Vehicle Dynamics Laboratory investigates the Castering Effect

[jtlan]

On 1/1/2018 at 5:50 AM, Hod Carrier said:

There may be times when you want the axles of a vehicle to steer in opposite directions, such as going through points/switches, which is why my test track includes a couple of S bends.

I was initially concerned about this as well; however, on the Umbauwagen 3yg the front and rear axles always turn together. The three axles are in a straight line in the middle of an S-bend, which works because the track is approximately straight there:

For a wheelbase of this length (20 studs axle-to-axle), the deviation is small enough that the wheel flanges don't rub on the track (Try it and see! Big Ben Bricks wheels are slightly thinner and so are affected less.). The articulation is mostly needed to reduce friction in turns, and to keep the wheels from riding up the point or guard rails of a switch.

[Hod Carrier]

This is where your three axle design has the advantage over the two axle designs.

Because all three of your axles influence and steer each other, the centre axle is centring the two outer axles and reducing the deflection which is the source of the unwanted friction. With a passive steering two axle design the axle at the blue end of the vehicle would still be turning hard left against the direction of the curve because the axle of the red end would be turning into the curve under the action of the coupling to the neighbouring car.

[Paperinik77pk]

I agree with @Hod Carrier - the third axle is an important input to the two other axles, since it can suggest "how the track is done in the middle"  - two axles only cannot have this kind of input and can only rely on themselves, or be helped by the pushing/pulling wagons. 

Great three axle wagon, BTW!!!   I wanted to create them in 12v style for my BR78  - may I try this kind of linking?

 

[Ludo]

I know it's a pain in the ... to get it working, specially on R40 radii, and most of us have more than a Curver box full of them.

I was wondering how the linked cars will behave on larger radii.

Would the problem persist, or should it behave better due to the larger radii?

I expect they would behave better when pushed.

And how would they pass the R104 point from BrickTracks?

see discussion on Eurobricks: 

see: 

Anyone who tried this yet?

 

[Paperinik77pk]

On very large radius curves (made with straight parts with custom mountings - so they form a curve) I can keep both axles fixed...or only one turning. 

I could try with Lego flexible track to create a long radius zigzag curve (emulating a switch) and see how the yellow wagon behaves 

 

[Hod Carrier]

You beat me to it!!

The bigger the curve radius the happier these vehicles will be. The trick is to tailor the amount of axle articulation to suit the smallest radius that they are likely to encounter; so the bigger the radius the less articulation you will need. Eventually, as @Paperinik77pk says, you will get to a radius big enough that the axles don't need to articulate at all and can be fixed.

Edited February 27, 2018 by Hod Carrier

[Paperinik77pk]

I totally agree with @Hod Carrier, we can manage to create longer radius curve with standard Lego parts, but points are always limited to R40...so we had to work on the "worst case" possible. 

BrickTracks points are way larger than R40, so I think the wagons will be veeery happy to travel over there!!! I just saw the video @Ludo posted yesterday - look at that crocodile locomotive changing track on standard points - it is a pain only to see it - and it has very flexible bogies!  

[jtlan]

5 hours ago, Paperinik77pk said:

I totally agree with @Hod Carrier, we can manage to create longer radius curve with standard Lego parts, but points are always limited to R40...so we had to work on the "worst case" possible. 

This is what I was getting at -- a rigid 2-axle car will stay on ordinary track (albeit with increased friction!), but the discontinuous geometry of switches will derail them.

[bradaz11]

how do they do this on real life long trains? or do they not have single axle bogie loooong trains, only double axle bogies?

it seems like you are trying to invent a soloution on train, for an issue that is made by the track, where the answer is, modify the track not the train.

the other thing with the buffers steering the single axles off. what happens if you remove the buffer and magnet from the axles, and attach them to the actual carriage, leaving the axles to free steer?

 

[Hod Carrier]

@bradaz11 Real trains work very differently from LEGO ones, and this is the main reason why vehicle dynamics have to be considered differently.

Real train axles naturally self-steer because of the cross-sectional profiles of the train wheels and track. The diameter of the wheel tread is largest next to the flange and reduces slightly as you measure away from it. As the axle enters a bend the wheels move laterally towards the outside of the bend. As a consequence, the diameter of the outer wheel where it is in contact with the rail is larger than the diameter of the inner wheel meaning that it will travel further per revolution which causes the axle to follow a curved rather than a straight path. It is this difference in wheel tread diameter that causes the axle to follow the bend, not the flange itself as is commonly believed. You can push a rail axle down a length of track and it will follow the bends happily without any intervention. Rail vehicles take advantage of this by allowing each axle a certain degree of movement within the suspension to permit each axle to steer itself relative to the position of the vehicle body, allowing the vehicle to take bends without creating unnecessary wear to rails or wheels due to excessive friction.

LEGO rail wheels and track are far cruder meaning that a LEGO axle will not naturally self-steer in the way that a real axle would. Believe me, it would be far, far easier if LEGO axles did behave this way because you could then be sure that they axles will follow the path of the tracks. But because they don't, any steering effect you get can only be achieved by applying some force to the axle assemblies directly. In the case of the vehicles that I and others were testing, this force was applied through the coupling to the neighbouring vehicle. Free steering axles that had no steering force applied would not follow the course of the track, refused to self-centre (even when at the very rear of the train) and were frequently the cause of derailments. I did not experience any problems with the buffers steering the axles off because I made sure there was sufficient articulation to ensure that the buffers never made contact with each other. This might be a problem if they were rigidly mounted to the vehicle itself, but mine were attached to the axle assemblies which prevented any interference.

Certainly one solution to this problem would be simply to use larger radius curves, but not everyone has the luxury of space to use them and many have to make do with LEGO's standard curves. As a result, focusing on the vehicle rather than the track makes the solution accessible to more people. I'm sure that those people or clubs lucky enough to have the space for large radius curves will have looked at this and decided it's not required for them, and that's fine. But for the majority of us it opens the possibility for running scale length vehicles on the standard track without the excessive friction and derailment issues previously experienced by trying to run long-wheelbase vehicles with rigidly mounted axles.

To answer your question about real rail vehicles, there are indeed limits to how large a two-axle vehicle can be. Partly this is down to vehicle dynamics but partly it is due to axle loads. The model VGA wagons that I built on the back of this testing are representations of the largest two-axle vehicle to run on the UK rail network. There may be larger vehicles of this configuration elsewhere in the world, but anything larger than this in the UK would require bogies. The trend in rail freight has moved away from trains formed of large numbers of small wagons towards smaller numbers of large wagons. This gives greater efficiency of operation and permits larger loads to be conveyed in trains of equivalent lengths by reducing wasted space thereby increasing the load density.

I hope this answers your questions, but if you'd like to ask more I will be happy to answer.

[bradaz11]

@Hod Carrier

thanks for the reply. When I say buffer, I mean the entire buffer brick, so magnet and buffer. I was refering to your bunching issue when pushing the carriages. If the buffer bricks were mounted to the chassis of the carriage, the connection wouldn't bunch would it? Or would it cause issue because the axle wouldn't align itself to the track, and so although it may not bunch, it may still have the wheels at weird angles or worse, derail?

 

thanks for explaining the real wheel relationship to the rails, that does help clear up what is going on IRL.

the thing I'm trying to ask is, if a real single axle train carriage length is governed by the curve radius in track, then are we not still limited to that in LEGO? so although the train could be scaled down, we have to adjust it to navigate our LEGO curve radius, so we have to change the dimensions of length, or add a bogie to get it to be compatible to the radius we have to work with, or if we change the radius to match the real life example that train carriage could navigate, then the real life carriage should work if scaled down?

or would you stil also need to change LEGO wheel shape?

[Hod Carrier]

4 hours ago, bradaz11 said:

When I say buffer, I mean the entire buffer brick, so magnet and buffer. I was refering to your bunching issue when pushing the carriages. If the buffer bricks were mounted to the chassis of the carriage, the connection wouldn't bunch would it?

Correct. The reason why the cars were "bunching" was because there were too many pivots between the fixed point which meant that the couplers would "fold up" when the cars are pushed. You are right to say that a rigid mounting to the chassis would prevent this from happening.

4 hours ago, bradaz11 said:

Or would it cause issue because the axle wouldn't align itself to the track, and so although it may not bunch, it may still have the wheels at weird angles or worse, derail?

This is the real problem. The axles need to be steered because they cannot self-steer themselves, and the best (only...?) way to do this is through the couplers. Without this there would be nothing to align the axles with the track whatsoever.

I did come up with a solution to the "bunching" issue, which was to add a small elastic band to the coupler magnet itself to keep it centred. This was sufficient to keep the magnets correctly aligned when the train was pushed which also kept the wheels correctly aligned with the track.

4 hours ago, bradaz11 said:

thanks for explaining the real wheel relationship to the rails, that does help clear up what is going on IRL.

the thing I'm trying to ask is, if a real single axle train carriage length is governed by the curve radius in track, then are we not still limited to that in LEGO? so although the train could be scaled down, we have to adjust it to navigate our LEGO curve radius, so we have to change the dimensions of length, or add a bogie to get it to be compatible to the radius we have to work with, or if we change the radius to match the real life example that train carriage could navigate, then the real life carriage should work if scaled down?

or would you stil also need to change LEGO wheel shape?

I'm not entirely sure that a re-profiled LEGO wheel would have sufficient effect to ever make it fully compatible with LEGO curves and make them work in the same way as real train wheels, but it might possible if the curve radius is generous enough.

I think you've asked a very valid question. Very few model railway systems ever truly mimic the operations of real railways in terms of vehicle dynamics, but the LEGO system is almost comically unsuited. No real railway has curves as freakishly tight as the LEGO system and so no vehicle designer ever has to consider how to make their vehicles traverse them.

I guess the answer for us depends on personal preferences, and this is often a factor that gets touched upon whenever the question of scale comes up. Do you design your cars to scale with the track with dynamic characteristics to suit or do you look at ways of modifying either the track or the cars to work together in a more harmonious way? There is no right or wrong answer to this question. Some people like playing with the scale to make shortened LEGO-friendly caricatures of real trains while others like to push the boundaries of what is possible with LEGO by creating correctly scaled behemoths and then engineering them to work on LEGO track geometry.

Personally I don't think we need to be limited by LEGO track geometry. I believe that there are ways of engineering solutions to most track-related problems, and this investigation was one example of this approach. There's no reason why a two-axle vehicle needs to use fixed axles with all the limitations this brings when there are alternative methods we can use to achieve compatibility between the train and the track. LEGO is traditionally seen as merely a toy and not worthy of serious consideration amongst modellers because of it's perceived crudeness, a perception that TLG seems unwilling to refute. However, this does not mean it is impossible to create some truly stupendous creations that, at first glance, really shouldn't work but somehow do. I like stuff to scale correctly if at all possible and try to get as close to realism as I can. This is one aspect of this hobby that I find incredibly attractive. The chance to show someone something and have them say "Is that really LEGO...??" and to undermine their preconceptions is priceless.

But those are just my thoughts. As I said before, there are no right or wrong answers to this question and it's up to everyone to make their own judgements. Often it's simply a question of space that dictates the size of everything.

[Roadmonkeytj]

I know this is an older post but I never saw this method dug into...  I'm the older style magnets (where the magnet clips into a holder)  would mounting the magnet rotated 90 so that it pivots up and down with only the magnet side to side thus limiting the degree of push the coupling can enact? 

[Hod Carrier]

I'm trying to visualise the arrangement you're suggesting. Perhaps you could post a quick diagram showing your proposal?

If the purpose is to try to prevent the phenomenon I referred to as "bunching" when the train is being pushed, the trick is to try to reduce the number of pivots between each vehicle. The trouble is that, out of necessity, these vehicles have too many. There is the pivot for each articulated axle together with the pivot for each magnet, giving a total of four pivots between each vehicle. If you've ever tried pushing something using a hinged bar you will know that it doesn't work because the bar will try and fold up the instant that any of the pivots go over centre.

One solution could be to fix the magnets so that they do not articulate, creating a solid connection across the axles between vehicles, and what you would have is a kind of Jacobs bogie. Another could be to force the axles to self-centre, perhaps by using rubber bands to pull them back to the centre. Personally, I found neither solution satisfactory.

The quasi-Jacobs bogie simply swapped having a two-axle car of a certain wheelbase for a two-axle bogie of a certain wheelbase, and it was possible that both would have the same problems taking curves. In the case of the vehicles I was testing, tying the axles together in the form of a Jacobs bogie between vehicles would create a fixed wheelbase barely less than that of the wagon itself. Therefore I wouldn't really have solved the problem that I had set out to solve.

Through experimentation, I also rejected the idea of forcing the axles to self-centre. Yes it works up to a point, but to eliminate "bunching" entirely the force that would have to be exerted on the axles to centre them would have been great. The real downside I found was that any force acting to centre the axles had to be overcome in order to induce them to steer. I couldn't see any way to tune these forces in order to get the right balance between centring and steering. All you'd end up with was something that would either centre or steer but not both, and that for me was to big a price to pay. I wanted them to steer so that the cars could take curves easily and smoothly, so any force that prevented them from doing so was unwelcome.

In the end, and slightly by accident, I discovered that the key was to influence the magnets. Allowing them enough movement to articulate slightly and yet centre again when needed seemed to work brilliantly. I guess what I came up with was a sort of flexible Jacobs bogie that could articulate through curves but would otherwise hold itself straight, even when pushed. If you can replicate this effect by changing the orientation of the magnets in the old-style couplers then that should be your aim. However, given that they freely articulate the same as (if not more than) the new-style couplers, I'm not sure if you can achieve the same effect without somehow inducing the magnets to self-centre.

[Hod Carrier]

Time enough for a quick update, I think.

After having designed a discreet power bogie for the Ferrobus I wondered if the principle could also be applied to a long wheelbase wagon.

If you were following this discussion last year you may remember that I was still struggling with how to control the last axle without having to run it coupled to a conventional vehicle in order to give the necessary steering inputs. If I turned it into a bogie the problem would go away, but how to do so without it being obvious?

Can you see it?

Here it is!! Admittedly it would be even less obvious if I hadn’t used a dark bley plate, but I hadn’t got a black one to hand.

A quick look underneath shows the simplicity of the design and construction. I’ve also been able to remove the plates that would normally limit the amount of articulation at this end of the wagon.

So how does it run? Really well!! Using free castering axles, self-centring couplers and this bogie at the very rear of the train it is able to run forwards, backwards and through points/switches without binding, derailing or catching on anything. If the small train wheels add any friction it is barely noticeable and has no discernible impact on performance. If you’ll permit a little immodesty on my part, I think I’ve finally cracked it!!

Edited March 18, 2019 by Hod Carrier
Picture re-sizing

[Unfinished_Projects]

3 hours ago, Hod Carrier said:

I think I’ve finally cracked it!!

Just looked through this thread for the first time, and I'm very impressed with the work you've done! Is there any chance that you'll be creating a digital version of the final solution? I'd love to try out this design! (I'd always give credit of course)

Unfinished_Projects

[Matt Dawson]

I think elastic bands will probably be the best method of centering but it's a hard thing to get right with LEGO track, especially due to variance in vehicle length and since you're sacrificing detail and under-frame space to fit the mechanisms...

[Hod Carrier]

@Unfinished_Projects Thanks. I was thinking of posting up an exploded view of all the critical components once I’ve rendered one, but I could make a file available too. The mechanisms are actually quite straightforward.

@Matt Dawson I tried the elastic band method and found it less effective. The problem is that any force that acts to centre the axles must be overcome in order to make them steer. If you take the elastic bands off the axles and put them on the couplers instead it will cause the axles to centre without affecting the steering and has the bonus of eliminating “bunching” when the wagons are being pushed.

Any attempt to either “spring” the axles or to link them together causes more problems than it solves. Using self-centring couplers rather than axles together with a bogie at the uncoupled end is the only reliable way to run these wagons both forwards and backwards, and taking points/switches without derailing.

[Unfinished_Projects]

52 minutes ago, Hod Carrier said:

I was thinking of posting up an exploded view of all the critical components once I’ve rendered one

Sounds awesome! I can't wait to try it out 

Unfinished_Projects

[Man with a hat]

That's clever. And interesting that the small wheels don't add too much friction. That's not what I expected. But maybe because of the combination it works and the wheels may slip?

[Hod Carrier]

@Man with a hat I think it's simply that the entire train only needs one pair of small wheels. If there were more the friction might become a problem, but as only one of these bogies is needed it's manageable. But they seem to roll fairly well on their holders, and I have seen entire trains running on small wheels at shows without too many issues.

[bogieman]

On 3/17/2019 at 11:59 AM, Hod Carrier said:

@Unfinished_Projects Thanks. I was thinking of posting up an exploded view of all the critical components once I’ve rendered one, but I could make a file available too. The mechanisms are actually quite straightforward.

@Matt Dawson I tried the elastic band method and found it less effective. The problem is that any force that acts to centre the axles must be overcome in order to make them steer. If you take the elastic bands off the axles and put them on the couplers instead it will cause the axles to centre without affecting the steering and has the bonus of eliminating “bunching” when the wagons are being pushed.

Any attempt to either “spring” the axles or to link them together causes more problems than it solves. Using self-centring couplers rather than axles together with a bogie at the uncoupled end is the only reliable way to run these wagons both forwards and backwards, and taking points/switches without derailing.

Just finished reading this thread.

It's interesting that you've found self-centering couplers to be a solution. Not sure how versed you are on NA railroading but all freight cars and freight locomotives are equipped with what are called alignment control draft gears that the couplers pull/push on and pivot from. The draft gears are designed such that at at a small angle of rotation of the couplers, at about 4 to 5 degrees rotation or so of the coupler relative to the draft gear, the draft gear imparts a progressive restoring force to keep the coupler near the centered position. This is necessary to prevent "jackknifing" of the train during application of independent air or dynamic braking on the locomotives going down grades. As it is, the RR's still have to limit the total dynamic brake force generated by the lead consist to avoid jackknifing, with DC traction locomotives generally 20 operating axles, less with AC traction. This is part of the reason why heavy haul RR's use distributed power, where the locomotives are placed at intervals within the train. Because passenger locomotives haul short, comparatively lightweight trains, alignment control draft gears are not used on those cars and locos. This has caused problems when delivering passenger locomotives dead-in-train at the head of the train - I can remember at least two derailments when we delivered F40PH's to customers via freight RR's. Switcher locomotives also do not use alignment control draft gears because they don't typically have dynamic brakes and it can be hard to couple to cars on a curve because the coupler has to be forced to angularly align with the car coupler.

Dave

[Hod Carrier]

@bogieman Hi Dave. Thanks for the background information.

Being UK-based I'm not very familiar with American practice and equipment, although I was made aware of the problem of jack-knifing a few years ago after chatting with an American engineer and took away an appreciation for the differences in train handling. Here in the UK freight trains are generally more modestly proportioned and the risk of jack-knifing is much lower so the methods of coupling are different. That said, the trend with multiple unit passenger trains has, since the 1980s, been to use various types of autocouplers, all of which employ centring springs to hold them straight and level to help ensure good alignment when coupling. In common with your switchers, this can make things tricky when trying to couple on a curve. However, we don't have to get between the units and physically force the couplers into alignment because the couplers themselves have features that align the coupler heads as they come together, such as gathering horns or "nose and pocket" arrangements. 

[Hod Carrier]

At the end of this investigation I think it's time to sum-up everything that I have learned.

I started out trying to find out whether or not the Castering Effect could be used in LEGO trains to enable long wheelbase vehicles to be run but the investigation quickly expanded into a more general quest to find the best solution for running vehicles of this type. Having looked at various methods from springing to passive steering to just leaving things to physics to sort out, I finally arrived at a solution that I believe to be the best possible.

Before delving into the mechanics of the solution it is probably a good idea to give a brief explanation of the problem. One of the biggest issues with running long wheelbase vehicles on LEGO track is friction between the wheels and the rails. Fixed non-articulating axles impose a natural limit on how long a vehicle's wheelbase can be before friction becomes so great that it starts to affect the running of the train. The reason for this is that when the vehicle enters a bend the axle is no longer perpendicular to the rail where it is contact with the wheels, as it would be on a straight section of track. This turns the wheels such that they are no longer following the direction of the rail and are, in effect, being driven across the direction of the rail. This forces the inside faces of the wheels to scrub or bind against the inside faces of the rails generating friction. The longer the wheelbase of the vehicle, the more that the wheels are turned across the rails and the more friction is generated. The perfect solution would be to find a way to keep the axles perpendicular to the rail through bends as well as on straights, and for this the axles would need to articulate.

While articulating bogies naturally follow the curves of the track due to having more than one axle, a single articulating axle requires some degree of external control in order to ensure smooth running. This usually takes the form of some sort of centring to bring the axles back to the straight-ahead position on straight track. Initially I hoped that the natural trail created by offsetting the pivot point from the line of the axle would be sufficient to cause the axles to caster, much as the wheels on a shopping trolley do, but the forces proved to be insufficient to cause this to happen reliably. I then considered using passive steering where the axles were linked together mechanically to transfer the steering impetus from one axle to the next but, while this worked well on simple curves, it caused derailments on points/switches due to the fact that at certain times on complex track configurations it is necessary for the axles to steer in opposite directions, which is something that this system did not permit. Following this I tried the solution most commonly tried by other builders which was to use elastic bands to pull the axles back into a centred position, but I discovered that this prevented the axles articulating as much as I wished them to while still not being able to reliably centre them. What all of these different approaches failed to permit was pushing of the wagons due to a phenomenon I referred to as "bunching" where all the axles are deflected causing high levels of friction.

The solution that I have settled on, and the one that I recommend to all train builders, came about almost by accident. However, it is the most reliable method that I have tried and the only one that permits these wagons to be pushed without "bunching". As anyone who has followed this thread will know already, the solution is to employ self-centring couplers attached to the axle assemblies. This method reliably brings the axles back to a central position on straight track while still permitting the full range of articulation on bends. It also allows each axle to steer itself fully independently and holds the couplers straight when the train is being pushed. Vehicles with this feature can safely traverse points/switches both in forward and reverse and, with the use of a small bogie under the last vehicle in any train, does not require coupling to a conventional vehicle.

Above is a render of the basic components of a long-wheelbase vehicle. (It is, in fact, the chassis used for my VGA vans.) The axle assembly at the left of the image is an articulating axle while the assembly at the right of the image is the low profile bogie used at the tail of the train.

The free-castering axle assembly. These pivot freely around the 2x2 turntable plate and do not require any springing to return them to the centre position. The red 1x2 plates are the restrictors that are attached to the underside of the body of the wagon to prevent over-articulation. The size, type and position of these can be varied to allow different amounts of articulation depending on wheelbase and minimum curve radius. This configuration works well for my VGA vans which have a 24 stud wheelbase and are required to traverse standard LEGO R40 radius curves.

The low-profile bogie which is needed if a long-wheelbase vehicle is at the rear of the train. Unless it is coupled to another vehicle the free-castering axles do not behave themselves correctly and can cause running problems. In particular, the train cannot be pushed without risking a derailment and it cannot take points/switches. Note that, as this is a bogie and will naturally follow the curvature of the track, no restrictors are needed, hence they have been omitted.

The construction is very simple and just requires a few parts to be added to the existing assembly. The blue 2x2 plates are there simply to represent the number of layers between the axle assembly and the wheel holder and can be used for detailing if necessary. On the VGA vans I have used these layers to represent the spring hangers for the suspension.

With the axle assembly removed it is possible to see the restrictors fixed to the bottom of the van chassis. Annoyingly they are black on black, but they should be more visible in the next photo.

It should be easier to see the restrictors now and to see also how they limit the amount of articulation. This is important because, to reduce the friction between the wheels and the rails, you want to keep the axles as close to 90 degrees to the rail where the wheels make contact. Over-articulation is just as bad as under-articulation, therefore it is important to tune these restrictors as much as possible to suit your vehicle and layout.

This is the other key component that makes the whole system work. It's the self-centring coupler. Exerting a force to centre the couplers is all that is required to centre the axles also. A strong force, such as is exerted using these small elastic bands, is enough to make it possible for these wagons to be both pulled and pushed and even take complex track layouts and points/switches.

Centring couplers are only required on vehicles of this type. If you want to run wagons like these mixed in with conventional fixed axle or bogie wagons it is not necessary to add the bands to their couplers also.

Edited March 19, 2019 by Hod Carrier
Wonky links

[Unfinished_Projects]

1 hour ago, Hod Carrier said:

At the end of this investigation I think it's time to sum-up everything that I have learned.

Thank you for sharing your findings!  I'm looking forward to trying this out when I get a chance.

Unfinished_Projects