MTB BSO rear hub – bearing size dilemma

Question

Background

I am fixing up an old MTB BSO (MTBSO? Or even MBSO?). I reckon it's from the 1990s or early noughties. My ambition is to do it myself and as cheaply as possible. The fault is that the axle snapped and some of the loose ball bearings were lost.

I've had a read of this: https://bicycles.stackexchange.com/a/43295/33048, in which the need for an educated guess is identified. I am hoping someone can help me make that guess.

The problem

The parts are not what I was expecting:

• the nuts are odd – I suspect it’s just terrible quality, but maybe it’s something else:
  • the edges seem sharper, or more pronounced, than I am used to
  • the nut sizes are funny: I can barely get a size 15 spanner on, then size 16 has lots of play
• the bearing balls are 3/16” and Sheldon Brown says 1/4" is normally used: https://www.sheldonbrown.com/harris/bearings.html

Rough, tentative plan

1. For the axle, my plan is to replace it like for like, I have no appetite for splashing out on a quick release.
2. For the bearings, my plan is to replace the existing loose ball bearings with cage bearings. I know loose ball bearings are better but here are my reasons:
   1. the bike is only for light, occasional use;
   2. I've once replaced a caged bearing with loose balls and found it very frustrating.
   3. I am struggling for time.

Concerns

1. I can’t tell what size caged bearing I should buy to get it right first time and only buy what I need.
2. Shops seem to market their caged bearings as one of the following:
   1. “3/16" Front Hub Caged Bearings” – I assume my axle (the existing and the replacement) is 3/4" = M10, so the concern is I might struggle to get the axle through the bearing, let alone the cones.
   2. “1/4" Rear Hub Caged Bearings” – my concern is that the cup in the hub will be too small to hold this, and I don’t know how to measure to be sure.

Speculation

It seems the wheel meets one of the following descriptions:

1. The factory used the wrong size balls, but otherwise everything is normal: the axle is 3/4" = M10, and the cups in the hub will fit one of those “1/4" Rear Hub Caged Bearings”
2. It is a rare-ish but reasonably standardized (not unheard of) system where I can use an M10 axle and a “3/16" Front Hub Caged Bearing”
3. It’s some weird, non-standard thing and it’s going to be pot luck, hit and miss

Main question requiring an answer

Which description from the “Speculation” section above is my wheel likely to meet, if any?

Supplementary questions - opinions would be appreciated but are not essential

I know I probably could find the answers to some of these if I put more hours in, but hopefully I can ask them here.

1. Is my general plan reasonable? Or am I overcomplicating it?
2. Are there any measurements I can take on the hub’s races to narrow down the search?
3. Will the cones fit? Can I buy a new axle complete with bog standard cones, and will they fit in the caged bearing, whether I go for 3/16” or 1/4"?
4. Will I even be able to get a caged bearing into place through the freewheel?

Some photos

Please excuse imperfect focus.

Answer 1

Unless you are lucky, the time taken to install loose bearings will be less than the time needed to track down a caged bearing. Cost wise a 'bucket' of loose bearings is the cheapest approach. As such, I would replace like for like and save a whole raft of potential issues, i.e. I suggest loose 3/16" bearings.

Installing loose bearings is not hard, but it can be frustrating the first few times, I don't think is a good reason to avoid them on this job.

Those cones don't look in great shape, if the cups are good, I would look to installing new cones. Getting ones that fit could become and exercise in trial and error (with bearing size coming into it), so may be a reason to stick with the cones you have. This kind of job - occasional, light use and lowest cost requires being pragmatic, when I have done it for myself, I accept possible rework down the line if I cheap-out too much. If doing for someone else, it get more professional and put in the new parts.