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I recently visited a railway museum with a lot of Soviet-era locomotives. The picture below shows the wheels on a locomotive from the 1930s or 1940s. Some of the wheels are thicker on one side (as it it were a partially filled cup). What is the purpose of that?

Picture of the wheels of a Soviet-era locomotive

(Now that I am looking at the picture again I wonder if they are balancing the weight of the coupling rods in some way.)

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    $\begingroup$ another point of interest in the picture is the gizmo above the rightmost wheel. That mechanism is what provides the ability change between forward and reverse drive. A nice video of simulation is at youtube.com/watch?v=8yRVMnPJmdQ. Also, one can google "steam locomotive reversing mechanism" or some such. $\endgroup$
    – David
    Jan 7, 2020 at 23:50

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Those are counterweights. They work exactly the same as those lead counterbalance weights on the wheels of your automobile.

If they left those out, then those connecting rods and bearings would create an out-of-balance condition, and the wheels would vibrate at higher speeds. That could very well damage the wheels. But as a couple of others have nicely pointed out, the violent shaking could derail the train.

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    $\begingroup$ Agree. And the mass of the unbalanced drive rods would do more than damage the machinery. It would probably throw the locomotive completely off the tracks. $\endgroup$
    – A. I. Breveleri
    Jan 4, 2020 at 22:41
  • $\begingroup$ Thank you for explaining the purpose as well! $\endgroup$
    – adam.baker
    Jan 5, 2020 at 5:58
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    $\begingroup$ Damaging wheels is nothing compared derailing whole locomotive going fast enough... $\endgroup$
    – Crowley
    Jan 6, 2020 at 23:33
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Those are balance weights against the joints used for the rods linking the wheels together.

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    $\begingroup$ Notice the largest weights are on the wheels with the largest connecting rod hardware. $\endgroup$
    – blacksmith37
    Jan 4, 2020 at 17:38
  • $\begingroup$ Are the balance weights added ("filled in", from the question title) separately, e.g. moulded on as molten lead, or is their size known in advance and so cast as part of the wheel? $\endgroup$
    – Andrew Morton
    Jan 6, 2020 at 14:45
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    $\begingroup$ @AndrewMorton Those wheels are cast in one piece. Sometimes there will be evidence of drilling to "fine tune" the masses involved. $\endgroup$
    – Solar Mike
    Jan 6, 2020 at 14:50
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The oversized counterweights on the second set of wheels are to help balance the additional inertia of the pistons, piston rods and crossheads, which are directly connected to the wheels on this axle. (In a former life I was a museum conservator and rebuilt, and operated, steam traction engines and a locomotive.) ronford

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    $\begingroup$ Welcome to Engineering.SE! You don't need to sign your posts, because the system automatically signs every question, answer, and comment for you. $\endgroup$
    – CJ Dennis
    Jan 6, 2020 at 9:57
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These counterweights are found on all piston-driven steam locomotives (not just Soviet designs), and even a few types of diesel locomotive using connecting-rod drive. As other answers note, their purpose is to balance the weight and momentum of the connecting and drive rods, which would otherwise cause heavy vibration when running at speed, to the extent of lifting the wheels off the track.

Here's a diesel example; the weights are relatively small here, but they can be seen on all three wheels to the lower left of the axle. On this shunting locomotive, the traction motors are connected to the front and rear axles, while the centre axle is driven through the connecting rods which also prevent any single axle from slipping under load.
BR Class 08 shunter

On this more elegant steam loco, designed for express passenger service, there are both strengthening webs on the crank side of the wheel, and balance counterweights on the opposite side. There's actually a second pair of cylinders between the frames, driving the leading axle, so the counterweighting is different for all three pair of driving wheels. Part of the counterweighting for the leading axle is built into the inner crank, rather than having it all on the wheels. Here you can also see that the carrying wheels on the leading bogie are not counterweighted, because they don't have any cranks.
GWR Castle

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  • $\begingroup$ That GWR locomotive nr 5043 is Earl of Mount Edgcumbe, a Castle class locomotive. Castle class locomotives is 4 cylinder simple expansion machines which have a fair number of advantages compared with a 2 or 3 cylinder simple expansion engine: - a more even beat over a wheel revolution - the weight of the drivning rods can be lessened because the necessary force can be transfered thru 4. on a Castle class, the front coupled axle is driven by the middle cylinders which complicated (according to the book The Railway: British tracks since 1804) the balancement of the machine. $\endgroup$
    – Stefan Skoglund
    Jan 7, 2020 at 3:58
  • $\begingroup$ [cont. Stefan's comment above] The book describes how the british railways in the late 1920's sent different machines around the country so that the engine's hammer blow could be measured on different bridges and bridge types. The conclusion was that 3 cylinder and especially 4 cylinder simple expansion engines exceded the 2 cylinder machines with regards to lessening the hammer blow impact on the rail head which also meant direct improvement in the interface between moving steel wheels and the permanent way (both normal lines on ground and on bridges of different types.) $\endgroup$
    – Wasabi ♦
    Jan 7, 2020 at 12:40
  • $\begingroup$ [cont. Stefan's comment above] If I understand the book correctly, the mass of the Castle's counterweights was reduced because it was found to be more advantageous to NOT completely balance out the moving masses. $\endgroup$
    – Wasabi ♦
    Jan 7, 2020 at 12:40
  • $\begingroup$ @Wasabi The "balanced four" design used on the Castle inherently balances out much of the motion of the piston rods and the pistons themselves. It also requires only two sets of valve gear. So for the most part, only the rotating mass of the connecting rods and strengthening webs needed to be balanced with weights, with a smaller compensation required for the big-end bearings being on different axles. $\endgroup$
    – Chromatix
    Jan 7, 2020 at 13:52
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Slightly different answer - aside from the hammer effect of having out of balance connecting rods, there is also a different problem set.

Since the left and right hand rods are at connected at 90 degrees wrt each other (deliberately, as this is how you avoid the dead center starting problems referred to above), what happens is that as they rotate, the whole engine starts to sway from side to side due to the unbalanced rotating load. If you happen to hit a resonant frequency with the rails, the engine (and train) can derail entirely. The faster you go, and the more driving wheels that the engine has, the worse the problem. 2-10-4 ("Texas"class) locomotives were notorious for having this problem, for example.

Finally, having one side 'pushing' whilst the other is 'pulling' can cause the axle boxes to work loose and this will severely increase wear on the axle boxes, wheels and brakes etc and in extreme cases, it can cause the loco chassis to fail (bend or even break) due to repeated flexing. Since both Berkshire (2-8-4) and Texas locomotives were designed to pull heavy freight loads, this can also cause the loco to 'fishtail' at any speed, which causes (different) problems again.

Rick

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These act similar to the flywheel of an engine, keeping the steam engine running smoothly, especially at the start of rolling when there is not much rolling momentum in the wheels.

They are positioned such that when the links are nearly expanded fully and there is a chance of wheel lock-up at the dead point, the gravity of the ballasts encourage the wheel to keep rolling and not lock up, or worse, back up.

EDIT

After some comments/ answers, I think a few points need to be clarified.

  • If these were meant to be just ballast for the wheels and counter the weight of joints or links attached to them, they needed to be installed off the plane of the wheel by the same amount as those links. Because as they are they create a considerable imbalance on the wheel if we look at the wheel's cross-section. A rotating wheel with an attached off-plane mass will not be balanced by adding weight in its plane; it will tend to turn about an axis which passes through the slanted axis of symmetry, therefore wobble.

  • The fact that they are elongated circular segments, as opposed to just a cylindrical shape similar to the mass of the links, helps them have greater angular momentum, hence additional rotational energy (parallel axis angular momentum: the sum of spinning momentum and rotation of CG about an axis momentum)

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    $\begingroup$ The right and left sides of driving rods are off set to avoid "dead center" starting problems. $\endgroup$
    – blacksmith37
    Jan 4, 2020 at 17:45
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    $\begingroup$ "... the gravity of the ballasts encourage the wheel to keep rolling ..." This seems very unlikely as any imbalance would cause destructive vibration at high speed. Have a look at p2steam.com/2016/10/31/getting-balance-right and p2steam.com/2016/10/31/getting-balance-right. $\endgroup$
    – Transistor
    Jan 4, 2020 at 21:55
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    $\begingroup$ -1 Incorrect. This is no part of the purpose of these weights. They are only to counter the mass of the drive rods and their bearings. $\endgroup$
    – A. I. Breveleri
    Jan 4, 2020 at 22:38
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    $\begingroup$ Wobbling will only be an issue if the wheel is insufficiently stiff. Note that the power input to the wheel is off-axis as well, which will also lead to wobble - but stiffness counters this. $\endgroup$
    – vidarlo
    Jan 5, 2020 at 13:35
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    $\begingroup$ @NuclearWang You seem to be only considering one side in your analysis - the other side is out-of-phase so that that there is no dead-spot... For a simple equivalent think of the pedal cranks on a bicycle. $\endgroup$
    – Solar Mike
    Jan 6, 2020 at 19:45

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