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Hod Carrier

Vehicle Dynamics Laboratory investigates the Castering Effect

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Posted (edited)

One of the questions that pops up here on a fairly regular basis concerns the maximum distance between axles without binding or derailment becoming an issue. On a couple of occasions I have mentioned the Castering Effect and it's possible application to the LEGO railway world. Having raised the possibility I thought I should find out for myself what use it might be and to see whether I could harness this effect and see what it might be made to do. And so I set about building myself some prototype vehicles and a test track and got to work.

This is the test vehicle I designed. It's a bit of a "parts bin special" but it does the trick.

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In the light of the lessons learned the test vehicle design was changed slightly and then retested.

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There is still much more work to be done with more prototypes and testing, but I'm hoping to come out with some sort of working MOC at the end of this process. I appreciate that there is rarely anything new under the sun and that I'm probably just replicating someone else's work.

Comments welcomed as always.

**EDIT**

By the way, those black boxes are video links.

Edited by Hod Carrier

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This is great! I really like the effort put into it. It would be really interesting to see if the vehicles behave differently if weight is added. Can you post more detailed pictures of the axles, so I can get an idea of how they work?

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@McWaffel The axle arrangement is very straightforward as they simply pivot independently. The key detail is the offset between the line of the pivot and the line of the axle, as this is what allows each axle to caster.

38719470554_40d5fc2b5b_z.jpg

Most of what you can find online concerning the castering effect is relating to car suspension and steering set-up. However, the basic principle can be observed by watching the behaviour of the wheels on a supermarket trolley. It is the offset between axle and pivot that makes the wheel effectively "trail" and the forces acting on it ensures that it self-steers and aligns itself with the direction of travel. It is this effect that I am attempting to harness to create self-steering axles and, for the most part, it seems to have worked.

@LEGO Train 12 Volts I'm already ahead of you. The second prototypes will be of more conventional "bricks and plates" construction (which I am hoping will form the basis of a heavier MOC) and will have the facility to use a passive steering link between axles. However, I am not confident of the results and it may actually be a step backwards.

The problem is the phenomenon I've been calling "bunching", which is what you can see in the last overhead shot of the second video. In normal hauled operation the couplings are kept in tension and that is what allows them to caster. However, when the vehicles are being propelled the couplings are in compression and this actively forces the axle out to one side or the other. All that a passive steering link will do is to transmit the steering impetus from one axle to the other, so if one axle is forced out of alignment it will force the other out of alignment also, and that is what is already happening without a passive steering link.

This "bunching" issue may be insurmountable without some means of centring at least one axle, but I'm currently at a loss to see how that might be achieved without somehow restricting the axles ability to free caster. However, I am hoping that a passive steering link may at least be enough to stabilise the rear axle sufficiently that it won't derail when propelling, so it will be tested.

The other potential issue with a passive steering link is that it may affect the train in forward motion too. 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. Free castering allows this to happen very successfully, but adding a passive steering link could prevent this from happening resulting in the friction I'm trying to design out.

That said, the concept seems to work very well within certain parameters. You could run an entire train formed of long wheelbase two axle vehicles with castering axles provided you don't want to propel (push) them. If propelling is on the agenda they should behave reasonably well provided you have a non-castering vehicle to stabilise the last axle and stop it from derailing. It's not shown in the video, but the test train did several laps of the track successfully in propelling mode.

I should also add the caveat that I have not yet tested the train through points/switches. I expect they should go through forwards safely but will probably derail if going through backwards due to the "bunching" issue.

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@zephyr1934 I absolutely will. I'm hoping this is something that other people will find helpful too.

Just as an aside:

Some people might be wondering why I haven't explored the use of some form of springing to help with centring the axles. Well, part of the reason has already been touched on elsewhere by someone else on this board, and that is to do with springing rates. Whatever method of springing that you choose it would need to be strong enough to centre the axle but not so strong as to prevent it from articulating at all. In order to overcome the "bunching" issue it would have to be quite strong indeed, and that would probably defeat the purpose.

But the real reason is that my interest was in exploring the castering effect and it's potential uses. I have no wish to try and prove whether one idea or another is best, but simply to discover whether or not castering works.

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Hello,

thanks again for sharing your work in such detail.

I noticed that you actually have two pivot points. One is connected to the buffer section and one is connected to the center beam. I suppose that the distance between the axle and both of the pivot points will have a big influence on how well the system works, including "bunching". Did you consider to change those distances?

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@Legopold Funny your question should pop up when it did because it's something I had thinking about just at that precise moment. :laugh:

Counting across the coupling from the centre beam of one test vehicle to the centre beam of the next, there are a total of four pivot points; one each for the axle assemblies and one each for the magnets on the couplers. This is why the test vehicles experience "bunching". To dial this out you wouldn't want any more than two pivots, ideally the ones for the axle assemblies only with the magnets mounted rigidly. Once coupled to a neighbouring car this would, in effect, create a Jacobs bogie across the coupling (assuming no flex between the magnet faces themselves) and "bunching" would be eliminated. On the down side, such a rigid coupling between the cars would not permit each axle to caster freely, generating friction between the wheels and the track. What you would be creating in effect would be rigid bogies with a wheelbase of @10.5 studs.

The biggest impact that I have noticed was with the amount of axle articulation you permit. Moving the axles either closer or further away from the pivot points doesn't seem to make as much difference because the amount of deflection is the same. The limiters on the test vehicles (the yellow structures behind each axle assembly in the renders) allow @16 degrees of deflection which, by happy chance, is about the correct amount of deflection needed for a 25 stud wheelbase vehicle to negotiate a standard LEGO R40 curve (obviously more or less articulation would be required depending on the wheelbase of the vehicle and the radius of the curve). In this configuration, no matter where you place the axle in relation to the pivot points, it will always deflect by up to @16 degrees when "bunching".

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Thanks for sharing your video Hod Carrier.

I'm very interested in this subject and I hope to see the next experiments soon.

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@Hod Carrier Thanks for your elaborate answer.

Interesting, I had expected that increasing the distance between center beam and wheel axle would make the bunching less a problem.

After thinking through your setup for a while I am concerned about something else. If you start building something on top of the centre beam, the whole weight will last on top of the two pivot points located at both ends of that beam. Since the axle cannot take the weight directly, the pins will suffer some serious stress and increased friction with increasing weight. I wonder, if your setup will be suitable for bigger (heavier) cars.

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@Legopold You’re most welcome. :classic:

I agree that adding weight to the centre beams of these prototypes would be likely to overstress the pivots and affect the performance, but these are just proof-of-concept models not designed for anything more than checking how the castoring effect might work. The second prototypes will be of a completely different design and construction which should be better able to carry more weight. 

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@Hod CarrierI believe designing the pivot points to carry the weight will be a major challenge. Maybe the small technic turntables can do the trick? 

I am looking forward to see your solution. Good luck!

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@Legopold The next prototypes will be conventional “brick and plate” construction rather than Technic, so the weight bearing pivots should be much easier to construct and more straightforward in operation. But we shall see. That’s the joy of prototyping. You build, you test, you learn and you adapt. :grin:

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On 1/1/2018 at 2:50 PM, Hod Carrier said:

 

@LEGO Train 12 Volts 

The other potential issue with a passive steering link is that it may affect the train in forward motion too. 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. Free castering allows this to happen very successfully, but adding a passive steering link could prevent this from happening resulting in the friction I'm trying to design out.

Oh I've never thought about to steer in opposite directions ...thanks for the analysis.

Now I'm waiting for your next prototypes :classic:

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On 1/3/2018 at 4:48 PM, Hod Carrier said:

@Legopold The next prototypes will be conventional “brick and plate” construction rather than Technic, so the weight bearing pivots should be much easier to construct and more straightforward in operation. But we shall see. That’s the joy of prototyping. You build, you test, you learn and you adapt. :grin:

My recommendation is to use axles instead of pins, and to support them at more than one point - say, with Technic bricks spaced vertically some distance apart - in order to avoid a cantilevering effect. This should also reduce the effect of friction within the joint somewhat as well.

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Posted (edited)

Great work!!! I've also tried to investigate a bit how to manage long wheelbase two axle. At first I used a 6x24 train base with fixed axles. Nice on long cuves and terrible on standard curves and switches. Then I began to experiment some kind of pivoting, basically creating a normal 4 axle car and removing the outer pair of wheels. Same problem...good if pulled and placed in the middle of the train, awful if pushed or at the end of the train. I began some testing with rubber bands which kept the axles a bit more under control, and it worked better, but was not perfect at all. Your cars are waaay bigger so forces and dynamics and angulations are very different. Really interesting discussion ,  makes me wanting to rebuld that  two axles car :grin:

Edited by Paperinik77pk

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How about using a 2x2 turntable plate as the pivot point?   Experiment with its offset from the centerline of the wheel axle.  Those standard wheelsets are 3 studs long, so a 2x2 turntable place could produce an offset pivot as small as 1/2 stud...

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A little update for you all. The second prototypes have been built and tested and the results are in.

39609314432_0db5fd0ec4_z.jpg

I have hit a bit of a snag, which you will see if you watch the video all the way to the end. The failure of the last axle to centre on it's own is vexing me. So far I've tried;

  • altering the distance between the pivot point and the axle to see if more force could be exerted on it to make it centre,
  • adding and removing weight,
  • changing the pivot design from a 2x2 turntable plate to a pin and hole, and
  • raising the chassis so that there is no way that the underside could possibly rub against the top of the axle assemblies and create friction preventing the assembly from turning.

Frustratingly none of these attempted fixes have had any affect whatsoever. About the only thing that makes the last axle behave correctly is increasing the speed. I can only conclude that the problem is being caused by internal friction in the pivot, so I'm giving serious thought to stopping at the RC model shop on my way to work and picking up some sort of plastic-safe grease to sparingly apply and see if that helps at all.

While I was tinkering I thought I'd have a look at passive steering.

27860986469_4732631c33_z.jpg

The results of this are mixed. The centring problem affecting the last axle makes this test a little inconclusive, and actually makes that problem worse. While the axles move independently it's only the last axle that fails to centre, but physically linking them using a passive steering system means that now both axles on the last car fail to centre. There is also some issues with axles being steered the wrong direction, but this is actually not as bad a problem as I anticipated before. It's actually quite a fleeting phenomena and the axles are not deflected too far for binding to be a big issue.

That said, it does help when propelling (pushing) a train because the last axle is being steered into the bend under the influence of the passive steering rather than doing it's own thing and potentially causing a derailment. However, as predicted, passive steering does not prevent "bunching" as that has more to do with the manner in which the vehicles are coupled. Basically what's happening is that I'm trying to push something with a hinged bar, and of course that's not a great recipe for success.

As a result of these tests I think that, on balance, if you were wanting to run a formation of long wheelbase vehicles you could get away with having free-castering vehicles and only the first and last vehicle using passive steering.

Your comments are invited. I'm interested to know what you all think and what suggestions you may have for things I might have missed.

**EDIT**

Images are clickable video links. Enjoy!!

Edited by Hod Carrier

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3 hours ago, Hod Carrier said:

A little update for you all. The second prototypes have been built and tested and the results are in.

39609314432_0db5fd0ec4_z.jpg

I have hit a bit of a snag, which you will see if you watch the video all the way to the end. The failure of the last axle to centre on it's own is vexing me. So far I've tried;

  • altering the distance between the pivot point and the axle to see if more force could be exerted on it to make it centre,
  • adding and removing weight,
  • changing the pivot design from a 2x2 turntable plate to a pin and hole, and
  • raising the chassis so that there is no way that the underside could possibly rub against the top of the axle assemblies and create friction preventing the assembly from turning.

Frustratingly none of these attempted fixes have had any affect whatsoever. About the only thing that makes the last axle behave correctly is increasing the speed. I can only conclude that the problem is being caused by internal friction in the pivot, so I'm giving serious thought to stopping at the RC model shop on my way to work and picking up some sort of plastic-safe grease to sparingly apply and see if that helps at all.

While I was tinkering I thought I'd have a look at passive steering.

27860986469_4732631c33_z.jpg

The results of this are mixed. The centring problem affecting the last axle makes this test a little inconclusive, and actually makes that problem worse. While the axles move independently it's only the last axle that fails to centre, but physically linking them using a passive steering system means that now both axles on the last car fail to centre. There is also some issues with axles being steered the wrong direction, but this is actually not as bad a problem as I anticipated before. It's actually quite a fleeting phenomena and the axles are not deflected too far for binding to be a big issue.

That said, it does help when propelling (pushing) a train because the last axle is being steered into the bend under the influence of the passive steering rather than doing it's own thing and potentially causing a derailment. However, as predicted, passive steering does not prevent "bunching" as that has more to do with the manner in which the vehicles are coupled. Basically what's happening is that I'm trying to push something with a hinged bar, and of course that's not a great recipe for success.

As a result of these tests I think that, on balance, if you were wanting to run a formation of long wheelbase vehicles you could get away with having free-castering vehicles and only the first and last vehicle using passive steering.

Your comments are invited. I'm interested to know what you all think and what suggestions you may have for things I might have missed.

**EDIT**

Images are clickable video links. Enjoy!!

Is it possible to add a locking mechanism for the trailing axle of the last car?   If the train goes in reverse, and the axle is locked, it acts like a rigid axle, which should prevent bunching in that direction.   I realize you're trying to create a solution that works without modification in either direction, but that might not be possible.   This seems like it might be the least-intrusive method to correct that "last car" issue.

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@icemorons The "bunching" issue isn't caused by the last axle but by the pivots for the magnets on the couplers. It's like trying to push something with wet spaghetti. It's true that locking the last axle should also have the effect of locking the other axle on the same car via the steering link, but the next car would still "bunch" because of the magnet pivots.

The simplest way to deal with "bunching" is to have rigid couplers between each car (effectively a Jacobs bogie), but the trade-off with that arrangement is that you limit the movement of each axle relative to each other and I think I'd probably lose something in the forward motion stakes if I did that. I'm sure that there may be other alternatives, but it's difficult to work out how each vehicle would "know" it's on a straight and not a curve. It couldn't do it through the motion of the couplers because "bunching" creates the same movement as going forwards through a curve, and in this circumstance it's a motion that I want to create. The only way would be by reference to the track, as @jtlan's Umbauwagen 3yg does, or by reference to the body positioning relative to the neighbouring car.

I'm starting to be of the opinion that I can live with "bunching" provided that it doesn't cause derailments, and the increased weight of these vehicles compared to the first proof-of-concept prototypes seems to prevent that. Using a passive steering link on the last car does at least steer the last axle into the bends and seems to keep things relatively ship-shape and Bristol-fashion.

The last car issue that I'm having at the moment is trying to get the axles to self-centre when they come out of a bend. They do manage this in the end, but it's mostly done by applying more speed which increases the draw force through the couplers. In this respect the passive steering link can help because if I apply enough power through the coupler to centre the first axle the link will see to it that the last axle centres also.

Edited by Hod Carrier

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I've been asked a couple of times over on Flickr how these vehicles perform on LEGO points/switches. Embarrassingly I hadn't actually got any points to test them on, but just today the postman brought me a pair that I had ordered specifically for the purpose. So this evening I set them up, put the train in motion and, well, click on the box below and see for yourselves.

39674534971_e68a5292c0_z.jpg

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Another little video to have a look at showing a few additional tests I carried out. Click on the pic below to see how things have progressed.

39766437451_e09242a7d2_z.jpg

If you'd like to build one of these vehicles yourself or use the principles for a MOC of your own you can download the .lxf file for the chassis mechanics.

Notes on the download:

  • Due to some issue with LEGO Digital Designer the centre axle in the passive steering link is not the correct length. It should be 7 studs long not 6 studs as shown in the file.
  • If using the steering link take a few moments to adjust the length of the link so that both axles centre correctly.
  • The floating 1x2 plates are the axle deflection stops which prevent excessive movement. These will need to be attached to the underside of whatever chassis you wish to build.

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