Slip Ring Motor

First off, that "slip ring motor" is likely a Wound Rotor Induction Motor (WRIM), which by definition IS an induction motor, so I assume you mean that you want to replace it with a Squirrel Cage Induction Motor (SCIM). The only other kind of "slip ring" motor would be a Synchronous motor, not usually used for high torque applications like that. If you have a resistor bank or electrolyte solution that controls the resistance to the rotor through the slip rings, then it is a WRIM. If you have a DC generator (or power supply) applying DC power TO the rotor through the slip rings, then it is a Synchronous motor.

Assuming it is a WRIM, you could possibly use an SCIM, but you will likely need to increase the HP to attain the necessary torque, or have a custom motor made. There is no simplistic formula for determining what size, it will depend upon the torque and speed you need. The only way to do that would be to observe the resistance value you are currently using successfully, compare that to motor data that includes torque-speed curves for each resistance value, then calculate backwards the torque and speed you need to accomplish that, translating it into a number of poles and HP for an induction motor. If you don't have and can't get the original motor manufacturer's data, you would need to have it dyno-tested to be sure.

But why? That WRIM is an almost perfect machine. What is your reasoning for making a costly change? Do you just not understand how simple it really is?