What does an AC-to-DC conversion require?

There is no equation that turns an AC gearmotor into a DC one. The temptation is to match rated watts, and it is wrong in both directions at once. A nameplate on a shaded-pole or permanent-split-capacitor gearmotor states input power at the motor's own efficiency, which can be under 30%. It is not a statement of what the mechanism needs, and it was chosen by whoever specified that unit for reasons that may have had nothing to do with the load: it was in the catalog, it fit the bracket, it started reliably.

What actually has to be replaced is the behavior of the machine. Start with timing. A line-frequency AC gearmotor runs at an essentially fixed speed whenever it is powered, because synchronous speed is set by the supply frequency and the pole count and slip is small. A brushed DC motor sits on a sloped curve and slows under load. Every cycle time that the product inherited from the AC unit becomes a requirement that has to be stated and then proven, not a property that comes for free.

Then holding, which is where most conversions fail. Many AC gearmotors use a worm reduction that is effectively self-locking, so the load stays where it was left with the power off. Planetary and spur DC gearheads back-drive. If a damper, a valve, a lift or an arm holds position today because the gearbox will not turn backwards, replacing it with a DC gearmotor of the same torque loses that property silently, and it is discovered in the field. The fix is a brake, a self-locking element, an over-center mechanism or a change in the mechanism, and it is decided before the motor is chosen.

Then starting. Single-phase AC motors have a starting torque characteristic engineers stop thinking about because it has always worked. A DC motor has a different one, and the breakaway torque of a cold, stiff mechanism is a real number that has to clear it.

Then the control. A line switch or a relay becomes a DC supply, a driver, a decision about inrush and current limiting, and often a change to the enclosure and the wiring. Stalling into an end stop, which a small AC motor may survive indefinitely, will cook a DC motor unless the drive limits current. Dynamic braking puts energy back into the driver, which has to be able to take it.

Then duty and thermal mass. The DC replacement is usually physically smaller, so it has less thermal mass and less surface area. A duty cycle that ran the old unit warm may not be survivable by the new one, and that is a measurement, not an assumption.

This worksheet exists so that all of that is on one sheet before anybody proposes a part. What it returns is the state of each question and the list of measurements still needed. It will not return an equivalent part number, because a part number issued against an incomplete worksheet is a guess with an authoritative format.