NOT the third amendment... Why are steam locomotives drive rods in quarter?
RJ
"Something hidden, Go and find it. Go and look behind the ranges, Something lost behind the ranges. Lost and waiting for you. Go." The Explorers - Rudyard Kipling
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Ah! That makes perfect sense!
Next question: did the PRR turbine 6-8-6 need to be quartered? Did siderod electrics need to be quartered? And siderod diesels?
(Answer is yes, but lots of people will say no.)
If I recall, with the PRR turbine the turbine was geared to one pair of driving wheels and the power was transferred to the others by the side rods....so if it was dead centered, again, there'd be no way to exert rotational force on the other driving wheels to get the locomotive moving...at least I would think.
WRONG! If the force is exerted as a torsional force throught gears, chains, etc then quartering is not necessary. Quartering is needed on an engine with rods connecting the piston to the wheel. If the cylinder was on TDC or BDC then the rod is trying to push in a straight line and no torque is produced. If the force is torsional to begin with then it does not matter.
Then why did the PRR Turbine need to be quartered?
The Dude With The Hair Then why did the PRR Turbine need to be quartered?
The drivers were side rod connected, meaning the drivers had two heavy spots, the crank pin (where the side rods were connected), and the counterweight, which were on opposite sides of the wheel. If they were perfectly aligned, there would be severe pounding on the rails, which would increase as the speed increased. Quartering reduced, but did not eliminate, this pounding
The Dude With The HairIf I recall, with the PRR turbine the turbine was geared to one pair of driving wheels
TomDiehl If they were perfectly aligned, there would be severe pounding on the rails
tdmidgetIf the force is torsional to begin with then it does not matter.
tdmidgetThe side rods have nothing to do with it .
Nothing to do with what?
We agree the PRR 6-8-6 has siderods? Tell us how the tension/compression in the rods would vary thru a rotation of the wheels, if the rods weren't quartered. (Assuming constant torque applied to the two middle axles, by the geared turbine.)
It does not matter how the first wheel is driven, whether through pistons and main rods, gears, quill drive, whatever. If you are transmitting torque from one wheel to a neighboring wheel through a siderod drive, you are going to need quartering. This fact has been rigorously proved by this German guy
Muller, A., 2002, "Higher order local analysis of singularities in parallel mechanisms," ASME 2002 Design Engineering Technical Conferences and Computer and Information in Engineering Conference, Anonymous ASME, New York, DETC2002/MECH-34258, pp. 515-522.
following up on a conjecture from this Austrian dude
Wohlhart, K., 2000, "Architectural shakiness or architectural mobility of platforms," Advances in Robot Kinematics, J. Lenarcic and M. M. Stanisic, eds. Kluwer, Dordrecht, pp. 365-374.
The American guys
Woo, L., and Freudenstein, F., 1970, "Application of Line Geometry to Theoretical Kinematics and the Kinematic Analysis of Mechanical Systems," Journal of Mechanisms, 5pp. 417-460.
knew this was a problem but did not have a mathematically-rigorous framework to solve it.
A pair of axles, where the wheels on one side are coupled through a connecting rod, is something the engineers call a "four-bar linkage", where the driving wheel constitutes the crank link, the connecting rod is the coupler link, the driven wheel is the follower link, and the locomotive wheel frame in which the axles rotate on bearings is the base link.
When the wheels are rotated so that the connecting rod is in a position inline with each of the two axles, this "mechanism pose" constitutes a "mechanisms singularity", where the mechanism needs help figuring out where it is going next. One allowed motion away from the singularity is for both wheels to continue to rotate the same way. The other allowed motion is for the driving wheel to continue rotating the same way, but for the driven wheel to start rotating in the other direction, putting the connecting rod in a kind of skewed position.
With a quartered siderod drive, when one side is at the singular pose, the opposite side is not, and this opposite side only allows one direction of rotation for the driven wheel of the two directions allowed for the singular side, so the bad direction of having the driven wheel rotate the wrong way is the path not taken.
Sheesh, the arguments people get into here. Don't you people keep current on reading technical conference proceedings papers?
If GM "killed the electric car", what am I doing standing next to an EV-1, a half a block from the WSOR tracks?
No idea what the articles are about-- but you'll agree the need for quartering isn't a recent discovery? We know the PRR DD1 was quartered; we assume the FF1 was too, and the L5 (?), and the Virginian and N&W siderod electrics, and all the siderod electrics in Europe and the rest of the world, and all the siderod diesels in England and the US and elsewhere. And the PRR 6-8-6.
Like the Captain said in "Cool Hand Luke" , "Some men you can't reach".
Let's try again. Quartering is due to the link between a piston and driven crankpin. If the pistons are at either end of their travel travel and pushing straight in line with the crankpin, no torque is developed and the no motion results. IF the rods are quartered then one them will always be off of center and able to provide torque which will the get the other off center.
If you still can't see it get a toy engine, disconnect the connecting rods and remove one side rod. You can still rotate the wheels because there is no reciprocating motion involved.
Quartering also spreads the power pulses evenly around the wheel rotation. Imagine if in your car or truck all cylinders fired at once. This is the effect you would have without quartering. The turbine had no pistons and no power pulses. There is no reason that its siderods could not have been balanced adequately.
And Timz: what is this about a "no 3 side rod"?
tdmidgetwhat is this about a "no 3 side rod"?
tdmidgetThere is no reason that its siderods could not have been balanced adequately.
Indeed, And there is also a place for a mathematical and theoretical understanding of things.
The submersible well pump motor over at my Dad's place froze up, and no amount of coaxing and switching of start winding wires could get that puppy turning. It was time to lift the pump out of the bore to see if I could get it turning, and I had to loosen this big brass nut to remove the pipe manifold.
I try a big honkin pipe wrench, nothing doing, the only "wrench extender" I had was a less-than-stiff length of PVC, so I put on the PVC, I start strainin' with the PVC bendin', and I call out "Moment vector M equals force vector F vector-cross-product lever-arm vector R!" and wouldn't ya know it, the brass nut starts to turn.
Any drive rod with a bearing at each end, whether it is a main rod from a piston steam engine crosshead or a side rod, can only apply a static force along the length of that rod. If the static force is off-axis, that vector cross product formula I just mentioned generates a turning moment at one or the other bearings, and the rod will turn about that end bearing, contradicting the claim that you can generate a static force in that direction.
Picture a siderod connecting a pair of wheels on one side, each wheel attached to a turning axle. The side rod can only apply a force along its length, so as mentioned earlier in another post, that side rod applies zero torque when the two wheel cranks are in line with the side rod.
The two wheel cranks connected by a side rod (and nothing else going on) is what the mechanical engineers call a four-bar linkage. The base link is the locomotive bed frame, the crank link is the crank of the first wheel and axle, the coupler link is the side rod, and the follower link is the second wheel and axle.
If anyone bothered to go to their local university engineering library and look up the Woo and Freudenstein article, you will see a picture of that arrangement and an explanation that the motion of this mechanism is indeterminate when the two wheel cranks are in line with the side rod. The article by the Andreas Muller is the first rigorous mathematical proof that starting from that position, there are two ways the mechanism can go: one way is for both wheels to turn together, the other way is for the wheels to turn in opposition.
I have an article that is moldering around in "peer review" for an ASME journal, where I have come up with what I think is a simpler but mathematically rigorous explanation of this effect. Peer review is sort of like this Web site, only people with seemingly more impressive credentials bat arguments around about the obvious.
In other words, when the pair of wheels connected by a siderod reaches that kind of top-dead-center postion of both wheel cranks in line with the side rod, not only can the side rod no longer transmit torque between the two wheels in that position, if you get both wheels on a locomotive model to spin around the same way going through that position with the quartered side rod disconnected, it is only because momentum is carrying the wheels around when you spin them. If you fiddled around with this locomotive model long enough, you will find out there is a way to get the two wheels to rotate in opposite directions with the side rod taking up a skewed position.
When you quarter side rods on each side, when one side rod is in this bad position, the other side rod is in a good position that only allows the two axles to rotate in the same direction, preventing the side rod that could go either way from taking the wrong direction.
Ergo, side rod drives need to be quartered as the man said, and this has been rigorously proven by some of the finest minds in the business (i.e., Columbia Mechanical Engineering Professor the late Ferdinand Freudenstein).
I agree with Paul, and I think Paul is confirming what timz suspects. That is, you need quartering on a wheelset where power is transmitted to it by side rods. It makes no difference whether those rods are being driven by a reciprocating engine or by another wheel that is being driven by a torsional motor or turbine. Either way, the rods impose a reciprocating force on the driven wheel. And when that wheel stops at the end of the reciprocating rod stroke, it does not know which way to turn when the rod reverses its stroke. So when that happens, the other side makes that decision because it is quartered, and therefore not in the same predicament.
I look at it like a bicycle,if one side of the crank is straight up and the other side straight down,the more you push on the one thats straight down it only wants to go down further.Put one petal half way and you will find it can turn from a dead stop.
"The side rod can only apply a force along its length, so as mentioned earlier in another post, that side rod applies zero torque when the two wheel cranks are in line with the side rod."-Paul Milenkovic
"It makes no difference whether those rods are being driven by a reciprocating engine or by another wheel that is being driven by a torsional motor or turbine"-Bucyrus
While I agree that in a non quartered wheelset the amount of torque would not be even throughout a revolution it does not mean no torque. Your quotes above indicate that your perception is that of a conventional rod engine where linear motion is applied. In this case the motion is applied to either the second(forward) or third (reverse) axle through a gear from the reduction box. So there is torque regardless of quartering. If no quartering then starting torque would I agree be very weak on the other three axles but not nonexistant. In a conventional rod engine if the connecting rod is inline with the axle there only linear thrust and no torque at all would be produced without quartering.
I have seen a Whitcomb 44 ton operated with one rod on each truck. It was able to start and pull and at the speeds it was capable of, with no noticeable vibration .
tdmidgetI agree that in a non quartered wheelset the amount of torque would not be even throughout a revolution
tdmidgetI have seen a Whitcomb 44 ton operated with one rod on each truck.
tdmidgetIn a conventional rod engine if the connecting rod is inline with the axle there only linear thrust and no torque at all would be produced without quartering.
The principle you have illustrated here applies to the second set of drivers even though the rods are being driven by the first driver set, and that driver set is being driven by a torque or rotational motor or engine. Even with torque powering the first set of drivers, the second set is being powered as though it were on a conventional rod engine.
Consider an 0-4-0 with a gear motor driving the first driver set and a pair of rods driving the second driver set, and no quartering with the opposite side. That second driver set is being driven by liner motion of the rods even though the first driver set is being driven by torque or rotational force.
Now while the stalling on center is a perfect geometrical response, it may be possible to run such a non-quartered 0-4-0 around all day and never get it stuck on center. Although, as you have mentioned, the power torque to the rod-driven second driver set will be very uneven, and very weak as the crank pins near dead center. But the chance of getting stopped with the crank pins on dead center is rather small.
You mentioned a 44-ton Whitcomb with both rods on one side removed. Although there would be no quartering under such a condition, the locomotive does have two trucks, and they are not synchronized with each other, so the chance of a coincidence of both trucks becoming synchronized through slippage during operation is remote. And if they do become synchronized, they won’t stay that way for long. And while they are synchronized briefly, there is only a small chance that they will stop with pins on center. So in lieu of quartering where one side takes care of the other to prevent centering, one truck will tend to take care of the other to prevent centering.
OK, OK, I guess I have to admit this, but there is a circumstance that you could run without quartering the side rods on the two sides.
Consider a model train locomotive, an 0-4-0, where one axle is driven from an electric motor with gears, and the second axle is linked with a single side rod, only on one side.
If you keep this model locomotive on the track, and if there is enough friction so that none of the wheels slip, there is a torque that will keep the second wheel turning, and no, this model will not get stuck at top dead center. The torque comes from the contact of the wheel with the track. At top dead center, the side rod is unable to transmit torque to the second axle, but the track certainly can. So long as the wheels do not slip, they have to turn the same way, hence that indeterminate condition at top dead center where the second wheel and axle turns the opposite way cannot happen.
So an 0-4-0 model train locomotive, gear driven from the first axle and with a single side rod connection to the second axle, that train can run all day without ever getting stuck. But at top dead center of the wheel cranks and side rod, all of the tractive effort will be applied through the geared wheel, and the second wheel and axle will be along for the ride, contributing nothing to tractive effort but being pulled off top dead center by motion of the train along the track.
Of course, you would never, ever build a real 12-inch to the foot scale 0-4-0 steam engine or side rod electric that way. In full-scale practice, you need all the traction you can get from as many wheels as possible, and the situation where for a certain wheel crank angle that you would be getting traction from only one axle, with the second axle being dragged along as an idler, this situation would be completely unacceptable.
That a locomotive with side rod drive needs quartering remains valid, the model train layout 0-4-0 locomotive notwithstanding.
Paul MilenkovicThe torque comes from the contact of the wheel with the track. At top dead center, the side rod is unable to transmit torque to the second axle, but the track certainly can. So long as the wheels do not slip, they have to turn the same way, hence that indeterminate condition at top dead center where the second wheel and axle turns the opposite way cannot happen.
That is an excellent point. I hadn't thought about the relationship through the rail contact.
Try to see it this way: Every time any machine trys to convert back-and-forth motion into rotary motion by means of a crank there's a "thump" generated and the possiblity of a stall at dead center. So, the machine's designer trys to smooth out the thump by balancing his machinery as much as possible. If he is working with more than one point where work effort meets resistance, he eliminates the possiblity of stalling on dead center by deliberately staggering the work thrusts. That also helps smooth out the thump ( called dynamic augment ). As long as Pennsy's Turbine ran some of its drivers with rods connected to cranks, balancing and stagering was necessary, otherwise the engine would "pound" or thmp excessively. With the tubine geared directly to its driving axle stalling on dead center was less of a problem but the crank driven axles still needed to be balanced against pounding. Norfolk and Western's turbine solved this problem by using the turbine to run a generator which fed current to traction motors. The gears in the traction motors turned the wheels smoothly, like a diesel locomotive does so no more thumping or stalling.
JimVallethe crank driven axles still needed to be balanced against pounding.
timzNo idea what the articles are about-- but you'll agree the need for quartering isn't a recent discovery?
No idea what the articles are about-- but you'll agree the need for quartering isn't a recent discovery?
The need for quartering seems like common sense to me, but a rigorous proof of the need for quartering may be as recent as the papers cited by Paul.
Putting on my Double-E hat, quartering is equivalent to a two phase electric power system, while the three cylinder approach is equivalent to a three phase electric power system.
Admittedly, I'm late to this party. Two things:
Unlike model locos, 1:1 scale siderod sets are not rigid in a vertical direction - they have to allow for the vertical movement of equalized driver axles. Therefore, they can only deliver force parallel to the rod, never perpendicular to it. As for expecting rail friction to prevent the piston-driven wheel from slipping and getting out of sync with the rod-connected wheels....
There was one occasion that saw a seriously wounded N&W J returned to Roanoke on a single cylinder, with the other main rod disconnected and chained up. The siderods on the 'dead' side had to remain in place to preserve proper quartering...
Chuck
I simply wish to complement Paul on being an excellent Mechanics (branch of Physics) teacher.
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