In automotive and machinery applications, if the manufacturers were producing large numbers of shafting, they would design the shafting to the exact/calculated diameter needed. In this way, they would save a small amount of money rather than going to "the next larger standard diameter". If an automaker was producing thousands of cars in a year, they could have the mills run shafting at the diameter they required. It might mean running the shafting as hot rolled steel at maybe 0.900" allowing 0.020" for cleanup to final diameter. The savings over using a "stock diameter" would add up to quite a bit over a year for a high production manufacturer. By this same token, with that kind of production volume, things like bearings or bushings to fit that shafting would be ordered or made in the same large quantities. The result is the end-users (or shops doing repair work) of those products would have to come back to the manufacturer for replacement parts.
In past years, before CAD came on the scene and before GDT (geometric dimensional tolerancing), working drawings for parts were made in the classic "mechanical drawing" ways and used a combination of fractional and decimal dimensions. Usually, there were some notes on the drawing which read something like:
".... Tolerances: Fractional dimensions: +/- 1/64"
Decimal dimensions: +/- 0.005" unless otherwise noted"
On decimal dimensions on the old style of working drawing, the tolerances would be called off on each dimension if required to make a fit with a mating part.
The rounding off of decimal dimensions based on fractional equivalents is a relatively new thing, and was the result of going over to CAD drawings and CNC machining.
The rounding off to two decimal places is often used on the "new" (hey, I am a dinosaur who still draws on a board with a pencil and instruments) CAD drawings is a handy way to indicate looser tolerances. Recently, I took a GDT course. It was quite interesting and an eye-opener for me. It was a logical enough way to make a drawing, but it took me some time to get a handle on it. One of the real eye-openers for me was the GDT course was given at a local manufacturer's shop. Working drawings and parts made routinely are made to tolerances measured in tenths of thousandths of an inch. As I was beginning to realize before I retired from the powerplant ( 5 1/2 years ago), with CNC machine tools, working to "tenths" is more the routine thing than the exception. Coming up in both the machinist's trade and the engineering professions over 45 years ago as I did, in regular machine shop work tolerances within a thousandth or two were the norm. Working to "tenths" was for the toolmakers, or for precise instrument machine work. It was the realm of those guys in the white aprons who got to work on the Hardinge HLV lathes and ran the jig bores or jig grinders. The rest of us mere mortals ran heavier machine tools and could split a thousandth if needed, such as for a shrink fit or a shaft journal for a bearing.
Another reason manufacturers might have gone to this odd diameter would be to allow enough "meat" to set down for a journal or for a spline. I've run into some
"oddball" shaft diameters along the way over the past 45 + years. I usually just shrug it off and figure the manufacturer had their reasons if it were on a production part such as something from automotive or heavy equipment. Where I have also run into oddball diameters is on very old machinery shafting. This was stuff made in the era when machinists used spring or firm joint calipers and rules to measure diameters and lathes did not have micrometer collars. It was also the era of poured babbitt bearings. The matter of a non-standard bearing was a non-issue since the shaft journals at whatever they finished up at would be used as mandrel for the babbitting. In other words: babbitt was cast using the shaft journal as the form or pattern. In the old shops, the lighting was bad (read: kersosene wick torches in winter, with dim natural lighting thru dirty windows diffused through a forest of belts from the linshafting overhead). A machinist would use calipers and steel rule and between bad lighting and parallax and eyes that maybe needed "corrective lenses", the shafting might well finish up at something other than the exact decimal equivalent of the fractional dimension called for on the drawing. Or, the shafting was turned to suit the bore in a pulley or gear hub. If that was a tad large to start with, the shafting was turned to suit.
Hot rolled round bar was usually sized by the 1/8ths. If an automotive manufacturer were making thousands of parts, they did not play around with hogging off any more steel than they absolutely had to. The result was round bar rolled to order, or forgings or rotary swagings which took care of stepped diameters on a shaft. Ford, probably the big daddy of this sort of thing, had their own "integrated" plant at the Rouge, where iron ore, limestone, coal and other raw materials arrived in bulk at one end and finished cars came out the other end. Ford had their own blast furnaces and steel mills on site with the rest of the plants needed to manufacture their cars and light trucks. If Ford engineers said a shaft of 0.880" was needed to transmit a given torque under the conditions it would see in service, the Rouge steel mills made rolls to roll maybe 0.900" hot rolled bar, or they set up to cold roll it right at 0.880" if the application allowed cold rolled to be used.
Plenty of reasons for this odd size. I make parts from chunks of old vehicle axles, and nothing in the way of diameters surprises me. Often, an axle will be forged on a taper to transition from the splines at the differential end to the bearing journal at the wheel hub end. Digressing a bit, Harley-Davidson abandoned the use of tapered roller bearings in the wheel hubs of their motorcycles some years back. They went to sealed ball bearings. Being H-D and making enough motorcycles to absorb (and pass along to the customers) the cost of a production run of specially sized bearings, and wanting a "captive audience", H-D designed a non-standard bearing. This bearing, being sealed, was non-maintainable and has a finite service life, IOW, "throw away and replace". Over time, aftermarket parts suppliers have started offering replacement axle bearings for H-D motorcycles, but if you were to mike an H-D axle or the bearing counterbores in the hubs, you'd likely find they were some off-the-wall diameter that made no sense in inches or metric units. Similarly, years ago, machinery makers sometimes used what were known as "bastard threads" on fasteners on their machinery. This forced people needing parts to come back to them for even something as mundane as bolts or machine screws. The 0.880" shafting may well be a combination of "trying to lean out the job" to save a fraction of a cent or more on each shaft in production, along with trying to create a captive audience for replacement parts.
