I have a vintage bike which requires a new crankset (and bottom bracket). Long story short, pedals fell off the old cranks, I bought new cranks and those cranks didn't fit the old square tapered bottom bracket. So, I am trying to get a new matching BB for the new cranks.

First, the cranks I got are the Sunlite Crankset, Cotterless Steel, 52/40 x 170mm that is square tapered

It didn't fit into the old BB, which was also square tapered, as the spindles were too big. So, i need a new BB.

Second, the BB shell is the standard 68mm. And, the spindle on the old BB is 127mm. That, having been said, what BB should I get? I was looking at the Shimano UN55 68x127 square taper. Would that work?

For what its worth, the old BB was manufactured by Tange and had the following numbers 1.37x24T inscribed on the lockring. And in the middle of the spindle (it's not a sealed BB), it has the following marking: "3S3"

So, any recommendations on a BB to fit those new replacement cranks?

You should post in the Bicycle Mechanics forum. They can help you there.

In what way did the cranks not fit? All square taper spindles have the same angle of taper, but vary in high and low dimensions as well as the length of taper. I believe the Sunlite Cranks are JIS and there is a good chance that your current BB is as well, being manufactured by Tange, so it should fit. When you install it, does the crank go too far on the spindle or does it not go on enough? Also, that is a double crank and your current spindle is probably for a triple. The way I decide on spindle length is to install the crank on whatever BB I have handy, take measurements for the chain line and then use those measurements tell me if I need shorter and longer (and how much).

it does not fit at all: that is, the spindle is too big for the hole (or square). i replaced the BB with the shimano UN55 taking the spindle length measurements of the old BB . . . and now, I have another problem . . . the Shimano UN55 which I got (68x127MM spindle) is too long for my cranks: i can't get the front derailleur to bring the chain up to the highest front chainring. So now, I need to get a shorter spindle!!! ugh!!!

If it is this crank, it says 122mm spindle.

https://www.niagaracycle.com/categor...th-steel-rings