David, you've asked questions here that could fill volumes. I can't even begin to give you detailed answers but here are some basic bits of information to get you started"
(K)ool. How many factories were there?
Six altogether (if you count Factory 183 in Kharkov and Nizhniy Tagil as one factory) though not all at once: Factory 183, STZ, Factory 112 Krasnoye Sormovo, ChKZ, UZTM (that last produced only around 730 tanks before switching to self propelled guns).
Did each factory make their own versions?
No, not entirely. UTZ (Factory 183 in Nizhniy Tagil), ChKZ, and UZTM are nearly identical and difficult to tell apart though many have tried.
Factory 174 is also very similar to UTZ, at least early on. By mid-1943 they had added a few of their own refinements including wider hinges on the rear plate and a different variation of the commander’s cupola made from rolled steel plate rather than cast.
STZ after its initial start up, which was accomplished using “kits” provided by UTZ, quickly changed aspects of hull and turret construction to lower costs and simplify assembly.
Factory 112, which also used UTZ kits for its initial runs, quickly made changes to the design to allow it produce the tank in their facilities the most notable of which was dispensing with the rolled lower rear plate replacing it with flat steel (this was the introduction of the “simplified hull”). They also used interlocking plates similar, though not identical, to STZ until later in 1943. Krasnoye Sormovo tanks can be easily identified from the back by the unique hinges they use and the fact that the upper rear plates overlap the lower rear plate unlike every other manufacturer other than STZ (who continued to use the “Model ‘41” type lower rear plate).
Sormovo also added bullet splash strips to protect the turret race, a feature also unique to them.
I heard Stalin moved the factories behind the mountains when the Germans invaded...would this affect the design in any way? ie- cut corners?
This is correct, some of the factories were moved most notably Factory 183. In as far as “cutting corners” goes a better term would be “simplification”. All factories participated in programs the intent of which was to cut costs, reduce the use of strategic materials, and lessen the time needed to produce an individual T-34. More successful changes were quickly shared between factories but, for STZ and to a slightly lesser extent Factory 112, some of the changes lead to greatly reduced reliability.
Was each factory given a specific model to produce or how did that work? Because we see so many variants that are so similar but with little differences between them?
No. Each factory was told to produce X number of T-34s and was given some leeway as to how to accomplish that. Remember though that there could be no great mechanical variations between each of the producers; they all had to use the same guns, engines, electrical, and other standardized systems.
That said, Factory 112 continued to make T-34’s with the “flat” turret well after everyone else had adopted the hex turret and Factory 174 continued to use the hex turret for some time after UTZ and Sormovo had switched to making the T-34-85.
With that said, was the armor protection for all of them the same for each year? When did they upgun the T-34 to 76mm?
There were changes to the hull armor. Initially the design called for 45mm of glacis armor and 40mm on the sides and rear. This was changed to 45mm all around in order to reduce the number of different thicknesses of plate needed to make the tank.
For a time some T-34s had an additional 15mm plate welded to the glacis but this was a short lived modification.
Krasnoye Sormovo produced a number of tanks with extra armor welded not only to the glacis but the turret as well. Still others from that factory had much thicker plate added to the glacis but I suspect this was more to save flawed glacis plates rather than to improve resistance to AP shot.
The thickness of the turret armor varied between welded and cast versions but generally speaking all turrets of a similar pattern would have the same wall thickness. The forged turrets of course were unique.
The Model 40/41/43 all had 76.2mm (3”) guns though the Model ’40 was fitted with the L-11 and the others with the F-34
The pic below is not mine but by Chris Wauchop & looks like the first photo. Dragon T-34/76 Model 1941, kit number 6205.
It’s not. The model represents a “standard” production, earlyish, Model ’41. The photo is a Model ’42 with its later “simplified” hull.
I think I could possibly be on a new mission..collect every T-34 (v)ariant. How many are there?
Dozens certainly. Perhaps hundreds when all the different T-34-85’s and factory rebuilds are added to the mix. Frankly, I’ve never even tried to count.