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But every production EV in which the motor shaft is not also the transmission input shaft couples the motor to the transmission input (which is exactly what we're talking about here) with a splined shaft connection and nothing flexible.
That's true for the Leaf and the legacy Hyundai/Kia family comprising the Kona/Niro/Soul and classic Ioniq. The splined coupling with adjacent radial locating diameter and closely-located bearings each side is clearly an over-constrained design but Nissan seems to have gotten away with it, presumably by precise production machining methods.

Hyundai/Kia on the other hand did not and there have been quite a few issues surrounding the spline, starting with a knocking noise. In many cases only the gearbox or motor are replaced under warranty and the noise returns. It seems that most successful fixes involve replacing both. This has been ongoing for 3 years now and they seem to be slowly addressing the problem. The motor costs around US$6.5k and the gearbox US$1.5k. I have a Kona from 2018 and am lucky, it's quiet.

The new E-GMP platform seems to have moved to the design tactic adopted by Tesla and no-doubt others where the spline provides support for one end of the pinion shaft, so three bearings in total across the motor and gearbox. The Bolt is even more simple, the pinion gear is simply cantilevered off the motor output shaft. This is not a mistake GM's experienced powertrain engineers would make and the entire gearbox design shows good attention to detail. The legacy H/K and Leaf to lesser extent look no more advanced than a 1950s BSA motorcycle.

Used oil analysis from Konas and Leafs show that the Kona has typically twice the contamination of the Leaf regarding iron and aluminium, and at half the distance driven.

It's fair to say that a gearbox to transfer case splined coupling on a typical 4x4 is not dissimilar in principle but generally one side will have a longer distance to the bearing such that a tiny amount of misalignment can be tolerated.

But there's another issue that legacy H/Kia seem to be weak on and that is draining shaft currents from the motor. There is a circular conductive brush at the motor output shaft but still the gear oil turns black in short order, under 10,000 km or miles. A small number of Ioniq and Kona owners have had unexplained bearing failures, tellingly one leaving no significant ferrous debris. The Leaf gearbox design uses a grounding brush assembly on the intermediate shaft but I'm not clear if there is also one on the motor output as well. Perhaps someone here can confirm that one way or the other? The problem I see with circular brushes is that a tiny amount of oil contamination can reduce the effectiveness. The Leaf's brush (pair) is contained in a dry, sealed cavity.
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Note the shagged out spline on this example.

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Kona/Niro gearbox showing proximity of pinion bearing to spline, upper-right.
 

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I'll stick my nose in because this sort of thing was within my profession before I retired. Assuming the Mini gearbox has a conventional input shaft the first issue is that the pilot end of the input shaft must be supported just like it had been by the crankshaft. Gearboxes normally rely on this, that's why they appear somewhat loose when you wiggle the input shaft on the bench.

Then you have to transfer the torque off the keyed motor shaft to the spline without loading the spline unevenly. You rely on the involute teeth under torque for alignment.
A normal clutch disk of course is rattle-loose in the middle so that can happen freely (and cheaply).

A huge problem with a keyway-type coupling half is that the constant back and forth torque can shag out the key if the coupling is "hard", but allowing slight rotational flex will help that, which is what the rubber does, another requirement to add to the list. The clamp style coupling half (as used in the type you've identified) can help or at least delay the issue. But a far better design is what's called a taper-lock hub (see image) where there is a tapered sleeve between the motor shaft and coupling half that is drawn in by screws. These are really effective, far better than what you've chosen.

Generally engineers send the dimensional details of the two sides to the coupling manufacturer with the maximum torque and RPM and they determine the best product for the job. Hacking something together especially involving welding may work for a while but it's not a professional solution unfortunately.

One suitable design would be a rubber-based flexible coupling (see image) with both radial and bending flexibility that is configured with a taper-lock on one side and machined to match the spline on the other, allowing the pilot journal to poke through the center and locate into the end of the motor shaft - with a bushing as needed. Or the pilot support can be part of the motor side coupling half. It's only holding it centered just like a pilot bushing or bearing in a crankshaft. This would allow a radial misalignment error of perhaps 0.001 to 0.003" between the motor and gearbox, entirely practical.

If you want more assistance a useful photo would be of the two physical parts set to the locations you need.

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They did a nicer job than I expected but I'd be impressed if it lasts, even if the parts are concentric.
1) there is evidence of shrinkage along the middle of the weld.
2) the coupling split will cause a stress concentration where it intersects the weld. (just below the arrowhead)

I would have welded up the coupling split on the gearbox half to stop movement at the weld. At least shim the gap tight and install some screws to limit flexing of that half.

In your favour, the gearbox input shaft will have some some wiggle tolerance and it's unlikely anything expensive will be damaged if the coupling fails. Grease the splines lightly at installation and make sure that the key(s) are a tight fit in the keyways.
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... but every rotation of the shaft is a cycle of distorting the rubber, by an amount dependent on misalignment.
An industrial coupling is a professional solution for the very-common motor to gearbox application. Properly sized these would last a long time. There are other types of less-flexible material of course; I only posted that particular photo to show that a spline can be machined into one half. The other half would use a tapered lock sleeve around the keyed shaft. Decoupling motor interia from the gearbox is never a bad thing as long as resonances are avoided.
I worked as an engineer in the field of engine and powertrain test equipment for a few years in the UK, 1980s, Froude Engineering.
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Presumably they've machined the clutch hub end (the end not visible) to fit the coupling so that it's centered but now that it's welded there's no reason to allow that side of the coupling to flex.
I was suggesting welding it along the red line but you'd want to grind a "V" first so that the weld can take good hold of the parent steel.

But before spending the money, perhaps check runout first in case it's not concentric and needs to be redone. If the minor diameter of the spline and/or the outside diameter is more than 0.002" out radially I'd scrap it. Oh, and that's when clamped to the motor shaft as mentioned by others.

I'd sure like to see photos of the actual gearbox input shaft and motor output shaft. And some idea of the spacing between them you're expecting.

I'll just add that my recommendation remains to use an industrial flexible coupling. That still requires the two sides to be well-aligned, perhaps 2-3 thousandths TIR.

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@sifawangiaEV, Thanks for posting the photos of the actual parts. Because it's now clear that the transmission input (clutch) shaft is already fully supported within the gearbox you should use a flexible coupling that can tolerate parallel misalignment. If you use a solid coupling your alignment must be perfect. That's a tall order and not something I'd recommend trying if any sort of reliability past a few weeks is your goal. So, when I say "should" I mean like an engineer speaking politely to his manager, I really mean "must". You're shooting yourself in the foot if you try to mickey-mouse this, which is regrettably the path you are already on.

There are a number of industrial coupling types that are suitable but you also have to ensure that the type chosen will be available with appropriate shaft options. Because of the frequent torque reversals I would stick to those that use clamping methods on the shaft(s), not just a split clamp but a proper taper-lock design. There may even be one for the spline according to the literature I'm referencing below. A small amount of torsional flexibility would not be a bad thing either, but not a lot.

Because the radial misalignment could be realistically kept to within 0.5mm TIR, one option that I found quickly is the Rexnord CentaFlex. It's quite complicated to navigate the engineering selection details but it's likely that their application department will do all that for you if you supply a fully-dimensioned drawing of both sides and max torque/RPM specs. You'll need to identify the spline dimensions as well and the desired gap between the shaft ends. When you get a recommendation from them you'll need to verify that it fits within the bellhousing.

There are many other coupling manufacturers but that's up to you to research. Following this advice will provide a reliable solution but I'm going to wish you the best of luck and leave the rest up to you, as I have to move on to other things.
 

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Yeah, 006" TIR is pretty horrific for the RPMs and physical scale of the system when using a rigid coupling. It will end in disaster. I'm not surprised that the splined hub warped during welding and that's an unfortunate compilation. But I'll repeat that using a rigid coupling is a bad idea anyway.

Almost all modular (meaning configurable) flexible couplings can be purchased with a blank end (with pilot hole only) and could be machined to suit your requirements. EDM would certainly be ideal, no-doubt pricey but you get what you pay for. I'm a bit surprised that in the US of A you can't get this sort of thing done easily? On a remote island in the South Pacific where I live I'd expect that.

I think your machine shop is leading you astray by telling you it will work. More research into flexible couplings is my recommendation. It would be useful if you can identify the spline size on the Mini gearbox. Additionally, creating a proper engineering drawing that you can send out for quote showing the two sides would make your search so much easier because application engineers can quickly interpret the requirements from that without any verbal or written explanation.
 
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