And if you absolutely have none of those alternatives available, I'd sooner solder (only) to the crimp terminal than to crimp to solder-tinned wire.
In theory this might be feasible but you'd have to dip the entire terminal in the solder along with the crimp, which might cause other problems. Might be ok for basic ring or spade terminals, never tried it.
I've also wondered if soldering the litz wire into a ferrule and crimping to that would be the best compromise. Asked NEW about it and they basically said "interesting, give it a try and let us know how it goes".
Hah. At least for smaller (pin-sized) litz, I've seen shops just dip the loose end in the pot -- tin the wire, then shove it into the board for a second (and final) soldering step. Avoid fraying the strands (or I suppose wrap them with a fine strand before dipping) and it works out fine. Needs a relatively large PTH of course, since some fraying is inevitable. Usually it's done as part of a lead frame operation: like mounting the e.g. transformer on a mounting base (sheet of FR-4 with holes drilled in it), with blobs of gel epoxy to secure wires on it. Also an alternative to pinned bobbins, just take the wires out and shove them through holes separately.
Ferrules should be fine, give or take if they're nickel plated I guess, heh. Disappointed NEWT didn't have anything to say about it. (I forget if we asked them about ferrules back in the day..)
Would imagine the crimp wire-in-board terminal thingys would do well enough too; I don't know that I would trust those to tin through (clearing out the enamel) if using litz with a fairly ordinary wave soldering process, but if you can spend some time "soaking" them, that would still be fine. (Customized selective solder, perhaps? Run the wave slower, if everything else is fine with it?) Pre-tinning of course does nothing, as you'd glom up the snap-in clip parts and not be able to assemble them in the board, or at least any better than as ferrules.
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At PPoE, we did industrial (up to sausage-sized) cables by crimping, dribbling in some liquid rosin, then dipping the whole lug, usually with a clean-up step blasting off dross / rough solder with a sanding disc. Not exactly ideal, but I'm not aware of any that came back to the service department with charred lugs. (Granted, that might only be a 1/1000s failure rate, hardly exemplary as industrial production is concerned.)
Regarding solder vs. crimp, my understanding is, the crimp has to pinch and stretch -- specifically, not just crush, but to hold in compression, necking down and thus squeezing the strands out lengthwise just a little bit, and the strands spring back against that force, acting to push them back into the crimp, sealing it tight. It isn't, and doesn't have to be, a cold weld; in fact the strands can move in the crimp, it's not necessarily a problem for the lug and wire to have mismatched thermal expansion for example (but, probably not a good thing if they are very different, lol).
Thus, if we make a very loose crimp (that isn't actually holding tension against the strands), it's better to fill it with solder, because it's not a gas-tight joint, and the solder will make the bond, like a tight-fitting solder pot. There's nothing wrong with solder pot terminals, in and of themselves. We have a soldered joint, and all the limitations thereof (creep, fatigue, corrosion). If you have terminals but no crimper, you can still do them with pliers and a soldering iron in this way -- badly, but you can likely make something that fits wires into a housing, and maybe that's good enough in a pinch.
If we fill a proper crimp with solder, we get the worst of both worlds: the fatigue and creep and corrosion of a soldered joint, without the natural movement (potentially) of the crimp joint; the soldering heat may also relieve some of the stress in the crimp joint, or by melting tin plating (when applicable), change the volume in the crimp, and thus the stress in a more exaggerated manner.
So that's why you don't crimp AND solder.
Then, what about litz? It's enameled, so there's a three-layer mix in the crimp cross-section: the barrel around the outside, then the matrix of copper and enamel. This will crimp just fine when cold, but when heated, the enamel breaks down and flows out, relieving stress. Whether that's bad, depends on how much is relieved: it seems to be enough to fill with solder, but, I mean obviously it's a solder wick, that's not saying a whole lot; possibly it's enough that strands could in fact come loose, but I can't say I've ever extracted strands from a terminal while the solder is molten. But that might also simply be because the strands are stuffed in there with enough congestion that they can't really pull out
It could also be that not enough stress is relieved by melting the enamel, to loosen it. We're not talking much strain here (<1%?), but a fair amount of enamel (several percent by diameter?), so I doubt this is the case. It seems plausible in the tin-plating case though.
But, I think for most applications, they're just not strenuous enough to be a problem: the soldered joint, the vast strand count, and the fact that the cable some inches behind the terminal remains stiff (from the enamel melting together), accounts for most of the strain relief, plus a generous layer of heatshrink does a bit more; and applications may simply be well enough secured, or low vibration, or clean environment, that the stress response (creep/fatigue) and corrosion concerns just don't manifest. Basically, you aren't usually running litz cables around for general cabling use, they're mostly at the terminals of a component and there's no slack length to couple vibration and handling into heavy flexing. The situation might be suboptimal in a broader sense, but further optimization may not even be perceptible (in terms of production yield and product quality/reliability).
You definitely don't want to tin AND THEN crimp, as the tinned end will have a substantial fraction of solder inside it, and the whole thing will mush down, getting severely strained and fatigued, while not holding nearly as much springback force as the crimp needs to be sealed against. The cracked, loose mass may be mechanically pinned (you can't yank it out, maybe even without breaking the wire), but it will be far more susceptible to fatigue and corrosion. This can be cured (or, probably not completely, but partially perhaps) by remelting the joint after crimping: apply flux, then heat it up; there may be enough excess solder to make a reasonable solder-pot joint, but probably some extra should be added to get a nice fillet. Plating around the lug ring can be unaffected (or at least, not blobbed up; usually the plating does change on heating, oxidizing or thickening the intermetallic layer), so it bolts down as good as new.
Tim