perhaps the engineer or the like-educated out there can help me out. We all know that XL motors can twist axles to their breaking point..... so I have a ? regarding axle strength. Would one long axle, say, 12L or longer be the same strength, weaker, or stronger than many 2L axles put together joined by many axle connectors (see attachment)?

I am thinking that the latter may be slightly stronger given that it is easier to twist and shear a long axle as opposed to a short axle. Much like it is easier to break a longer stick as opposed to a shorter stick of the same diameter. What do others think?

[Omikron]

2nd

[Corvette3]

i was thinking about this when building the 42009 and placing the 32l axle would two 16s not have worked better? the 32 was bent slightly in the box and does not transfer drive as well as it should.

[weavil]

From what have seen on others that connector and 2L is stronger! But only if 8L or shorter, if 12L it would twist and pop something.

[DrJB]

You need first to define what is 'stronger'. Some people (non engineers) define 'strength' as the max load a component would take before breaking. Others define strength as the net deformation under a given load.

If you're looking for the max load before breaking, then both variants (a single long axle vs. one made with stacked 2L axles and 2L connectors) would have the same strength. The failure mode here is when the torsion-induced shear stress exceeds the max that the axle(s) can take. The 2L connectors will not fail as they are stronger/stiffer in torsion than the axles.

If you're looking to get max torsional stiffness, then stacked 2L axles + connectors would definitely be much stiffer in torsion than a single long axle.

Someone said once that engineering is 10% science and 90% terminology (people calling the same thing by different names). Case in point, in this specific case, you need to clarify EXACTLY what you mean by 'strong'.

PS. In all above discussion, I have assumed that the failure mode is attributed to shear only. With long axles, sometimes imperfections in the geometry cause a bending mode in addition to twisting (so called non-pure twisting). In such case, the failure mode is due to both shear+normal stresses. Some call this torsional buckling.

Edited February 11, 2015 by DrJB

[Seasider]

CSA vs l

The short connector piece has a very good torsional stiffness. The 2l red axle has notches in it so has sectional weakness. The only issue is possible weakness with an increased number of connections

[Tommy Styrvoky]

the option of using 2 long axles will be stronger, as they are less likely to torsionally twist because of a shorter length axles. maybe 3 long axles may work better, as it will require less connectors and lacks the notches as mentioned above.

[DrJB]

... The 2L red axle has notches in it so has sectional weakness ...

Good observation. However, not sure that the notch makes a difference. The reason is, when the 2L axle is inserted into 2x 2L connectors, the notch area is essentially 'stress-free'. The torsional load is transmitted by a very tiny part of the 2L axle: the part in between the 2x 2L connectors.

Edited February 11, 2015 by DrJB

[Tommy Styrvoky]

What are you planning to build ? if you support the axle and keep axles in short lengths, it should work, as I have never had XLs directly twist axles, but I have had them bend 5.5 axles on sprockets.

[nerdsforprez]

All good information.... thanks everyone. I am modifying my Unimog (see avatar or mocpages) further for even more torque. I like driving things with pneumatic engines, and so not ever PF, and the pneumatic engine I am using is pretty powerful for LEGO standards. This will be a slow, high-torque vehicle, so concern about twisting axles will be a concern for me. But it is nearly, done, look for a post soon. I decided to go with the shorter axles and multiple connectors, but just wanted to make sure I made the correct decision. Also, the axles do have consistent support, so I think that it will work fine.

[Anio]

If you have a bit more space than 1 stud wide (cause they will do more than 1 stud when rotating), parts 32034 and 18948 might be even stronger than build with regular axle joiner.

I mean, for a given length, you will have less connections between parts (they are 3L whereas axle joiner is 2L).

[andythenorth]

Length might make no difference. For a given part, in a given material, for a given torque, the shear under rotation should be the same. Adding more strong parts doesn't make the weakest part stronger.

OTOH, length allows more deformation, and deformation might contribute to shear. Dunno.

Eh, it's a long time since I saw an actual engineering test rig, I might have forgotten something.

Edited February 11, 2015 by andythenorth

[Boxerlego]

I am modifying my Unimog (see avatar or mocpages) further for even more torque. I like driving things with pneumatic engines, and so not ever PF, and the pneumatic engine I am using is pretty powerful for LEGO standards. This will be a slow, high-torque vehicle, so concern about twisting axles will be a concern for me.

Now this getting interesting. Why didn't you say so in the beginning. Axle breaking isn't really a problem, Twisting is. I don't think you will break an axle unless you experience some kind of shock loads. When the LEGO Axle has achieve a certain RPM Friction will be the problem that you will be encountering.

[Zerobricks]

Hmm theoretically both axles should be capable of sustaining same torque but in reality the longer axle gets twisted so much, it becomes thinner and weaker. Thats why I suggest you to use lots of small axles and connectors.

[camaudio]

I have a few axles that look like that, but none have broken

[nicjasno]

I reinforce all axles with half bushes.

[Blakbird]

I was going to give a nice technical answer, but it looks like DrJB already nailed it. To summarize, the strength of an axle in torsion is unrelated to length. The critical section in torsional shear is the same whether you are using a 12L axle or 6 2L axles with connectors, so the max torque that the axle can carry is exactly the same. However, the longer unreinforced axle will have more twist than the built up axle. Because of the higher spring rate, the reinforced axle may also perform better because there will be less "bounce" between the motor and the load.

[N-4K0]

With enough force, wouldn't the connectors have a risk at cracking, in a setup with e.g. 6x 2L axle vs. 12L axle?

Either way, I do see how and why 6x 2L would be stronger in resisting the twisting better.

[DrJB]

... To summarize, the strength of an axle in torsion is unrelated to length. The critical section in torsional shear is the same whether you are using a 12L axle or 6 2L axles with connectors, so the max torque that the axle can carry is exactly the same. However, the longer non-reinforced axle will have more twist than the built up axle ...

You sure have a very 'eloquent' way to explain such concepts in simple words.

When on here, I need to learn to dis-associate myself from what I do for a living ... not easy though!

[dr_spock]

You sure have a very 'eloquent' way to explain such concepts in simple words.

When on here, I need to learn to dis-associate myself from what I do for a living ... not easy though!

What do you do a for a living? Do you have a way to measure forces on axles and connectors? It might be fun to test out which is "stronger" by sacrificing some LEGO.

[DrJB]

What do you do a for a living? Do you have a way to measure forces on axles and connectors? It might be fun to test out which is "stronger" by sacrificing some LEGO.

I'm an engineer, work on noise and vibration, essentially everything that shakes and makes noise.

Measuring a force is typically not easy. There is however a way to calculate the forces from measured deformations (strains) by use of 'strain-gauges'. In this case however, the 'easiest' way would be to take the two constructions side by side and keep on increasing the load until one of them fails. I must warn though that testing for failures is not very 'repeatable' and one must test several times and run some statistics/averages, unless you want a simple answer of A vs. B. That said, in my view there is no need to test as the answer to this problem is known, as explained by both Blakbird and myself in prior posts.

Edited February 12, 2015 by DrJB

[Captainowie]

i was thinking about this when building the 42009 and placing the 32l axle would two 16s not have worked better? the 32 was bent slightly in the box and does not transfer drive as well as it should.

I thought that too, but there's nowhere to put the axle joiner in the middle of the axle - it would get in the way of _something_. Presumably it was easier to just drop in a 32 axle than redesign the model.

[andythenorth]

Presumably it was easier to just drop in a 32 axle than redesign the model.

Needed for the B model

[aol000xw]

From a non purist point of view

if I understood correctly using reinforcements in axles like half bushes is mostly useless because there is always a critical section between every half bush, at the point where an axle crosses a beam or where gears are put. So unless spreading torque among several axles and gears there is not much to do

2x2 round bricks reinforcing an axle -yeah bulky- given the diameter and the design of the parts and having an axle at the core would increase the strength by a high margin right? But unless the 24 and 40 teeth gears can fit the 4 studs without modification it is a non purist options because:

• If a gear sits next to a 2x2 round brick, it needs to be firmly attached to it, otherwise everything is reduced to a critical section at the axle.
  
• If two or more consecutive gears are used to increase "gear strength" then those should be attached or glued together and to the round bricks next to them if any.
  
• Axles can never cross a beam
  
• CV or UV joints would need to be custom if some are needed before the "reinforced axle" is spread among several standard axles, one to each of several wheels for example.
  

in doing so, the limits of the axle could theoretically be overcome by a very high margin, for example in a big truck using several XL motors and a main shaft to transfer all the torque.