Flexi Chassis an Appreciation

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martinm
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Re: Flexi Chassis an Appreciation

Postby martinm » Sun Apr 23, 2017 4:34 pm

What I'm saying I'm suspecting, is that in any particular example CSB solution, the wire can be slid to the full extent to say the front, with the front loop being the only one fully extended. Or the exact reverse, with the wire slid fully to the rear and the real loop fully extended.
And that after letting the chassis settle back from each case, there could well be different equilibrium states for each. E.g. the wire isn't going to slide fully back to a single central position. And so the settling position of each loop will also be offset to which ever end was stretched last. Basically the sliding action creates an hysteresis in the CSB stability position. Just as in most most other mechanical systems that have reversing.

Am i missing somethig here?
I will admit to being a CSB virgin, but I am about to tackle one.
I don't recognize this talk of 'loops,' 'stretch' and 'extended' and am worried I'm missing something.
I don't see that there is going to be much movement/sliding back and forth of the suspension wire, nor how that can impact upon the strength/rate of springing, nor can I imagine it stretching.
Nor do I understand the point
Which presumably complicates CSB systems even more if you want the axle boxes to move up and down correctly with the suspension a

since surely that is how the system works. As Bill Bedford put it
Because the wheels are, and should be, fixed to the axles, it is the most practical and economic way of getting wheelset in and out of the frames.
What other system is there, apart from the 'original' one of holes in frames, with a minimal bearing surface to allow twist?

regards,

martin

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grovenor-2685
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Re: Flexi Chassis an Appreciation

Postby grovenor-2685 » Sun Apr 23, 2017 6:12 pm

Am i missing somethig here?
No Andy was.
Regards

proto87

Re: Flexi Chassis an Appreciation

Postby proto87 » Sun Apr 23, 2017 6:37 pm

My apologies to the CSB proponents who I am sure already fully understand this. But I would like to be sure I have it right too.

After looking at the more popular springing ideas proposed as improving Flexi-chas, it seems clear to me that the use of horizontal wire(s) as relatively soft springs for model use absolutely depends on their ends being able to slide through their end supports. This allows for the easy bending over a wide ranger of movement (as opposed to the huge forces needed for longitudinally stretching) of the original unloaded straight wire into some form of curve - which is of necessity becomes a longer wire length than in the straight wire position.

But, this also means that every suspension movement, no matter how small or frequent, also requires a matching sliding of the wire through its supports. So the friction damping of that sliding already mentioned is also an additional force resisting the easy upward/downward movement of such a sprung wheel over a bump or dip. In the case of a CSB, that extra resisting force would multiplied by the number of extra supports the wire needs to move through at that time. So the frictional effects could be widely different for different locomotive wheel configurations and different methods of wire support construction.

One other aspect that is presumably important is having sufficient excess wire (and space) to allow for full displacement of all wheels to their upper and lower stops. Will has said that properly fitted CSB's allow for sprung manual depression of the model. So I assume that's not a practical difficulty.

On the other hand, the surprising apparent ability of CSB systems to not exhibit the far less stable (wobbly) characteristics and difficulties of individually tuned wheels springs may mean that the excess wire length is more critical. Or that the powerful spread sheets used for CSB's could be used for setting the spring rates of non-continuous individual wheel wire springs, equally successfully, but has anyone tried that?

Andy

billbedford
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Re: Flexi Chassis an Appreciation

Postby billbedford » Sun Apr 23, 2017 7:23 pm

proto87 wrote:One other aspect that is presumably important is having sufficient excess wire (and space) to allow for full displacement of all wheels to their upper and lower stops. Will has said that properly fitted CSB's allow for sprung manual depression of the model. So I assume that's not a practical difficulty.


You can calculate the change in length of the spring wire for known displacements with simple trigonometry.
Bill Bedford
Mousa Models
http://www.mousa.biz

proto87

Re: Flexi Chassis an Appreciation

Postby proto87 » Sun Apr 23, 2017 8:07 pm

billbedford wrote:
proto87 wrote:One other aspect that is presumably important is having sufficient excess wire (and space) to allow for full displacement of all wheels to their upper and lower stops. Will has said that properly fitted CSB's allow for sprung manual depression of the model. So I assume that's not a practical difficulty.


You can calculate the change in length of the spring wire for known displacements with simple trigonometry.


Hopefully that's taken care of on the spreadsheets. Beams don't need it.

But looking forward with what seems to be the comparison case:

The resistance to a wheel following an upward perturbation in the track is;

1. For beams: The weight on the wheel + inertia of 13%-25% the body (4 point corner mounting, possible 1 or 2 layers of beams)
2. For simple springs: The weight on the wheel + the spring compression force + inertia of between 25%-50% the body (depending on wheel location).
3. For CSB's : The weight on the wheel + the spring extra compression force + inertia of between 25%-50% the body + the friction of the wire mounts.

That comparison excludes the extra parts of (and needed space) of fitting wires, mounts, and sticking with hornblocks. But please note that in my version of Flexichas, I will be using ball bearings, which does simplify the beam manufacturing. Part of the reason being they don't seem to be significantly more expensive than low volume machined miniature plain bearings, which are otherwise required.

Andy

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Will L
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Re: Flexi Chassis an Appreciation

Postby Will L » Mon Apr 24, 2017 9:33 am

proto87 wrote:One other aspect that is presumably important is having sufficient excess wire (and space) to allow for full displacement of all wheels to their upper and lower stops. Will has said that properly fitted CSB's allow for sprung manual depression of the model. So I assume that's not a practical difficulty.


CSB must extend beyond the outer fulcrum points and be free to slide through all of them, but it is logically constrained from sliding out of the outer fulcrums by fixed points on the loco, typically by the loco buffer beams. The wire is of such length that it is shorter than the distance between the constraining fixed points but long enough to ensure that it would meet the fixed point at one end before it disengages with the fixed fulcrum point at the other. I said it is "logically constrained" because you obviously leave clearance at both ends when you fit the springs and I've never come across one on a working loco where they had moved to the point of being in contact with the constraining fixed points. I agree you can postulate that they could work sideways till they meet the fixed points and hard contact with that might effect performance, but it doesn't seem to be an issue in practice.

A strait line calculation gives the amount that the spring moves to take up a deflection of 0.5mm is rather less than 0.02 per per axle, or 0,06 for 3 axles, which will be shared between the end so the amount of movement through the end fulcrums would be 0.03 which you might be able to measure but you certainly can't see. Working out the true curved length over those short arks isn't going to change the figures very much.

On the other hand, the surprising apparent ability of CSB systems to not exhibit the far less stable (wobbly) characteristics and difficulties of individually tuned wheels springs may mean that the excess wire length is more critical.

It is just necessary rather then critical if you see what I mean, but a good part of the damping is in the fiction between the axle blocks and the slots they slide in.
Or that the powerful spread sheets used for CSB's could be used for setting the spring rates of non-continuous individual wheel wire springs, equally successfully, but has anyone tried that?


Courtesy of Russ I can now do the calculation for a wire between only two fixed fulcrums.

billbedford
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Re: Flexi Chassis an Appreciation

Postby billbedford » Mon Apr 24, 2017 9:40 am

Will L wrote:A strait line calculation gives the amount that the spring moves to take up a deflection of 0.5mm is rather less than 0.02 per per axle, or 0,06 for 3 axles, which will be shared between the end so the amount of movement through the end fulcrums would be 0.03 which you might be able to measure but you certainly can't see.


...which is appreciably less than the slop in the pivot point of a fixed equalisation beam.
Bill Bedford
Mousa Models
http://www.mousa.biz

proto87

Re: Flexi Chassis an Appreciation

Postby proto87 » Mon Apr 24, 2017 2:44 pm

Will L wrote:A strait line calculation gives the amount that the spring moves to take up a deflection of 0.5mm is rather less than 0.02 per per axle, or 0,06 for 3 axles, which will be shared between the end so the amount of movement through the end fulcrums would be 0.03 which you might be able to measure but you certainly can't see. Working out the true curved length over those short arks isn't going to change the figures very much.


I agree with all you said except I'm going to quibble with the wire movement amount. I put the axle spacings of my N7 into my CAD program and then just drew simple circular arcs for 0.5 mm and 1mm and measured the differences. While the extension from straight to 0.5 mm is correct, the extension from 0.5 mm to 1mm comes out at over 4 times the amount. Just over 0.1 mm. That would be at least 0.5 mm for an x-10-x loco.

The reason this matters is that the straight line represents the loco off the track. The equilibrium position on the track (no bumps or twist) will be the 0.5 m deflection. And the bumps will cause the +/- sliding around that level.

Also note that the force needed for overcoming the wires sliding is intermittent. I.e you are working against static friction, rather than moving friction, for each track perturbation.

Andy

proto87stores

Re: Flexi Chassis an Appreciation

Postby proto87stores » Mon Apr 24, 2017 3:49 pm

billbedford wrote:
Will L wrote:A strait line calculation gives the amount that the spring moves to take up a deflection of 0.5mm is rather less than 0.02 per per axle, or 0,06 for 3 axles, which will be shared between the end so the amount of movement through the end fulcrums would be 0.03 which you might be able to measure but you certainly can't see.


...which is appreciably less than the slop in the pivot point of a fixed equalisation beam.


Using CAD, the sideways movement of a beam end on my N7 wheel spacing is +/- 0.006 mm over the whole vertical range of +/- 0.5 mm. I'm not sure the sideways slop of a typical P4 well installed hornblock is that good. Or that free to move.

Andy

proto87stores

Whoops - small maths error

Postby proto87stores » Mon Apr 24, 2017 5:10 pm

I just realised that I used 0.050 INCHES for my max up/down displacement. That's 20% bigger than +/- 0.5 mm, so before I (or some of you) redo the figures, the CSB max sliding distance I calculated is likely to be ~25% less than I said, but the beam vs. hornblock sideways slop comparison is going to be ~25% better for beams.

Probably a not big a deal in the overall conclusions, but I prefer my figures to be accurate and stand up to scrutiny.

And a point I overlooked earlier. The up/down sliding resistance for CSB's was 4 times higher moving upwards than downwards. Now that's an interesting entry of a major dynamic non-linearity into the equations. I suspect it's the opposite of a good damping factor, but it could explain a lot of the good performance results.

See http://auto.howstuffworks.com/car-suspension2.htm, especially the compression vs. extension cycles paragraph form those who may not be familiar with shock absorbers.

Andy

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Russ Elliott
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Re: Whoops - small maths error

Postby Russ Elliott » Tue Apr 25, 2017 9:12 am

proto87stores wrote:The up/down sliding resistance for CSB's was 4 times higher moving upwards than downwards.

???

Proto87stores

Re: Whoops - small maths error

Postby Proto87stores » Tue Apr 25, 2017 2:29 pm

Russ Elliott wrote:
proto87stores wrote:The up/down sliding resistance for CSB's was 4 times higher moving upwards than downwards.

???


See previous post on curvature of wire to hold loco in equilibrium position.

The additional length of wire that has to move into some curve shape from the straight line, off the track rest state, to the sitting on the track, weight carrying equilibrium position is much less than the extra additional amount of wire need to move into the sharper curve shape if the wheel rises from the static equilibrium position to accommodate going over a bump.

I.e. the rate of increase of wire length and friction resistance to upward wheel movement from static equilibrium, is greater than the rate of decrease of wire length and friction resistance to downward wheel movement into a dip. It's considerably non linear.

My error was in using a 25% greater up/down movement range to discover that effect than I claimed. (+/- 0.625 mm instead of the more usual +/- 0.5mm). However, the non linear trend is the same whichever displacement range you use.

Andy

proto87stores

Re: Flexi Chassis an Appreciation

Postby proto87stores » Tue Apr 25, 2017 5:36 pm

Image

Here's the corrected CAD sketch of the 3 different wire heights, along the N7 wheelbase, with the resultant different wire lengths dimensions. These are shown individually, without any adjustments for any "equalization" effects to adjacent wheels. And of course, I've just used circular arcs to save calculating the true "bell shapes".

Sorry my CAD is set up to use inches. Please multiply by 25.4 to get mm values.

Andy

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Will L
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Re: Flexi Chassis an Appreciation

Postby Will L » Tue Apr 25, 2017 8:50 pm

proto87 wrote:
Will L wrote:A strait line calculation gives the amount that the spring moves to take up a deflection of 0.5mm is rather less than 0.02 per per axle, or 0,06 for 3 axles, which will be shared between the end so the amount of movement through the end fulcrums would be 0.03 which you might be able to measure but you certainly can't see. Working out the true curved length over those short arks isn't going to change the figures very much.


I agree with all you said except I'm going to quibble with the wire movement amount. I put the axle spacings of my N7 into my CAD program and then just drew simple circular arcs for 0.5 mm and 1mm and measured the differences. While the extension from straight to 0.5 mm is correct, the extension from 0.5 mm to 1mm comes out at over 4 times the amount. Just over 0.1 mm. That would be at least 0.5 mm for an x-10-x loco.

The reason this matters is that the straight line represents the loco off the track. The equilibrium position on the track (no bumps or twist) will be the 0.5 m deflection. And the bumps will cause the +/- sliding around that level.

I chose the 0.5mm measure as this is the one that, as you said, will occur when the loco is placed on the track and will affect all wheels equally. Further deflections from that point in traffic will generally be relatively small, and, because an increase in deflection/wire length on one wheel (hence the weight carried by that wheel) implies a decrease in the deflection/wire length on the wheel(s) next to it (as the loco weight is unchanged), the wire length changes will tend to net out. Therefore, the actual net amount of movement along the whole wire for all but the most dire of track faults will be significantly less than you are suggesting (i.e. the maximum deflection/wire movement you have calculated could only occur if a loco was running with all its weight on the wheels on one side and none on the other).

It should also be remembered that even a 0.5mm step under one wheel will not produce an additional defection of anything like 0.5mm for exactly the same reasons. The calculations aren't that strait forward but I reckon an additional 0.25 for a static 4 wheeled vehicle. Actually the ability to deal with steps of that size is really only a party trick and is not required by any competent track builder. The true "detrimental to reliable running" issue that we ought to be thinking about isn't steps in the track at all, but the "rate of change of cant". That is the rate at which the height of the top of one rail changes in relation to the other. On the real thing this is limited to never more than 1 in 600 (1 in 1200 for high speed line) see this Network Rail document A Guide to Permanent Way Design, although a rather more extreme but perhaps more easily attainable limit for model railways of 1 in 300 has been suggested in the past. Using that, even a real monster (long fixed wheelbase) loco like a 9f with a 21' 8" wheelbase, will see no more than 0.3mm over the full coupled wheelbase, resulting in deflections of ± 0.15 from the static point over the rigid wheelbase of the vehicle.

Also note that the force needed for overcoming the wires sliding is intermittent. I.e you are working against static friction, rather than moving friction, for each track perturbation.


Initially I thought I agreed that was true, but I thought some more and now I'm not so sure. Static friction applies when there is no movement, dynamic when movement is happening. Static is generally higher, so more force is required to start the movement than to keep it moving. Therefore the differential between a short movement and a slightly longer one isn't, as you are suggesting, purely proportional to the length of the movement. Anyway, practical experience suggests whichever one you getting, it is only sufficient to help dampen the system nicely.

Proto87stores wrote:
Russ Elliott wrote:
proto87stores wrote:The up/down sliding resistance for CSB's was 4 times higher moving upwards than downwards.

???


See previous post on curvature of wire to hold loco in equilibrium position.

The additional length of wire that has to move into some curve shape from the straight line, off the track rest state, to the sitting on the track, weight carrying equilibrium position is much less than the extra additional amount of wire need to move into the sharper curve shape if the wheel rises from the static equilibrium position to accommodate going over a bump.

I.e. the rate of increase of wire length and friction resistance to upward wheel movement from static equilibrium, is greater than the rate of decrease of wire length and friction resistance to downward wheel movement into a dip. It's considerably non linear.

My error was in using a 25% greater up/down movement range to discover that effect than I claimed. (+/- 0.625 mm instead of the more usual +/- 0.5mm). However, the non linear trend is the same whichever displacement range you use.


So you see, I rather suspect there are more things you didn't take into account than just the difference between mm and inches

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Will L
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Re: Whoops - small maths error

Postby Will L » Tue Apr 25, 2017 10:56 pm

proto87stores wrote:IAnd a point I overlooked earlier. The up/down sliding resistance for CSB's was 4 times higher moving upwards than downwards.


And there is another reason why that' isn't a valid interpretation. I agree the increase in wire length will accompany the deflection increase and hence the frictional resistance to that movement, but the increase in wire length between no deflection and 1mm deflection isn't linier, it's actually a segment of a sign curve with the wire length increasing most quickly as the 1mm limit of deflection is approached, as your diagram shows. As I have shown above, the actual practical movements are both small and close to (either side of) the 0.5 static deflection point. So while there may be a difference between the upward and downward resistance it won't be anything like the x4 you suggest, and as it isn't the only frictional resistance to the up and down movement of the axle, it just gets lost in a general and very desirable dampening effect.

This is all very interesting, if this sort of thing turns you on, but whatever theoretical objections you may see we have practical experience of CSB producing reliable sprung steam era loco chassis, which:-
1. are truly riding the springs and not, either the top, or the bottom, stops
2. fully decouples the body from the wheels, with the improved ride characteristics you expect from functional suspension
2. give good weight distribution and hence good haulage characteristics
3. are mechanically and constructionally simple, when compared to other methods which implements suspension on all wheels.

I will be interested to see just how well your N7 gets on. Compared to a CSB, I'm sure you ought to be able to get it to pull just as well, and we may be hard put to differentiate the ride quality. It can never be decoupled like a sprung loco and I have questions about just how mechanically and constructionally simple implementing equalisation on a rigid steam loco chassis will prove, but the proof as they say.....

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Re: Flexi Chassis an Appreciation

Postby Crepello » Wed Apr 26, 2017 12:57 pm

There's also the consideration that the friction generated in the changing of the suspended wire length only leads to changes of wire tension. These tensile forces (one each side of an axlebox) then need to be resolved into their vertical components to arrive at the contribution to axlebox load perturbation. The calculation would be simple if infinitely flexible strings were involved, but our wires have continuously changing gradients. Nevertheless, the worst case would be at the point of inflexion between positive and negative curvature in the spring wire. Taking the sine of that gradient angle multiplied by the frictional force each side of an axlebox, that's a miniscule amount, because even the maximum wire gradient is so shallow.

proto87stores

Re: Flexi Chassis an Appreciation

Postby proto87stores » Wed Apr 26, 2017 2:17 pm

Crepello wrote:There's also the consideration that the friction generated in the changing of the suspended wire length only leads to changes of wire tension. These tensile forces (one each side of an axlebox) then need to be resolved into their vertical components to arrive at the contribution to axlebox load perturbation. The calculation would be simple if infinitely flexible strings were involved, but our wires have continuously changing gradients. Nevertheless, the worst case would be at the point of inflexion between positive and negative curvature in the spring wire. Taking the sine of that gradient angle multiplied by the frictional force each side of an axlebox, that's a miniscule amount, because even the maximum wire gradient is so shallow.


The idea that the wire may be significantly stretched by small scale model suspension movement has to be reconciled with the relatively enormous forces generated when a taut steel wire is heated or cooled.The mechanical stretching forces are exactly the same as those required/produced for thermal expansion.

I would suggest that low force wire linear tensioning is not a contributing factor in sliding CSB suspension operation.

Andy

Crepello
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Re: Flexi Chassis an Appreciation

Postby Crepello » Wed Apr 26, 2017 10:06 pm

proto87stores wrote:I would suggest that low force wire linear tensioning is not a contributing factor in sliding CSB suspension operation.

Why are you worrying so much about friction in the supports then??

proto87stores

Re: Flexi Chassis an Appreciation

Postby proto87stores » Wed Apr 26, 2017 10:48 pm

Crepello wrote:
proto87stores wrote:I would suggest that low force wire linear tensioning is not a contributing factor in sliding CSB suspension operation.

Why are you worrying so much about friction in the supports then??


Damping is intended only to prevent the sprung suspension from continuing to oscillate after being disturbed. As per the shock absorber link I provided previously, in your normal sprung road vehicle, the added damping is specifically designed to allow much freer wheel upward movement, than downward. Otherwise you just end up with damping partly (or worse wholly) negating the sprung freedom of movement and a bumpier ride. Increasing the damping upward considerably will make the dynamic performance of hitting a bump much closer to having a rigid chassis than a sprung one.

Since sprung suspension only has a "smoothing" advantage over equalization in a dynamic case (proportional to speed) , too much damping, or reverse damping, will tend to cancel out some or all of the dynamic springing effect.

Andy

proto87stores

Re: Whoops - small maths error

Postby proto87stores » Wed Apr 26, 2017 11:12 pm

Will L wrote:
proto87stores wrote:IAnd a point I overlooked earlier. The up/down sliding resistance for CSB's was 4 times higher moving upwards than downwards.


And there is another reason why that' isn't a valid interpretation. I agree the increase in wire length will accompany the deflection increase and hence the frictional resistance to that movement, but the increase in wire length between no deflection and 1mm deflection isn't linier, it's actually a segment of a sign curve with the wire length increasing most quickly as the 1mm limit of deflection is approached, as your diagram shows. As I have shown above, the actual practical movements are both small and close to (either side of) the 0.5 static deflection point. So while there may be a difference between the upward and downward resistance it won't be anything like the x4 you suggest, and as it isn't the only frictional resistance to the up and down movement of the axle, it just gets lost in a general and very desirable dampening effect.

This is all very interesting, if this sort of thing turns you on, but whatever theoretical objections you may see we have practical experience of CSB producing reliable sprung steam era loco chassis, which:-
1. are truly riding the springs and not, either the top, or the bottom, stops
2. fully decouples the body from the wheels, with the improved ride characteristics you expect from functional suspension
2. give good weight distribution and hence good haulage characteristics
3. are mechanically and constructionally simple, when compared to other methods which implements suspension on all wheels.

I will be interested to see just how well your N7 gets on. Compared to a CSB, I'm sure you ought to be able to get it to pull just as well, and we may be hard put to differentiate the ride quality. It can never be decoupled like a sprung loco and I have questions about just how mechanically and constructionally simple implementing equalisation on a rigid steam loco chassis will prove, but the proof as they say.....


Sorry, I was adding up the number of fully extended loops for the x-10-x example to determine the max movement necessary statically . I.e if you did that "press down test" We talked about earlier to show that you do have full springing. If you just allowed for the expansion of one wheel loop, you wouldn't be able to push down any noticeable distance on the loco at all.

Even with my corrected figures, the upward needed increase in wire length for a + 0.5 mm displacement is still 3 times that of the downward decrease of - 0.5 mm.

If you want that to "net out", then that will have to move the wire along and out of the curvature over three other wheels. Even if the amount of the running perturbations is far less, you still have the problem that the added wire sliding resistance to restricting slight upward movement is fundamentally much higher than for slight downward. And further, that resistance is still higher than for merely flexing springs, which in turn is higher than for free to rotate beams.

There is a practical issue with only designing a CSB model to have a much smaller up/down movement than +/- 0.5 mm. How does a newcomer with only basic hand tools manage to set the static height correctly at 50% of say +/-0.1 mm instead of +/- 0.5 mm, if the movement range is so small, you can barely detect it even with a professional dial height gauge??? If the static equiilbrium height isn't pretty close the midpoint of a much smaller movement, it won't be working suspension.

Again this is where leaving the fixed beam designs behind creates new added complications. None of the above is any concern for a properly equalized flexi-chas. It's just a case of build it, and it will run perfectly on completion.

Andy

proto87stores

Re: Flexi Chassis an Appreciation

Postby proto87stores » Thu Apr 27, 2017 2:03 am

Will L wrote:It should also be remembered that even a 0.5mm step under one wheel will not produce an additional defection of anything like 0.5mm for exactly the same reasons.

I'm not sure I understand what you are saying above?

The calculations aren't that strait forward but I reckon an additional 0.25 for a static 4 wheeled vehicle. Actually the ability to deal with steps of that size is really only a party trick and is not required by any competent track builder. The true "detrimental to reliable running" issue that we ought to be thinking about isn't steps in the track at all, but the "rate of change of cant". That is the rate at which the height of the top of one rail changes in relation to the other. On the real thing this is limited to never more than 1 in 600 (1 in 1200 for high speed line) see this Network Rail document A Guide to Permanent Way Design, although a rather more extreme but perhaps more easily attainable limit for model railways of 1 in 300 has been suggested in the past. Using that, even a real monster (long fixed wheelbase) loco like a 9f with a 21' 8" wheelbase, will see no more than 0.3mm over the full coupled wheelbase, resulting in deflections of ± 0.15 from the static point over the rigid wheelbase of the vehicle.



FWIW, we have a cant issue in the US due to so many larger layouts having curves on grades, and of course the helix often used for transferring between between levels. But with the normal coarse scale flanges in HO, they are not overly problematic. Future US P:87 vehicles will however have to sufficient static equalizing freedom to run safely on them.

I did make up a table of the cant effect for P4 (18.83) and your 9F example over a range of grades and radii as follows:

Cant in mm for a 4m 9F Real in. Model in. Model mm

9F wheelbase units 21 ft 8 in 260 3.412073491 86.66666667

Radius inches 18 24 36 48
Grade 1% 0.022726397 0.017044798 0.011363199 0.008522399
Grade 2% 0.045452795 0.034089596 0.022726397 0.017044798
Grade 3% 0.068179192 0.051134394 0.034089596 0.025567197

The tight radii and grades are actually prototypical for my local San Francisco streetcars. Although those also need to take major vertical curves into account as well.

[youtube]https://www.youtube.com/watch?v=pp9RNGXlQQY[/youtube]

Andy

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Russ Elliott
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Re: Flexi Chassis an Appreciation

Postby Russ Elliott » Thu Apr 27, 2017 2:43 am

Our beams do not stretch. It would take about 1.5kg to stretch a 100mm length of 0.012" guitar string by 1mm. We don't have those kind of longitudinal forces in our models. Our beams merely bend.

All our beam curves are cubics. Taking the simple case of a single point load F midway between two supports spaced at L apart, the equation of the curve, for x < 0.5L, is:

y = F(4x3 - 3L2x)/48EI

(The deflection y is at a maximum for a midpoint load, and where the slope of the curve, i.e. dx/dy, is zero.)

The arc length L' of each section of this curve can be derived from the differential of the equation of curvature:

L' = integral[{(1 + (dx/dy)2)0.5}dy]

In the case of multiple spans, as in a CSB, the beam curve equations are vastly more complex, because of the adjacent bending moments, but they are still cubics, and arc lengths can be derived if one is feeling nutty enough.

Prototype bridge designers are not overly concerned with changes in arc length - they are concerned more with beam rotation and temperature expansion - these (and friction) are avoided by using suitable bearings:

bridge-roller-bearing.png
bridge-roller-bearing.png (158.48 KiB) Viewed 2968 times

Victorian engineers tended to slosh a gallon or two of heavy grease onto such bridge bearings.

In our models, as the beam bends and moves a little bit over its fulcrum points and its axleboxes, the values of the frictional forces at these points are in proportion to the reaction load at each point. This proportion is given by the coefficient of friction u. These frictional forces will be highest toward the middle of an 0-6-0 frame, because this is where the frame loads are higher. The determinant of the frame loads is the CofG. For a typical 'balanced' 0-6-0, the two outermost fulcrum points each have approx 15% of the frame load, and the two inner ones have approx 35% each. Likewise, the frictional forces at the hornblocks are proportional to the axle load.

continuous-friction-sources3.png
continuous-friction-sources3.png (4.6 KiB) Viewed 2968 times

The direction of these frictional forces will depend on the direction the beam is moving over each support or axlebox. In all cases, the axis of the frictional force is horizontal, and will be in the opposite direction to the beam movement. Thus the frictional force(s) will tend to tighten a span as it becomes more tensioned, and weaken a span as it relaxes. Although the extent of the movement of the beam over a load point will alter the work done by the beam, it does not alter the frictional force at each load point, which remains proportional to the reaction force at the load point. In other words, the effect of friction will increase the degree of equalisation along the beam.

Taking the example of the 2-axle case where the left-hand axle encounters a bump and compresses its span, and likewise there is a relaxation of the right-hand span, the likely scenario for the directions of the frictional forces at the frame fulcrum points is:

continuous-friction-sources4.png
continuous-friction-sources4.png (2.46 KiB) Viewed 2903 times

In this case, the high frictional force at the middle of the frame pointing to the right (the mid-frame load is about 60%, say, for a typical 2-axle case) is countered (although to an unknown extent) by the two lesser frame frictional forces pointing to the left. The situation for an 0-6-0 is more complex, but, notwithstanding the disparity of the values of the frame load frictional forces, I agree with Will that the effects of the frictional forces generally tend to 'net out'. Because our beams are jiggling around over their load points all the time (on undulating track), I'm also inclined to agree with Will that we are dealing with sliding friction rather than static friction values, so I can understand why he doesn't get too excited about the 'finessing' of the friction situation by using lube. Some guitarists however feel inclined to provide a smidgeon of lubrication at nutbridges, to keep string tensions in good order:

Image

The concentration of the largest frictional forces in the middle of the frame will I think tend to prevent beam creep along the frame.

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Will L
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Re: Flexi Chassis an Appreciation

Postby Will L » Thu Apr 27, 2017 4:09 pm

proto87stores wrote:
Will L wrote:It should also be remembered that even a 0.5mm step under one wheel will not produce an additional defection of anything like 0.5mm for exactly the same reasons.

I'm not sure I understand what you are saying above?


On any effectively sprung chassis (and more so on a CSB) when one wheel is forced up, it takes more of the vehicle weight, so the deflection on the other wheels gets smaller, and the vehicle will rise to compensate. The net result is to get a single wheel over a 0.5mm step, the extra upward deflection needed isn't anything like 0.5. Analysis suggest this is never more than 0.25, giving a 0.75 deflection on one wheel and a reduction below the static deflection point on all the rest. So worrying about the implications of a full 0.5mm additional deflection all seems a bit pointless.

FWIW, we have a cant issue in the US due to so many larger layouts having curves on grades...





Its interesting that when you go to look up stuff on cant, real railway engineers are far more worried about the implications for speeding on corners, which as was pointed out recently here is a problem much reduced (by a factor of 76) for us 4mm scale devotees. From the point of view of the chassis design, the amount of twist (rate of change of cant) that a vehicle can tolerate in the track is much more interesting. This is unaffected by any scaling factors (as it is based on a linear relationship) and is sensitive to relatively small, hard to measure reliably, differences in track top height.

Also I fixed your Youtube refetence.

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Will L
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Re: Whoops - small maths error

Postby Will L » Thu Apr 27, 2017 5:33 pm

proto87stores wrote:[re a 0-10-0 ... if you did that "press down test" We talked about earlier to show that you do have full springing. If you just allowed for the expansion of one wheel loop, you wouldn't be able to push down any noticeable distance on the loco at all.


Can't offer you a 0-10-0, I'm not sure anybody's done that as a CSB yet, but how about my O4 - (an 2-8-0)



That passes the bounce test!. It was also the first CSB I did and the thing that convinced me I was on to a winner. Easier to do than a compensated 2-8-0 chassis, and very effective. It is definitely riding the springs both up and down and runs as rock steady as 73 tons of heavy metal should.

If you want that to "net out", then that will have to move the wire along and out of the curvature over three other wheels.


I think Russ explained what's going on better than I can, and the picture above shows you that this isn't a theoretical thing. CSB work so isn't it a bit pointless to go on thinking of good reasons why they might not?

There is a practical issue with only designing a CSB model to have a much smaller up/down movement than +/- 0.5 mm.


No problem using the spread sheets to design CSB with less than 0.5mm static deflection, if that's what turns you on. You only need to be able to set the fulcrum points out reasonably accurately (to the nearest 0.5mm) and fit the right size wire. I agree that wouldn't work if you went as low as .1mm which. as you point out, is as near as dammit rigid anyway. However what I was pointing out was, not that the deflection was limited to a small value, but that with the full normal 0.5mm static deflection, the actual range the suspension normally works over is no more than 0.15 either side of the static deflection point, or 0.25 if you must indulge in party trick size track faults. You'll only ever get the full 0.5 if you can persuade the loco to balance on all the wheels on one side, stunt driver style.

Again this is where leaving the fixed beam designs behind creates new added complications. None of the above is any concern for a properly equalized flexi-chas. It's just a case of build it, and it will run perfectly on completion.


Thing is all these "additional complications" are not things that trouble us in practice, if they exist at all. When I built the O4, all I did was apply the method to define the fulcrum points, build a mechanically simple chassis to the tolerances I was used to, and bingo it worked like a charm.

proto87stores

Re: Flexi Chassis an Appreciation

Postby proto87stores » Sun Apr 30, 2017 9:40 pm

Will,

Thanks for your impressive video of the 2-8-0 static springing functionality and for fixing my SF Muni clip.

I think I'm seeing at least a 1mm overall up/down movement range capability in the 2-8-0. And the equilibrium near centre or a little below. So you obviously were able to achieve those.

I'm now quite convinced that a single sliding wire spring over a single wheel is likely the nearest to a non-linear prototype single wheel leaf spring that modellers can easily achieve. Which is a good thing to know clearly practical for models. And I note, used on Bill B's successful 4 wheel wagon chassis'.

What I still can't understand is how that quite simple and effective springing solution came to be pretty much bypassed in thought and deed, so many years ago, by the rush to go to a single continuous wire with all the obvious extra wheel movement resistance and dubious compromise equalization effects.

Earlier Bill suggested I build a CSB steam loco chassis. Iif the theory supported it as an improvement, and I had nothing else to do, I would. Sadly, I still have many years other committed work to do first. However, I have a related question. Given the large number of P4 Steam Loco Builders in the Society, did anyone build a steam loco chassis with single independent sliding wire springs per wheel and do a running comparison with a similar model with the then new CSB's? Obviously the prototype does it that way, but I don't seem to see that subject, or a comparison, coming up here or elsewhere. And presumably Bill chose not to make his 4 wheel wagon wire continuous for more than just convenience reasons.

On the subject of cant, yes my Muni (and other model) examples do go round some very tight radii between hill sections. Fortunately, many of the curve portions are leveled out, due to them being mostly on the horizontal cross streets. But the possible graded corner cant figures are still much worse than for 1st class railways. E,g 50 ft radii and up to 9% grade worst case. Even just a 6% grade in HO, would give rise to a 1 mm cant along less than 10 model inches of track. While the historic single cars the track was originally laid for would have been in the proto 30-40 ft length range, the modern articulated pair cars are 70 ft long and are run as double pair units much of the time. Proto mandatory speed limit on those corners is 3 mph.

Image

Andy


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