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Originally Posted by DuaneB
Are the motors tied together in a gearbox
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Yes.
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If so, there isn't really a free speed. Free speed means there's no load on the motor.
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Free speed in this context means "no load on the output shaft of the gearbox" (and ignoring friction in the gearbox with no load on it).
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The maximum speed of the system, barring additional loads, will be somewhat less than the lowest free speed of the three.
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False. It will be somewhere between the slowest and fastest.
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Whenever you're ganging motors together, you want their free speeds to be as closely matched as possible, taking into account any difference in gearing.
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The equation shown works whether the individual free speeds are matched (with a speed reducing gearhead on the faster motors) or not. If speed reduction is used on any of the motors, then use the Free Speed and Stall Torque of the gear+motor for that motor.