To get an idea of the relationship between size and bore in Far Eastern lathes have a look at Warco's website. If you click on a lathe's photo it will take you to its specification including the spindle bore. (Scroll down to the table at bottom of each lathe's blurb.)
I think the first Warco machine to meet your criteria is the WM290. At 230kg it's the largest of the 'Variable Speed Lathes'. After that, look at the Gear Head machines which go up to 80mm but weigh about 2500kg.
A lot of the 12x?? advertised 37mm but there were reports some time back that they could be on or more mm shy of that. However owners have been known to correct that without detriment. Some sellers may be knocking off a bit from the manufacturer's 'spec' to avoid comeback.
In the USA they advertise 'gunsmith' models which usually means a larger bore on a basic model.
My Taiwanese copy of a 14"x40" Harisson M300 has a 40mm bore. A necessity for me doing mainly motorcycle work and needing to hold fork stanchions. Lathe brand name is Excel.
Hi Bill in the past I had to turn long pieces and to prevent wobble of the piece sticking out of the rear we made a tube which fastened on the rear of the spindle like an extension and a ring cam closed down three jaws on to the long piece to hold and prevent run out.
The smallest lathe I know of which qualifies is a South Bend Heavy 10 which passes 1-3/8" (34.925mm) through the spindle.
Edited By Pete Rimmer on 15/02/2019 16:49:22
That may depend on the year of the "Heavy Ten" my 1942 model sold about 6 years ago was only around 1 1/8"
Good point. It's not the year, but the spec but yes there were some heavy 10's with the smaller bore just like there were some other sizes with the larger. The larger bore are by far the more common and identified by the 2-1/4" spindle thread.