Rotary converter is almost certainly too small. The high speed setting of these two speed motors is notoriously demanding on start up current and many of the standard rotary converters aren't up to the job despite theoretically having enough power capability. If its new talk to the supplier. They ought to be able to supply an extra boost set of capacitors with automatic switching which might give it enough kick to get going.
Quick and dirty option is to add a free running pilot motor. 3 HP should do. With the pilot running there should be enough "generating" capacity to supply the start load on the motor to get things moving. Cut the extra pilot out as soon as the lathe motor comes up to speed. Besides acting as a third phase generator and rotary transformer the pilot motor on a rotary converter also acts as a spinning mass energy store. When the load motor comes on some of the rotational energy gets converted into generated power. If there is ever next "Help sort my converter" time I'd be tempted to try flywheel.
In my view commercial rotary converters are usually undersized in the rotary department. Usually the motor rating is less than the actual converter rating. Old line advice is that it should be bigger. When I converted a 3 KW MotorRun static converter to rotary I put a 5 HP pilot on it. Worked very well even on two speed motors. Brute force has its moments. I'm somewhat skeptical of the claims for "more sophisticated" rotary converters with so called load matching capacitor switching to more exactly match the motor demand and specially wound rotary elements instead of standard motors. My limited experience suggest that although they work OK in less demanding applications they can't handle the tough jobs. More to go wrong too.
Clive.
Edited By Clive Foster on 26/09/2017 23:43:32