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Is this a suitable 9A, VFD setup?

The general spec's seem just fine although you don't need 1 HP for a 9A lathe. If yours is a bench model lathe, that junction box on the motor may cause you trouble if you have tight clearance between the lathe and countershaft. (Assuming the picture is what's really being supplied) For an undermount model, it should not be an issue. Teco-Westinghouse seems to have a good reputation for VFD's. I've never heard of Brooks motors but there's not much to go wrong in a 3 phase motor.
 
Thanks...haven't heard of Brooks, either.
They have another package with a refurbed Baldor- but the Baldor has a 7/8" shaft.
 
A 7/8" shaft isn't necessarily bad. You just need to get a new motor pulley. That size shaft is typical on motors in the 3-5 HP range. There are 56 frame motors rated as high as 5 HP. I have a couple and they have 7/8" shafts. You'll also find 7/8" shafts on larger frame motors but you don't need to go there for a 9A lathe!
 
True, I'll look around to see if I can find a similar size 2-step pulley in 7/8"
 
As a practical matter, I think you'll find that with the VFD, you won't find any use for the higher speed option for driving the countershaft. If you need more speed, it's pretty easy to bump up the VFD's output frequency and just raise the speed of the drive motor. You can easily get by with a single groove pulley for the motor. Pick the smaller diameter of the two groove pulley.
 
The original motor was 1/2HP. Anything more than 3/4HP is a waste and will likely cause a space issue, so why do that. The flat belt on a SB9 simply won't couple the additional torque of a larger motor without slipping.
 
V- belt drive...
I've read that it's advantageous to go slightly larger on motor size when changing to VFD.
 
FYI Brook are a well known and highly regarded British motor manufacturer http://www.brookcrompton.com/home.aspx

Plus I agree, 1/2Hp on your 9A is adequate, .apart from anything else, the (A while a good machine of its type, .simply hasn't the rigidity and mass to handle much more power, Even IF you could transmit it to the spindle!
 








 
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