Variable Speed Tread Mill D.C. Motor Conversion Shop Fox Drill Press.

[tonyfoale]

..... my controller does not have that large transformer on it.

I think that you will find that the "transformer" is a just a choke (inductance) which is used to filter or smooth the current through the motor. The speed control system works by chopping part of the AC cycle which at lower speeds and when rectified results in a series of narrowed pulses rather than the wider ones from a rectified full sine wave. Neither are smooth DC.
These are DC brush commutated motors which prefer feeding on smooth DC rather than out of phase rectified and chopped AC. At any given speed the commutator segments pass under a brush at a certain frequency which mostly will be out of phase with the supply frequency. The choke helps by evening out the current pulses. These motors run much smoother and quieter with the choke in series.
The above applies to TRIAC controllers which are the only type that I have seen in treadmills, but if some controllers are based on a PWM system then there would be less need for a large choke due to the much higher frequency of the pulses. 1000s of times higher.