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I've bought one of the shims so I can fit my Eagle crank to a Hollowtech II BB (on a Whyte 909). I've tried lots of combinations of spacers on both sides, but the cranks either tighten with play left or the drive side binds to the BB face. I can't seem to find a perfect width.
The Hope adaptors go each side of the non-drive side bearing.
Have you got a wave washer installed behind the crank?
On my Spark with Hope bb I had to leave the outside shim off and just use one on the inner side of the bearing as it bound tight when torquing up correctly.
The GXP system works by the end of axle and left arm clamping the left side bearing.
Your adapter should be the same depth as a GXP left bearing - measure it to be sure.
Insert the adapter from inside the bearing.
Mount to bike then add shell spacers to get desired chain line.
There will be a gap driveside between. Crank and bearing. You can put a wavy washer there if you want.
If the axle and Crank does not tighten onto your bearing adapter then something it amiss. I had a left Crank with trashed splines from the Crank bolt once that wouldn't tighten down.
Have you got a wave washer installed behind the crank?
On my Spark with Hope bb I had to leave the outside shim off and just use one on the inner side of the bearing as it bound tight when torquing up correctly.
@Blazin-saddles - the two parts of the Hope adapter fit around the bearing and seal, the seal won't be correctly aligned if you try to fit it outside the adapter - if that was what you were trying. This stack should make up the correct width and spacing for the LH crank arm.
I am not sure the Hope system would be ideal with other bearings with soft rubber on the seal as that would get squished when you tighten the LH crank bolt up. I would think the single sleeve type would be better there, though I have never had to convert that type of bb.
@wzzzz - out if interest, if you had the flange on the outside (which is as I read your post) - how did you fit the seal?
Um the last one I assembled looks like this diagram, note orientation of "GXP adapter" in each assembly:

Here is my mash up road bike with deore MTB BB and Truvativ Elita GXP road crankset. Note I didn't use any spacers on the shell, should maybe stick a 1-1.5mm in the left to get better chainline. Hence also note the size of gap on the driveside between crank and bb face ~1.5/2mm

A road BB + road crank or mountain bike with wider shell and wider axle will need likely different combinations of spacers depending on your particular GXP adapter, BB and desired chainline.
Just stick it all together, measure the chainline and add spacers to taste. You can add spacers on the driveside last if you want to close the gap up, but IIRC GXP is designed with a gap there.
Ah that is the way round I thought it oughta go, must have misinterpreted your earlier post wzzzz
I got an adapter like wzzzz's, but the shoulder wouldn't fit against the bearing due to an internal feature on the BB cup. A bit of swearing and grinding it off carefully has led to some smooth spinning cranks (which aren't supported as per design, but one bearing will take load on each side, so shouldn't fall to pieces.)
The bearings will fill with water and rust out or seize up with grit long before they wear out.
I managed to secure the cranks with no play by not fitting any spacers to the driveside. This has thrown the chainline out by about 1mm as the Shimano BB cups are narrower than the Truvativ ones. But I'll live with it for now. I only want to see if the Shimano BBs are worth sticking with. If not, it'll be a Hope next.
The cheap adapters have their extended bit on one side. The hope is two piece and splits it either side.
I can see why people just go with shimano....
Not cheap, designed for a differnt type of BB. Hope's rigid non-contact seals can be in the sandwich and compressed by the LH crank bolt, rubber coated contact seals might not take to that, so with that type of HTII bb (eg Enduro) the single piece sleeve takes all the compression (I think). Actual GXP seals are different on the LH side, the rubber coating does not extend to the middle bit which is exposed metal, so it can be compressed.