That's a lot of torque, assuming that's the input. At that level, a continuously variable transmission is likely - as in a locomotive - an electric drive of generator and motor, rather than a mechanical transmission. Or it could be hydrostatic. The automotive CVTs which are available handle about one-tenth of that input torque.Are there CVTs that support high torque applications, such as 3,000 to 5,000 ft lbs of torque?
In belt CVTs, rubber belts are for power toys (snowmobiles, ATVs...) and steel "belts" are used in automotive applications. It isn't just strength - a rubber-belt CVT for high torque would be very bulky, and the heat generated due to hysteresis and slippage would be a problem.With more robust components, would a go kart style CVT be feasible with the high torque application? One challenge is the chain or belt being strong enough, as well as having enough grip with the pulleys that there is limited slip.
If you don't mind my asking, why do you want a CVT, anyway? Assuming this is for a vehicle converted to electric drive, a fixed ratio is usually enough and a few ratios are plenty... continuously variable is pointless.