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Optimum Gear Ratio

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Equation (2-43) shows that the electromagnetic torque required from the motor to accelerate a motor‐load combination depends on the gear ratio. In a basically inertial load where TL can be assumed to be negligible, Tem can be minimized, for a given load‐acceleration , by selecting an optimum gear ratio (r1/r2)opt.. The derivation of the optimum gear ratio shows that the load inertia “seen” by the motor should equal the motor inertia, that is, in Eq. (2-44),

(2-45a)

and, consequently,

(2-45b)

With the optimum gear ratio, in Eq. (2-43), using TL = 0, and using Eq. (2-41),

(2-46)

Similar calculations can be made for other types of coupling mechanisms (see homework problems).

Analysis and Control of Electric Drives

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