Tuesday, January 19, 2010

69> About That Angled Wheel Design...

First a reiteration of the big picture. Designing a PRT system as logically as possible must start with a track that won’t put unnecessary limits on future usefulness of the system.  Unfortunately, in an effort to get a product to market, most PRT venders have produced designs that fall short of having the potential to do anything but be small players in the transportation mix. Current systems, by and large, are not versatile enough to be used for anything other than supplemental vehicles in very densely populated city areas. That may be a perfectly fine business model, but the resultant designs fall far short of embodying PRT’s transformative potential. Where would the internet (for example) be today if it relied on proprietary networking cables rolled out according to the business plan of a single company for specific, cherry-picked markets?  Standards based PRT track design is sorely needed.

I recently posted bogie design with tilted wheels. The purpose of design effort was not so much the bogie itself, but to see if such a design would require modifications to the track profile. Actually it has, but only slightly. The general design first described in post 39 has stood up to many challenges (outlined in subsequent posts) including multiple weight classes, speed ranges, station types, freight and industrial uses, propulsion types, turning radii and pitch angles, etc. What remains to be done is to explore braking and traction issues, to address the issue of forking (adding) track with minimal deconstruction, and general track construction methods. 

All of that being said, here are some explanations regarding that tilted wheel design. First of all, it is a response to the challenges of high speed. The design makes no sense for anything less than, say, 30 mph. It gets much more attractive at speeds over 80. The rationale is this. At very high speeds the guide wheels really get a workout. In order to provide a smoother ride and make less noise, all wheels should be made of a material with some give. (rubber or plastic, not steel) Such materials wear out, especially on very small wheels. The bearings, too, take a beating.  Centering the bogie without guide wheels is a challenge, however, because of issues that are particular to the remedies. Flanges on wheels can wear and heat up. Having a wheel running in a trough generally means that all wear occurs only on a very limited ring around the wheel. The same is true if the trough is in the wheel. (Pulley wheel profile) While this can be tolerated to a degree, the issue is most acute on the drive wheels, which support the full weight of the vehicle. V-shaped wheels in a V groove wear rapidly because the wheel has multiple diameters contacting at once. This creates wheel slippage.

In the illustration below it can be seen that the angled wheels, through gravity, work to minimize any contact with the flange, which has a radius to minimize friction wear, and could be made of a harder material. The inserted detail shows how the bogie becoming off-center causes the entire wheel (and whole vehicle) to be lifted against gravity.

These drive wheels are characterized by their large diameters, which have plenty tread surface to distribute the wear, and revolve at slower speeds than smaller wheels would. It is assumed that these wheels would use tapered roller bearings, like cars, and so cannot tolerate very high rotational speeds like ball bearings, but can better support the vehicle weight and the sideways “thrust” forces associated with fast tight turns.


In the illustration above note that the running surfaces have been replaced by half-round, or bull nosed rails. (shown in white) While it is obvious that such a design would greatly increase wear on both rails and wheels, such a profile also allows an extremely tight turning radius. My thinking is that at very slow speeds, such as for station maneuvers, the wear will be a minor factor.  After all, by definition, the sharper the turn, the slower the speed and the less distance traveled.  What about medium turns? One thing that occurred to me is that such inserts could provide a banking angle, which would treat the bogie like it was going straight. With wheel motors the wheels toward the outside of the curve can be made to rotate faster, facilitating (if not actually causing) the turn. This is a work in progress…I don’t have all of the answers at this time.

This all raises another very interesting point. In the last post, it was pointed out that the steering guide wheels would come into and out of contact with running surfaces as needed, so they would not spin and wear unnecessarily.  Here we have described other running surfaces that are not of a continuous, unchanging profile. There are other situations as well, such as very steep slopes, which might call for special “sticky” rails or other inserts. Having various inserts has a lot of advantages. They may be replaced and upgraded. They can be precisely finger-jointed to allow for thermal expansion to eliminate the repeating noise and vibration associated of expansion joints in train tracks and some roads. They allow one basic structural track profile to perform many functions without modification. They can be made of materials (such as stainless steel) that are too expensive to be used structurally. They can be rubber mounted for noise and vibration control. It becomes easier to add a diverging or converging track to a previously completed one when the running surfaces are modularized into precisely sized components. One interesting application for inserts is the technique used by Disney to detect any breaks in the tracks of their rides. They fill the tracks with compressed air. If there is any break or crack the pressure drops and they know it immediately and can stop the ride.

Finally, a note about the fifth wheel shown below; (in the center of everything else) There are several possible functions for such a part, from centering and holding down the bogie to additional braking, power and traction. Such a part can eliminate the possibility of wear on the wheel flanges altogether on straightaways. The truth is, however, that to do the design I had to either add it or not. Because it is easier to take it out than add it later, I added it. It could, in theory, prevent extraordinary forces, such as extreme cross winds or earth tremors from lifting the bogie inside of the track. It has a smaller diameter than the main drive wheels but it supports no weight, so ball bearings would suffice and wheel-wear would also be minimal. It is largely redundant, I know, but this is all a work in progress, and, as I mentioned before, it is really all about the track anyway.


cmfseattle said...

have you worked out the frog design? are the steering guide wheels capable of supporting the vehicle?

my other concern is your mention of varying the coefficient of friction along the guideway. because you can't rely on this to be constant, wouldn't you need every passing vehicle to test it somehow, so that the control system would be able to function safely? if you haven't already, read anderson's Overcoming Headway Limitations, specifically pp.7-8.

Dan said...

The design doesn't require a "frog". The guide wheels do, indeed, hold the bogie captive in whichever side of the track is engaged. The other side is just there to distribute the load and wear where convenient, and to keep out the weather.
As for the "variable coefficient of friction" as you call it, I just want to reiterate that complete traction between a dry wheel and a dry surface is pretty well assured, unless there are truly extraordinary forces at work, which a good design should eliminate.
Anderson first creates a design which is susceptible to ice induced skidding and then offers the only logical solution to his own design shortcoming. He never mentions that hanging systems don't have a weather problem, and uses the most rudimentary mechanical brakes as examples of "stste of the art". No ABS. No Magnetic braking.

cmfseattle said...

1) hanging systems are not immune from the weather.
2) suspended-vehicle guideways will behave more like simply-supported beams than like clamped beams.
3) cabinentaxi proved that linear electric motors can consistently perform brick-wall stops at 2.5-seconds headway, in icy conditions.

Dan said...

Dan the Blogger Responds -

I’m not sure what you are driving at with comments 1 and especially 2, cmfseattle.
Behave? In what respect? As for the weather thing, you’re right, they are not immune to condensation, possibly even frozen. This would be quite easy to manage compared with continuing snow or ice accumulation, however. By the way, the running surfaces are rubber mounted, so the thermal mass is minimal. Therefore the running surface temperature will tend to follow the ambient temperature, inhibiting condensation. Why do I suspect you were referring to something else? Have I overlooked something? As for the headway speeds…

It skids or it doesn’t, and not skidding is good enough, imho. I see no additional advantage to really, really, really not skidding. I think emergency, brick-wall stops would never happen, but to satisfy insurance companies and the like this should be done by clamping to the track anyway, even with linear, so to me traction is a manageable, if not minor, issue.

If you can show me any way to match the combination of speed, turning and price performance I have been talking about with a linear system, I will be “all ears.” A great big (horizontal) turning radius is a deal killer for me because of all of the issues that result from inflexible routing options. It’s extremely hard to get ANY route through an approval process. Needing the space over corner properties is opening a Pandora’s box. A big vertical turning radius is somewhat better, but for me still requires a complete system redesign or custom LIMs. Anyway, It’s pretty hard to critique or try to improve upon proprietary systems whose details are trade secrets. I personally don’t see a practical way to do it.

To those readers out there who don’t know, Linear Induction Motors are shaped like big blocks that must be held within about an 1/8th inch of a reactor plate which runs along the track. (closer is even better, efficiency-wise) It’s a bit like having a car that hangs so low it can’t even clear a cockroach. It’s going to want to scrape when you crest a hill. The more power you want, the bigger the block’s “almost” contacting surface must be and the more magnetic forces must presumably be held at bay. These inter-reacting surfaces are normally held apart by little wheels. Engineering all of this for highway speeds is a challenge. The required power, and therefore these surface areas, must increase geometrically compared to the resultant speed increase, with this effect becoming more and more pronounced the faster you want to go. In other words, what works great for lower speeds and fairly straight track becomes more and more cumbersome for curvy or fast applications. The concept of a motor with no moving parts sounds great at first, but for vehicular use it actually uses more parts than direct drive rotary motors mounted within the vehicles wheels. I favor the rotary option, but only because I have not currently seen or invented a practical solution to the problems outlined above.

cmfseattle said...

Marsden Burger on LIMs, weather, noise and reality

1800 inches/sec = 100mph. how fast do you need to go? how roller-coaster does it need to be? if you used 4 LIMs instead of 2, and used 8-inch casters (~4000rpm @ 100mph) instead of 4-inch casters, would your requirements be met?

Minimum Curve Radius

36 feet


"PRT need not have lower line speed. Line speed is an economic factor, not technical."

"There must be sufficient tread on the tires and the running surface must be sufficiently rough to make the
coefficient of friction as high as practical." Safe Design, (Time Headway and the Linear Induction Motor), pp.5-7

bottom line: the failure deceleration rate should not be greater than a following vehicle's emergency braking rate.

Transit Systems Theory

Dan said...

The roller coaster aspect you refer to is all about being able to maneuver in close quarters, because a system that needs to be laid out like a mini freeway is only useful for the few routes that have such right-of-way is available. Making a cheap track can only go so far. The real cost might just be in the wrangling over real estate.

The RPMs that bearings can handle is determined by how even and heavy the load and how large the shaft diameter. At 4000 rpm, they won’t wear out right away, but I’m not real comfortable with them lasting years either. I built a woodworking machine years ago with dual 1.5” shafts, (4 bearing units) @ 3500 rpm, and the first sign of slop and roughness was after only about, (I’m guessing) 1500 hrs., and within about that amount of time again, a second started to go. The machine, now in storage, never had a problem with the other two. Actually I attribute the failures to them being off-brand, more than anything else. There are also noise, vibration, and general complexity factors.

I prefer to start a design with very high performance expectations and then dial it back. Otherwise you might end up with the PRT equivalent to a three-wheeled racecar.

I believe all reasonably fast bottom supported PRT systems should be propelled by linear motors because of icy track issues. I can see no way out of it, save continuous, high-powered track defrosting.

I am very surprised that Skyweb Express lists 60 mph as a top speed. That is quite an achievement for their design architecture. I would be curious as to if those numbers are really practical in the field, and what would be the maintenance schedules.

LIM surface area (power) doubling might add 25% to speed. All of that is contingent on aerodynamics and the speed range involved. But doubling power doesn’t double speed, as I am sure you know. I guess it is theoretically possible to design LIMs that could be doubled up closely, although it might require a special, dual channel controller..

Do they allow individual speeds, or do bunches of podcars tend to stay bunched, and take all turns at “line-speed” no matter how sharp the turn? I admit to never really conclusively gleaning that info from Anderson’s discussions on “Asynchronous point-following” or whatever it is…

cmfseattle said...


Osaka Subway Line No.7

each LIM looks to have ~9sqft. of area facing the stator and produces ~135hp. the vehicles go up to ~40mph.

T2k says, "The power will peak at about 20 kw per vehicle and will average about 4 kW per vehicle including air conditioning and heating."

from p.5 of Transit Energy Use, ~2kw of that would be Auxiliary Energy if there are 3 passengers. so the LIMs are probably each rated at ~9kw or ~12hp. for whatever it might be worth, the smart fortwo weighs 1800lbs empty and is rated at 52kw.

the idea of 4 LIMs was similar to your method in post 26, except horizontally and using 6 wheels in order to achieve articulation.

as for the control system, as i understand it: the guideway is logically divided into segments, some long, others (e.g., merge zones or station zones) short. the zone controllers use the same code as the vehicle controllers to calculate where the vehicle should be by the next time its position is checked.

along with local guideway alignment, line speed depends on local wind speed. basically, you'd go as fast as safely possible, except to facilitate merges. the main difference between Anderson's asynchronous and a synchronous system (e.g., ULTra) is that merge conflicts are resolved locally as the vehicles approach. vehicle routing can be revised by the central computer through fiber-optic comms with zone controllers. Control of PRT, beginning on page 7.

i think that routing intelligence could be improved and/or distributed later.