Below: Normally, on a good speedometer the needle spindle sits in a nylon bushing that screw into the clear plastic frame under the white odometer carrier. The bushing serves to center the spindle, since it is attached to a loose/wobbly electro-spring set up below. As an aside, that bushing all but confirms the overall shaft is an assembly of pieces pressed together. There would be no way to get the nylon bushing on the thin part of the shaft otherwise. However, when the shaft breaks, that nylon piece can just be unscrewed by hand and removed to room to make the repair.
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Below: the needle's shaft starts out as maybe 2.5mm in diameter, but then transitions to a very fine shaft about the size of a sewing needle. This is where the shaft typically break. Mine broke very close to the thicker base shaft, which seems common. The nylon bushing has already been removed so you can see the break and get to it.
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Below: I discovered these 'telescoping' rods the other day at an Ace Hardware store. The kit shown includes a number of copper rods, each just small enough to fit in the next bigger rod.
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Below: By pure luck, the 1/16" rod has an inside diameter that fits over the broken speedometer shaft almost perfectly. I cut a tiny piece off, equal to the length of the stub left on the needle, and put it on the stub. With a soldering iron, I heated up the copper/needle combo on the very end and let a small amount of solder wick into the tube to secure it onto the stub. It's important, ultimately, to get the tube straight on the broken shaft, but you have to do the final straightening later, as described below. There is vey little play between the tube and the shaft, but just enough that the tube can be ever so slightly crooked.
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Below: Again by pure luck, the 3/32" tube fits almost perfectly over the thicker base of the diameter shaft. So I cut a length of it off and slid it over the broken shaft. I found it easiest just to cut it long enough so that it bottoms out on the lower end and sticks out on top just long enough for the other copper piece on the needle to slide all the way in. This way, when you slide the broken needle into the 3/32" tube, the height of the needle will be correct. Making the tube longer like this also makes it easier to solder in place and helps ensure the tube is straight. This time, I took a small length of solder and dropped it into the tube, then heated up the tube until the solder melted and wicked own and around the broken shaft, securing the 3/32" tube to the broken shaft.
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Below: Then I melted a bit of solder on the outside of the 1/16" tube on the broken needle and heated up the 3/32" receiver tube until it melted the solder already on the smaller tube, allowing it to slide in and solder itself in place. Forgot to get a pic of that before putting the odometer carrier on, but you can see the tubes assembled below. Now is the time to ensure the assembled shaft spins straight, with no noticeable wobble in the shaft as it turns. You can turn the little splined hub clockwise and watch it rotate back. The hub should rotate around its axis without little to no wobble / run out. I ended up straightening mine with brute determination -- i.e., I'd melt the solder and try to hold the hub straight with an awl until the solder cooled, then tested, then did that another 50 times until I got it just right.
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Below: At this point the shaft is stronger than new, and the speedometer functions again. However, without the nylon bushing keeping the shaft on center, the needle is a bit wobbly. To fix that, I 3D-printed a 2-piece busing that fits in the recess above the shaft. I made it in two pieces, like valve spring retainers, so that they could hug the 3/32" tube. [Edit: see post 5 below for an improved approach.] Had to take care to make sure that was sized 'just' right, and smooth inside so that the speedometer would not hang up on it. These bushings get trapped in place by the faceplate, once it is screwed back on. With that, I now have a functioning speedometer! I compared this speedometer, as repaired, to a known good speedometer on my bench tester and they both read the same MPH at any given input rate, so it seems the repair does not alter the accuracy of the gauge.
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These are tiny little things to 3D print, so part of the taper was just was printing practicality. The printer deals with the taper better than a chamfer when the chamfer is so small. The key is getting the hub true and straight. The more out of round it is, the more pressure it will exert on the bushing and the more likely to stick, so if it needs more clearance lower in the bushing, it's more likely to stick.
