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Does your controller control the speed of the motor? You will need some form of governor due to the wildly varying torque requirements of a hydraulic pump.
 

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You still need reduction gears in the transaxle, but everything else is a loss. Although getting enough reduction in the trans for an electric drive motor might prove a challenge.
 

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Dc motors have gobs of torque but not compared to the hydraulic motor on a Case transaxle. Would take a very large electric motor to replicate the low end torque of the present drive motor. My buggy has 12 to 1 reduction behind an aftermarket torque motor and that is with 22" tall tires, and while good, still won't pull like my 446, at least continuously.
 

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Sorry, I was meaning if one was to use an electric motor directly on the axle in place of the hydraulic one. But you do raise a concern I had too about the motor being used running the pump, but the Kohler had to run the pump AND power the deck or caster off the other end at the same time. Just for reference, my buggy in 6" deep snow this morning was pulling over 200 amps continuously and took 300 at times at 48 volts.
 

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Your oil cooler fan draw is negligible. Even if you forgot it on for a day or 2, it isn't going to affect runtime. If you were basing runtime on mileage, you would need a tape measure to see the difference. LOL
 
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