Articulated beams?

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grovenor-2685
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Re: Articulated beams?

Postby grovenor-2685 » Mon Apr 10, 2017 7:45 am

I think you need to rethink those weight distribution diagrams, they seem to be assuming a CofG midway betwen the support points, which is not what is shown on the triangle diagrams.
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Julian Roberts
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Re: Articulated beams?

Postby Julian Roberts » Mon Apr 10, 2017 10:53 am

Sure Keith. One post edited. Not saying this is fully pukka stuff but it works. Of course I need to put somewhere that all this is assuming central CofG.
Last edited by Julian Roberts on Mon Apr 10, 2017 10:58 am, edited 1 time in total.

andrew jukes
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Re: Articulated beams?

Postby andrew jukes » Mon Apr 10, 2017 10:55 am

Julian - Not sure how you work out the weight distributions but I reckon it’s easiest to do it by taking moments about the beam pivot(s). For diagrams 1. and 2., the CofG is 12mm from the pivot(S) and the end axle supporting the weight not carried by the beam(s) is 36mm from the pivot(s). If W is the weight of the vehicle, this means 12 x W = 36 x load on end axle -> load on end axle = 1/3 x W. The balance of the weight (2/3 x W) is split 50/50 between the axles supporting the beam(s). Hence all three axles carry 1/3 x W.

Moving to your drawing 4., and assuming the CofG is still over the centre axle, we now have 18 x W = 42 x load on end axle -> load on end axle = 0.43 x W. The balance of the weight (0.57 x W) is split 25/75 between the axles supporting the beam. Hence, the end axle gets 0.57 x 0.75 W = 0.43 x W and the centre axle gets 0.57 x 0.25 = 0.14 x W. So what this layout achieves is a big reduction in the load on the centre axle, with the reduction shared equally between the end axles.

What I’m not sure you’ve accepted - and the point of drawing these triangles in the first place - is the contrast in stability (indicated by closeness of the CofG to a side of the triangle) between diagrams 1. and 2.

Once one starts considering weight distribution (particularly if both springs and beams are involved) it is worth doing some actual measurements. I picked up pocket calculator-sized 0 - 500gm scales for £7 and arranged things so I can use them to measure individual axle loads. Definitely worth doing if you’re trying to achieve a particular result by shifting the CofG.

Regards Andrew

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grovenor-2685
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Re: Articulated beams?

Postby grovenor-2685 » Mon Apr 10, 2017 12:56 pm

Julian Roberts wrote:Sure Keith. One post edited. Not saying this is fully pukka stuff but it works. Of course I need to put somewhere that all this is assuming central CofG.

Exactly my point, a central CoG does NOT give the weight distributions you have shown.
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Re: Articulated beams?

Postby Julian Roberts » Mon Apr 10, 2017 4:42 pm

Keith I put on Diagram 7 that the 50% is not strictly accurate before disappearing off the internet on the W Highland line round Ben Nevis.

So yes as 50% is inaccurate 25% is too, and it is not enough just to imply that. What I will change the sketches to say is, on that diagram, each axle is 50% of whatever the number is where I have put 50%, and so on.

Or perhaps you can tell me, assuming central CofG, what the numbers are where I have written 50% in each of Diagrams 7, 8 & 9? I can do the maths from there.

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Re: Articulated beams?

Postby andrew jukes » Mon Apr 10, 2017 5:09 pm

Julian - Doesn't my 10.55am posting answer at least part of your question?

Andrew

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Re: Articulated beams?

Postby Julian Roberts » Mon Apr 10, 2017 5:25 pm

Andrew you are talking to a maths dunce here. 'Fraid your first and second paragraphs are too obscure for me not least because the common symbols ^ etc are meaningless to me.

But yes my objective was exactly that, to lighten the load on the centre axle sharing it to the outer ones, though I didn't know they shared it equally.

I see that there is a difference in stability between Drawings 1 & 2 but struggle to see why you say this is so important and that axle loading is so much less so.

Going back to this diagram as a tender it seems to me totally obvious that with 50% of the load the fixed axle at the rear is going to go backwards much more reliably than one with 25%. Going forwards the loco will tend to draw the front wheels of the tender behind it so they won't seek out each track fault. At least we all seem to be agreed the leading wheel (i.e. the rear wheel when going backwards) is the one that is most at risk of derailing on small track faults.

I can't see in comparison why stability is so important - assuming it is made heavy. I don't expect any brass kit made train to stay on the rails without being made as heavy as its whitemetal equivalent. You will have seen the weights I gave in my article.

There is just no issue with stability on the models I have made. Where the weight of the tender is born
on the back of a loco, this is balanced by filling the boiler with lead.

I haven't felt the need to get anything better than kitchen scales so far but with some Comet and Brassmasters kits awaiting their turn with associated springy adventures that is a useful idea

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Re: Articulated beams?

Postby Julian Roberts » Mon Apr 10, 2017 5:43 pm

I did say on both Drawings 7 & 8,....

Approximate!!

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Re: Articulated beams?

Postby Julian Roberts » Mon Apr 10, 2017 6:19 pm

Will L wrote:
Anybody who has tried to get 6 wheel carriages to perform reliably will know that it is lightly loaded centre wheels that are very prone to be first off when track conditions are less than perfect. Getting adequate weight on the centre axle without unloading the first and last axles as the vehicle navigates twists lumps and bumps in the track is a very nice trick if you can do it.

The examples in Julian's snooze articles will only achieve what he is after if you assume the CofG is central on the chassis, but you must understand that this needs to be true to get the result desired

.


Having not made one I suppose I shouldn't say this but surely it can't be harder to get a 6 wheel coach to stay on the rails than a 6 wheel loco? I would start from the presumption it has got to behave properly as a 4 wheeler, and be
compensated at one end or sprung. Then the
middle wheel has got to be sprung or simply weighted enough to keep it on the rails. Assuming a hornblock is used to locate the wheels it's got to work freely and be able to tilt, and the axle must be
able to slide sideways freely. Sufficient sideplay and vertical travel must be allowed for in the design for the intended ...route availability, let's say. So then the total vehicle weight must be sufficient to counteract those independent sideplay and up and down forces.

Yet as one guy so eloquently put it on yourGW thread Will (how could I forget it?), 6 wheel coaches derail if anyone farts in the same
postcode. How can it be so hard?

You say "will" achieve what I am after. The objective is not in the future, it has been achieved, for the last ten years.
Last edited by Julian Roberts on Mon Apr 10, 2017 6:34 pm, edited 2 times in total.

andrew jukes
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Re: Articulated beams?

Postby andrew jukes » Mon Apr 10, 2017 6:23 pm

Julian - Let me try to take out anything that I suspect might be confusing.

For diagrams 1. and 2., the CofG is 12mm from the pivot(S) and the end axle supporting the weight not carried by the beam(s) is 12 + 24 = 36mm from the pivot(s).
If W is the weight of the vehicle, this means 12 x W = 36 x load on end axle [This is where I 'take moments' thinking of the pivot as the fixed point.]
So, load on end axle = 12/36 x W = 1/3 x W
The balance of the weight (2/3 x W) is split 50/50 between the axles supporting the beam(s).
So each of the 'beam axles' carries 1/2 x 2/3 x W = 1/3 x W
Hence all three axles carry 1/3 x W.
This case gives 33%/33%/33% axle loadings.

Moving to your drawing 4., and assuming the CofG is still over the centre axle, the CofG is now 18mm from the pivot(S) and the end axle supporting the weight not carried by the beam(s) is 18 + 24 = 42mm from the pivot(s).
Again using W as the weight of the vehicle, this means 18 x W = 42 x load on end axle. [Again, I 'take moments' thinking of the pivot as fixed.]
So, load on end axle = 18/42 x W = 0.43 x W
The balance of the weight (W - 0.43W = 0.57W) is split 25/75 between the axles supporting the beam(s).
So the end 'beam axle' carries 0.75 x 0.57 x W = 0.43 x W
The centre axle carries 0.25 x 0.57 x W = 0.14 x W
This case gives 43%/14%/43% axle loadings

Hope that helps a bit

Andrew

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Noel
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Re: Articulated beams?

Postby Noel » Mon Apr 10, 2017 6:59 pm

Julian Roberts wrote:'Fraid your first and second paragraphs are too obscure for me not least because the common symbols ^ etc are meaningless to me


The ^ sign means 'to the power of', so (1/76)^3 is 1 divided by 76, cubed, a fairly small number. The brackets show the order the operations are applied in, so divide first and then take the cube of the result. Likewise (the vehicle’s speed)^2 is the square of the vehicle speed, a rather larger number. The ^ sign is used because it's generally easier to write and read in ordinary text than the small raised numbers commonly used in maths to show powers. It's also clearer if the power is a fraction.
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Will L
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Re: Articulated beams?

Postby Will L » Mon Apr 10, 2017 7:08 pm

Julian

in the spirt of helpfull cooperation for which the forum is known, I have calculated out what the actual axle loads (as a percentace of the loco weight) would be carried for your diagrams 7, 8 & 9.
Diagram 7
julian 7.jpg
julian 7.jpg (78.81 KiB) Viewed 2764 times

Diagram 8
julian 8.jpg
julian 8.jpg (77.43 KiB) Viewed 2764 times

Diagram 9
julian 9.jpg
julian 9.jpg (75.84 KiB) Viewed 2764 times


Given what you trying to achieve you there is no reason why you shouldn't be quite happy with the actual figures.

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Re: Articulated beams?

Postby Julian Roberts » Mon Apr 10, 2017 7:22 pm

Ah well Andrew you can see I fundamentally misunderstood the axle weights of the basic model, though I take your word for it of course that to my surprise they are all equal.

You may or may not see me work out how to apply the same logic to Drawing 9....

Weighting in favour of outside wheels is not hereby proven misguided or unnecessary I maintain...but what I was just saying about tenders in reverse needs my rethinking.

What our whole discussion has not mentioned is the David Franks modification where the outside axle beam is made into a flat level rather than rounded design, 6mm wide as far as I recall offhand. The idea from earlier P4 days of a wagon compensation beam using a sleeper placed lengthways seems equivalent for the lesser
weight....

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Re: Articulated beams?

Postby Julian Roberts » Mon Apr 10, 2017 7:28 pm

Hi Will that is so helpful on my fairly done in grey matter! Saved me a whole sleepless night probably with those numbers dancing round my head! Thanks. Also to Noel for your keyboard signs translation.

I will edit the original posts now but may not get round to changing the drawings as my long journey from Ft William to Birmingham is nearing its end.

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Will L
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Re: Articulated beams?

Postby Will L » Mon Apr 10, 2017 9:53 pm

Julian Roberts wrote:
Will L wrote:
Anybody who has tried to get 6 wheel carriages to perform reliably will know that it is lightly loaded centre wheels that are very prone to be first off when track conditions are less than perfect. Getting adequate weight on the centre axle without unloading the first and last axles as the vehicle navigates twists lumps and bumps in the track is a very nice trick if you can do it.....


Having not made one I suppose I shouldn't say this but surely it can't be harder to get a 6 wheel coach to stay on the rails than a 6 wheel loco? I would start from the presumption it has got to behave properly as a 4 wheeler, and be compensated at one end or sprung. Then the middle wheel has got to be sprung or simply weighted enough to keep it on the rails. Assuming a hornblock is used to locate the wheels it's got to work freely and be able to tilt, and the axle must be able to slide sideways freely. Sufficient sideplay and vertical travel must be allowed for in the design for the intended route availability, let's say. So then the total vehicle weight must be sufficient to counteract those independent sideplay and up and down forces.

Yet as one guy so eloquently put it on yourGW thread Will (how could I forget it?), 6 wheel coaches derail if anyone farts in the same
postcode. How can it be so hard?

Its a function of the much longer wheelbase. This means you need a lot more lateral flexibility on the middle axle, and it is more sensitive to vertical curvature of the rail head. I.e. it is likely to find itself suspended over any dip in the track, or standing on a high spot with the end wheels waving in the air. My last effort was really just a 4 wheel compensated vehicle much as you suggested, with the middle wheel W iron not supporting any vehicle weight but with a significant amount of lead attached keep it on the track, and laterally sprung to keep it somewhere near the centre line of the vehicle. Worked OK in 00 but doesn't cope well with p4 sized flanges. I've got a lot of GER 6 Wheelers in stock, if/when I get to the next one, it will be built sprung, which I'm pretty sure will work better, but there is still the question of how you arrange enough lateral flexibility on the middle axle.

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Re: Articulated beams?

Postby billbedford » Tue Apr 11, 2017 9:52 am

Noel wrote:
Guy Rixon wrote:This business of off-loading the central axle of 3 seems to have happened on the full-sized railway.


Assuming that the springs and axleboxes are original, which is, I would suggest, unlikely in a coach more than a century old. If its the one at Tenterden, it's on an ex-LMS Stove R chassis, which is itself around 80 years old...


I have a couple of MS&L six-wheel carriage underframe GAs that show the middle springs to have fewer leaves than the outer ones.
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Noel
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Re: Articulated beams?

Postby Noel » Tue Apr 11, 2017 10:34 am

billbedford wrote:I have a couple of MS&L six-wheel carriage underframe GAs that show the middle springs to have fewer leaves than the outer ones.


On investigation, so do photographs of GWR 6-wheel siphons, where it's possible to see them clearly. So, why?

LMSR 6-wheel fish vans and milk vans though had the same number of leaves in all six springs. However, on both the spring shackles were attached to rods bracketed to the solebars, and those rods were longer on the centre set. Presumably it is not a coincidence that this only applies to the centre axle springs, but, again, I don't know why.

My concern with the earlier comment was just to make the point that preserved vehicles may not still be as the original builders intended.
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Noel

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Russ Elliott
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Re: Articulated beams?

Postby Russ Elliott » Tue Apr 11, 2017 3:21 pm

Julian Roberts wrote:Well Andrew I appreciate your patience here but I wonder how many other readers understand all this. I saw something like it in the Digest and soon glazed over.

I think the key here, Julian, is in the definition of 'digest' - understand or assimilate by a period of reflection.

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Re: Articulated beams?

Postby Julian Roberts » Tue Apr 11, 2017 5:41 pm

You are kind Russ, I am sorry I put a simple lack of intelligence and willingness to learn like that.

As the Prayer Book says though of a different matter, "mark, learn and inwardly digest"... I wonder if you consider we have dealt with the issue of stability sufficiently?

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Russ Elliott
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Re: Articulated beams?

Postby Russ Elliott » Wed Apr 12, 2017 10:25 am

Julian Roberts wrote:I wonder if you consider we have dealt with the issue of stability sufficiently?

Probably not. In qualitative terms, lateral stability is easy to explain (we know a CofG towards the left improves lateral stability but gives a silly axle weight distribution, whilst one towards the triangle apex improves that distribution slighty but makes the lateral stability critical), but I have always found it impossible to quantify such instability. I think there are aspects about the lateral CofG position, beams possibly wiggling laterally very slightly, and the effects of beams impinging on axles moving (albeit very slightly) laterally under sideplay that we don't fully appreciate. Essentially, our '3-legged stools' were always a lot more precarious than had been originally envisaged.

basic-compensation-triangle.png
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Armchair Modeller
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Re: Articulated beams?

Postby Armchair Modeller » Wed Apr 12, 2017 11:21 am

For a 2-axle chassis, this is an alternative configuration to the traditional fixed + rocking axle configuration.

a-3jaa0p3u.jpg
a-3jaa0p3u.jpg (5.91 KiB) Viewed 2909 times


This uses a pivoting beam on one side of the chassis, with the other side fixed.

My impression from limited testing is that this alternative is more stable and requires less weight to stay on the track.

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Re: Articulated beams?

Postby Julian Roberts » Wed Apr 12, 2017 11:40 am

Hopefully correct Diagrams 7 - 9 attached. Please let me know if there are still any wrong numbers.

I will attach these singly to the earlier posts of 2 days ago.

20170412_114738.jpg

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Re: Articulated beams?

Postby grovenor-2685 » Wed Apr 12, 2017 11:45 am

I will attach these singly to the earlier posts of 2 days ago.

Julian,
Be careful how you do that, just replacing your original drawings will make the next half dozen posts totally confusing.
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Re: Articulated beams?

Postby Julian Roberts » Wed Apr 12, 2017 11:54 am

Yes Keith I will add them not replace them and with explanatory note, later on.

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Russ Elliott
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Re: Articulated beams?

Postby Russ Elliott » Wed Apr 12, 2017 12:34 pm

Armchair Modeller wrote:For a 2-axle chassis, this is an alternative configuration to the traditional fixed + rocking axle configuration.
a-3jaa0p3u.jpg
My impression from limited testing is that this alternative is more stable and requires less weight to stay on the track.

I agree. It's like an MJT torsion-bar CCU, for example. But it's a significantly different principle, namely where the rotation is in the pitch plane, i.e. 'longitudinal compensation' (and where one could argue the 'triangle' is irrelevant because of its symmetry over the wheelbase), as opposed to rotation in the roll plane, which is the traditional 'transverse compensation'.


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