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2‐7‐2 Gears

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For matching speeds, Fig. 2-15 shows a gear mechanism where the shafts are assumed to be of infinite stiffness, and the masses of the gears are ignored. We will further assume that there is no power loss in the gears. Both gears must have the same linear speed at the point of contact. Therefore, their angular speeds are related by their respective radii r1 and r2 such that

(2-39)

and

(2-40)

Combining Eqs. (2-39) and (2-40),

(2-41)

where T1 and T2 are the torques at the ends of the gear mechanism, as shown in Fig. 2-15. Expressing T1 and T2 in terms of Tem and TL in Eq. (2-41),

(2-42)

From Eq. (2-42), the electromagnetic torque required from the motor is

(2-43)

where the equivalent inertia at the motor side is

(2-44)


Fig. 2-15 Gear mechanism for coupling the motor to the load.

Analysis and Control of Electric Drives

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